v.- i The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924012388363 THE ELEMENTS OF PHYSICAL CHEMISTET '4 THE MACMILLAN COMPANY NEW YORK • BOSTON • CHICAGO ATLANTA ■ SAN FRANCISCO MACMILLAN & CO., Limited LONDON • BOMBAY ■ CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, Ltd. TORONTO THE ELEMENTS OF PHYSICAL CHEMISTRY BY HARRY C. JONES PROFESSOR OV PHYSICAL CHEMISTRY IN THE JOHNS HOPKINS UNIVERSITY FOURTH EDITION, REVISED AND ENLARGED Neto gorfe THE MACMILLAN COMPANY 1914 i <* V"*" ' t ( AU rights reserved , ^f Y ^ 5 l r !iif Coptbight, 1902, 1907, 1909, By THE MACMILLAN COMPANY. Set up and electrotyped. Published January, 1902. Reprinted August, 1903. New edition, revised, with additions, August, 1907. New edition, revised, with additions, February, 1909 ; October, 1910; September, 1914. / J. S. Cushing Co. —Berwick & Smith Co. Norwood, Mass., U.S.A. PREFACE It is now generally known that within the last fifteen years a new branch of science has come into existence. This branch, occu- pying a position between physics and chemistry, is known as physi- cal chemistry. The term, however, is by no means a new one. We have had physical chemistry since the beginning of the last century. In order to distinguish the new science from the old, from which it differs in kind, it has been termed the new physical chemistry. There seems to be a tendency in the last few years to ignore the work of the older physical chemists, and to regard that physical chemistry which is of any value as dating not earlier than 1885. To any one who holds this view, this work will seem to lay undue stress upon, and devote an unnecessary amount of space to the older work. It, however, appears to the writer that in order to appreciate the gigantic strides made by the new physical chemistry, it is not neces- sary to reject, or even ignore the work of such men as Kopp, Bun- sen, Gladstone, Kegnault, and the other great founders of chemical and physical science. If we would study their work more closely, we would see that it lies at the foundation of much that has been developed within the last few years. It has been the aim of the author to deal with the whole subject of physical chemistry in an elementary manner. The rapidly increasing desire, on the part of students of chemistry and physics, to know more of physical chemistry is manifesting itself in every direction. It is with the object of helping such students in the later stages of their college work and in the earlier part of their university career that this work has been prepared. The question might be raised that if this is meant to be an ele- mentary text-book, why is so much presupposed ? No one can use this book successfully without an elementary knowledge of physics, of chemistry, and of mathematics. The answer is that this is partly inherent in the nature of the subject. Physical chemistry involves at least the elements of physics, and of chemistry inorganic and vi PREFACE organic ; and the student must also be familiar with the elementary calculus if he would go deeply into the subject, and it would be well to add the elements of thermodynamics and differential equations. It is, however, true that much may be learned about physical chem- istry without any knowledge of the higher mathematics ; but such information must always be more or less unsatisfactory. In reference to the contents of that portion of the work which deals with the newer physical chemistry, a few words should be added in this connection. The new physical chemistry really begins with the chapter on solutions, and this is one of the most important chapters. The discovery of the relations between dilute solutions and gases has placed the subject of solutions at the very foundation of the new developments in physical chemistry. The subject of thermochemistry, while important and interesting, has never acquired that prominence which, for a long time, it seemed likely to attain, partly because the data are often so com- plex that it is difficult to interpret them and discover their meaning. Electrochemistry, on the other hand, is of the very greatest im- portance. In no chapter of physical chemistry have greater advances been made in recent time, and nowhere do we find experimental work of greater value. The study of chemical dynamics and statics has been very much to the front ever since the recognition of the importance of the law of mass action. It will be observed that reaction velocities, and equilibrium in chemical reactions have been dealt with from the standpoint of this law. This appeals to the author as being the most exact and by far the simplest method of treating these prob- lems. The phase rule, however, is considered at sufficient length, and applied, it is hoped, to a sufficient number of cases to make clear this important generalization. An attempt has been made to prepare a balanced work. The danger of treating certain subjects too fully and of following certain deductions beyond the scope of the remainder of the book has been felt, and an earnest endeavor has been made to avoid this defect. In dealing with the older as well as with the newer work the author has endeavored to obtain his information from original articles wherever it was possible, and in most cases it has been possible. He, however, wishes to express his indebtedness espe- cially to Lothar Meyer's Die modernen Theorien der Chemie, to Ost- wald's great Lehrbuch der allgemeinen Chemie, to Nernst's Theoretische Chemie, and to Van't Hoff' s Vorlesungen iiber theoretische und physi- kalische Cliemie for references to the literature. These have made PREFACE vu it a much simpler matter to find just what was desired at any moment. Little need be said at this date in reference to the importance of the whole subject of physical chemistry. It has already extended into nearly every field of chemical science, contributing largely to the interpretation of phenomena hitherto not understood. It has thrown light on so many problems in chemistry that it has now become an integral part of that science. And it is recognized that no chemist to-day, scientific or technical, can omit physical chem- istry without losing an essential part of his training. Physical chemistry has also thrown light on a number of physical problems, especially in connection with the study of primary cells, as we shall see when we study electrochemistry. It has also reached out into biology, and has become essential to the physiologist and pharmacologist. This has been shown by the work of Loeb, Dreser, and others. And that physical chemistry is to find its way into the geological sciences has become obvious from the work of Van't Hoff in the last two or three years. The wide- reaching significance of the subject would account for its almost unprecedented growth in the last decade and a half of the nine- teenth century. HARRY C. JONES. PREFACE TO THE THIRD EDITION The aim in preparing the third edition of this book has been to bring it up to date The growth of physical chemistry in the last few years has been unusually rapid, and an enormous amount of new and important material has been published since the first edition of this book appeared in 1902. The more important developments have been discussed, as far as possible, without unduly enlarging the book. Since, however, much that is both new and valuable could not be brought directly within the scope of the text, it has been decided to give a fairly large number of references at the bottom of the pages, to the more important investigations bearing on the subject under discussion. In this connection practically all of the original papers in the Zeitschrift fur physikalische Ohemie have been exam- ined, and, further, the "Eeferate" in this same journal have been carefully consulted up to the appearance of the PhysikaliscJt-che- misches Centralblatt in 1904. All of the volumes of the latter have been examined, and a number of references to important papers taken from them. In this way it is believed that this work can be made more useful as a book of reference, without detracting in the least from its value as a text-book. The author is indebted to a large number of those who have used the work for valuable suggestions; and especially to Prof. E. C. Franklin of Leland Stanford, Jr. University. He hopes that those who may use the work in the future will continue to favor him with such suggestions. H. C. J. PREFACE TO THE FOURTH EDITION The third edition of this book having been carefully revised and brought up to the date of its appearance (1907), makes the prepara- tion of the fourth edition a comparatively simple matter. It is chiefly necessary in this addition to add an account of the more important investigations in physical chemistry during the last two years, or to give references to them. A number of minor correc- tions have, however, been made, and some few matters omitted. The large and increasing demand for this work shows that it is meeting a growing need, and this is a source of personal gratification to its author ; more than repaying for the amount of labor spent in its preparation and revisions. H. C. J. CONTENTS CHAPTER I Atoms and Molecules FAGB The Atomic Theory 1 Determination of Relative Atomic Weights 4 Relations between Atomic Weights and Properties .... 18 Thomson's Theory of the Relation between the Elements ... 37 CHAPTER II Gases Laws of Gas-pressure 46 The Kinetic Theory of Gases 54 Densities and Molecular Weights of Gases 57 Specific Heat of Gases 68 The Spectra of Gases 79 CHAPTER III Liquids Relations between Liquids and Gases 84 The Vapor-pressure and Boiling-point of Liquids 99 ■ Heat of Vaporization 109 Specific Heat of Liquids Ill The Refractive Power of Liquids 115 Rotation of the Plane of Polarized Light 125 Magnetic Rotation of the Plane of Polarization 135 Magnetic Property 138 Specific Gravity and Volume Relations of Liquids .... 139 Viscosity of Liquids 141 Surface-tension of Liquids 143 Dielectric Constants of Liquids 154 XL xii CONTENTS CHAPTER IV Solids PAGB Crystals 158 Properties of Crystals — Relations between Form and Properties . .161 Crystallographic Form and Chemical Composition .... 165 Melting-points of Solids 167 Latent Heat of Fusion 170 Specific Heat of Solids 171 CHAPTER V Solutions Solutions in Gases 176 Solutions in Liquids 177 Osmotic Pressure 188 Relations between Osmotic Pressure and Gas-pressure .... 202 Origin of the Theory of Electrolytic Dissociation 208 Recent Measurements of Osmotic Pressure 214 Lowering of the Freezing-point of Solvents by Dissolved Substances . 222 Lowering of the Vapor-tension of Solvents by Dissolved Substances (Rise in Boiling-point) 256 Diffusion 273 Color of Solutions 287 Other Properties of Solutions 298 Solutions in Solids 305 CHAPTER VI Thermochemistry Development of Thermochemistry 318 Conservation of Energy applied to Thermochemistry .... 322 Thermochemical Methods 325 Thermochemical Units and Symbols 329 Some Results with the Elements 331 Neutralization of Acids and Bases 333 Some Results with Organic Compounds 339 CHAPTER Vn Electrochemistry Development of Electrochemistry 347 Electrical Energy ; Units ; Nomenclature 358 The Law of Faraday . . - 362 CONTENTS xni PAGE The Migration Velocities of Ions 366 The Conductivity of Solutions of Electrolytes 377 Applications of the Conductivities of Solutions of Electrolytes . . 393 Dissociating Action of Water and Other Solvents 419 Electromotive Force of Primary Cells 442 Measurement of Differences of Potential between Metals and Electro- lytes — Calculation of the Solution-tension of Metals . . . 471 Electrolysis and Polarization 482 Batteries in General Use 491 CHAPTER VIII Photochemistry Actinometry 493 Results of Photochemical Measurements 496 Photochemical Action of Newly Discovered Forms of Radiation . . 499 CHAPTER IX Chemical Dynamics and Equilibrium Historical Sketch 514 The Law of Mass Action 526 Chemical Dynamics 530 Chemical Equilibrium 565 The Phase Rule and its Application to Chemical Equilibrium . . 574 Equilibrium in Solutions of Electrolytes 593 CHAPTER X Measurements op Chemical Activity Methods employed and Some of the Results obtained .... 601 Effect of Composition and Constitution on Chemical Activity . . 611 THE ELEMENTS OF PHYSICAL CHEMISTRY CHAPTER I ATOMS AND MOLECULES THE ATOMIC THEORY The Law of the Conservation of Mass. — The study of chemical phenomena, like the study of natural phenomena in general, was at first purely qualitative. It was early observed that when certain substances are brought together they react, giving rise to new sub- stances, and it was also noted that the substances formed as the result of the reaction have many properties which are very different from those of the substances from which they were formed. These qualitative observations, however, while absolutely necessary in the earlier stages of any branch of science, are far from sufficient. The mere fact that from certain things other things are formed is not only empiricism, but empiricism in the earliest stage; since it is but the result of the observation of the more superficial side of the phenomenon of chemical activity, and entirely lacks any quantita- tive basis. The qualitative stage is followed, wherever it is possi- ble, by the quantitative; and so it has been in chemistry. Known quantities of substances were used, and the amounts of the sub- stances formed determined. Almost as soon as chemists began to work with known masses of substances, the remarkable fact was discovered that in chemical transformations mass remains unaltered. This is remarkable because it is the only property which remains unchanged in chemical reaction. When two or more substances react, nearly all of the properties of the products of the reaction are different from those of the substances which enter into the reaction. This is well illustrated by the reaction between metallic sodium and chlorine, resulting in the formation of sodium chloride. The salt formed has properties very different from either constituent. 2 THE ELEMENTS OF PHYSICAL CHEMISTRY Indeed, all of the most striking properties of both constituents are lost during the reaction. Yet, in the midst of ■ all this change of properties which takes place in chemical reactions, the one property, mass, stands immutable. We measure mass by weight, and are accustomed to say that in chemical reactions weight remains unchanged ; the weight of all the products of the reaction, under the same conditions, is exactly equal to the weight of all the substances which enter into the reaction. This is true ; but since weight is but a measure of mass, it is the conservation of the mass and not of the weight upon which we should fix our attention. This law of the conservation of mass is sometimes referred to as the law of the conservation of matter. The former expression is greatly to be preferred to the latter, since it states just what we have established by experiment. The latter goes far beyond the facts and, as Ostwald has pointed out, is pure theory. The question as to whether there is any change in weight in chemical reaction has recently been thoroughly investigated by Landolt. 1 In his work the most refined balances that have ever been made were employed; and in every detail the work is a classic for thoroughness and accuracy. Landolt studied about a half-dozen reactions, and found always a small loss in weight as the result of the reaction. His most recent work shows that this is due to the expansion of the vessels by heat. The Law of Constant Proportion. — The second important general- ization which was reached through the quantitative study of chemical phenomena, was that the constituents of a chemical compound are always present in a constant proportion. If two substances unite and form a third, they enter into combination in a constant propor- tion by mass. The law may be stated thus: — Any given chemical compound always contains the same constituents, and there is a constant proportion between the masses of the constituents present. The law of constant proportions was called in question in the early years of the nineteenth century by Berthollet. 2 He was im- pressed by the effect on the chemical reaction of the quantity of substance used, and saw in outline what has since been established as the law of mass action. He thought that not only the nature and magnitude of the reaction were affected by the masses of the sub- 1 Ztschr. phys. Chem. 12, 1 (1893) ; 65, 589 (1906). 2 Essai de statique chimique (1803). ATOMS AND MOLECULES 3 stances used, but also the composition of the products formed. Two substances could unite in a great many proportions, and the com- position of the product depended chiefly on the relation between the amounts of the substances used. The error of Berthollet was corrected by Proust, who showed that many of the substances which were supposed by Berthollet to be compounds were simply mixtures. The result of the most accurate investigations is to show that the law of constant proportions is a fundamental law of chemical reaction. Law of Multiple Proportions. — While it is true that substances combine in constant proportions, it is also true that two substances may combine in more than one proportion. Dalton ' examined the two compounds, methane and ethylene, and found that the ratio of carbon to hydrogen in the former was as 3 to 1 ; in the latter as 6 to 1. The latter compound evidently contains twice as much carbon with respect to hydrogen as the former. Similarly, there is just twice as much carbon with respect to oxygen in carbon monoxide as in carbon dioxide. A large number of other compounds were examined, in which simple ratios between the masses of the con- stituents were discovered. Prom these and similar facts Dalton arrived at the law of multiple proportions, which may be stated thus : — If two elements combine, in more than one proportion, the masses of the one which combine with a given mass of the other, bear a simple rational relation to one another. The Law of Combining Weights. — There is a third law to which the masses of substances which combine with one another conform. . This has been termed the law of combining weights. If we deter- mine the weights of different substances which combine with a given weight of a definite substance, these weights, or simple multiples of them, represent the quantities of the different substances which will combine with one another. The quantities of substances which combine with one another have been termed their combining numbers. Substances combine either in the ratio of their combining numbers, or in simple rational multiples of these numbers. This law, like the laws of constant and multiple proportions, has been subjected to the most careful experimental test, and has been shown to be true to within the limit of error of some of the most refined experimental work. Origin of the Atomic Theory. — The discovery of empirical rela- 1 New System of Chemical Philosophy (1808). 4 THE ELEMENTS OF PHYSICAL CHEMISTRY tions, such as the three laws of chemical combination just considered, is of great importance, and is absolutely essential to scientific prog- ress; but these are chiefly of interest as they lead to correct theories and wide-reaching generalizations. Dalton raised the question, What does the law of multiple proportions really mean ? Why do such relations obtain ? His answer is what has come to be known as the scientific atomic theory, in contradistinction to the older imaginative speculations about atoms and molecules. The view that matter is composed of indivisible particles or atoms, which have definite weights, and that chemical action takes place between these parti- cles, was to Dalton the only rational explanation of the laws of mul- tiple proportion and combining weights. If matter is composed of such ultimate parts or atoms, then a constant number of atoms of one substance combine with one atom of another substance to form a definite compound, and we have the law of constant proportions. One atom of one substance may combine with one atom of another substance, or a number of atoms of one substance may combine with one of another; but the number must be a simple rational whole number; whence the law of multiple proportions. Since the atoms have definite weights, and the laws of constant and multiple proportions are true, the law of combining numbers follows as a necessary consequence of the atomic theory. And, further, if the same number of atoms of the two substances combine, the combining numbers represent the relative weights of the atoms which enter into combination. This furnished a means of determin- ing the relative atomic weights. DETERMINATION OF RELATIVE ATOMIC WEIGHTS Combining Numbers and Atomic Weights. — The problem of de- termining the relative weights of atoms seems at first sight a very simple matter, from what was stated above. It is only necessary to determine the relative weights of substances which combine — the combining numbers — in order to find out the relative weights of the atoms of these substances. This would be true if a given number of atoms of one substance always combined with an equal number of atoms of another. But we know that this is not the case, since it often happens that two elementary substances combine in several proportions. To determine the relative atomic weights of the ele- ments, we must, therefore, know the combining numbers of the ele- ments, and also the number of atoms of the different elements which ATOMS AND MOLECULES 5 combine -with one another. We will take up first the method of determining the combining numbers of the elements. Chemical Methods of determining Combining Numbers. — The simplest method would be to take some element as our standard, and call its combining number one. Then allow all of the other elements to combine with this one, and determine the weights of the different elements which combined with unit weight of our standard element. Since hydrogen has the smallest combining number, it would natu- rally be chosen as the unit. The problem then would be to determine, say, the number of grams of the different elements which combine with one gram of hydrogen, and these figures would represent the combining weights of the elements in terms of hydrogen as unity. Since it is true that comparatively few of the elements combine directly with hydrogen, the direct comparison with hydrogen cannot be made in many cases. A large number of the elements, however, combine directly with oxygen. We can determine the ratio between the combining numbers of these elements and oxygen, and then the ratio between the com- bining number of oxygen and that of hydrogen, and thus calculate the combining numbers of the elements in terms of our unit hydrogen. We might thus work out a table of the combining numbers of all of the elements in terms of hydrogen as unity. This part of the prob- lem is, however, not as simple as would be indicated from the above. Many of the elements combine in more than one proportion. Take the case of hydrogen and carbon. The combining number of carbon in terms of hydrogen as unity would be 3 if determined by the analysis of marsh gas. From the analysis of ethylene we would conclude that it was 6, while from the analysis of acetylene it would appear to be 12. A similar complexity would result in the case of carbon and oxygen. If we take oxygen as 16 in terms of hydrogen 1, the combining number of carbon, as determined from carbon monoxide, would be 12, while as determined from carbon dioxide it would be 6. We would thus obtain different combining numbers for the same element, depending upon which of its compounds we selected. It is perfectly clear that neither the chemical analysis of the compound, nor its synthesis from the elements, throws any light on the problem as to the number of atoms of one substance combined with one atom of the other. Berzelius attempted to solve this part of the problem of atomic weights by means of certain dogmatic rules, which have only this value, that they brought out a large amount 6 THE ELEMENTS OF PHYSICAL CHEMISTRY of experimental work which resulted in new and improved methods of analysis. Chemical methods alone can lead only to the combin- ing weights or numbers of the elements, and, as already stated, in many cases more than one combining weight for an element would be obtained. Other methods must be employed in order to deter- mine the number of atoms of the one element which have com- bined with one atom of the other. To these we will now turn. Molecular Weights determined from the Densities of Gases. — Gay Lussac 1 showed in 1808 that the densities of gases are proportional to their combining weights, or to simple rational multiples of them. If two gases react chemically, the volumes which react are either equal, or bear a simple rational relation to one another. And, further, if the product formed is a gas, its volume bears a simple rational relation to the volumes of the gases from which it was formed. Thus, one volume of hydrogen combines with one volume of chlorine, and forms two volumes of hydrochloric acid gas. One volume of oxygen combines with two volumes of hydrogen, form- ing two volumes of water-vapor. One volume of nitrogen com- bines with three volumes of hydrogen, forming two volumes of ammonia. From the laws of definite and multiple proportions, the law of combining numbers, and the atomic theory which was proposed to account for these, we see that every chemical reaction takes place between a definite number of atoms, and the number is usually small. Therefore, the discovery of Gay Lussac leads to the con- clusion that — The number of atoms contained in a given volume of any gas 'must bear a simple rational relation to the number of atoms contained in an equal volume (at the same temperature and pressure) of any other gas. We have thus far, however, no means of determining the numeri- cal value of this relation, and, therefore, cannot use the discovery of Gay Lussac alone to determine relative atomic weights. Avogadro's Hypothesis. — Avogadro 2 in 1811, taking into account all of the facts known, advanced the hypothesis that — In equal volumes of all gases, at the same temperature and pressure, there is an equal number of ultimate parts or molecules. Avogadro extended his hypothesis to all gases, including even the elementary gases, and regarded the molecules of these substances 1 Mem d. Arcueil, T., II. (1808). 2 Journ. de Phys. 73, 58-76 (1811). ATOMS AND MOLECULES 7 as made up of atoms of the same kind, 'which had united with one another. This was a necessary consequence of his hypothesis. One volume of hydrogen gas combines with one volume of chlorine gas, and forms two volumes of hydrochloric acid gas. If there are the same number of molecules in equal volumes of all gases, there would be twice as many in the two volumes of hydrochloric acid as in the one volume of hydrogen, or the one volume of chlorine. Since each molecule of hydrochloric acid must contain at least one atom of hydrogen and one atom of chlorine, the molecule of hydrogen and of chlorine must be made up of at least two atoms. Ampere, 1 in 1814, advanced essentially the same hypothesis as had been pro- posed three years before by Avogadro. The hypothesis of Avogadro has been confirmed by such an abundance of subsequent work, in so many directions, that it is now placed among the well-established laws of nature. It points out distinctly the difference between atoms and molecules, and rationally explains why different gases should obey the same law of volume and of pressure, and have the same temperature coefficient of expansion. It has been tested from both the physical and mathematical standpoints, and now lies at the basis of much of our knowledge of gases. Avogadro's Hypothesis and Molecular Weights. — Given the hypothesis of Avogadro, the determination of the relative molecular weights of gases is very simple. If there is an equal number of molecules contained in equal volumes of the different gases, the relative weights of equal volumes of these gases give at once the relative weights of the molecules contained in them. It is only necessary to choose some substance as our standard, and express the molecular weights of other substances in terms of this standard. We would naturally select as the unit that substance which has the smallest density, and this is hydrogen. From what has been said, however, in reference to the union of hydrogen and chlorine, forming hydrochloric acid, it is certain that the molecule of hydro- gen contains at least two atoms. We will, therefore, call the molec- ular weight of hydrogen two, and calculate the molecular weights of other elements in terms of this standard. The densities of sub- stances are usually determined in terms of air as the unit. It is a simple matter to recalculate these in terms of hydrogen as two. The density of hydrogen in terms of air as the unit is 0.06926. 2 We must multiply this by 28.88 to obtain our new unit two 1 Lettre de M. Ampere a le Berthollet, Ann. de Chim. 90, 43. 2 Later determinations give 0.0696. 8 THE ELEMENTS OF PHYSICAL CHEMISTRY (2 -i- 0.06926 = 28.88). Similarly, for other substances whose den- sities are known with reference to air ; these densities must be multiplied by the constant 28.88 to transform them into densities in terms of hydrogen = 2. These latter values are the relative molecular weights of the substances in the form of gas, referred to the molecular weight of hydrogen as two. A few results are given in the following table, showing in column I the densities in terms of air as the unit ; in column II the densities or relative molecular weights in terms of hydrogen = 2. The results in column II are obtained by multiplying the results in column I by 28.88. I II Hydrogen, 0° C 0.06926 2 Oxygen, 0° C. 1.10563 31.93 Nitrogen, 0° C. 0.9713 28.05 Sulphur, 1400° C. . 2.17 X 28.88 62.67 Chlorine, 200° C. . 2.45 70.75 Bromine, 100° C. . 5.54 159.99 Mercury, 1400° C. 6.81 196.67 Iodine, 940" C. . 8.72 251.83 The molecular weights of compounds can be determined in exactly the same manner from the densities of their vapors. If these have been determined on the basis of air as unity, we must multiply by 28.88 to obtain the molecular weight referred to hydrogen as two. The molecular weights of compounds thus obtained must bear a rational relation to the combining weights of the elements which enter into the compound. The molecular weights as obtained from vapor-densities can, therefore, be corrected by the most careful analytical or synthetical determination of the combining weights of the elements which enter into the compounds. Atomic Weights from Molecular Weights. — If we knew the num- ber of atoms contained in the molecule of elements in the gaseous state, the problem of relative atomic weights would be solved at once by dividing the molecular weight of the gas by the number of atoms in the molecule. The problem is, however, not as simple as this, since we do not know at once the number of atoms in the molecules of elements. Other lines of thought have enabled us to solve this the second part of our problem. The definition of an atom as an indivisible particle of matter shows that fractions of atoms cannot exist. No molecule can con- ATOMS AND MOLECULES 9 tain a fraction of any atom. The quantity of any substance which enters into a molecule must be at least one atom. It may be more than one, but it cannot be less. This is the key to the problem. Suppose we wish to determine the number of hydrogen atoms in a molecule of hydrogen. "We must examine compounds into which hydrogen enters, and find out what is the smallest quantity of hydrogen which enters into the molecule of the compound. Let us take hydrochloric acid, whose molecular weight is 36.45. This is shown by analysis to be composed of 1 part of hydrogen and 35.45 parts of chlorine. This 1 part of hydrogen is at least one atom ; it may be more, but it cannot be less. By examining a large num- ber of compounds into which hydrogen enters, it has been found that hydrogen never enters into a molecule of any substance in a smaller quantity than in hydrochloric acid. This is, therefore, for us the atom of hydrogen, but it may in reality be composed of a great number of smaller parts. The hydrogen which enters into the molecule of hydrochloric acid is just half the quantity which forms the molecule of hydrogen gas, since one volume of hydrogen com- bining with one volume of chlorine yields two volumes of hydro- chloric acid gas. The molecule of hydrogen, therefore, contains at least two atoms, and since there is no experimental reason for assuming that it contains more than two, we say that the molecule of hydrogen is made up by the union of two hydrogen atoms. Know- ing the number of atoms in the molecule, the atomic weight follows at once from the molecular weight determined by vapor-density, and corrected by the most refined methods of chemical analysis. By methods similar to the above the molecules of many elements have been shown to be composed of two atoms. But this by no means applies to all elementary substances. The molecules of some elementary substances contain more than two atoms, and in a very few cases the molecule and atom seem to be identical. And, further, the number of atoms contained in the molecule has been shown to vary in some cases with change in conditions, especially with change of temperature. But by studying a large number of compounds of an element, and ascertaining what is the smallest quantity of the element which ever enters into a compound, we can determine the number of atoms contained in a molecule of the element itself. Knowing the number of atoms in the molecule of the element, and the weight of the molecule, we can determine relative atomic weights. The relations between the molecular weights of a few of the elements and their atomic weights are given in the follow- ing table: — 10 THE ELEMENTS OF PHYSICAL CHEMISTRY Elements Atomic Weights Molecui*ab Weights Iodine . .... 1 14.01 15.88 30.96 31.98 35.18 74.9 78.9 79.34 111.7 126.3 125.89 199.8 2 28.02 31.76 123.84 r 63.96 above 800° C. 1191.88 at 500° C. 70.36 299.6 157.8 158.68 111.7 252.6 251.78 under 600° C. 199.8 This table brings out a number of facts to which reference has already been made. The molecular weight of a number of the elements is twice as great as the atomic weight. In some cases, as with sulphur, the molecular weight is twice the atomic weight at a given temperature, and then varies with the temperature. In the cases of cadmium and mercury the molecular weights are apparently identical with the atomic weights. This matter will be taken up later in other connections. It frequently happens that an element boils at such a high tempera- ture that we cannot determine accurately its vapor-density. In such cases volatile compounds of the element are used, and their molecular weights determined. These compounds are then analyzed, and the one containing the smallest quantity of the given element in its molecule is said to contain one atom of the element. The real atom of the element may be a fraction of this quantity, but this is for all chemical or physical chemical purposes the atom, and its relative weight is the atomic weight of the element in question. Atomic Weights from Specific Heats. — Dulong and Petit 1 in 1819 showed that a very simple relation exists between the specific heats of elements in the solid state and their atomic weights. They found that the specific heats varied inversely as the atomic weights, and, consequently, that the product of the specific heats and atomic weights of the elements is a constant. This will be seen from the following data : — 1 Ann. Chim. Phys. 10, 396 (1819). ATOMS AND MOLECULES 11 Specific! Heat Atomic Weight Product Lithium 0.941 7.01 6.6 Sodium . 0.293 22.99 6.7 Magnesium 0.250 23.94 6.0 Potassium 0.166 39.03 6.5 ■Calcium 0.170 39.91 6.8 Iron 0.112 55.90 6.3 Cobalt . 0.107 58.60 6.3 Nickel . 0.108 58.60 6.4 Zinc 0.0932 64.9 6.1 From these and similar facts Dulong and Petit announced their law: — ■ Tlie atoms of all elements have the same capacity for heat energy. After the discovery of this law it was a comparatively simple matter to determine the atomic weights of solid elements from their specific heats. If specific heat multiplied by atomic weight is a constant, the atomic weight is equal to the constant divided by the specific heat. The numerical value of the constant, taken as the average for a number of elements, is about 6.25. Exceptions to the law of Dulong and Petit were early recognized. "Weber 1 determined the specific heats of the elements carbon, boron, and silicon, at temperatures between 0° and 100° C, and obtained much smaller values than would be expected from the law of Dulong and Petit, using the atomic weights of these elements as determined from Avogadro's law. He found, however, that the specific heats of these elements varied widely with change in temperature, and that above a certain temperature the specific heats became constant. At these elevated temperatures, where the specific heats became con- stant, they conformed to the law of Dulong and Petit. These constant specific heats were obtained only at comparatively high temperatures ; for silicon at about 200° C, for the different modifica- tions of carbon at about 600° C, for boron at about 500° C. The different modifications of carbon had different specific heats at low temperatures, but at elevated temperatures this difference also was found to vanish, the different varieties of carbon at red heat show- ing the same specific heats. Similar observations were made on glucinum by Nilson and Pettersson. 2 1 Pogg. Ann. 184, 367 (1875). Ber. d. chem. Gesell. 5, 303 (1872). 2 Ber. d. chem. Gesell. 13, 1451 (1880). 12 THE ELEMENTS OF PHYSICAL CHEMISTRY The law of Dulong and Petit is, in general, only approximately true, and holds only within certain limits of temperature. The relation between the specific heats of compounds and the specific heats of their constituents was next investigated. Neumann 1 showed that equivalent quantities of analogous compounds have the same capacity for heat, and Eegnault, Kopp, 2 and others pointed out the following relation between the specific heats of compounds and the specific heats of their constituents. The capacity of the atoms for heat energy is not appreciably changed when they unite and form compounds. In a word, the capacity of the molecule for heat is the sum of the capacities of the atoms in the molecule. The recognition of this relation makes it possible to greatly extend the method of determining atomic weights by specific heats. Many of the elements are solids only at temperatures which are too ' low to be dealt with by the methods of measuring specific heats. But these elements form solid compounds with other elements whose specific heats and atomic weights can be determined. Let us take an example. 8 Chlorine is an element whose specific heat in the solid state would be very diificult to determine. Chlorine, however, forms a solid compound with the element lead. The specific heat of lead chloride has been found by Eegnault to be 0.0664 ; 206.4 parts of lead yield 277.1 parts of lead chloride. Multiplying this number by the spe- cific heat of lead chloride, we obtain the molecular heat. 277.1 x 0.0664 = 18.4. Subtracting the atomic heat of lead, 6.5, we have 11.9 as the atomic heat, corresponding to 70.7 parts of chlorine. Since the atomic heat of the elements is about 6, we have in 70.7 twice the atomic weight of chlorine, or the atomic weight of chlorine = 35.35. This agrees very closely with the atomic weight of chlorine determined by the vapor-density method, based upon the law of Avogadro. The above example serves to illustrate the way in which the spe- cific heats of compounds are used to determine atomic weights. The method has been widely applied, and it may be said in general, that the atomic weights determined from the law of Dulong and Petit agree with those obtained from the law of Avogadro, although some discrepancies exist. Isomorphism an Aid in determining Atomic Weights. — It was 1 Pogg. Ann. 23, 1 (1831). 2 Lieb. Ann. (1864), Suppl. 3, 5. 3 Meyer : Die modernen Theorien der Chemie, p. 100. ATOMS AND MOLECULES 13 recognized even in the eighteenth century that substances of different composition often have the same, or very nearly the same, crystal form. This was at first explained by assuming that certain substances have the power of forcing other substances to take their own crystal form. Mitscherlich 1 interpreted this fact quite differently. He studied the salts of arsenic and phosphoric acids, and found that those which contained an equal number of atoms in the molecule had the same or very similar crystal forms. Mitscherlich concluded at first that it was only the number and not the nature of the atom which condi- tioned the crystal form. Later, he recognized that the way in which the atom was united in the compound was an important factor in determining its crystal form, and then arrived at the generalization that, " An equal number of atoms combined in the same way produce the same crystal form, and that the same crystal form is independent of the chemical nature of the atoms, but depends only on their number and position." If this relation was true, it would throw much light on the num- ber of atoms in a compound, and therefore be of service in deter- mining atomic weights. Given two isomorphous substances such as BaCl 2 2 H 2 and BaBr 2 2 H 2 0, from the law of Mitscherlich their molecules must contain the same number of atoms. If we know the atomic weights of all of the elements in the former compound, we can find the atomic weight of the bromine in the latter sub- stance. This relation pointed out by Mitscherlich was accepted at once by Berzelius, who made it the basis of atomic weight determinations. The law, however, did not long remain without exceptions. Mit- scherlich 2 showed that the compounds BaMn 2 O s , Na 2 S0 4 , and Na 2 Se0 4 are isomorphous, and they evidently contain a very different number of atoms in the molecule. An attempt was made to overcome this difficulty by ascribing to these compounds the formulas, BaMn 2 8 , NaS 2 8 , and NaSe 2 8 , but these were so strongly at variance with all the facts known that they had to be abandoned, and a number of other substances were soon discovered to be isomorphous which could not possibly be regarded as containing the same number of atoms in the molecules. The generalization of Mitscherlich is then only an approximation to which there are many exceptions, and this method of determining atomic weights must be used with great caution. 1 Ann. Chim. Phys. [2], 14, 172 (1820). 2 Fogg. Ann. 25, 287 (1832). 14 THE ELEMENTS OF PHYSICAL CHEMISTRY The modifications of the law of Mitscherlich proposed by Marig- nac 1 and Kopp 2 have scarcely increased our confidence in it as a means of determining atomic weights. The former has shown that equality in the number of atoms in compounds is not necessary in order that we may have isomorphism, and Kopp would limit the term isomorphism to substances which will grow in each other's so- lutions. The application of the conception of isomorphism to the problem of atomic weights has, however, been of much service, especially in the earlier stages of such work. Most Accurate Method of determining Atomic Weights. — The general methods described for determining the relative atomic weights of the elements differ greatly in their relative accuracy. Of these the various chemical methods for determining the constituents of compounds are by far the most accurate. Indeed, the other methods described, such as the vapor-density method, and the methods based upon specific heat of solids, and upon isomorphism, must be regarded simply as checks upon the chemical methods. By means of chemical analysis or synthesis we determine with the greatest degree of accuracy the combining weights of elements, and then make use of the other methods to decide whether we are dealing with one or more atoms. In determining atomic weights we must choose some element as our standard. We would naturally take the lightest element, hydro- gen, and call it unity. This has been done, and all atomic weights referred to this unit. But it is unfortunately true, as has been stated, that hydrogen does not combine directly with many of the elements and form stable compounds which can be analyzed. Oxygen, on the other hand, does combine with a large number of the elements, forming some of the most stable compounds with which we are acquainted. It therefore seemed best to compare the atomic weights of the elements directly with the atomic weight of oxygen, and then compare oxygen with hydrogen, with which it forms the very stable compound, water. It should be stated, however, that this method is by no means free from objections, and many prefer retaining hydrogen as the unit. The atomic weight of oxygen, in terms of hydrogen as the unit, was supposed for a long time to be the whole number 16. If this was true, it would obviously make no difference whether we called hydrogen 1 or oxygen 16, and then compare all other atomic weights with these standards. It has 1 Lieb. Ann. 132, 29 (1864). 2 Ber. d. chem. Gesell. 12, 909 (1879). ATOMS AND MOLECULES 15 recently been shown beyond question that when hydrogen is 1, oxy- gen is not 16, but considerably less (15.88). We must, therefore, choose between these two substances as the basis of the system of atomic weights. The majority of investigators at present seem inclined to select oxygen as the standard, taking its atomic weight as 16, and referring the atomic weights of all the other elements to this basis. The most direct method of determining the combining weight of an element, in terms of oxygen as our standard, would be to deter- mine the weight of the element which would combine with a known weight of oxygen. The combining weight of the element would then be calculated by the simple proportion, — Wt. oxygen : wt. element = at. wt. oxygen : combining wt. element. We should then have to determine, by some of the methods already referred to, how many atoms of the element in question combined with one atom of oxygen. While it is true that oxygen combines directly with many of the elements, forming stable compounds, it is by no means true that it forms such compounds with all of the elements. And further, some of the elements form compounds with oxygen which are gaseous or liquid at ordinary temperatures, and for these or other reasons are not adapted to atomic weight determinations. In such cases the atomic weight of the element must be compared with that of some element other than oxygen, which in turn has been compared with oxygen. Thus, the atomic weights of the halogens have been determined in terms of the atomic weight of silver, and the latter then determined in terms of oxygen. Even more complex cases may arise, where it is necessary to compare the atomic weight of an element with the sum of the atomic weights of two or more elements, each of which has been determined in terms of oxygen. It is evident that the more direct the comparison of the atomic weight of the element with that of oxygen, the better; since the accumulation of experimental errors, resulting from indirect com- parisons, is avoided. Some of the most refined experimental work which has ever been done has had to do with the problem of relative atomic weights. It is obviously necessary that these constants should be determined with the very greatest degree of accuracy, since all chemical analysis and much of the most refined work in physical chemistry and in physics depends upon them. In this connection we should mention, 16 THE ELEMENTS OF PHYSICAL CHEMISTRY especially among the earlier work, that of Stas 1 and Marignac, 2 and among the more recent investigations those of Morley 3 and Eichards. 4 The work of Stas had to do more especially with the relations between silver and the halogens, but included, also, a large number of other elements, especially lithium, sodium, potassium, sulphur, lead, and nitrogen. The work of Stas, as a whole, has become a model for refinement and accuracy, and is simply wonderful when we consider the comparatively crude apparatus with which it was carried out. Marignac has done an enormous amount of work on the problem of atomic weights. He has determined the atomic weights not only of chlorine, bromine, and iodine, but of carbon and nitrogen, calcium, barium, magnesium, zinc, manganese, nickel, cobalt, lead, bismuth, and many of the rarer elements. The comparatively recent work of Morley on the ratio between the atomic weights of oxygen and hydrogen is one of the finest pieces of scientific work in modern times. He has established this ratio by different methods, with an unusual concordance in the re- sults, to be 1 : 15.879. The work of T. W. Eichards on the atomic weights of a large number of the metals should receive special mention. He has im- proved old methods, devised new ones, and applied them with a skill which is rare. His determinations are to be ranked among the very best which have ever been made. Table of Atomic Weights. — The most probable atomic weights of the elements, based upon the best determinations, are given in the following table. In preparing this table the tables of Clarke, of Eichards, and of the committee of the German Chemical Society have all been carefully considered ; also the original determinations themselves, wherever there were appreciable differences between the values chosen by the different authorities. The basis of this table is oxygen = 16. 1 Untersuch. iiber die Gesetze der ckemischen Proportionen. Leipzig, 1867. 2 Lieb. Ann. 59, 284, 289 (1846); Ann. Chim. Phys. [6], 1, 303, 321 (1884); Journ. prakt. Chem. 74, 214, 216 (1858). 3 Densities of and H, and the Ratios of their Atomic Weights. (Smith- sonian publication.) * Amer. Chem. Journ. 10, 187; Ztschr. anorg. Chem. (1894-1901). ATOMS AND MOLECULES 17 Element Atomic Weight Element Atomic Weioht Aluminium .... 27.1 Neodymium .... 143.6 Antimony . 120.2 Neon . . . 20.0 Argon . 39.9 Nickel . . . 58.7 Arsenic . 75.0 Nitrogen . . 14.01 Barium . 137.4 Osmium . . 191.0 Bismuth 208.0 Oxygen . . 16.0 Boron . 11.0 Palladium 106.5 Bromine 79.96 Phosphorus . 31.0 Cadmium 112.4 Platinum . . 194.8 Caesium . 132.9 Potassium 39.15 Calcium 40.1 Praseodymium 140.5 Carbon . 12.0 Badium . . 227.0 Cerium . 140.25 Bhodium . . 103.0 Chlorine 35.45 llubidium 85.6 Chromium 52.1 Ruthenium . 101.7 Cobalt . 59.0 Samarium 150.3 Columbium 94.0 Scandium . . 44.1 Copper . 63.6 Selenium . . 79.2 Erbium . 166.0 Silicon . . . 28.4 Fluorine 19.0 Silver . . . 107.93 Gallium . 70.0 Sodium . . 23.05 Germanium 72.5 Strontium 87.6 Glucinum 9.1 Sulphur . . 32.06 Gold . . 197.2 Tantalum . . 181.0 Helium . 4.0 Tellurium 127.6 Hydrogen 1.008 Terbium . . 159.2 Indium . 115.0 Thallium . . 204.1 Iodine . 126.97 Thorium . . 232.5 Iridium . 193.0 Thulium . . 171.0 Iron . . 55.9 Tin ... . 119.0 Krypton 81.8 Titanium . . 48.1 Lanthanum 138.9 Tungsten . . 184.0 Lead . . . 206.9 Uranium . . 238.5 Lithium 7.03 Vanadium . 51.2 Magnesium 24.36 Xenon. . . . 128.0 Manganese 55.0 Ytterbium . 173.0 Mercury . . 200.0 Yttrium . . 89.0 Molybdenum . 96.0 Zinc . . . 65.4 Zirconium . 90.6 18 THE ELEMENTS OF PHYSICAL CHEMISTRY RELATIONS BETWEEN ATOMIC WEIGHTS AND PROPERTIES The Hypothesis of Prout. — It was early noted that if we chose the atomic weight of hydrogen as one, the atomic weights of a large number of elements were either whole numbers or very nearly whole numbers. The slight differences from whole numbers, which were found in several cases, were attributed for the most part to experi- mental error. Prout observed this relation between the atomic weights, and suggested in 1815 that the explanation of this numeri- cal regularity might be found in the assumption that all the ele- ments are simply condensations of hydrogen. The atoms of the different elements are composed of hydrogen atoms, the number being expressed by the atomic weight of the element. This as- sumption, which has come to be known as the hypothesis of Prout, was also made some three years later by Meinecke. 1 The hypothesis of Prout was kindly received, especially by Thomson in England, but was strongly opposed by the great Swedish chemist Berzelius. The latter had devoted much time and labor to the determination of atomic weights, and at this time was the leading authority on such matters. He objected to the method of testing the hypothesis by dropping the fractional part of the atomic weight which had been found experimentally, and of course this point was well taken. Gmelin, 2 on the other hand, was well inclined toward Prout's generalization, and Dumas became a warm supporter of it, after he and Stas had redetermined the atomic weight of carbon and found it to be very nearly 12, in terms of hydrogen as unity. The element chlorine was, however, very troublesome. The best determinations showed that its atomic weight was 35.5. This led Marignac in 1844 to propose that one-half the atomic weight of hydrogen be taken as the unit. This was the beginning of the downfall of Prout's hypothesis. Having once begun to subdivide the atomic weight of hydrogen to obtain the fundamental unit, there was no limit to the process. The next step was taken by Dumas in 1859, when he suggested that one-fourth the atomic weight of hydrogen be taken as the unit, so as to avoid fractions in the more accurately determined atomic weights. Stas, in 1860, undertook to settle the question as to the correct- 1 Schweigger's Journal, 22, 138. 2 Handbuch d. theoret. Chemie. ATOMS AND MOLECULES 19 ness of Prout's original hypothesis. He began that series of atomic weight determinations to which reference has already been made, and which far exceeded in accuracy anything done up to that time. The result is well known. The atomic weights of a number of the elements did not prove to be whole numbers, and the differences from whole, numbers were far greater than could reasonably be accounted for on the basis of experimental error. Stas was thus led to abandon the hypothesis, as it was not supported by the facts. Attention was again turned to Prout's hypothesis, in 1880, by Mallet. 1 The result of his investigation on the atomic weight of aluminium was to add another element to the list of those which conform to the hypothesis. He took the view that the deviations of the best-known atomic weights from whole numbers may be due to constant errors in the determinations, and pointed out that ten out of eighteen of the best-known atomic weights differed from whole numbers by less than one-tenth of a unit. While there is then some difference in opinion, even at present, 2 in reference to the real merit of the hypothesis of Prout, there is a strong tendency to reject it as the ultimate expression of the truth. That it is an effort in the right direction is certain, and, indeed, this will be seen when we come to consider, later in this section, the most recent theory of one of the leading physicists of to-day. The Triads of Dbbereiner. — On examining the atomic weights of correlated elements, Dobereiner observed the striking relation, that the atomic weight of the middle member of a group of three such elements was almost exactly the mean between the atomic weights of the first and last members. This will be seen from the following examples : — Atomic Weight Atomic Weight Atomic Weight Calcium . . Strontium . . Barium . . . 40.1 87.7 137.4 Chlorine . . Bromine . . Iodine . . . 35.4 80.0 126.8 Sulphur . . Selenium . . Tellurium 32.1 79.2 127.5 The atomic weight of strontium is close to the mean of calcium and barium (88.7) ; that of bromine is not widely different from the 1 Amer. Chem. Journ. 3, 95 (1881). 2 Strutt: Phil. Mag. [6], 1, 311 (1901). 8 Fogg. Ann. 15, 301 (1825). 20 THE ELEMENTS OF PHYSICAL CHEMISTRY mean of chlorine and iodine (81.1) ; while the atomic weight of selenium is very close to the mean of sulphur and tellurium (79.8). These correlated groups of three elements came to be known as triads, and from their discoverer as Dobereiner triads. The Work of Cannizzaro and of De Chancourtois. — It was impossible that any comprehensive generalization should be reached connecting atomic weights with any property, until some uniform system of atomic weights had been adopted. Confusion was reduced to order in this line by Cannizzaro. He considered Avogadro's law as the basis of atomic weight determinations, and gave us the con- ception of atom which still prevails. With these, comparable atomic weights chemists could now deal, and relations between those weights and properties of the elements, which have proved to be of the greatest service in the development of inorganic chemistry, were soon pointed out. It is thought by some that De Chancourtois was the first to call attention to relations which can fairly be regarded as the logical precursors of the periodic law. He suggested l that the atomic weights be arranged in a particular way in the form of a screw, and showed that relations existed between the positions of the elements and their properties. In an obscure way he seems to have hinted at the fundamental idea underlying the later discovery, that the properties depend upon the atomic weights, but certainly this was neither clearly conceived nor tersely expressed. The Octaves of Newlands. — The question of relations between the atomic weights was taken up by Newlands shortly after the work of De Chancourtois. In his earlier papers 2 he pointed out connections between atomic weights and chemical properties, but it was not until 1864 that he announced any important discovery. In a brief note to the CheimtiklNews, 3 " On Relations among the Equiva- lents," he arranged the el*ients in the order of their equivalents, and stated that " it will belobserved that elements having consecu- tive numbers frequently either belong to the same group or occupy similar positions in different groups. . . . The difference between the number of the lowest member of a-- group and that immediately above it is 7; in other words, the eighth element starting from a given one is a kind of repetition of the first, like the eighth note of an octave in music." In the following year Newlands announced his " Law of Octaves " in a very brief note : * "If the elements are 1 Vis Tellurique, Classement naturel des Corps Simples, etc. Paris, 1863. * Chem. News, 7, 70 (1863); 10, 11, 59 (1864). » Ibid. 10, 94 (1864). 4 Ibid. 12, 83 (1865). ATOMS AND MOLECULES 21 arranged in the order of their equivalents with a few slight trans- positions, it will be observed that elements belonging to the same group usually appear on the same horizontal line. It will be seen that the members of analogous elements generally differ either by 7, or by some multiple of 7. In other words, members of the same group stand to each other in the same relation as the extremi- ties of one or more octaves in music." The table given by New- lands brings out the relation to which he refers. It is of such historical interest that it should be given in this connection. Newlands' Table H 1 F 8 CI 15 Co & Ni 22 Br 29 Pd 36 I 42 Pt&Ir 50 Li 2 Na 9 K 16 Cu • 23 Rb 30 Ag 37 Cs 44 Tl 53 G 3 Mg 10 Ca 17 Zn 25 Sr 31 Cd 38 Ba & V 45 Pb 54 Bo 4 Al 11 Cr 19 Y 24 Ce & La 33 U 40 Ta 46 Th 56 C 5 Si 12 Ti 18 In 26 Zr 32 Sn 39 W 47 Hg 52 N 6 P 13 Mn 20 As 27 Di & Mo 34 Sb 41 Nb '48 Bi 55 7 S 14 Fe 21 Se 28 Ro&Ru 35 Te 43 Au 49 Os 51 A comparison of this table with the periodic system proper will show that it contains more than the germ of this important general- ization. The Periodic System of Mendele'eff and Lothar Meyer. — The periodic system of the elements, as we now have it, was undoubtedly discovered independently, and very nearly simultaneously, by the Russian, Mendeleeff, and the German, Lothar Meyer. The latter published in 1864 x a table containing most of the then known ele- ments, arranged in the order of their atomic weights. In this arrangement elements which are closely allied in their chemical properties appear in the same columns, but the system is so incom- plete that it is scarcely an advance on that of Newlands. The first to point out the most important features in the arrange- ment of the elements according to their atomic weights was undoubtedly Mendeleeff. In 1869 2 he arranged the elements in a table in the order of their atomic weights, and showed clearly that there is a periodic recurrence of properties as the atomic weights increase. This will be seen best in the following table : 3 — 1 Die modernen Theorien der Chemie. 2 Journ. Buss. Chem. Soe. 60 (1869). » Lieb. Ann. Suppl. 8, 133 (18741. 22 THE ELEMENTS OF PHYSICAL CHEMISTRY Mendeleeff's Original Table - Zn -< As 7 Ag >- Cd 1 -*— In -<— Sn -«— Sb 1 11 Au— >- Hg -< — Tl ~t— Pb -< — Bi Fig. 2. Old Atomic Weights corrected and New Elements predicted by Means of the Periodic System. — A scientific theory to be of the high- est value must not simply be able to account for all the facts known, but must suggest new possibilities which were not realized when the theory was first announced. The Periodic Law has fulfilled the lat- ter condition in a beautiful way. By means of it a number of erroneous atomic weights were corrected. The atomic weight of indium was supposed to be 75.6, and the composition of the oxide, InO. This would place it in the Periodic System between arsenic and selenium. The chemical properties and atomic volume showed that it belonged rather between cadmium and tin. Meyer ' gave it the atomic weight 113.4 (75.6 x 1|), and regarded the oxide as having the composition ln 2 3 . This was confirmed by Bunsen 2 from specific heat determinations. The atomic weight of beryllium was thought to be 4.54, or 4.54 x 2 = 9.08, or 4.54 x 3 = 13.62. The chemical i Lieb. Ann. Suppl. 7, 362 (1870). 2 Pogg. Ann. 141, 1 (1870). 32 THE ELEMENTS OF PHYSICAL CHEMISTRY and physical nature of the element showed that it must come be- tween lithium and boron, and, indeed, be the head of the magnesium- calcium group. The true atomic weight was subsequently shown to be 9.08. Similarly, uranium was supposed to have the atomic weight 60, 120, or 180, and it was difficult to decide between these values. But it was more probably 240 in terms of the Periodic System ; and this conjecture has also been verified. It should be observed that in these cases the vapor-density method of determining the number of atoms in the molecule could not be employed. The Periodic System has been used not simply to decide between an atomic weight and a multiple of this quantity, but to actually correct atomic weights imperfectly determined. Bunsen found the atomic weight of caesium to be 123.4. This value was smaller than would be expected from the Periodic System. The correct atomic weight of caesium was found later 1 to be 132.9, which is in perfect accord with the system. More recent work in connection with osmium, iridium, platinum, and gold make it very probable that the order for these four elements suggested by the system is the correct one, and that the earlier determinations of atomic weights contain considerable error. The prediction of the existence of unknown elements and the nature of their properties has been so beautifully verified in a num- ber of cases that this has become the most striking application of the Periodic Law. Mendeleeff 2 recognized that the atomic weight and other properties of an element can be determined from the properties of the two neighboring elements in the same series and the two neighboring elements in the same half of the same group. The properties are as a rule the mean of those of the four elements. These four elements were termed by Mendeleeff the Atomic Analogues of the element in question. This will be clear from the following example : — Ca 40 Eb Sr Yt 85 87 88 Ba 137 1 Bunsen: Fogg. Ann. 119, 1 (1863). 1 Lieb. Ann. Suppl. 8, 165 (1872). ATOMS AND MOLECULES 33 The atomic weight of strontium is the mean of the atomic weights of its four analogues, and the same holds in general for the other properties. On the basis of this fact Mendeleeff l predicted the existence and properties of a number of elements which had not been discovered when the Periodic Law was announced. The element predicted was named from the element in the same group which immediately pre- cedes it, adding the prefix " eka." In the third group the element immediately following boron was unknown, and was termed eka- boron. Since it followed calcium with an atomic weight of 40, and preceded titanium whose atomic weight is 48, its atomic weight must be 44. The oxide must have the composition Eb 2 3 and have the same relation to aluminium oxide as calcium oxide does to magnesium oxide. The sulphate must be less soluble than alumin- ium sulphate, just as calcium sulphate is less soluble than magnesium sulphate. The carbonate would be insoluble in water. The salts would be colorless and form gelatinous precipitates with potassium hydroxide and carbonate, and disodium phosphate. The sulphate would yield a double salt with potassium sulphate. Few of the salts would be well crystallized. The chloride would pi-obably be less volatile than aluminium chloride, since titanium chloride boils higher than silicon chloride, and calcium chloride is less volatile than magnesium chloride. The chloride would be a solid, and its density about 2. The specific gravity of the oxide would be about 3.5, and its volume about 39. Ekaboron would be a light, non-volatile, diffi- cultly fusible metal, which would decompose water only on warming ; would dissolve in acids with evolution of hydrogen, and would have a specific gravity of about 3. In a similar manner Mendeleeff predicted the existence and prop- erties of an element between aluminium and indium, terming it ekaaluminium. The atomic weight would be approximately 68. , Again, an element should exist between silicon and tin, and this was termed ekasilicium, with an atomic weight of 72. The properties of the last two elements and their compounds are described in considerable detail from the properties of their atomic analogues, but for these the original paper 2 must be consulted. These elements have now all been discovered. The element described by Nilson 3 as scandium, proved to be ekaboron, having an atomic weight of 44. Gallium, discovered by Lecoq de Boisbau- i Lieb. Ann. Suppl. 8, 196 (1872). 2 Loc. cit. 8 Ber. d. chem. Gesell. 12, 554 (1879). 34 THE ELEMENTS OF PHYSICAL CHEMISTRY dran, 1 was the predicted ekaaluminium, with an atomic weight of 70. And germanium, discovered by Winkler, 2 proved to be the ekasilicon, having an atomic weight of 72. The properties of these elements and their compounds corresponded about as closely with the properties predicted for them as the atomic weights. Imperfections in the Periodic System. — While admiring the many deep-seated relations which are brought out by the Periodic System, we must not fail to observe that it is far from complete. At the very outset there is evidence of this incompleteness — hydrogen does not fit at all into the scheme, and yet it is one of the most im- portant elements. In the very first group of the elements, again, there is apparent inconsistency. Along with lithium, potassium, rubidium, and caesium, we find copper, silver, and gold. There is evidently no very close connection between the last three elements and the first four. Further, sodium does not fall into the same divi- sion of the group with the other strongly alkaline metals, but with copper, silver, and gold. It is at once apparent that sodium is not as closely allied to these elements as to the alkali metals which con- stitute the other division of group I. Passing over the intermediate groups, which contain a number of more or less serious inconsistencies, we find in group VII manganese placed with the halogens and not falling into the same group either with chromium or with iron. The relations of manganese to the halogens are not more striking than the differences, and we do not find manganese falling into the same division of the group with chlorine, bromine, and iodine, but with fluorine, to which it bears a much less close resemblance than to the remaining halogens. When we come to group VIII, we find nothing but discrepancies. These elements do not fit into the system at all, and are placed by themselves as a separate group. It is questionable whether it is desirable to call this group VIII, since it is in no chemical or physi- cal sense a true extension of the system one step beyond group VII. Take as an example the power of the elements to combine with oxygen. There is a regular increase in this power from unity in group I, through the several groups up to group VII, — where we find the compounds C1 2 7 , Br 2 7 , I 2 7 , — fluorine not combining at all with oxygen. Of all the elements in the so-called group VIII, there is only one, osmium, which has a valence of eight 1 Compt. rend. 81, 493, 1100; 82, 168, 1036, 1098 ; 83, 611, 636, 663, 824, 1044 ; 86, 941, 1240 (1875-1878). 2 Ber. d. chem. Gesell. 19, 210 (1886) ; Journ. prakt. Chem. [2], 34, 177 (1886) ; 36, 177 (1887). ATOMS AND MOLECULES 35 towards oxygen. The remainder all show a lower valence towards this element. It seems better to recognize these elements as distinct exceptions, which do not fit into the Periodic System at all satisfactorily ; yet even here we must recognize a certain periodicity in the recurrence of these exceptions, and that they occur in every case in groups of three. The Periodic System seemed to be hard pressed for a time to find a place for some of the elements described by Ramsay as occur- ring in the atmospheric air. Quite recently, however, Ramsay has shown that these elements have a place in the Periodic System. These apparent discrepancies in the Periodic System have not been pointed out with the desire to undervalue the merits of this impor- tant generalization, but simply to arrest attention to the fact that the system is still far from complete. What has already been ac- complished is of tremendous importance, as is shown by the single fact that we can correct atomic weights and predict the properties of elements entirely unknown. Indeed, we can do more ; we can pre- dict with what elements the unknown element in question would form compounds, the composition of these compounds, and even the color and other physical properties possessed by them. 1 Modification of Mendeleeff' s Table. — A modification of the Peri- odic System as proposed by Mendeleeff has been suggested by Brauner. 2 It also contains group 0, or the rare elements discovered by Ramsey in the atmosphere. The important suggestion made by Brauner is that a number of closely related rare elements be placed together in group IV, series 8. These elements have atomic weights ranging from 140 to 173. By placing these closely allied elements together in one position in the system, the latter is very much shortened. The ninth series, which contains no elements, is abandoned ; the . tenth series is made an extension of the eighth, while the eleventh and twelfth series in the Mendeleeff table are made the ninth and tenth series in the new table. This system has marked advantages over the earlier forms. It includes all the known elements, and what is more important, it omits the ninth series in the Mendeleeff table, which never had any real existence ; since not a member of this series has ever been dis- covered. It also simplifies the system by reducing the number of series from twelve to ten; and it brings together those elements which differ from one another in properties less than any other known elements. iSeeLoew: Zschr. phys. Chem. 23, 1 (1897). Staigmuller : Ibid. 39, 245 (1901). Monoman : Chem. Neios, 95, 5 (1907). 2 Ztschr. anorg. Chem. 33, 1 (1902). 36 THE ELEMENTS OF PHYSICAL CHEMISTRY > o O o °op2 JO 1 * II II E6 ©"©" ido» o o II II Oh & O « n o OS II CO II ■ 3 II B © Cv fe- ll « ©* 7 i—i > & o M O a? O © S3 tH II o o o CN « II CO tH cn* id) II o II 03 o to II o © CM 7 II > a o « CiJ — O T-t ■*' *-* II © CO II Ph II © id II & O M 3 q o II CN Jl CO s II cn II o SO ©" OB II IT a GQ o ^3 O ^ ia 1 « OS o CM II Ph CO CN II -a a o M i o © II II CO © o I'- ll ej CD o CO II O a i-i CO* CO IT 3 CN II m o pa O i o OS II 0) H © CO a © II 0) o in eo II C © ii Li co CO S) PS <3 O o CM II CJD 04 & O « i o p? 00 © o 7 a O © II 3 CO M CO s' m" CO U CO o bo CO II cn 7 s © a o as ■ P3 © II H o CN II e OS CO II -a CO CO II o 7 99] raS ~ CN CO -* «o to t- CO A o If ATOMS AND MOLECULES 87 THOMSON'S THEORY OF THE RELATION BETWEEN THE ELEMENTS The Ratio — for the Cathode Particle. — The recent work of m J. J. Thomson has thrown entirely new light on the relation between the several chemical elements. This result is really the outcome of Thomson's brilliant investigations on the conduction of electricity through gases. It has to do especially with the cathode rays, or those rays which are sent off from the cathode when an electric discharge is passed through a dilute gas, as in a high-vacuum discharge tube. These rays, as Sir William Crookes has proved, are composed of charged particles, shot off with high velocities from the cathode. This was shown by such facts as that they can set in motion easily movable systems placed in their path. J. J. Thomson 1 determined the ratio of the charge e to the mass m of these particles. He established the remarkable fact that the ratio — was constant, m regardless of the nature of the gas through which the discharge was passed. He then tested whether the nature of the cathode had any effect on the value of this ratio. He made his cathode of widely different metals such as platinum, silver, aluminium, zinc, iron, copper, tin, etc., and found the same value of — for all of the metals used. This m value was about 1 x 10 7 . The value of — for the hydrogen ion of acids is 1 X 10 4 . Thus, m the value of this ratio for the cathode particle is one thousand times its value for the hydrogen ion of acids. In order to determine the relative masses of the ion in the gas, and the ion in solution of acids, we must know the relative values of e in the two cases. Determination of the Charge carried by the Cathode Particle. — In order to determine the mass m of the negative ion in a gas, knowing the ratio — , it is necessary to know e, or the charge carried by the m ion. To determine e for gaseous ions, Thomson devised and carried out an unusually beautiful experiment. The experiment was based on the observation made by Wilson 2 that the ions in a gas act as 1 Phil. Mag. 44, 293 (1897). 2 Phil. Trans. A., 265 (1897). 38 THE ELEMENTS OF PHYSICAL CHEMISTRY nuclei around which water-vapor condenses. When a gas in which ions are present is expanded, a part of the water-vapor present con- denses, and condenses around the ions, producing a fog or mist in the gas. Every ion acts as a centre of coudensation, so that there are as many droplets of water formed in the gas as there are ions present. If we knew the number of such droplets, we would know the number of ions present in the gas. To determine the number of water-particles in a given volume of the gas, Thomson made use 1 of an equation deduced by Stokes, con- necting the velocity with which the water-particles fall or settle with their size. The equation of Stokes is — 2gr i 9 u in which v is the velocity with which the particles fall, or the cloud or mist settles, g the gravitational constant, r the radius of the drop, and u the coefficient of viscosity of the gas. By measuring v, the velocity with which the cloud settles, we can determine r, the radius of the drop. The volume of the drop is obtained at once from its radius. Knowing the volume of the drop, it is only necessary to know the total amount of water precipitated from a given volume of the gas, to know the number of drops formed in that volume of the gas. The total amount of water precipitated is ascertained from the heat that is liberated when the water-vapor condenses. In this way the number of ions contained in a given volume of the gas is determined. It is necessary to know the total charge carried by these ions, in order to determine the charge carried by one ion. This is ascertained by measuring the current that passes through the gas under a given electrical force. It was found in this way that the value of e, or the charge carried by the gaseous ion, is the same as that carried by a univalent ion, such as the hydrogen ion in the solution of acids. The Mass of the Cathode Particle. — Since — for gases is of the m order of magnitude 10 7 , and — for the hydrogen ion in solution is 10 4 , m and since e is the same in both cases, it follows that m, or the mass of the hydrogen ion, is one thousand times that of the negative gase- ous ion such as exists in the cathode ray. 1 Phil. Mag. 46, 528 (1898). ATOMS AND MOLECULES 39 Since the value of — is the same for the negative ion of all gases, m no matter how produced, and since e is also the same for all negative gaseous ions, it follows that the mass of the negative ion that is split off from all gases is the same, and is about one one-thousandth that of the hydrogen ion. More accurate determinations give the value j^. This ion, which can be split off from all gases, regardless of their chemical nature, is a common constituent of the atoms of all matter. This ultimate .unit of matter of which all the atoms are composed, having a mass about y^ of that of the hydrogen atom, and carrying a unit negative electrical charge, Thomson called the Corpuscle. The Corpuscle — its Nature. — The corpuscle is then a small par- ticle of matter having a mass about -jr® °^ the mass of the hydrogen ion, carrying unit electrical charge. The corpuscle is then both' material and electrical. We shall now take up the work of Thomson on the nature of the corpuscle itself. If we ask what reason have we for thinking that the corpuscle contains any matter at all, the answer would be that it has both mass and inertia. Thomson pointed out a number of years ago that inertia may itself be of electrical origin. Townsend showed that a rapidly mov- ing sphere, when charged, would have greater inertia than when uncharged. In order that appreciable changes in mass should be produced, the particle must, however, move with very high velocity — with a velocity approaching that of light. The problem is then to determine whether there is any change in mass with change in the velocity of the particle that can be detected experimentally. The experiments of Kaufmann 1 bear directly on this problem. The particles shot off from radium have very different velocities. Kaufmann determined the velocities and the ratio — for these parti- m cles. The following results were obtained — the velocities for con- venience being divided by 10 10 , and the values of — by 10 7 : V e m 2.36 1.31 2.48 1.17 2.59 0.975 2.72 0.77 2.83 0.63 1 Phys. Zeit. 4, 54 (1902). 40 THE ELEMENTS OF PHYSICAL CHEMISTRY It is obvious from these results that, as v becomes greater, — be- m comes less. Since e, or the charge, remains constant, independent of the velocity, m, or the mass, must become greater and greater as the velocity increases. This shows that the mass of the particle in- creases as the velocity increases, and that at least a part of the mass is of electrical origin. This raises the further question, is all the mass electrical ? If not, what part of the mass is of electrical origin? Thomson has thrown light on this question. Assuming that the whole mass is electrical, Thomson calculated the ratios of the masses of the parti- cles moving with different velocities, to the mass of a slowly moving particle which is constant. He compared his calculated values with those found experimentally by Kaufmann, and a surprisingly satis- factory agreement manifested itself. This agreement makes it highly probable that the whole of the mass of the corpuscle is of elec- trical origin. If all of the mass of a corpuscle is of electrical origin, why assume that the corpuscle contains anything but electrical energy ? Since the fundamental properties of what we have been accustomed to regard as matter, viz., mass and inertia, are due solely to the electrical charge, there is no reason for assuming that there is anything in the corpuscle but the charge. The Electron. — The corpuscle is, then, solely of electrical nature. Thomson applied the term electron formerly used by Larmor 1 and others to this particle. The electron is a unit charge of negative electricity, entirely dis- embodied from what we have hitherto regarded as matter. It is the ultimate unit of which all matter is composed. It is the fundamental unit of all the chemical atoms ; the atom of one substance differing from the atom of another substance in the number and arrangement of the electrons contained in it. Ostwald's Conception of Matter. — This conclusion suggests a paper published by Ostwald 2 in 1895, in which he pointed out that matter is a pure hypothesis. What we really know are changes in energy. Energy is the reality, and matter an hypothesis. We have created matter in our imagination in order to have something to which energy can be thought of as attached. We usually take just the opposite view. We are inclined to regard matter as the reality, and energy as hypothetical. It is interest- iSee Theory of Electrons : J. Larmor, Phil. Trans. (1895), 695. 2 Ztsehr. phys. chem. 18, 305 (1895). ATOMS AND MOLECULES 41 ing to see that exactly the same conclusion as that arrived at by Ostwald on purely theoretical grounds, has now been reached experi- mentally by Thomson, as the result of one of the most brilliant investigations in modern physics. 1 The Electron Theory and the Periodic System. — Perhaps the most important application of the electron theory thus far made is in con- nection with the Periodic System. According to this theory the atoms of all of the elements are made up of electrons, which are nothing but disembodied negative charges of electricity. We might at first thought conclude that the atom of one element differs from the atom of another element only in the number of electrons contained in it. This would account for the different masses possessed by the atoms of different elementary substances, but would not explain their chemical or physical properties in general. This, for example, would not be in accord with the facts of spectrum analysis. It could not deal with such fundamental chemical properties as the acid-forming and the base-forming power of the different elements. Further, it would not account at all for valence, without which we would have no chemistry. The electron theory, if not developed beyond the stage which simply says that the atom of one element differs from the atom of another element only in the number of electrons contained in it, would be at best only a qualitative suggestion which did not even take into account the question of the stability of the different elementary atoms. This was, of course, recognized by Thomson, who has, however, placed his theory, in part at least, upon a quantitative basis. It is necessary that the different atoms, with their different atomic masses, should have different numbers of electrons in them, but this is far from sufficient. We must, if possible, solve the problem as to how these electrons are arranged within the atom. This has already been partially accomplished by Thomson. 2 Arrangement of the Electrons within the Atom. — An atom, in terms of the electron theory, is made up of a large number of elec- trons, the number being expressed by the atomic weight of the element multiplied by 770. The electrons are moving with high 1 For a fuller discussion of these matters see the following work by the author of this volume, from which a part of the above sketch was taken : The Electrical Nature of Matter and Badioactivity. New York, 1906, D. Van Nostrand Company. 2 Phil. Mag. 7, 237 (1904). 42 THE ELEMENTS OF PHYSICAL CHEMISTRY velocities within the atom, themselves filling only a small part of the space occupied by the atom as a whole. This is the same as to say that the spaces taken by the electrons are incomparably small, as compared with the distances between them. The atom can be looked upon as a small solar system in which the electrons are play- ing just about the same role as the planets. These electrons, 1 or negative charges, are moving in a sphere of uniform positive electrification. Thomson has not yet been able to solve the problem as to the arrangement of the electrons within the entire sphere, but has solved it for a plane through the sphere. In order that we may have equilibrium, the electrons must ar- range themselves in a series of concentric rings. A large number of corpuscles arranged in a single ring would not be stable, while such a system would become stable by placing some of the corpuscles on the inside. In a word, the concentric rings are necessary for stability. The total number of electrons in the plane with an outer ring of twenty is given by Thomson. Total Number of Electrons in the Plane 59 60 61 62 63 64 65 66 67 Number in Successive Rings 20 20 20 20 20 20 20 20 20 16 16 16 17 17 17 17 17 17 13 13 13 13 13 13 14 14 15 8 8 9 9 10 10 10 10 10 2 3 3 3 3 4 4 5 5 It is obvious from this table that the smallest total number of electrons in the plane, which can have an outer ring of 20, is 59; and the largest total number with an outer ring of 20 is 67. Thomson points out that systems built up in this way would have properties analogous to some of the properties of the chemical atoms. The various rings of corpuscles can be classified in groups or fami- lies. In such an arrangement we should expect relations between the spectral lines such as exist. The frequency of the vibrations produced by a ring would be proportional to the number of corpuscles within the ring. Since these bear simple relations to one another for correlated elements, we should expect to find simple relations be- tween the wave-lengths given out by such elements. Chemical Relations shown by this Arrangement. — The chemical relations brought out by the above arrangement of electrons are very 1 See Electrical Nature of Matter and Radioactivity, pp. 30-34. New York, 1906, D. Van Nostrand Company. ATOMS AND MOLECULES 43, striking, especially in connection with the Periodic System. Let us take first the system with a total of 59 electrons in the plane. This is the smallest total number of electrons that can have 20 in the outer ring. This system is near the limit of stability, and might easily lose an electron and thus become positively charged. As soon, however, as it did so, it would pass over into a stable form for 58 electrons, containing 19 in the outer ring. This would be very stable and would attract the surrounding electrons. Such a system could not be permanently charged, for as soon as it had lost one electron, it would be replaced by another electron. An atom corresponding to this arrangement would not be capable of becoming charged either positively or negatively — it would have no valence, and could not enter into chemical combination. The system with 60 electrons could lose one electron, but only one, without destroying the equilibrium and producing a new ar- rangement. If it lost two, it would pass into a system with a total of 58 electrons, which would contain only 19 in the outer row. The system with 60 electrons would, therefore, correspond to a univalent positive element, since the loss of one negative charge is equal to the gaining of a positive charge. The system with 61 electrons could lose two without necessitating a rearrangement. It would then correspond to a bivalent electro- positive element. It would, however, part with its electrons less readily than the system with 60, and would, therefore, be less strongly electropositive than the system with 60. Similarly, the system with 62 electrons could lose three, and thus hecome a trivalent electropositive element. Turning now to the other end of the series, we have the system with 67 electrons. We cannot add even one electron to this system without making it unstable and necessitating a rearrangement, since the system with 68 electrons would have 21 in the outer ring. The system with 66 electrons, like the system with 59, would then correspond to an atom with no valence. The group with 66 electrons could add one, and only one electron, without passing beyond the number 67, which is the limit of stability with 20 in the outer ring. It would correspond to a univalent electro- negative element. The group with 65 electrons could acquire two, and would thus become a bivalent electronegative element. It would, however, be less liable than the group with 66 to acquire electrons, and would, there- fore, not be as strongly electronegative. Similarly, the group with 64 could add three electrons, and thus 44 THE ELEMENTS OF PHYSICAL CHEMISTRY become a trivalent electronegative element, and the group with. 63 could acquire four electrons and become a tetrivalent electronegative element. If we compare the above deductions with the facts as brought out by the Periodic System, the agreement is most striking. The first two series of nine elements are : He Li Gl B C N F Ne Ne Na Mg Al Si P S CI Arg It will be seen that the fijst and last member of each of these series has no valence. The second member is univalent and positive ; the third bivalent and positive; the fourth trivalent and positive; the fifth tetravalent and negative; the sixth trivalent and nega- tive ; the seventh bivalent and negative ; the eighth univalent and negative ; and the ninth without valence. It is difficult to see how relations so general and satisfactory as these could exist, unless there was a fundamental truth at the basis of the generalization which led to them. The electron theory of Thomson is now accepted tentatively by a large number of the more progressive physicists and physical chem- ists. It is probably an epoch-making contribution to science. 1 In a very recent paper 2 Thomson seems to arrive at the conclu- sion that there is a very different number of electrons in the atom from what he formerly supposed. It is impossible at present to pass judgment upon this conclusion. We must wait until the sub- ject-is further developed. The Size of Molecules. — This chapter on atoms and molecules should not be closed without a brief reference to Kelvin's calculation of the approximate size of molecules. He 3 calls attention to the fact that atoms cannot be infinitesimally small, since if they were, chemical reactions would have to take place with infinite velocity. Recognizing that atoms have finite size, he obtained data from several sources, and especially from the study of the electrical relations between copper and zinc, and also from the study of the thickness of the soap-bubble, for calculating the size of molecules. The results obtained by some four different methods were of the same order of 1 For a fuller discussion of these matters see The Electrical Nature of Matter and Radioactivity by H. C. Jones (New York, 1906, D. Van Nostrand Com- pany), from which a part of the abstract has been taken. For a more mathemat- ical discussion see Conductivity of Electricity through Gases, by J. J. Thomson. » Phil. Mag.U, 769 (1906). "Electrons," Orr: Phil. Mag. [3], 50, 26» (1900). "Electron Theory of Metals," see Drude: Ann. d. Phys. [4], 3, 369 (1900). 8 Nature, March 31st, 1870. Reprinted in Amer. Journ. Science [2], 50, 38 (1871). Also Lieb. Ann. 157, 54 (1871). ATOMS AND MOLECULES 45 magnitude. If two millions of molecules were arranged side by side, the row would be a millimetre in length, and two hundred million, million, million of hydrogen molecules would weigh a milligram. The number of molecules in a cubic centimetre of gas under normal conditions cannot be greater than 6 x 10 21 , or six thousand, million, million, million. Since the densities of liquids and solids are from five hundred to sixteen thousand times that of the air, the number of molecules in a cubic centimetre of the. liquid or solid must be from 3 x 10 24 to 3 x 10 26 . Numbers of such magnitude are entirely incomprehensible, and in order to form any conception of them, we must translate them into terms with which the mind can deal. This has already been done for us by Lord Kelvin in the last paragraph of his paper : 1 — "To form some conception of the degree of coarse-grainedness indicated by this conclusion, imagine a raindrop, or a globe of glass as large as a pea, to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be coarser-grained than a heap of small shot, but probably less coarse-grained than a heap of cricket balls." Perhaps the best demonstration of the almost unlimited divisi- bility of matter is furnished by some of the aniline dyes or by fluo- rescein, where one part is capable of coloring or rendering fluorescent at least one hundred million parts of water. The absolute size of the molecules has been calculated on entirely different grounds by Nernst, J. J. Thomson, and others. The results obtained are, in general, of the same order of magnitude, and in many cases agree as closely as we could expect when we consider the enor- mous difficulties involved in such calculations. 1 Loc. cit. "Weight of Atoms." See Kelvin : Phil. Mag. (6), 4, 177, 281 (1902). CHAPTER II GASES LAWS OF GAS-PRESSURE Properties of Gases. — We know matter in three states of aggrega- tion : gas, liquid, and solid. These differ from one another in many respects ; but the most striking difference is in the relative ease with which the particles can move among' one another. In a gas there is comparatively little resistance offered to the movements of the mole- cules ; the friction of one particle against another is comparatively small. In a liquid there is much greater resistance offered to the movement of the parts, the inner friction being many times greater than in a gas ; while in a solid the parts are relatively fixed, and movement is accomplished only by subjecting the solid to very great pressures. Another striking difference between gases, and liquids and solids, probably due to the same cause, is the almost unlimited power of expansion possessed by the former. A gas expands and fills the entire space placed at its disposal. A liquid takes the form of the containing vessel on all sides except above, but has its own definite volume for a definite temperature, and this varies but little for large changes in pressure. A solid has its own definite shape and volume, independent of the shape and size of the containing vessel. This volume varies with the temperature according to definite laws, and is only slightly changed by change in pressure. Gases differ from liquids and solids also in that they represent matter in a very dilute form. A little matter is distributed through a large space, or as it is usually expressed, the density of gases is small. Some of these differences are not as fundamental as they might at first sight appear, since a gas can be compressed to a liquid, and a liquid con- verted into a solid. And, similarly, a solid can be liquefied, and a liquid converted into a gas. Indeed, most of the forms of matter with which we are acquainted are known in all three states of aggregation. 46 GASES 47 Of the three states of aggregation, the gaseous is the simplest, since it represents matter in the most tenuous condition, and will, therefore, be studied first. Law of Boyle. — The fact that a gas always fills the entire space placed at its disposal makes it easy to change the volume of a gas at will. This can be also accomplished by simply changing the pressure to which the gas is subjected. With increase in pressure the volume of a gas becomes smaller, and with increase in pressure the density of a gas becomes greater. There is a very simple rela- tion connecting these quantities. The pressure of a gas is pro- portional to its density, and both are inversely proportional to the volume. If we represent the pressure by p, and the density by d, p = cd. If v is the volume and m the mass of the gas, Boyle's law may be expressed thus : — pv = cm. c is a constant for a gas at a given temperature. If p is the pressure and v the volume of a given mass of gas, and p^ and v x the pressure and volume of the same mass of gas under other conditions, Boyle's law may be expressed thus : — pv=p 1 v 1 . The product of the pressure and volume of a given mass of gas at constant temperature is a constant. Boyle's law may be expressed in still another way. Since the pressure and density of a gas are proportional, the pressure exerted by a gas varies directly as its concentration, or directly as the number of parts contained in unit volume. Exceptions to the Law of Boyle. — It was early shown that the law of Boyle does not hold under all conditions. Deviations were observed especially when the gas was subjected to high pressures ; the change in volume being less at these pressures than would be supposed from the law of Boyle, as Natterer 1 and others have shown. The investigation of Amagat 2 on this problem is probably the best, and is certainly the most fundamental which has ever been carried out. He arrived at the same conclusion as that reached by i Journ. prakt. Ghem. 56, 127 (1852). 2 Ann. Chim. Phys. [5], 19, 345 (1880). 48 THE ELEMENTS OF PHYSICAL CHEMISTRY Natterer, that the product of pressure and volume, pv, increases with increase in pressure for very high pressures. Arnagat plotted the results obtained for hydrogen, nitrogen, carbon dioxide, oxygen, ethylene, etc., in curves. 1 For the smaller pressures the gases were more strongly compressed than would be expected from Boyle's law, — pv decreasing with increase in pressure. The value of pv, with in- 38 36 3+ - /s /, % 28 y /, "4 r s \V '/ y, '/ V, #, // 24 g,22 u. O 20 16 S; \\ ~-i23l°__- '/ 30° vor^y 16°3 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 Pressures in metres of mercury. Fig. 3. Ethylene. creasing pressure, reached a minimum, conformed closely to Boyle's law for a short range of pressure, and then began to increase as the pressure increased. This will be seen at once from the curves in Fig. 3. Hydrogen, however, is a marked exception. The value of pv increases regularly with increase in pressure from comparatively 1 Ann. Chim. Phys. 19, p. 379 (1880). GASES 49 small pressures, so that the curve for hydrogen does not show any minimum, but is very nearly a straight line. This will be seen from Fig. 4. Amagat studied also the effect of temperature on the deviations from the law of Boyle. Some of his earlier work l indicated that the values of pv, with increase in pressure, remained more nearly constant at higher temperatures. This led him to carry out an elaborate in- vestigation, which was published in 1880, 2 and which is probably the most important paper bearing upon the exceptions to Boyle's law. He took a gas, say ethylene, and worked out the values of pv with change in pressure at a given temperature. He then found the values of pv for the same range in pressure, using a different temperature. In the case of ethylene, the temperatures ranged from 44 A38 u. o ra 36 30 \o£ . - s£- 1 — " __-- 6tf* ' __„ _-— 5^5 v£l 1 20 40 60 80 100 120 140 160. 180 200 220 240 260 280 300 320 Pressures in metres of mercury. Fia. i. Hydrogen. 16°.3 to 100°. Amagat used a number of gases, — nitrogen, carbon dioxide, ethylene, marsh gas, and hydrogen, — and plotted the results obtained for each gas at the different temperatures in a curve. The curves for two gases, ethylene and hydrogen, are given in Figs. 3 and 4. The abscissas are the pressures expressed in metres of mer- cury. The ordinates are the values of pv. The values of pv for ethylene and all the other gases studied, with the exception of hydrogen, at first decreased, then reached a mini- mum, and finally increased as the pressure increased. It will, how- ever, be seen from Fig. 3 that the deviation from the law of Boyle i Ann. Chim. Phys. [4], 29, 246 (1873). 2 Ibid. [5], 22, 353 (1881), Scientific Memoir Series, V, p. 13. 50 THE ELEMENTS OF PHYSICAL CHEMISTRY becomes less and less as the temperature increases. If the law of Boyle applied, the curve would be a straight line parallel to the abscissa. This condition is more and more nearly realized as the temperature rises ; and for ethylene at 100° the minimum is far less sharp or pronounced than at 16°.3. The deviation from Boyle's law becomes less and less with rise in temperature also in the case of carbon dioxide and methane, as will be seen by consulting the curves for these gases as worked out by Amagat. 1 Hydrogen, as has already been mentioned, is a marked exception. The value of pv increases regularly from the smallest pressure used up to the largest ; and further, the curves for different temperatures are very nearly parallel, showing that the deviation from Boyle's law in this case is as great at the higher as at the lower temperature. The question as to the applicability of Boyle's law to gases under very small pressure has also been studied experimentally. The re- sults obtained are so conflicting that it is impossible to decide between them. It, however, seems quite probable that there is no large devia- tion from Boyle's law shown by very dilute gases ; i.e. where the pressure is small and there are relatively few gas particles in a given space. The Law of Gay-Lussac. — If a gas is kept under constant pressure and its temperature raised, the volume will increase. If the volume is kept constant as the temperature rises, the pressure will increase. The remarkable fact has been discovered that the increase in the vol- ume of a gas for a given rise in temperature is a constant, independent of the nature of the gas. All gases increase about ^\-g (=0.00367) of their volume at 0° C. for every rise of one degree in temperature. Gay-Lussac's law states that this temperature coefficient, which we will call B, is constant for all gases. Its approximate value is 0.003665. If we keep the volume constant and warm the gas to t°, the pressure P, at this temperature, is calculated from, the pressure p at 0°, as follows : — P=p (1 + 0.003665 0- If, on the other hand, the pressure is kept constant and the vol- ume allowed to increase with rise in temperature, the volume at f, V, is calculated from the volume at 0°, v , thus : — V= v (1 + 0.003665 t). If both pressure and volume are allowed to change when the gas is heated, the pressure and volume at t°, p and v, are calculated from the pressure and volume at 0° in this manner : — 1 Loc. cit. GASES 51 pv = p v <> (1+0.003665 t) from "which, v n = — ' ° p (1+0.003665 ty This is the expression generally employed for reducing a gas to ■what are termed normal conditions. If the volume v of the gas is read at a given pressure, p, and temperature, t, we can calculate at once the volume v at 0° C. and normal pressure p which is taken as 760 mm. of mercury. The value of the constant 0.003665 is determined either by keeping the pressure constant and measuring the increase in volume with rise in temperature, or by keeping the volume constant and measuring the increase in pressure as the temperature rises. The values found by the two methods differ only slightly, and we take 0.003665 as very nearly the true value of the temperature coefficient of a gas. This is veiy nearly ¥ ^ F , which means that if a gas is cooled down to — 273° C. its volume would become zero if the law of Gay-Lussac held down to the limit. This temperature, termed the absolute zero, has now been nearly realized experimentally. It is quite certain that temperatures have been produced which are within twenty degrees of this point. It is, however, very probable that the laws of gas-pressure would not hold at these extreme limits. If we represent temperature as measured from the absolute zero by T, the combined expression of the laws of Boyle and Gay-Lussac is: — ■ pv = ^T. * 273 We usually represent ^^ by B, when the above becomes, pv = BT. Deviations from the Law of Gay-Lussac. — There are frequent ex- ceptions to the law of Gay-Lussac as well as to the law of Boyle. The coefficient of expansion varies considerably from one gas to another, and varies considerably for the same gas under different temperatures and pressures. This was shown very clearly by the same work of Amagat, 1 in which the exceptions to the law of Boyle were studied. The effect of both temperature and pressure on the coefficient of expansion of ethylene is seen in the following table of results taken from the work of Amagat. 2 1 Ann. Chim. Phys. [5], 22, 353 (1881). * Ibid., p. 383. 52 THE ELEMENTS OF PHYSICAL CHEMISTRY Ethylene Pressure in Metres of Hg. 20°-40° 40°-60° 60°-80° 80°-100° 30 0.0084 0.0064 0.0046 0.0040 60 0.0166 0.0178 0.0097 0.0067 80 0.0121 0.0195 0.0132 0.0088 100 0.0079 0.0108 0.0121 0.0100 120 0.0062 0.0075 0.0095 0.0082 140 0.0048 0.0062 0.0076 0.0068 160 0.0041 0.0057 0.0061 0.0058 200 0.0034 0.0043 0.0044 0.0044 240 0.0030 0.0035 0.0036 0.0034 280 0.0027 0.0031 0.0030 0.0029 320 0.0025 0.0027 0.0024 0.0024 The horizontal lines show the variation in the coefficient of expansion, with change in temperature, the pressure remaining constant. While there is no sharply defined law in this con- nection, it will be seen from the results that the coefficient increases with the temperature up to a certain point, and then begins to diminish. At higher temperatures the coefficient be- comes still less. The vertical columns, however, bring out a well-defined relation between the coefficient of expansion at a definite temperature and the pressure. The coefficient increases with the pressure to a maximum and then decreases regularly. If we examine the curves for ethylene (Fig. 3), we will see that the maximum value of the coefficient of expansion corresponds closely to the pressure at which the value of pv is a minimum. As the temperature rises this maxi- mum becomes less and less sharply defined, just as the minimum for pv becomes less sharply defined. The decrease in the coefficient of expansion with rise in tem- perature beyond a certain point is also shown by the curves in Fig. 3- The distance between the curves for any given pressure becomes less and less as the temperature rises. The applicability of the law of Gay-Lussac to gases under very small pressure has been studied by a number of experimenters. The work of Baly and Eamsay 1 should, however, receive special 1 Phil. Mag. 38, 301 (1894). GASES 53 notice. They worked with a number of gases, from a few milli- metre's pressure down to a very small fraction of a millimetre. The pressure used with hydrogen varied from 4.7 mm. to 0.077 mm. The coefficient of expansion at the higher pressure was * s . This remained practically constant until the pressure was diminished to 0.4 mm. When still further diminished the coefficient of expansion decreased and was only ^L_ at a pressure of 0.077 mm. Oxygen behaves very differently from hydrogen. Its coefficient of expansion at 5.1 mm. is ^t, which is larger than would correspond to the law of Gay-Lussac. It increases with decrease in pressure, being -^ at 2.5 mm., and at 0.07 mm. it is about ^-jVr With nitrogen we find at 5.3 mm. that the coefficient of expansion is ^j, being much less than would be expected from the law of Gay-Lussac. This value becomes still less as the pressure decreases, being only ^ at a pressure of' 0.8 mm. The law of Gay-Lussac, like the law of Boyle, must be regarded as an approximation, which holds rigidly only under special con- ditions. There are many exceptions known to both laws, but those already considered suffice to show the general character of the exceptions most frequently met with. The Law of Avogadro. — The law of Avogadro has been already referred to in connection with the determination of the molecular weights of vapors. It will be recalled that the law was proposed to account especially for the simple volume ratios in which gases combine, and the simple ratios between the volumes of the constitu- ents and those of the products formed. The law is usually stated thus: equal volumes of all gases at the same temperature and pressure contain the same number of ultimate parts. This law cannot be proved directly by experiment, but is in accord with so many facts that it is very probably true. Indeed, it has been tested, indirectly, in so many directions that it is now given a place among the laws of nature. It is true, however, that it does not seem to hold absolutely in some cases. Thus, two volumes of hydrogen do not combine with exactly one volume of oxygen to form water. We must, therefore, assume either that water is not H 2 0, or that the law of Avogadro does not hold rigidly in this case. The latter assumption is, of course, by far the most probable, and is therefore the one accepted. We can combine the three laws of gas-pressure in one expression, 1 iHorstmann: Ber. d. them. Gesell. 14, 1242 (1881). Van't Hofi: Ztschr. phys. Chem. 1, 491 (1887), Scientific Memoir Series, IV, p. 24. 54 THE ELEMENTS OF PHYSICAL CHEMISTRY just as we combined the two laws, those of Boyle and Gay-Lussac, in the equation PV= BT. Let us deal with gram-molecular weighbs * of gases. The pressure exerted by a gram-molecular weight of a gas at 0° C, in the space of a litre, is about 22.4 atmospheres. If we use the equation — P 273 ' and substitute for p the above pressure, and for v e the value 1, we have — 22.4 _, pV= 273 r = 0.082 T. This is the combined expression of the laws of Boyle, Gay-Lussac, and Avogadro. Apparent Exceptions to the Law of Avogadro. — There are a num- ber of substances known which, for a time, were regarded as excep- tions to the law of Avogadro. The densities of their vapors were smaller than would be expected from the law of Avogadro. Among these substances are ammonium chloride, ammonium cyanide, ammo- nium sulphide, ammonium hydrosulphide, phosphorus pentachloride, and chloral hydrate. It has, however, been shown that these com- pounds are not exceptions to the law of Avogadro, but agree very well with it. "The very small vapor-densities are satisfactorily explained, as will be seen when we come to deal with this phase of our subject. THE KINETIC THEORY OF GASES The Kinetic Theory. — We have considered thus far the laws to which the pressure of gases conforms, and have found that gases in general obey approximately the laws of Boyle, Gay-Lussac, and Avogadro. The question has thus far not been raised, why a gas exerts any pressure at all. It is more than probable that the pressure exerted by all gases is due to the same cause, since differ- ent gases obey so nearly the same laws of pressure. Further, the nature of these laws makes it highly probable that the structure of gases is comparatively simple, and the nature of gas-pressure, me- chanically considered, not very complex. 1 A gram-molecular weight is the molecular weight of the gas In grams. OASES 55 The theory which has been proposed to account for gas-pressure is known as the kinetic theory. According to this theory, the parti- cles or molecules of a gas are continually moving in all directions in straight lines; the velocity being very great, and each particle moving independently of all others. These particles would frequently strike one another and also the walls of the containing vessel, and thus the pressure of gases would be produced. The pressure of the gas on the walls of the confining vessel is then due to the blows or impacts of the gas particles against these walls. Deviations from the Gas Laws explained by the Kinetic Theory. Van der Waals' Equation. — We have seen that the laws of gas-press- ure are only approximations and hold only under very special con- ditions. We will now examine gases in the light of the kinetic theory and see whether any explanation of the exceptions to the gas laws can be found. If gas-pressure is due to the impacts of the gas particles against the walls of the vessel, the space in which these particles move is evidently not the whole volume of the gas, as we have thus far assumed, but is not greater than the volume of the gas minus the space occupied by the particles themselves. If the press- ure is small, or what amounts to the same thing, the volume large, there are relatively few particles in a large space, and the space occupied by the particles themselves is so small compared with the spaces between the particles that it is negligible. If the gas is under high pressure there are many more particles in a given volume, and the space occupied by the gas molecules themselves becomes quite considerable. We have seen that the gas laws hold much more closely when the gas is dilute or under small pressure, than when the pressure is great. It is, therefore, evident that we must take into account the space occupied by the gas molecules themselves. We must introduce into the equation which expresses both the laws of Boyle and Gay-Lussac (pv = BT) a factor for the volume of the gas molecules. If we call this factor, which is a constant for every gas, b, the above equation becomes — p(v-b) = BT. There is one factor, however, which is still not taken into account. The assumption is made that the particles of gas do not exert any attraction upon one another, and it is quite certain that such an attraction exists. Van der Waals 1 has taken this into account, and 1 Die Kontinuitat des gaaformigen und flussigen Zustandes, Leipzig, 1881. 56 THE ELEMENTS OF PHYSICAL CHEMISTRY has modified the gas equation accordingly. The attraction exerted by the gas particles is proportional to the specific attraction a, and inversely proportional to the square of the volume v. This term ~ must be added to the pressure p, since the attraction of particles for each other has the same effect as subjecting the gas to an increase in pressure. Van der Waals' equation is then — (p + ^(v-b) = BT. This equation explains many of the exceptions shown by gases to the simpler laws of Boyle and Gay-Lussac. If the pressure is small, — becomes negligible because of the large value of v, and 6 the space occupied by the molecules is also small. The gas under these condi- tions would be more likely to accord with the simpler expressions, and such is in general the fact, with perhaps a few exceptions at very small pressures, and here experimental errors are large. As the pressure increases the two correction terms acquire finite values, but act in opposite senses. If a has a large value, the volume is appre- ciably diminished, and pv decreases, as is shown in the curves for ethylene (Fig. 3). As the pressure still further increases, a becomes relatively smaller with respect to p, and the influence of b begins to manifest itself. The gas becomes relatively less compressible, or pv increases with the pressure. This is also seen in the curves for ethylene. The two correction terms have the same value at a press- ure of from 40 to 100 m. of mercury depending upon the tem- perature, and at this pressure the gas obeys the simpler expression of Boyle's law. In the case of hydrogen (Fig. 4), the value of pv continually increases with the pressure. This means that the value of the con- stant a is so small that it is more than counterbalanced by b at all pressures. The determination of the values of the constants a and b for any gas is comparatively simple. Eeference only can be given here to the methods 1 which are used. The exceptions to the laws of Boyle and Gay-Lussac, which were pointed out when these laws were considered, are, then, fully explained by means of the kinetic theory of gases. 1 Ostwald : Lehrb. d. Allg. Chem. I, p. 226. GASES 57 DENSITIES AND MOLECULAR WEIGHTS OF GASES Densities and Molecular Weights. — The determination of the relative densities of gases consists in determining the relative weights of equal volumes of gases at the same temperature and pressure. Since equal volumes of gases under the same conditions contain an equal number of molecules, the densities stand in the same relation as the molecular weights. Thus, by means of Avogadro's law we can determine the molecular weights of substances in the gaseous state. Some substance must be taken as the unit in determining the densities in gases. Air has generally been selected as the unit, and the weights of equal volumes of other gases, at the same temperature and pressure, compared with that of air. Hydrogen has also been used as the unit, and is to be preferred to air, since the composition of the latter varies slightly from time to time and from place to place. The density of air is 14.37 times the density of hydrogen, and since the molecular weight of hydrogen is 2, we must multiply the density referred to air as the unit by 28.74, to obtain the molecular weight of the gas. If we represent the molecular weight of the gas by m, and the density referred to air as the unit by d, m = d x 28.74. In this way the molecular weights of gases can be calculated from their densities. A number of methods and a large number of modifications of methods have been proposed for determining the densities of gases. The more important will be briefly considered. Method of Dumas. — The method of Dumas * consists in deter- mining the amount of substance which in the form of vapor, at a given temperature, just fills a flask whose volume is afterwards determined. The flask is weighed full of air. Knowing the volume of the flask, we know the weight of air contained in it ; therefore we know the weight of the empty flask. The weight of the flask being known, and the weight of the flask plus the substance which just filled it with vapor, we know the weight of the substance. By deter- mining the weights of the vapors of different substances which fill a flask of given volume, we have the relative densities of the vapors. The apparatus used is a balloon flask (Fig. 5) holding from 100 to 250 cc. i Ann. Chim. Phys. [2], 33, 337 (1826). 58 THE ELEMENTS OF PHYSICAL CHEMISTRY The flask is carefully dried and weighed, using as a tare another flask of very nearly the same size. We are in this way made inde- pendent of the conditions of temperature, moisture, etc., under which the weighing is made. A few grams of the substance whose vapor-density is to be deter- mined are introduced into the flask, the neck drawn out to a capillary, and the flask placed in a bath which is at least ten or fifteen de- grees above the boiling-point of the substance. The substance vaporizes, drives out the air, and when the vapor of the substance ceases to escape, the capillary is fused shut. The flask after cool- ing is weighed. The fine point is then cut off under mercury and the flask filled with mercury. The flask may then be weighed again, or the mercury poured out and measured, giving the volume of the flask. 1 The method of Dumas is not as well adapted to higher tempera- tures as other methods to be con- sidered later. In the first place, it is difficult to measure high tem- peratures accurately; and, further, the amount of substance contained in the bulb at high temperatures is so small that relatively large errors result from this source. Deville and Troost 2 have used this method at fairly high tempera- tures, employing porcelain balloons, but their results are not very accu- rate. The method of Dumas can- Fig. 5. not be used with even a fair degree of accuracy above 600° to 700° C. An attempt has been made to use the Dumas method under diminished pressure. Habermann 3 has so arranged the bulb that a low pressure can be maintained constant, and the pressure read on a manometer. Larger bulbs are required for work under diminished pressure, and even then the quantity of substance is so small that considerable errors are introduced. 1 For details in carrying out the method and calculating the results, see Kohl- rausch : Leitfaden der Praktischen Physi/c, p. 69. H. Biltz : Practical Methods for Determining Molecular Weights; translated by Jones and King, p. 40. Also, Trauhe : Physikalisch-chemische Methoden, pp. 25-27. 2 Ann. Chim. Phys. [3], 58, 257 (1860). 8 Lieb. Ann. 187, 341 (1877). GASES 59 A large number of modifications of the method of Dumas have been proposed, 1 but that of Bunsen 2 should be especially mentioned. He used three vessels of the same volume and weight. One was empty, one was filled with air at a given temperature and pressure, and the third was filled with the vapor at the same temperature and pressure. If we represent by Wi the weight of the vessel filled with the vapor, by W 2 the weight of the vessel filled with air, and by W$ the weight of the vessel in which there is a vacuum, the relative density of the vapor and air is expressed thus : — Wl- W s After vessels of the same volume and weight have once been prepared, this method of procedure is more convenient and far more rapid than that originally described by Dumas. The method of Dumas is used less to-day than it was formerly, having been largely supplanted by better methods, especially at elevated temperatures. The apparatus used in this method is, how- ever, exceedingly simple, and even at present the Dumas method is employed in certain cases where the presence of a foreign gas in the vapor must be avoided. The Method of Gay-Lussac. — The method devised by Gay-Lussac a for determining the densities of vapors is based upon a principle which is quite different from that which we have just considered. In the method of Dumas the vapor required to fill a given volume was weighed. In the method of Gay-Lussac a weighed amount of substance is converted into vapor, and the volume of the vapor measured. The method as originally proposed by Gay-Lussac con- sists in placing a known weight of liquid in a calibrated vessel over mercury. The whole is then warmed until the liquid is converted into vapor. The temperature is noted, also the volume of the vapor. The latter is reduced to standard conditions, a correction being in- troduced for the tension of the mercury vapor. This method has been so greatly improved that the original is no longer used. Hofmann's Modification of the Gay-Lussac Method. — The modifi- cation of the Gay-Lussac apparatus proposed by Hofmann* consists in elongating the inner tube beyond the barometric height so that iBuff: Pogg. Ann. 22,242 (1831). Marchand: Journ.prakt. Ohem.4A, 88 (1848). Victor Meyer: Ber. d. chem. Gesell. 13, 399, 2019 (1880). 2 Gasornet. Methoden, second edition, p. 154. 8 Biot: Traite, I, p. 291. * Ber. d. chem. Gesell. 1, 198 (1868) ; 9, 1304 (1876). 60 THE ELEMENTS OF PHYSICAL CHEMISTRY ="^ «3» t*h a vacuum will exist in the top of the tube. The substance is intro- duced into the tube over the mercury and volatilized under diminished pressure. The apparatus is shown in the following figure. The calibrated tube A rests in a mercury reservoir R, and is more than 76 cm. long. It is fastened into a vapor-jacket J into which vapor enters at a, and leaves at b. m is a bar of metal terminating in an adjustable point, which is brought down to the surface of the mercury ; the cross-hairs attached to the bar at h serving to read more accurately the height of the mercury in the tube A. After the substance is converted into vapor the volume of the vapor is read and reduced to standard con- ditions. Knowing the weight of the substance and the volume of vapor, the density of the vapor is calculated at once. The advantage of the modi- fication proposed by Hofmann is that the substance is converted into vapor at a temperature below its boiling- point under atmospheric pressure. Thus, the vapor-density of many substances which would decompose if boiled under atmospheric pressure can be determined. Indeed, Hofmann devised this method especially for use with organic sub- stances which would easily decompose. The Gas-displacement Method of Victor Meyer. — A method for determining vapor-densities was devised by Victor Meyer 1 in 1878, which has practically supplanted all other methods, except in very special cases. The method consists in volatilizing a small weighed portion of substance in a tube filled with air, and collecting and measuring the volume of air which is displaced. The apparatus used is seen in Fig. 7. The inner vessel A is surrounded by a glass jacket J, in which is boiled some substance which will heat A to a constant temperature, and at the same time to the temperature desired. The tube A is closed above with a Fig. 6. 1 Ber. d. chem. Gesell. 11, 1867, 2253 (1878). GASES 61 stopper, and from the central tube a side tube runs over to, and under, a calibrated tube filled with water and dipping into a water reservoir. The substance to be used is weighed in a weighing tube which is closed loosely at the top, and introduced, when desired, into the top of A. In carrying out a determination, a liquid which has a higher boiling-point than the substance whose vapor-density is to be determined is placed in the outer jacket. This liquid is J boiled, and a part of the air in the inner vessel pi t is driven out. When no more air escapes from j the side-tube, the tube containing a weighed -^ rj amount of substance is introduced into the top of A, and rests on the rod r. When temperature equilibrium has been perfectly established, the mouth of the side-tube is placed under the measuring tube in the water tank, the rod r drawn back, and the small vessel containing a weighed amount of the substance allowed to drop to the bottom of A. The substance volatilizes, drives out the loosely fitting cork from the weighing tube, and then displaces air from the tube A. The displaced air is received in the measuring tube t, and its volume is equal to the volume of vapor formed in the tube A by the known weight of the substance introduced. We know the amount of substance used, also the volume of the air displaced, which is equal to the volume of vapor formed; consequently the density of the vapor of the substance. A very small amount of substance suffices for determining vapor-density by this method, and the method can be used at very high temperatures. At higher temperatures vessels of glass cannot of course be employed, but porcelain can be used. Berlin porcelain can be employed up to 1600°, and other more resistant forms of porcelain 1 can be used up to 1700°, or perhaps a little higher. Platinum vessels can be used up to 1700°. There is no material known which can be 'used above 1800°. The great advantage of this method, in addition to the small Fig. 7. i Biltz : Ztschr. phys. Chem. 19, 406 (1887). 62 THE ELEMENTS OF PHYSICAL CHEMISTRY amount of substance required, is that the temperature of the experi- ment does not need to be known. It is only necessary to keep the temperature constant before and after the introduction of the sub- stance. The gas-displacement method is so far superior to all others at high temperatures that it has practically supplanted them all. It is not necessary to fill the vessel A with air. This may be replaced by an indifferent gas, in case the oxygen of the air would act chemically upon the substance to be vaporized. Thus, if we were determining the vapor-density of arsenic or sulphur, oxygen must be excluded, and the vaporizing vessel could be filled with nitrogen or hydrogen. If the vapor of magnesium was being studied, nitrogen could not be used, since it would act chemically upon the magnesium. The gas-displacement method of Victor Meyer has also been used under diminished pressure, 1 and the vapor-densities of substances determined considerably below their boiling-points. The advantage of increased stability of the substance at the lower temperature has already been mentioned. A number of modifications of Meyer's method have been devised for working at diminished pressures. La Coste 2 places the whole apparatus under diminished pressure. Lunge and Neuberg 3 also work at known pressure, while Traube * reads the volume of displaced air at the diminished pressure of the experiment. Bleier 5 devised an ingenious manometer for measuring accurately very small pressures, and together with Kohn determined the vapor-density of sulphur at very small pressures. Method of Bunsen. — Bunsen 6 has devised a rough method of determining the relative densities of gases. Gases under the same pressure pass through a small opening with velocities which are in- versely as the square roots of their densities. The method consists in allowing equal volumes of different gases to pass through a very fine hole in a platinum plate, which covers the top of the cylinder containing the gas, and noting the time required. The cylinder is immersed in mercury, which enters from below as the gas escapes at the top. The method is not capable of any very great refinement, and the results obtained by means of it are only close approximations. 1 Ber. d. chem. Gesell. 23, 311 (1890). Bleier : Monatsh. 20, 505, 909 (1899) ; 21, 575 (1900). 2 Ber. d. chem. Gesell. 18, 2122 (1885). 8 Ibid. 24, 729 (1891). See Traube : Physikalisch-chemische Methoden, p. 34. 4 Physikalisch-chemische Methoden, p. 34. 6 Monatsh. 20, 909 (1900). 6 Gasomet. Method., p. 160. GASES 63 Of the methods considered for determining the densities of vapors, that of Meyer is by far the most generally applicable. The method of Gay-Lussac and the modification proposed by Hofmann are seldom used. The method of Dumas is used at present only in special cases, to which reference will be made in detail a little later. Results of Vapor-density Measurements. — The vapor-densities of elementary gases have shown many interesting and surprising rela- tions between the number of atoms contained in the molecules of these substances. The molecular weights of a number of elementary gases, calculated from their densities, show that the molecule is made up of two atoms. This applies to hydrogen, oxygen, nitrogen, chlo- rine, bromine, and a number of others. The vapor-densities of mer- cury, cadmium, and glucinum show that the molecule is monatomic, or that the molecule and atom are identical. On the other hand, the molecules of phosphorus, sulphur, etc., contain more than two atoms, if the temperature to which they are heated is not too high. The vapor-density, and, therefore, the number of atoms contained in the molecule, varies in some cases with the temperature. Take the case of sulphur. The vapor-density at about 500° C. gives a molecular weight which is about six times the atomic weight of sulphur ; or, in a word, at this temperature the molecule of sulphur consists of six atoms. The vapor-density of sulphur at about 800° shows a molecular weight of 70, and at about 1100° of approxi- mately 64. The molecule of sulphur, which contains six or eight 1 atoms at the lower temperature, has therefore broken down at the higher temperature into three molecules, containing two atoms each. Similar results were obtained with phosphorus. At 500° C. there are four atoms in the molecule. The vapor-density becomes con- tinually less with rise in temperature, until at about 1700° C. the molecule of phosphorus contains only three atoms. The case of iodine is especially interesting. At temperatures from 200° to 600° the molecule of iodine consists of two atoms. As the temperature rises, V. Meyer 2 on the one hand, and Crafts and F. Meier 3 on the other, found that the vapor-density decreases, and that above 1400° the density is only about one-half the value at the \ lower temperature. Above 1600° it is quite certain that the vapor- density of iodine would remain constant, since at this temperature the atom and molecule would be identical, and no further dissoci- ation of the molecules could take place. 1 See Bleier and Cohn : Monatsch. 21, 575. 2 Ber. d. chem. Oesell. 13, 394 ? 1010 (1880). 8 Ibid. 13, 851 (1880). Compt. rend. 92, 39 (1881). 64: THE ELEMENTS OF PHYSICAL CHEMISTRY This dissociation of more complex into simpler molecules is not limited to elementary gases. The molecule of arsenious oxide from 500°-700° is shown by its vapor-density to have the composition As 4 6 . As the temperature rises, the vapor-density becomes less and less, and at 1800° it corresponds to the simpler formula As 2 3 . Similarly, vapor-density methods make it very probable that the molecules of ferric chloride and aluminium chloride correspond to the double formulas at lower temperatures; and that these more complex molecules break down into the simplest molecules, FeCl 3 and AICI3, as the temperature rises. In working either with elementary gases or with the vapors of compounds which undergo dissociation, the method of Dumas is greatly to be preferred to that of Meyer, since in the latter there is always present a considerable quantity of some foreign gas, which affects the amount of dissociation. This foreign gas dilutes the vapor whose density is being determined, and it is well known that this will change the amount by which the vapor will be dissociated. This accounts for the difference between the results obtained in such cases by the gas-displacement method and the method of Dumas. Abnormal Vapor-densities. Apparent Exceptions to the Law of Avogadro. — The vapor-densities of the elementary substances men- tioned above showed that the molecules of some vapors contain a number of atoms, the molecules of others two atoms, while in some vapors at low temperatures, and in others at higher temperatures, the molecule contains one atom, or the molecular weight is identical with the atomic weight. In the case of no elementary substance, however, was the molecular weight found from vapor-density less than the atomic weight of the element, and in none of the com- pounds thus far mentioned was the molecular weight less than the sum of the atomic weights of the elements entering into the com- pound. In a number of cases the molecular weight showed that the molecule of the compound was the simplest possible, but there was nothing to indicate that the simplest molecule had in any case broken down into its constituents. We must now turn to another class of phenomena. The molecular weights of substances like ammonium chloride, phosphorus pentachloride, choral hydrate, etc., calculated from their vapor-densities, were less than the sum of the atomic weights of their constituent elements. Thus, the vapor- density of ammonium chloride, corresponding to the formula NH 4 C1 must be 1.89, while Bineau ' found the value 0.89. The vapor-density 1 Ann. Chim. Phys. [2], 68, 440 (1838). GASES 65 of phosphorus pentachloride of the formula PC1 5 must be 7.20. Neu- mann l found by the method of Dumas at 182° the value 5.08. This decreased with rise in temperature up to 290°, where it became con- stant at 3.7. Similar results were found by Cahours. 2 A number of other examples similar to the above were known, but these suffice to illustrate the point. The explanation of these abnormal results was not furnished at once, and for a time the hypothesis of Avogadro was rather at a discount because of their existence. The explanation, however, has been furnished, as we shall now see, and the law of Avogadro thoroughly substantiated. Explanation of the Abnormal Vapor-densities. — After Deville 3 had shown in 1857 that many chemical compounds are broken down or dissociated by heat, it occurred to Cannizzaro, 4 Kopp, 5 and others, that the abnormal vapor-densities of substances like ammonium chloride, phosphorus pentachloride, etc., might be due to the disso- ciation of these substances by heat. If a substance like ammonium chloride was dissociated, one molecule would yield one molecule of ammonia and one of hydrochloric acid. One molecule of phosphorus pentachloride would break down into one molecule of phosphorus trichloride and one molecule of chlorine. If such a dissociation did take place, it would account for the abnormally small vapor-densities found, since the substances in the form of vapor would occupy a greater space than if there was no dissociation. But this did not prove that such a dissociation actually took place. How could this point be tested ? Take the case of ammonium chloride ; if it is dissociated by heat, it would yield ammonia and hydrochloric acid in equivalent quanti- ties. It would, however, be exceedingly difficult, if not impossible, to detect either ammonia or hydrochloric acid when the two gases were mixed in equivalent quantities. This problem was solved by Pebal. 6 He made use of the different rates at which these two gases diffuse to separate them, in part, in case they were present in the vapor of ammonium chloride. The apparatus which he used is seen in Fig. 8. The ammonium chloride d, rests on a plug of asbestos c, near the top of the inner tube, which is open above. A stream of hydrogen is passed through a into the outer part of the apparatus, i Lieb. Ann. Suppl. 5, 341 (1867). "Ann. Chim. Phys. [3], 20, 373 (1847). 8 Compt. rend. 45, 857. 4 Nuovo Cimento, 6, 428. 6 Lieb. Ann. 105, 390 (1858). « Ibid. 123, 199 (1862). 66 THE ELEMENTS OF PHYSICAL CHEMISTRY r^ Fio. 8. and another stream through b into the inner part of the apparatus. The whole is heated above the boiling-point of ammonium chloride. If the salt is decomposed when it volatilizes, the ammonia being lighter than the hydro- chloric acid would diffuse more rapidly through the plug of asbestos. The vapor in the inner tube below the plug would therefore contain an excess of ammonia. This vapor is swept out by means of the stream of hydrogen gas, and made to pass over a piece of moist red litmus paper in the vessel B. It was found that this was colored blue, proving the presence of an excess of ammonia. The vapor remaining in the inner tube above the wad of asbestos must contain an excess of hydrochloric acid, since more ammonia has passed through the asbestos than hydrochloric acid. This is swept out by means of the stream of hydrogen in the outer vessel, and passed over a piece of blue litmus in the vessel A. This turned red at once, showing the presence of free hydrochloric acid in this gas. It would seem, then, that Pebal had demonstrated beyond doubt that the vapor of ammonium chloride contains both free ammonia and free hydrochloric acid, and, therefore, that this substance is dissociated by heat. The objection was, however, raised to the experiment of Pebal, that a foreign substance, asbestos, had been used in con- tact with the vapor of ammonium chloride, and that this might have caused the vapor to dis- sociate, or at least might have facilitated the breaking down of the salt by heat. This objec- tion, while apparently having but little foundation, could not be ignored. To test this point Than 1 devised the following appar- atus (Fig. 9): The tube AB, in which the ammonium chloride is contained, is placed horizontally, and the septum is made out of 1 Lieb. Ann. 131, 129 (1864). GASES 67 ammonium chloride. Nitrogen is passed through the tube, the ammonium chloride d heated with a lamp, and the vapors in the two sides passed over colored litmus, as in the experiment of Pebal. The vapor in the side next to the ammonium chloride was found to contain free hydrochloric acid, and free ammonia was shown to be present in the vapor which had diffused through the plug of am- monium chloride. It is thus shown beyond question that the vapor of ammonium chloride is broken down, in part, into ammonia and hydrochloric acid, by heat alone. The work of Wanklyn and Eobinson 1 has shown that phosphorus pentachloride is dissociated by heat into the trichloride and chlorine. The pentachloride was placed in a short-necked glass flask, in which it was to be converted into vapor. Over the neck of this flask a wider glass tube was placed, so that the two were separated by an air-space. Air was passed in through the upper tube and escaped through the space between the two glass tubes. If the vapor of the pentachloride was dissociated by heat into the trichloride and chlo- rine, these would diffuse with different velocities into the upper portion of the vessel, since they have different vapor-densities. They would then be swept out by the current of air in different quantities, the chlorine being in excess since it is the lighter, and would, therefore, diffuse more rapidly into the upper portion of the vessel. Free chlorine was proved to be present in the vapors which escaped, and analysis showed an excess of phosphorus trichloride remaining in the flask. Therefore, the phosphorus pentachloride was broken down, in part at least, by heat into its constituents. This conclusion was confirmed by the observation that as the vapor of phosphorus pentachloride is heated higher and higher it becomes colored more deeply greenish yellow, — the characteristic color of chlorine itself. The vapor of chloral hydrate — CC1 3 COH . H 2 — was shown by Wiirtz 2 to contain water-vapor. Dehydrated potassium oxalate absorbed water from the vapor of this substance, and thus dimin- ished its vapor-tension very considerably. It was thus shown that the compounds, ammonium chloride, phosphorus pentachloride, and chloral hydrate, are dissociated by heat. The abnormal vapor-densities are then satisfactorily ac- 1 Compt. rend. 52, 549 ; Journ. prakt. Chem. 88, 490 (1863). * Compt. rend. 84, 977 (1877); 86, 1170 (1878). 68 THE ELEMENTS OF PHYSICAL CHEMISTRY counted for, and instead of these substances presenting any real ex- ceptions to the law of Avogadro, they furnish a beautiful confirma- tion of the law. The same explanation undoubtedly applies to other substances whose vapor-densities are abnormally small. They are more or less broken down by heat into their constituents ; the amount of the dis- sociation increasing with the temperature. Dissociation of Vapors diminished by an Excess of One of the Products of Dissociation. — A discovery was made in connection with the study of dissociating vapors, which has proved to be of the very highest importance. If there is present an excess of either of the products of dissociation, the amount of the substance decom- posed is lessened. Thus, ammonium chloride is less dissociated if there is present an excess of either ammonia or hydrochloric acid. Similarly, phosphorus pentachloride is much less decomposed at a given temperature if there is present an excess of either phosphorus trichloride or chlorine, as Witrtz 1 has shown. Indeed, the vapor of phosphorus pentachloride is scarcely dissociated at all by heat in the presence of an atmosphere of phosphorus trichloride, or of chlo- rine. The vapor-density of phosphorus pentachloride in an atmos- phere of the trichloride was found to be about 209, while the calculated vapor-density is 208. This is a perfectly general principle, illustrated by phosphorus pentachloride and ammonium chloride. The dissociation of sub- stances in general by heat is driven back by an excess of any one of the products of dissociation. This is the first example thus far met with of the effect of mass on chemical activity. The importance of the action of mass will be more clearly seen as the subject develops. SPECIFIC HEAT OF GASES Specific Heats at Constant Pressure and at Constant Volume. — The amount of heat required to produce a given rise in temperature in equal quantities of different gases, under the same conditions, varies from gas to gas. This is usually expressed by saying that each gas has its own definite capacity for heat. If we represent the amount of heat added by dd, and the rise in temperature by dt, the heat capacity c is expressed thus : — = d0 dt 1 Oompt. rend. 76, 601. GASES 69 The heat capacities of unit quantities of gases are termed their specific heats. If we represent unit mass by m, the specific heat C is expressed thus : — C=- — m dt The specific heat of a gas has been found to vary greatly with the pressure. If the gas is allowed to expand as it is heated, so that the pressure remains constant, it has a definite specific heat, which is termed its specific heat at constant pressure. This is usu- ally represented by C p . If, on the contrary, the volume of the gas is kept constant as the temperature rises, — the pressure increasing, — the gas has a different specific heat. This is termed its specific heat at constant volume, and is usually written C v . These two specific heats for the same gas are very different, as we shall see, and we must always carefully distinguish between them. Determination of Specific Heats at Constant Pressure and at Constant Volume. — The gas is warmed to a known temperature and then allowed to flow through a tube surrounded by water in a care- fully protected calorimeter. The original and final temperatures of the gas and its mass being known, also the mass, specific heat, and rise in the temperature of the water, we have the data necessary for calculating the specific heat of the gas under constant pressure. In connection with the specific heat of gases at constant pressure, we should mention especially the older work of Regnault x and the more recent work of E. Wiedemann. 2 Regnault found that the specific heat of a number of gases, such as oxygen, hydrogen, etc., was a constant, independent of the tem- perature, while the specific heat of carbon dioxide changed very considerably with the temperature. That the specific heat of gases is somewhat dependent upon the temperature has been shown by the more recent work of Le Chatelier 3 and others. The specific heats of different gases tend more nearly to the same value, the lower the temperature. A few of the results of Regnault are given below. These are calculated, not for equal weights of the different gases, but for quantities which bear the same relation to one another as the molec- ular weights. These are known as "molecular heats." 1 Paris, 1862. 2 Fogg. Ann. 157, 1 (1876). Wied. Ann. 2, 195 (1877). 3 Compt. rend. 93, 962 (1881). Beibl : Wied. Ann. 14, 364 (1890). Ztschr. phys. Chem. 1, 456 (1887). 70 THE ELEMENTS OF PHYSICAL CHEMISTRY Molecular Molecular Heat Weight at Constant Pbesbuke Oxygen, 2 32 6.96 Nitrogen, N 2 28 6.83 Hydrogen, H 2 . 2 6.82 Chlorine, Cl2 . 70.9 8.58 Hydrochloric acid, HC1 36.5 6.68 Carbon dioxide, CO2 44.0 9.55 Hydrogen sulphide, H 2 S 34.0 8.27 Carbon bisulphide, CS2 76.0 11.93 Benzene, CeH 6 . 78.0 29.28 Ether, C4H10O . 74.0 35.50 Acetone,CsH 6 58.0 23.92 Stannic chloride, SnCU 259.8 24.39 E. Wiedemann improved the method of Eegnauit in a number of ways. With less elaborate apparatus he was able to obtain as satis- factory results as Eegnauit had done. Instead of using such a long tube and large calorimeter through which the gas must pass to restore temperature equilibrium, he filled the tube with silver turn- ings. 1 This offered a larger surface to the gas, and temperature equilibrium was established in a much shorter tube. The results of Wiedemann's investigations are quite as accurate as Eegnault's. He also found that the specific heats of gases are somewhat depend- ent upon the temperature. To measure directly the specific heats of gases at constant volume, the gas must be placed in a vessel which will withstand great press- ure without change in volume, and the gas and vessel must be heated to the desired temperature. The gas and vessel must then be introduced into the calorimeter. A moment's reflection will show that the heat given out by the vessel will be much greater than that by the gas, and, therefore, all experimental errors will accumulate on the comparatively small quantity of heat given up to the calorim- eter by the gas when it cools. For this reason accurate measure- ments of the specific heats of gases at constant volume are impos- sible. It, however, has been found that the specific heat at constant volume is always less than at constant pressure. The specific heats of gases at constant volume have, however, been calculated from the specific heats at constant pressure by the 1 Wied Ann., 157, 1 (1876). GASES 71 aid of thermodynamics. Instead of using specific heats referred to equal weights of gases, molecular heats have been employed, and an unusually interesting and important relation between the molecular heats at constant pressure and the molecular heats at constant vol- ume has been discovered. We will now follow in some detail the method by which this relation has been pointed out. The Mechanical Theory of Heat and the Mechanical Equivalent of Heat. — Before attempting to deduce any relation between the specific heat at constant pressure and the specific heat at constant volume, we should raise the question as to why there should be any difference between the two; and further, why should the specific heat at constant pressure be greater than at constant volume ? If we inquire into what takes place when a gas is warmed, on the one hand at constant pressure, and on the other at constant volume, we would be impressed at once by this difference. When a gas is heated at constant pressure, it expands, occupying a larger volume. In expanding it must drive back the air, or, as we say, do work. When a gas is heated at constant volume it cannot expand, and, therefore, does not do external work. There is thus a marked dif- ference in the conditions under which the gas is warmed. If heat were consumed in doing work, then we could understand why the amount of heat required to raise the temperature of a gas a given amount was greater at constant pressure than at constant volume. And since, under the same conditions, a gas always gives out the same amount of heat when cooled over a certain range in temperature, as was required to raise it over this same range of tem- perature, we could see why the specific heat at constant pressure would be greater than the specific heat at constant volume. As is well known, this is exactly what takes place. When work is done by an expanding gas, heat is always consumed. Indeed, a gas can be made to cool itself very considerably by simply allowing it to expand and do work. We have then a qualitative relation be- tween heat and work. This qualitative relation was pointed out in 1841 by Julius Robert Mayer, and this marks the beginning of the mechanical theory of heat. Mayer went much farther than the merely qualitative stage, and made it probable that the amount of heat consumed in compressing a gas was exactly equivalent to the amount of work done. He thus showed that heat and work are of similar nature, and that force, or what we now call energy, is as indestructible as matter. If heat and work are equivalent, and if the disappearance of a definite amount of heat means the production of a fixed amount of 72 THE ELEMENTS OF PHYSICAL CHEMISTRY work, it still remains to determine the relation between the two — to determine the mechanical equivalent of heat. The mechanical equivalent of heat was determined with unusual accuracy, for the time when the experiment was carried out, by Joule. He converted a known amount of work into heat by friction, and measured the amount of heat produced. According to Eowland the amount of heat required to raise one gram of water from zero to one degree is equivalent to about 42,550 gram-centimetres of work. We have now expressed, in the mechanical equivalent of heat, the quantitative relation between heat and work. Ratio between the Specific Heats calculated from the First Law of Thermodynamics. — It was shown by the combined labors of Mayer, Joule, Helmholtz, and others, that heat and all other forms of energy are indestructible, and also cannot be created. This is usually stated as the first law of thermodynamics. As this law denies the possi- bility of creating energy, it shows that the so-called perpetual motion of the first class, which would depend upon the creation of energy, is impossible. The relation between the specific heat of a gas at constant pressure and the specific heat at constant volume, can be calculated at once from the first law of thermodynamics. If we have a substance containing E amount of energy and we add d0 amount of heat, the change in the energy of the body, dE, will be equal to the amount of heat added, if no external work is done. If d W external work is done, we would have the following relation : — 06 = 0E + 0W. (1) But the external work, dW, is equal to the pressiire, p, times the change in volume Ov, supposing the pressure to remain constant : — 06 = 0E+p0v. (2) The energy, E, will be dealt with as a function of the temperature and volume — 0E = ^dT+^dv. dT dv The last member of this equation, the change in energy with the change in volume, t— dv, is equal to zero for gases ; since the inner energy of a gas does not change with change in volume, when no ex- ternal work is done. Equation (2) becomes then — d6=^dT + pdv. (3) (X JL GASES 73 If the volume is constant, dv = 0. v — = The term — - ' dT dT dT is the specific heat of the gas at constant volume, which we will now call C'„. If the pressure is constant, — = C„+ p— . But — -is the specific heat at constant pressure, C p . Therefore, — dv 'dT' O r =G.+p^. (4) Returning to the general equation for gas-pressure, pv = RT, we see that if p is constant, pdv = BdT. Substituting this value of pdv in equation (4), we obtain — 0, = C, + R. (5) The specific heat at constant pressure is equal to the specific heat at constant volume plus the gas-constant R. 1 It only remains to determine the value of R in heat units in order to calculate the specific heat at constant volume from the specific heat at constant pressure. The equation G p — C„ = R shows that the work done in expanding under constant pressure, for a rise of one degree in temperature, is the same for all gases, since R is a constant for all gases. Let us deal with gram-molecular weights, and we can calculate the value of R very simply, since R = ^^, as we have seen. A gram-molecular weight of a gas under a pressure of one atmosphere (76 cm. of Hg and at 0°) occupies a volume of 22,376 cc. Since the weight of an atmosphere is 1033.2 grams, we have — B = 22376^1033.2 = g^ R is equal to 84,685 gram-centimetres of work. We know, however, that 42,550 gram-centimetres of work are equivalent to the amount of heat required to raise one gram of water from 0° to 1° 0. — to one calorie. Therefore, — R = 2 calories, or more exactly, according to recent determinations of the mechani- cal equivalent of heat, to 1.99 calories. This applies to the molecular heats of gases. In case we are dealing with unit weights, we repre- sent the specific heat at constant pressure by C p and the specific heat 1 For a fuller discussion see Ostwald : Lehrb. d. allg. Chem. I, 234. 74 THE ELEMENTS OF PHYSICAL CHEMISTRY at constant volume by O,. becomes then — The above equation for molecular heats C p — C v ■■ 2 "where M is the molecular weight of the gas. Returning to the molecular heats at constant pressure, it is neces- sary to subtract 2 from them to obtain the molecular heats at con- stant volume. The following table contains the molecular heats of a few gases at constant pressure and at constant volume. In the last column the ratio between the two is given. Molecular Heat Molecular Heat Cp at Constant at Constant a Pressure, Cp Volume, Cv Ratio Oxygen 6.96 4.96 1.40 Nitrogen . 6.83 4.83 1.41 Hydrogen . 6.82 4.82 1.41 Chlorine . 8.58 6.58 1.30 Bromine . 8.88 6.88 1.29 Hydrochloric acid 6.68 4.68 1.43 ■Carbon dioxide . 9.55 7.55 1.26 Sulphur dioxide 9.88 7.88 1.25 •Carbon bisulphide 11.93 9.93 1.20 Ethylene . 11.31 9.31 1.21 Methyl alcohol . 14.66 12.66 1.16 Chloroform 18.71 16.71 1.12 Ethyl bromide . 19.66 17.66 1.11 Ethylene chloride 22.67 20.67 1.10 Acetone 23.92 21.92 1.09 Stannic chloride 24.39 22.19 1.09 Ether 35.50 33.50 1.06 Oil of turpentine 68.80 66.80 1.03 The last column in this table contains the most interesting results. The ratio between the specific heats is not a constant, as could be foreseen from the method of calculating the specific heat at constant volume from the specific heat at constant pressure. The ratio neces- sarily decreases as the specific heats of the substances increase. It should be noted that the specific heats of compounds are, in general, higher than the specific heats of the elements ; and, further, that the compounds with a large number of atoms in the molecule have a greater specific heat than those with a smaller number. There are exceptions to these statements, but they are in general true. GASES 75 The specific heat at constant volume is thus calculated from the specific heat at constant pressure, and the ratio of the two ascertained in this way. It is a matter of importance to determine the ratio be- tween the two specific heats directly by experiment. This has been successfully accomplished. Determination of the Relation between the Specific Heats of a Gas. — A number of methods have been suggested and used to determine the ratio of the two specific heats of a gas, but of these only one — - the best and most convenient of them all — will be considered. Reference 1 is, however, given to other modes of procedure. Dulong 2 first employed the velocity of sound in the gas to deter- mine the ratio between its specific heats. Instead of measuring the velocity of sound in the gas directly, Kundt 3 measures the wave-lengths, which are proportional to the velocity. A glass rod, with one end terminating in a glass tube filled with the gas to be investigated, is rubbed along its length. The gas in the tube is thus thrown into vibrations, and it remains to measure the wave-lengths of these vibrations. For this purpose some light powder, say lycopodium or finely divided cork, is added to the tube. The powder moves from the points of disturbance to the points of rest in the gas — from the loops to the nodes. It is then only necessary to measure the distance between two loops or two nodes to ascertain the length of the wave in the gas. Since the velocity of the sound is proportional to the wave-length, we know at once the velocity of the sound in the gas. The ratio between the specific heats of any gas is determined at once from the relative lengths between the nodes in the gas in ques- tion and in air, knowing the ratio for air. Let M be the molecular weight of the gas, l x and l 2 the distance between two nodes in the gas and in air under the same conditions ; and the ratio between the specific heats of air is 1.4. The ratio between the specific heats of the gas K is obtained thus : — Ml? K=1A 28.88 V The ratio between the specific heats of a gas, determined by the acoustical method, agrees very closely with that calculated from the first law of thermodynamics for a large number of gases. By exam- 1 Laplace : Mecan. CUeste. V, 223. Assmann : Pogg. Ann. 85, 1 (1852). Mttller: Wied. Ann. 18, 94 (1883). » Ann. Chim. Phys. [2], 41, 113 (1829). Pogg. Ann. 16, 438 (1829). » Pogg. Ann. 127, 497 (1866) ; 135, 337, and 527 (1868). 76 THE ELEMENTS OF PHYSICAL CHEMISTRY ining the table of results on page 69, it will be seen that the ratio between the two specific heats — the one determined, the other cal- culated — does not exceed 1.43. The direct determination of the ratio between the two specific heats in the case of mercury 1 gives a considerably higher value. And the same applies to argon and helium, as will be seen below : — Molecular Heat at Constant Prebsure, Cp Molecular Heat at Constant Volume, Cv LR Mercury Argon Helium 1.66 1.66 1.66 The ratio between the specific heats in each of the above cases is not only higher than the ratio for many other gases, as previously calculated, but the surprising fact comes out that the ratio is the same for all three elements. What can this mean ? It can scarcely be an accidental agreement. We shall now see that, on the contrary, it is a very important fact and has a profound significance, throwing much light on the inner nature of the molecule itself. Ratio between the Specific Heats of a Gas deduced from the Kinetic Theory. — The ratio between the specific heats of a gas can be calculated from the kinetic theory of gases. 2 We have already seen that the difference between the molecular heat at constant pressure and at constant volume is equal to the gas-constant B, and that R is equal to £— : — C' ' 273 It has been shown from the kinetic theory of gases that the pressure times the volume is equal to two-thirds the kinetic energy of the gas: — Therefore, pv = - K. * 3 " - 273 K. (1) i Kundt and Warburg : Fogg. Ann. 157, 353 (1876). 2 For a fuller discussion see Ostwald : Lehrb. d. allg. Chem. I, 261. GASES 77 The entire energy in the gas (E) is the heat required to warm it from absolute zero to the temperature in question at constant volume. This is increased by the heat required to warm the gas from 0° to 1° by -^ of E. But the heat required to warm the gas from 0° to 1° at constant volume is the specific heat at constant volume C„. Therefore, C v = ^fg- E- Dividing this value of C„ into equation (1), we have — P,-C, _2g, C, 3E' f-KV) (2) In case the total energy in the gas is the kinetic energy of the molecules, K= E, and we would have — &=£ = ?; or C„ 3' ^ = ^=1.666. C,. 3 This ratio (1.666) between the specific heats is calculated on the assumption that the total energy in the gas is kinetic, or that there is no intramolecular energy. This value of the ratio is, therefore, a. maximum value. If we examine the ratios between the specific heats of elementary gases already given, either as determined directly by the acoustical method or as calculated, we shall find that in most cases the ratio is less than 1.666, and in no case does it exceed this value. Yet this value is reached with mercury, argon, and helium. This raises the question why is the ratio found experimentally less in most cases than that calculated above, and why is the calcu- lated value realized in a few cases ? This question has apparently been answered quite satisfactorily. In order that the entire energy in the gas should be kinetic, it is necessary that the molecules of the gas should be made up of one atom each. If there was more than one atom in the molecule, there would be intramolecular movement, and the total energy in the gas would not be the kinetic energy due to the movements of the mole- cules as a whole, but this quantity plus the intramolecular energy of the gas. If there was more than one atom in the molecule, K C — C would not be equal to E, but less than E, Therefore — £-— — - would not be equal to two-thirds, but less than this quantity. Conse- quently jf < 1.666. Gv 78 THE ELEMENTS OF PHYSICAL CHEMISTRY This is exactly what we find in most elementary gases. The ratio of the two specific heats is less than 1.666, and we would con- clude that these gases contain more than one atom in the molecule. We will recall that the molecular weights of most of the elementary gases, as determined by the densities of their vapors, showed that there was more than one atom in the molecule. The conclusion in reference to mercury, argon, and helium is evident from what was stated above. Their molecules contain one atom each, or the molecule and atom are identical. The conclusion that the ratio between the specific heats of a gas being 1.666 points to monatomic molecules has been called in question by some physicists, on purely physical grounds. A number of points have been raised, but perhaps the most important objec- tion has been based upon the comparatively complex spectrum shown even by mercury vapor, which is monatomic in terms of the specific heat ratio. This element shows a number of lines in the spectrum, and it has been claimed that no monatomic molecule could give out so many wave-lengths of light. While it is evident that this objection applies if the ultimate atom were meant, its force is not so clear if we recall that what we mean by the chemical atom is simply that unit of matter which we have not thus far been able to break down or subdivide. Indeed, as we have seen, the most probable theory as to the ultimate nature of matter states that what we must regard as the chemical atom must be enormously complex, and in all probability the atoms of what to us are different elements are simply complexes of the same ultimate " corpuscles.'' Whatever weight we are inclined to attach to these objections from the physical side, we must not forget that in those cases where the ratio between the specific heats points to monatomic molecules, the vapor-density method also shows that the molecule and atom are identical. This has been verified in a manner which can leave no doubt in the case of mercury, and it is almost certain that the same result would be obtained with argon and helium. The Second Law of Thermodynamics. — The calculation of the specific heat of a gas at constant volume from the specific heat at constant pressure involves, as we have seen, the first law of ther- modynamics. For the sake of future reference this section should not be closed without a brief reference to the second law of ther- modynamics. The first law of thermodynamics states that it is impossible to create energy, and, therefore, perpetual motion of the first class is GASES 79 impossible. We might, however, conceive of a machine which could convert into mechanical work the heat of surrounding objects at the same temperature as itself. This would evidently be a perpetual motion ; but since it differs from the first kind, it has been called perpetual motion of the second kind. The second law of thermody- namics states that perpetual motion of the second kind is impossible. In a word, heat cannot flow from a colder to a warmer body. Given a gas of volume v and allow it to expand at constant tem- perature to a volume v^ . The maximum amount of work obtainable from this process is exactly equal to the work required to compress the same amount of gas from volume v x to volume v at constant temperature. This can easily be determined. If we are dealing with a gram-molecular weight of a gas with a volume v x and com- press it to a volume v, the pressure being p, the work done is — Ji \pdv. Since pv = BT, the work done, W, is expressed thus: — W= Cpdv v =btC *2 J V v = RTlnl 1 . v The maximum amount of work obtainable from a gram-molecular weight of a gas expanding from a volume v to a volume v 1 is given by the above equation, since this is equal to the work required to compress the gas under the same conditions from the volume v x to volume v. On examining this equation we see that the maximum amount of work obtainable depends only on the relation between the original and final volumes of the gas, and is independent of the absolute values of either. Frequent applications of this deduction will be made, especially in the chapter on electrochemistry. THE SPECTRA OF GASES Emission Spectra of Gases. — When a gas is heated to a sufficiently high temperature, it sends out light of definite wave-lengths. These wave-lengths were recognized by Kirchhoff and Bunsen l to be de- i Pogg. Ann. 110, 160 (1860); 113, 337 (1861). 80 THE ELEMENTS OF PHYSICAL CHEMISTRY pendent upon the chemical nature of the" gas, and to be character- istic of it. Upon this fact is based a method of chemical analysis, •which has proved to be one of the most convenient and fruitful in the whole field of chemistry. It is only necessary to pass the light from a highly heated gas through a prism, or throw it upon a grating, when it will be refracted or diffracted, and the lines characteristic of the gas will appear. In this way it is possible to detect the presence of most of the chemical elements. If the element is a solid or liquid, it is only necessary to convert it into a gas to obtain its characteristic lines. This is easily accomplished if the boiling-point of the element is not too high. Those elements which boil only at very high temperatures are converted into vapor between the carbon poles of an electric arc, and then their spectra examined. By means of spectrum analysis, then, the lines which are char- acteristic of the elements can be studied, and their wave-lengths determined. Having mapped out the lines which are characteristic of all the known elements, we are in a position to detect the presence of any new element. If when we examine the spectrum of a sub- stance a line appears which can be shown not to belong to any known element, we conclude that we are dealing with a new substance, and then proceed to separate it and purify it by chemical methods. As is well known, many of our chemical elements were discovered by means of spectrum analysis. We need mention only caesium, rubidium, thallium, indium, and gallium, and quite recently the spectroscope has proved of incalculable service in the discovery of the new substances in the atmosphere, by Ramsay. Spectrum analysis has now reached such a high degree of perfection, due especially to the concave grating designed by Rowland, 1 that it is certainly the most sensitive means at our disposal for detecting small traces of substances. In examining any substance to-day for unknown elements, or in testing any element in which some foreign material is suspected, resort is always had, whenever possible, to the spectroscope. Absorption Spectra of Gases; Law of Kirchhoff. — If white light is passed through a gas and then through a prism or thrown upon a grating, it is seen to contain dark lines exactly in the places occupied by the bright lines of the gas. Kirchhoff recognized this fact and announced his law : A gas absorbs exactly the same wave- lengths of light as, under the same conditions, it can itself emit. This discovery was of great importance as throwing light on a class of 1 Phil. Mag. 16, 197 (1883). GASES 81 phenomena up to that time not understood. Fraunhofer had early discovered that when sunlight is refracted and separated into its colors the spectrum is not continuous, but is marked by a large num- ber of dark lines. The law of Kirchhoff explained the presence of these dark lines. The light coming from the sun had passed through the vapors of certain elements, and the same wave-lengths which these gases could emit had been absorbed by them. If this is true, we have a means of determining at least some of the elements which exist in the sun. It is only necessary to find out with what char- acteristic bright lines of our terrestrial elements the dark lines in the solar spectrum correspond, in order to determine which of our elements are present in the sun. In this way a large number' of the dark lines in the solar spectrum have been " identified," as it is stated ; i.e. shown to have the same wave-lengths as the bright lines of known elements. We can now state that about half ' of the known terrestrial elements certainly occur in the sun, and about eight of the remaining terrestrial elements may occur in the sun. Among the solar elements we find most of the metals which occur on the earth. Spectrum analysis has not been oontent with determining the elements which occur in the sun, but an attempt has been made to determine the elements which occur in different parts of the sun. Work during the total eclipse of the sun, or by specially devised methods, has shown that the chromosphere always contains hydro- gen, titanium, helium, and calcium, and frequently contains a large number of other elements, such as sodium, barium, iron, and magne- sium. Similarly, the spectroscope has been applied to the corona during a total eclipse, but the composition of the corona is still in doubt. The spectroscope has also been applied to the stars, planets, com- ets, moon, nebulae, etc. ; but for the results obtained reference only can be made to the excellent little book of Landauer, Die Spectral- analyse. Relations between the Spectrum Lines of the Elements. — An ele- ment may give out light of a few wave-lengths, or of many. Some elements are represented by comparatively few lines in the spectrum, while others are represented by a large number — the lines of iron and uranium may number thousands. We will look first for relations between the lines of the same element. Since light is regarded as a 1 Janssen : Compt. rend. 68, 93. Lockyer: Proc. Boy. Soc. 17, 91, 104, 128 (1868). Zollner: Fogg. Ann. 138, 32 (1869). Huggins: Proc. Boy. Soc. 17, 302 (1868). 82 THE ELEMENTS OF PHYSICAL CHEMISTRY ■wave-motion of the ether, the different spectrum lines correspond to different wave-lengths. It would seem probable that the different wave-lengths sent out by the same kind of atoms or molecules would bear some simple relation to one another. , One naturally thinks of the wave-lengths of sound sent out by a vibrating string, and recalls the simple relations between them. Relations as simple as these have not been discovered in the case of light, but generalizations of value have been reached. The first attempt to point out relations between the wave-lengths of the vibrations sent out by the same ele- ment was made by Lecoq de Boisbaudran, 1 but the first successful attempt was made by Balmer. 2 He showed that the wave-lengths of the first spectrum of hydrogen can be accurately calculated from the equation — n 2 -4' n having the values 3 to 15, and A the value 3647.20. It was, however, Kayser and Kunge, 3 who first deduced any gen- eral relation which obtained for a number of the elements. Their equation is — - = A + Bn-* + On-*, A taking instead of the wave-length A, its reciprocal. To test their for- mula they redetermined more accurately the wave-lengths of the lines of many of the elements, and pointed out the existence of distinct series of lines. In the spectra of the alkali metals they found three distinct series of lines. The first series, known as the Primary Se- ries, occurring only with the alkalies, was very bright, containing some of the strongest lines in the whole spectrum, and had unequal differences in period. The First Subordinate Series was composed of very bright lines, but not so bright as the Primary Series, and the differences in period were equal. The Second Subordinate Series was composed of weaker lines, and the differences in period were equal. The relations between the lines of other elements were not as well defined as with the alkalies. Certain elements showed the existence of secondary series, but, in general, as we pass farther and farther from the alkalies in the Periodic System, the relations between the i Compt. rend. 69, 694. 2 Wied. Ann. 25, 80 (1885). 8 Abhandl. Berlin. Akad. 1888, 1889, 1890, 1891, 1892, 1893. Wied. Ann. 52, 114 (1894). British Ass. Beport, 1888, p. 576. Chem. Zeitg. 16, 533. GASES 83 lines of any element become less distinct. For further details in this connection reference must be had to the original papers. 1 Tlie relations between the spectrum lines of different elements are of greater interest, from the physical-chemical standpoint. Lecoq de Boisbaudran 2 thought he had discovered certain relations between the spectra of potassium, rubidium, and caesium, and concluded that as the atomic weight increases, the spectra of the alkalies and alka- line earths tend more and more toward the red. This has since been shown by Ames 3 not to be strictly true in the case of magnesium, zinc, and cadmium. The work of Kayser and Eunge, and of Eydberg, 4 are again of chief importance in connection with the relations between the lines of different elements. Elements belonging to the same groups of the Mendeleeff Table /have analogous spectra. It has already been pointed out that the primary series of lines appears only with the alkali metals. The first three groups of elements have been arranged in the following order with respect to relations between their spectra : 5 — (1) Li, Na, K, Eb, Cs. (2) Cu, Ag. (3) Mg, Ca, Sr. (4) Zn, Cd, Hg. (5) Al, In, Th. Within these groups the spectrum tends more and more toward the red, with increasing atomic weight. This is what we might ex- pect, the heavier atom vibrating more slowly and sending out fewer waves in a given time. As we pass, however, from one group of these elements to another, the spectrum tends toward the violet, with increase in atomic weight. These relations must, of course, be re- garded as only first approximations to any general truth, and when we consider that some elements vibrate in thousands of periods, or at least give thousands of lines in the spectrum, it will probably be a long time before any comprehensive generalization will be reached connecting anything like all the wave-lengths sent out by the differ- ent elements. That there are, however, fundamental relations be- tween these wave-lengths no one can doubt. 1 Rydberg: Compt. rend. 110, 394 (1890). Ztschr. phys. Ohem. 6, 227 (1890). Wied. Ann. 50, 629 (1893) ; 52, 119 (1894). Landauer : Die Spectralanalyse, p. 64. 2 Compt. rend. 69, 610. a Phil. Mag. 30, 33 (1890). 4 Loc. cit. 6 Landauer : Die Spectralanalyse, p. 69. CHAPTER III LIQUIDS RELATIONS BETWEEN LIQUIDS AND GASES General Properties of Liquids. — The properties of liquids as such are so different from the properties of gases that we would suspect little or no connection between these two states of aggre- gation. Liquids have their own definite volumes, which are only slightly changed by change in conditions. The volume of a liquid is slightly diminished by increase in pressure, and increased by rise in temperature; but the change in either case is small. Accord- ing to Amagat, 1 the coefficient of compression of water varies from 0.000043 at comparatively low pressures to 0.000024 at pressures in the neighborhood of 3000 atmospheres. The compression coeffi- cient of mercury is only about 0.0000032 for pressures of a few atmospheres. The increase in the volume of water with increase in temperature is seen in the few results given in the following table, which is taken from the work of Volkmann. 2 The unit is water at + 4° C. Expansion op Watbk Temprrature Volume Temperature Volume 0° 1.000122 40" 1.00770 2° 1.000028 50° 1.01197 4° 1.000000 75° 1.02572 6° 1.000031 90° 1.03574 10° 1.000261 100° 1.04323 20° 1.001731 Similarly, the expansion coefficient of mercury varies from 0.0001813 at 0° to 0.0001884 at 360°. i Oompt. rend. 103, 429 (1886); Journ. de Phys. [2], 8, 197. 2 Wied. Ann. 14, 260 (1881). 84 LIQUIDS 85 If we recall that the volume of a gas decreases with the pressure according to the law of Boyle, and increases with the temperature according to the law of Gay-Lussae, we will see the marked difference between the persistency of the volume of a gas and that of a liquid. The particles of a liquid move comparatively freely over one another, but the resistance to movement is much greater here than with gases. This is usually expressed by saying that the inner friction of liquids is greater than that of gases. Liquids in general represent matter in a much more condensed form than gases. A given volume of a liquid when converted into a gas occupies many times its volume in the liquid state ; but here, again, pressure must be taken into account, since the density of a gas can be greatly increased by pressure alone. These are some of the most striking differences between matter in the liquid and matter in the gaseous state. If, however, we examine gases and liquids more closely, we shall see that the differences are mainly differences of degree — the state of aggregation depending chiefly upon temperature and pressure. That there are close relations between the gaseous and liquid states is clearly brought out by a study of the transformation of gases into liquids and of liquids into gases. The Liquefaction of Gases. — The problem of the liquefaction of gases early attracted attention. It was very easy to liquefy some substances, while others remained in the gaseous state even at quite low temperatures. Van Helmont 1 distinguished between those sub- stances which cannot be liquefied and those which can, by calling the former " gases " and the latter " vapors." The first really important step in the liquefaction of gases which condense only at very low temperatures we owe to Faraday (1823). He heated chlorine hydrate in a glass tube, one end of which was kept cool, and obtained chlorine as a yellow liquid. This was followed 2 by the liquefaction of a number of other gases, such as sulphurous acid, hydrogen sulphide, carbon dioxide, cyanogen, ammonia, etc. In these experiments, Faraday made use both of high pressure and low temperature, — the two conditions which underlie all subsequent work. Bussy 3 woiked at low temperatures, but did not use high press- ures. He liquefied sulphurous acid, and made the important dis- covery that when this liquid was allowed to evaporate in the air, a 1 Kopp : Oeschiehte der Chemie, I, p. 121. 2 Phil. Trans. 113, 189. s Ann. Chim. Phys. [2], 26, 63 (1824). Pogg. Ann. 1, 237 (1824). 86 THE ELEMENTS OF PHYSICAL CHEMISTRY much, lower temperature was produced. This, as we shall see, has proved to be of fundamental importance in connection with the lique- faction of the more resistant gases. Utilizing this fact, Bussy was able to liquefy chlorine and ammonia. Carbon dioxide was liquefied in fairly large quantities by Thilorier 1 in 1834, by means of a new apparatus 2 which he devised for this purpose. He studied a number of the physical properties of liquid carbon dioxide, — its vapor pressure, solubility, etc., — and then turned his attention to the production of low temperatures by allowing the liquid to volatilize. By means of a spray of carbon dioxide low temperatures could be reached ; but by mixing solid carbon dioxide and liquid ether, powerful refrigerating effects could be produced. Thilorier not only liquefied, but succeeded in solidifying carbon dioxide. The liquid carbon dioxide was allowed to expand, when a part volatilized, and in doing so extracted enough heat from the remainder to convert it into a solid. When the solid carbon dioxide is mixed with ether, a powerful refrigerant is produced, which has proved to be of great service in obtaining comparatively low tem- peratures. Under reduced pressure temperatures of from — 100° C. to — 110° C. can be produced by means of this mixture, which has come to be known as Thilorier's Mixture. Faraday published the results of his second attempt to liquefy gases in 1845. s The incentive, as he says himself, was to obtain the so-called " permanent gases " in liquid or solid form. He worked with higher pressures than in his first experiments, and also used lower temperatures, now made possible by the discovery of Thilo- rier's mixture. A number of gases such as ethylene, hydrobromic acid, phosphine, etc., succumbed to this treatment, and were ob- tained as liquids. A number of gases were also solidified, such as hydriodic, sulphurous, and hydrobromic acids, ammonia, cyanogen, and nitrous oxide. Faraday did not succeed in liquefying hydrogen, oxygen, nitrogen, carbon monoxide, or nitric oxide. Natterer 4 devised an apparatus for producing very high pressures, and then attempted to liquefy the so-called permanent gases — oxygen, hydrogen, etc. 5 He subjected these gases to higher and higher pressures, until finally a pressure of between three and four thousand atmospheres was used. At the same time he used the lowest temperature which he could obtain by mixing solid carbon 1 Ann. Chim. Phys. [2], 60, 427 (1835). 2 Lieb. Ann. 30, 122 (1839). 8 Phil. Trans. 135, 155 (1845). * Joum.prakt. Ohem. 35, 169 (1845). 6 Wien. Ber. 5, 361 ; 6, 557 and 570 ; 12, 199. LIQUIDS 87 dioxide and ether. He was unsuccessful, and the permanent gases still remained unliquefied. During the next thirty years (1845-1875) not many gases -were added to the list of those which had been liquefied. The so-called "permanent gases" had baffled all attempts to liquefy them, and still continued to do so. But during this period the nature of gases was studied more closely, and knowledge acquired which made possible the subsequent liquefaction of all gases. Some of the results of the work of this period will be considered in more detail a little later. Suffice it to say here that it was shown that for every gas there is a temperature above which it cannot be liquefied, no matter how great the pressure to which it is subjected. This is called the critical temperature of the gas. It soon became obvious, then, that every gas must be cooled down at least to its critical temperature, before it can be converted into a liquid by pressure. After this fact became clearly recognized, experimenters saw that they must look rather to the securing of low temperatures than of high pressures, in order to convert the "permanent gases" into liquids. It was not until 1877 that Oailletet x succeeded in liquefying oxygen and carbon monoxide; and it was only a few weeks later that oxygen was also liquefied by Pictet. 2 The method employed by Cailletet consisted in subjecting the gas to a fairly high (300 atmospheres) pressure in a very simple apparatus, 3 cooling the gas down to a low temperature by means of liquid sulphur dioxide, and then allowing the gas to expand suddenly by releasing the pressure. In addition to oxygen and carbon monoxide, Cailletet succeeded also in liquefying nitrogen and air, but the experiments with hydrogen were not as satisfactory, although it is stated that a mist was seen in the tube containing the hydrogen, when the pressure was re- moved. The experiments of Pictet 4 cannot be described in detail. He succeeded in liquefying oxygen, as has been stated, and pos- sibly hydrogen also, and, indeed, may have obtained a little solid hydrogen. We now come to the very important and successful work of the Poles, Wroblewski and Olszewski. 1 Their method consists in sub- jecting the gas to be liquefied to considerable pressure, but at the same time cooling it down to a very low temperature. The low 1 Compt. rend. 85, 1217 (1877). 2 Ibid. 85, 1214, 1220 (1877). *Ann. Chim. Phys. [5], 15, 132 (1878). *Ibid. [5], 13,145 (1878). « Wied. Ann. 20, 243 (1883). 88 THE ELEMENTS OF PHYSICAL CHEMISTRY temperature is secured by causing a liquid with low boiling-point to boil under diminished pressure. Thus, in the liquefaction of oxygen a temperature of — 130° was secured by boiling liquid ethylene under diminished pressure. The oxygen was then lique- fied at a pressure not much above twenty atmospheres. Similarly, when nitrogen was cooled to a very low temperature, subjected to a pressure of 150 atmospheres, and part of the pressure released, it was obtained as a liquid. In 1884 Wroblewski 1 liquefied hydrogen, using liquid oxygen under diminished pressure as the refrigerating agent. He assigned the following boiling-points to four of the more common gases : — Pressure Boiling-point Oxygen .... Nitrogen .... Carbon Monoxide 1 atmosphere 1 atmosphere 1 atmosphere 1 atmosphere - 184°. C. - 194°.3 C. - 192°.2 C. - 186°.0 C. When these liquids were boiled under diminished pressure, a temperature somewhat lower than — 200° C. could be obtained. Olszewski made use of the low temperature obtained in this way to liquefy hydrogen. 2 The gas was subjected to a pressure of nearly two hundred atmospheres, and cooled as low as possible by boiling oxygen under a pressure of a few millimetres of mercury. He was not able to obtain any quantity of liquid hydrogen. Olszewski solidified a number of the very low-boiling liquids. Liquid carbon monoxide, 3 which boiled at —190°, was evaporated under diminished pressure. The temperature sank to — 211°, and a part of the liquid solidified. Nitrogen 4 was solidified in a similar manner at a temperature of —214°. Solid nitrogen, when boiled under diminished pressure, produced a temperature of —225°. Liquid air evaporated under low pressure gave — 220°. Olszewski found the boiling-point of oxygen to be — 181°.4, of nitrogen — 194°.4, and of carbon monoxide — 190°. In 1891 he made another attempt to liquefy hydrogen, 5 using liquid air and liquid oxygen as the re- frigerants. While not successful to any marked extent, he was able to fix the boiling-point of hydrogen at about — 243°.5. 1 Compt. rend. 98, 149 (1884). 8 Ibid. 99, 706 (1884). 2 Ibid. 98, 365, 913 (1884). * Ibid. 100, 350 (1885). 6 Phil. Mag. [5], 39, 188 (1895). LIQUIDS 89 The experiments of Dewar 1 contributed much to our knowledge of lew-boiling liquids. He devised an apparatus 2 for liquefying such gases as oxygen, nitrogen, etc., on a comparatively large scale, and in 1893 solidified air. 8 Dewar greatly facilitated the work with these low-boiling liquids, by devising double-walled bulbs and test- tubes, 4 and pumping out the air between the two walls. In this "vacuum-jacketed" apparatus these liquids evaporate comparatively slowly and could be preserved for a relatively long time; At this time the problem of liquefying gases was solved by a new method, which made it possible to liquefy such gases as the air on a commercial scale. Hitherto, the gas had been cooled chiefly by evaporating some low-boiling liquid under diminished pressure, but plainly this was not economical. The final cooling of the gas was effected by allowing it to expand. The methods of liquefying air used by Linde, and also by Hampson and Tripler, are apparently based upon essentially the same principle. The gas is compressed, and the heat which is liberated removed. The gas is then allowed to expand, usually through a small opening, and thus its temperature lowered. This cold gas is then allowed to cool more of the compressed gas, and finally some of the latter is obtained in liquid form. Quite recently some extremely interesting results have been obtained in connection with the liquefaction of the most resistent gases. Argon was liquefied by Olszewski* in 1895, using liquid Oxygen as the re- frigerating agent. It boiled at — 187° and froze at — 191°. Fluorine was liquefied by Moissan and Dewar 6 in 1897. This is, of course, a remarkable experiment, when we think of the chemical nature of fluorine. The fluorine was cooled to — 190° by means of liquid air, liquefied, and received in a glass bulb. Fluorine boils at — 187°, and at this low temperature loses much of its chemical activ- ity. It does not act upon iron, and does not replace iodine from its compounds. The liquid fluorine was cooled to — 210° without solidi- fying. Fluorine has, however, been recently 7 solidified. The problem of liquefying hydrogen in any appreciable quantity was solved by Dewar 8 in 1898. A mixture of liquid nitrogen and hydrogen was used to cool down the gas. Under diminished press- ure this would give a temperature of at least — 205°. Hydrogen 1 Phil. Mag. 18, 210 (1884). 8 Chem. News, 67, 126 (1893). 2 Proc. Roy. Inst. 1886, 550. 4 Proc. Boy. Inst. 14, 1 (1896). 6 Trans. Boy. Soc. 186, 253 (1895). Communicated by Ramsay. » Compt. rend. 124, 1202 (1897); 125, 505 (1897). 7 Nature, March 26th, 1903, 497. » Proc. Boy. Soc. 63, 256 (1898). 90 THE ELEMENTS OF PHYSICAL CHEMISTRY gas cooled to this temperature, and under a pressure of about 180 atmospheres, was allowed to flow through a fine opening into a "vacuum-jacketed" vessel, kept below — 200°. Hydrogen liquefied under these conditions at the rate of some four or five cubic centi- metres of liquid per minute. The boiling-point of liquid hydrogen, as determined by the platinum thermometer, is — 252°. This has since been redetermined by a platinum-rhodium thermometer, and found to be - 246°. Dewar l did not succeed in liquefying helium although he placed a tube containing this gas in liquid hydrogen. He obtained hydro- gen in the solid form. 2 He attempted to solidify hydrogen by plac- ing some of the liquid in a tube surrounded by liquid hydrogen in a vacuum-jacketed vessel, and boiling the hydrogen in the outer vessel under diminished pressure. This experiment was not successful. The hydrogen in the inner vessel may have been cooled below its freezing-point, but remained undercooled and did not solidify. How- ever, by means of a simple apparatus in which the refrigerating effect of evaporation under diminished pressure could be better realized, Dewar obtained hydrogen in the solid form. The melting-point of hydrogen must be about — 255°, and a slightly lower temperature can be obtained by evaporating solid hydrogen. 3 Helium has recently been liquefied by Kamerlingh Onnes, 4 using liquid hydrogen boiling under diminished pressure as the refrigerating agent, and then allowing the compressed gas to expand. Helium boils at 4°.3. Liquid helium under diminished pressure does not solidify. We see, then, from the above, that all known gases have been liquefied, and all, with the exception of helium, have been solidified. The relation between the gaseous and liquid state is evidently a very close one — the state of aggregation which obtains depending obviously upon temperature and pressure, but chiefly upon tempera- ture. A. further point of very great interest comes out in connec- tion with the liquefaction of the more permanent gases. We are able to realize experimentally a temperature which is but slightly above the absolute zero. That many important discoveries will be made by working in this region of extreme cold is almost certain, now that we have refrigerating agents of such intensity and in such quantity at hand. In tracing the development of the principles and methods in- volved in liquefying gases, it was pointed out that there is a temper- 1 Proa. Roy. Soc. 63, 257 (1898). 2 Chem. News, 80, 132 (1899). 8 For details in connection with the liquefaction of gases, see the admirable little book by Hardin, Liquefaction of Gases. * Chem. News, 98, 37 (1908). LIQUIDS 91 ature for every gas, above which it cannot be liquefied by pressure. This and certain analogous constants for gases must be studied more closely. Critical Temperature and Critical Pressure. — Cagnaird de la Tour ' observed in 1822 that ether and alcohol pass completely into vapor in a very small space, when the temperature is above a certain point. Also, that two volumes of ether volatilize at the same temper- ature as one volume into the same space. This made it probable that there was a temperature above which these liquids could not remain in the liquid state, but would pass over into vapor regardless of the pressure. This observation made but little impression, until Andrews 2 showed much later (1869) that there is a temperature for every gas, above which it cannot be liquefied. This temperature was called by Andrews the Critical Temperature of the gas. The i work of Andrews was done largely with carbon dioxide. When the tube containing this gas was brought to a temperature of 13°.l, and the gas subjected to a pressure of 48.9 atmospheres, a liquid began to appear, and the volume of the gas continued to dimin- ish without any con- siderable increase in pressure being required. At 21°.5 similar results were obtained. At some- what higher tempera- tures, however (31°.l and 32°.5), results of a very different character manifested themselves. Although there was a marked decrease in vol- ume at a certain definite pressure, yet no liquid separated. There was no evidence that any liquid had been formed. At still higher temperatures the abrupt- i Ann. Chim. Phys. 81, 127, 178 (1822); 22, 410 (1823). 2 Trans. Boy. Soc. 1869 [2], 575. 92 THE ELEMENTS OF PHYSICAL CHEMISTRY ness of change in volume at any definite pressure became less and less, and entirely disappeared at 48°.l. These results are seen best by plotting them in curves ; the abscissas are volumes, the ordinates pressures. The curve for 13°.l shows that when a pressure of nearly 50 at- mospheres is reached, the volume diminishes very greatly without any marked increase in pressure. This means that the gas has passed over into liquid at this pressure. The curve for 21°.l is similar to the lower curve. An abrupt transition from gas to liquid takes place, but at a higher pressure. The curves for 31°.l, 32°.5, and 35°.5 show less and less abruptness, but at none of these tem- peratures is any liquid produced. The curve at 48°.l shows no break, being perfectly smooth throughout. The temperature above which carbon dioxide cannot be liquefied was found by Andrews to be 30°.92, and this is, therefore, the critical temperature of the gas. The temperature above which a gas cannot be liquefied has been termed by Mendeleeff 1 the absolute boiling-point of the gas. This is obviously the same as Andrews' critical temperature. The pressure which will just liquefy the gas at the critical tem- perature has been termed the critical pressure. The substance has a certain definite density under these conditions, and this is its critical density. The reciprocal of the critical density is the critical volume. Many of the critical constants of liquids will be found in a paper by Heilborn, 2 but since some of these have been quite recently deter- mined with greater accuracy, the original papers bearing upon the liquefaction of gases and the properties of the liquids formed must be consulted. The critical temperatures and pressures of some well- known liquids are given in the following table : — Critical Temperature Critical Pressure Hydrogen .... - 225°. 16.0 atmospheres Nitrogen . - 146°. 35.0 atmospheres Carbon monoxide - 141°.0 36.0 atmospheres Argon . - 120°. 40.0 atmospheres Fluorine - 121°.0 50.6 atmospheres Oxygen . - 118°. 8 50.8 atmospheres Methane - 95°. 5 50.0 atmospheres Carbon dioxide - 31°.Q 75.0 atmospheres Ammonia - 130°.0 115.0 atmospheres Chlorine - 144°.0 83.9 atmospheres Bromine - 302°.2 i Lieb. Ann. 119, 1 (1861). 1 Ztschr.phys: Chem. 7, 601 (1891). LIQUIDS 93 The examples given in this table show the great differences in the critical temperatures of different liquids. It also shows that the critical pressures of liquids are, in general, not high. If the tem- perature of the gas is below the critical temperature, the pressure required to liquefy the gas is below the critical pressure. In the liquefaction of gases, then, low temperature is far more important than high pressure. Indeed, the temperature must be at least down to the critical temperature. If the temperature is still lower, very- slight pressure may liquefy the gas. We can now see why the earlier experimenters were not successful when they tried to liquefy such gases as oxygen, nitrogen, hydrogen, etc. They used in some cases enormous pressures amounting to thousands of atmospheres; but did not cool the gases down to the critical temperatures. After these gases were sufficiently cooled they were liquefied at moderate pressures. Continuity of Passage from the Liquid to the Gaseous State. — It will be seen from what has been said in reference to critical tempera^ ture and pressure, that a liquid can be transformed into vapor with- out becoming heterogeneous at any time. If the liquid is warmed above its critical temperature, a pressure is produced which is greater than the critical pressure. The volume may now be increased to any extent, yet the substance which was originally liquid remains homogeneous. The passage from the liquid to the gas is thus perfectly continuous, and it is impossible to say where the liquid state ends and the gaseous begins. The condition of matter at and near the critical point has always perplexed men of science, and many opinions have been expressed concerning it. Andrews discussed this condition in connection with carbonic acid. He pointed out that if this gas above the critical temperature is sub- jected to a pressure considerably above the critical pressure, there is an enormous decrease in volume. The carbon dioxide under this condition is neither gas nor liquid, but occupies a position between the two. Certain phenomena manifested by substances around the critical point have been very carefully studied. Clark 1 showed that the density of the vapor was equal to that of the liquid at the critical point. This has been defined as the critical density. The critical point is, then, that at which the density of vapor and liquid are equal. Ramsay 2 concluded from the experiments of others and from his own that the liquid state may persist beyond the critical 1 Proc. Phys. Soc. 4, 41. a Proc. Boy. Soc. 31, 194 (1881). 94 THE ELEMENTS OF PHYSICAL CHEMISTRY point, and this opinion is shared by other experimenters. 1 Hannay, 2 on the contrary, is of the opinion from, his own work, that the criti- cal point marks the limit of the liquid condition, and suggests the term "vapor" for matter just above the critical point. It, however, seems best to still limit the states of matter to three, — gas, liquid, and solid, — as Hardin points out. 3 Defining gas as we do, as having neither any definite form nor occupying any fixed volume, but capable of nearly indefinite expansion, it is ob- vious that a substance above the critical point is in the gaseous condition. Just as a liquid can be transformed into a gas without any break in continuity, so can a gas be transformed into a liquid by a continu- ous process. The gaseous and liquid states, then, approach as the critical point is reached, and either can be made to pass into the other without any breach in continuity. The Kinetic Theory of Liquids. — The close relation which we have just seen to exist between liquids and gases has led to the application of the kinetic theory of gases also to liquids. Since the passage from a liquid to a gas, and vice versa, under certain condi- tions is so gradual that we cannot say where the one state of aggrega- tion ends and the other begins, it is highly probable that any theory which obtains for the one state would apply, to some extent at least, to the other. The liquid state, as we have seen, represents matter in a much more concentrated condition than the gaseous state. There is a much larger number of molecules in a given volume of a liquid, and consequently the collisions between the moving molecules are much more frequent. There would thus result in the liquid an enormous pressure, were it not for the attractive forces between the molecules. These attractive forces hold the molecules together and prevent them from flying off with explosive violence. Only those molecules which approach the surface of the liquid with unusually great velocity can so far escape from the attractions of the other liquid molecules as to fly off into the space above the liquid. This explains the existence of vapor above every liquid. We know, however, that if these mole- cules fly off into a closed space above the liquid, the vapor-pressure thus produced cannot exceed a certain limit at any given tempera- 1 Jamin : Phil. Mag. [5], 16, 75 (1883). Cailletet and Colardeau : Ann. Chim. Phys. [6], 18, 269 (1889). 2 Proc. Boy. Soc. 30, 478 (1880). 8 Liquefaction of Oases, p. 95. LIQUIDS 95 ture. We can clearly see the reason for this in terms of our theory. The molecules of the vapor, in their movements through the confin- ing space, come in contact with the surface of the liquid. Some of these are continually coining within the range of the attractive forces of the liquid molecules, and are drawn down, as it were, into the liquid again. There is thus a continual exchange going on between the liquid and the vapor, some liquid particles passing off as vapor, and some vapor particles condensing as liquid, until a condition of equilibrium is reached. Equilibrium is established when the vapor- pressure has reached such a point that the same number of gaseous molecules are condensed in any unit of time as there are liquid mole- cules converted into vapor. We have seen that it is only the mole- cules with the greatest kinetic energy which can so far overcome the molecular attractions as to escape from the liquid as vapor, and this of course lowers the mean kinetic energy of the liquid. We know that when a liquid evaporates, the mean kinetic energy of the liquid molecules decreases, or, as we say, the temperature is lowered. If the liquid is in such a position that it can absorb heat, it does so ; and the heat required to effect complete vaporization of a liquid is very great. This explains why the vapor-tension of a liquid is increased with rise in temperature. The addition of heat increases the kinetic energy of the liquid molecules, and more are capable of overcoming the molecular attractions and flying off as vapor in a given unit of time. The number of molecules in the condition of vapor is therefore greater, and the vapor-pressure is greater the higher the temperature. So much for the qualitative application of the kinetic theory of gases to liquids. The quantitative application will be made by attempting to apply the equation of Van der Waals for gases also to the continuous passage from the gaseous to the liquid condition. Van der Waals' Equation applied to the Continuous Passage from the Gaseous to the Liquid Condition. — The equation of Van der Waals for gases, it will be remembered, is : — (* + *)(. ->)-** When this is arranged with respect to the powers of v, we have: — \P J P P 96 THE ELEMENTS OF PHYSICAL CHEMISTRY This equation has three solutions, being a cubic equation, -which means that there are three values of v for any given value of p. We can understand the significance of two volumes for one pressure, the one that of the liquid, the other that of the vapor ; but of the third we know nothing. If we construct the curve corresponding to the above equation, we will have the following figure (Fig. 11). The abscissas represent volumes, and the ordinates pressures. Each is an isothermal curve, and the temperature increases from curve 1 to curve 6. Curve 1 represents a temperature below the critical temperature, and curve 6 is above the critical temperature. If we follow one of these isothermals, say 1, we find that as the pressure increases from A to C, the volume continually decreases ; but as the pressure decreases from C to E, the volume still continues to de- crease. As the pressure increases again from E, the volume contin- ues to decrease. If we compare this curve with the results of experi- ment, — say Andrews' work with carbon dioxide, — we find that the first part of curve 1 corresponds to the results obtained. When gaseous carbon dioxide was subjected to increasing pressure, the volume de- creased as represented by the curve AB. Since the temperature is below the critical, when a certain pressure was reached, rep- resented by the point B, the gas liquefied. The volume thus changed very rapidly without any change in pressure, until a volume corresponding to that of the liquid was reached. This is represented by the straight line BF. With further increase in pressure beyond the point F there was very slight diminution in volume, since the volume of a liquid is only slightly changed with large changes in pressure. The portion of the curve which cannot be verified experimentally VOLUMES Fig. 11. LIQUIDS 97 is that represented by BCDEF. The temperature here is below the critical, and when a certain pressure is reached there is an abrupt transition from the gas to the liquid. The substance at this volume is heterogeneous, i.e. part gas and part vapor. Since the equation of Van der Waals applies only to homogeneous conditions, — to a continuous transformation from one state of aggregation to the other, — it is obvious that it cannot apply to this condition. It is possible to follow the curve a little beyond B by studying a super- saturated vapor, and to proceed a short way from F toward E by studying a superheated liquid, but it is impossible to proceed to any considerable distance because of the instability of these states. If we now examine curves 2, 3, etc., corresponding to increasing temperatures, we find that the three volumes corresponding to a given pressure more and more nearly coincide. The middle portion of the curve deviates less and less from the straight line, until in 4 we have the three volumes absolutely coinciding. The physical significance of this point, where the three volumes become equal, is very interesting. It is the point where the volume of the gas is equal to that of the liquid, or where there is no discontinuity be- tween the two states. It is only at this point that gas and liquid can be transformed into one another isothermally and without loss in continuity. The temperature, pressure, and volume at this point are, respectively, the critical temperature, critical pressure, and critical volume. In a word, this is the Critical Point of the sub- stance. The method of obtaining this point is evident from Fig. 11. It is only necessary to draw a number of isothermal curves for con- stant values of a and b in the Van der Waals equation, starting at a temperature considerably below the critical temperature. As the temperature of the isothermal approaches the critical temperature, the values for the three volumes approach one another and finally become equal when the isothermal corresponding to the critical temperature is reached. We can thus calculate the point K from the constants in Van der Waals' equation, which is the same as to say that we can calculate the critical temperature, critical pressure, and critical volume of a substance. In concluding this section attention should be called again to the fact that the application of Van der Waals' equation to liquids has been only partially successful. While it has shown relations between properties as different as the deviations from the ordinary gas laws and the critical constants, yet there are many and quite 98 THE ELEMENTS OE PHYSICAL CHEMISTRY appreciable differences between the values as calculated by means of this equation and as found experimentally. The explanation of many of these differences cannot be given, but a suggestion made by Nernst * will doubtless account for some of them. As he says, in the development of Van der Waals' equation, the assumption is always made that in the passage from the gaseous to the liquid con- dition, and vice versa, there is no change in the molecular condition. We know, however, at present that this assumption is not true. Many substances in passing from gas to liquid form complex molecules to a greater or less extent. As we shall see later, it has been shown that the molecules of liquid water are made up of four of the sim- plest molecules, while the molecule of water-vapor is the simplest possible. We shall also see that the molecules of many substances in the liquid state are complex, while in the gaseous state the mole- cule is generally the simplest conceivable. On account of the very incomplete state of our knowledge with respect to the molecular weights of substances in the liquid condition, it is impossible to say at present whether molecular aggregation in the liquid state can account for all of the deviations of liquids from the equation of Van der Waals. In this section the attempt has been made to point out the most striking relations between liquids and gases, and in doing this some general properties of liquids have been considered. We must now study the several properties of liquids more closely, and especially any relations which may exist between properties and chemical com- position on the one hand, and properties and constitution on the other. Indeed, it was right in this field that much of the earlier physical chemical work was done. The question was raised, and answered as far as possible, how does the introduction of a CH 2 group, or of an oxygen or chlorine atom, affect the physical properties of the compound into which it enters ? Or what is the difference between the effect on one compound produced by a given atom or group, and the effect on other compounds ? Then the question of the effect on physical properties of an atom or group in one state of combination, as compared with the effect produced by the same atom or group in a different state of combination, arose. What, for ex- ample, would be the effect on the physical properties of compounds produced by an oxygen atom in the hydroxyl condition, with respect to an oxygen atom in the carbonyl condition ? In a word, how would constitution affect properties ? 1 See Nernst : Theoretische Chemie, p. 237. LIQUIDS 98 A great many interesting and important relations between compo- sition and properties, and constitution and properties have been discovered. Most of this work has been done, as we would expect, with liquids, and will, therefore, be taken up in this chapter. We shall now take up in turn the thermal properties of liquids, the optical properties, and, in addition, a number of more or less appar- ently disconnected physical properties of liquids ; and shall especially point out in every case the more important relations which have been discovered between the property in question and chemical composition and constitution. THE VAPOR-PRESSURE AND BOILING-POINT OF LIQUIDS The Vapor-pressure of Liquids. — When a liquid is in contact with free space, it continually sends off particles into this space, as we have seen. Given a liquid in contact with an inclosed space; particles are constantly escaping from the surface of the liquid, but at the same time vapor-particles are condensing. Finally, an equilibrium will be established between the liquid and its vapor, when the same number of particles escape in unit time as con- dense in the same time. The vapor-pressure exerted by a liquid is the pressure of its vapor when this condition of equilibrium has been reached. The condition of equilibrium varies, as we have seen, with the temperature, and the vapor-pressure also varies ; the higher the tem- perature the greater the vapor-pressure. In speaking of the vapor- pressure of liquids we must, then, always state the temperature to which the vapor-pressure refers. In comparing the vapor-pressures of liquids we could select some temperature and measure the pressures of their vapors at this temperature ; this method has been extensively used. The liquid whose vapor-pressure it is desired to measure is placed most conveniently above the mercury in the vacuum of a barometer tube, and brought to the desired temperature. The column of mercury is depressed, and the amount of the depression is measured by reading the height of the mercury in the tube and also on a second barometer. From the difference in the height of the two columns the vapor-pressure of the liquid at the temperature in question is determined by reduction to normal conditions. The objection to this method, which has been termed the statical method, is that the presence of any volatile impurity in the liquid 100 THE ELEMENTS OF PHYSICAL CHEMISTRY would greatly vitiate the results. The vapor-pressure of the impurity would add itself to that of the pure liquid, giving a vapor-pressure which is too great. This error may be very considerable if there is only a trace of the impurity present, as Tammann J has shown. A far better method, and one which can be used at much higher temperatures and pressures, is that known as the dynamical method. The principle is very different from that of the statical method. In the latter, as we have just seen, the temperature is kept constant and the vapor-pressures of the different liquids measured at this constant temperature. In the dynamical method the pressure is maintained constant over the different liquids, and the temperatures at which they boil determined accurately by means of fine ther- mometers. In the statical method we measure vapor-pressures, while in the dynamical method we measure temperatures. Any convenient pressure can be chosen, and the temperature at which liquids boil under this pressure can be measured. The pressure must be very carefully regulated, since the boiling-point of a liquid is greatly affected by comparatively slight changes in pressure. The results obtained by the two methods for perfectly pure sub- stances agree very closely, showing that there is for any liquid a definite vapor-pressure for any given temperature. The apparent differences between the results of the two methods have been shown to be due to the large error produced by traces of volatile impurities, when the statical method is used. 2 A number of attempts have been made to formulate the relation between vapor-pressure and temperature, 8 but none of these has been entirely successful. The expressions which hold at one temperature generally do not hold at other temperatures. Relations between the Vapor-pressures of Different Substances. — More interesting are the relations which have been discovered be- tween the vapor-pressures of different substances. Dalton 4 thought that the vapor-pressures of all liquids, at temperatures equally distant from their boiling-points, were equal. While this holds approxi- mately for certain classes of substances, it is far from the truth in many cases. The expression proposed by Diihring is more rational, and holds in a much larger number of cases. The vapor-pressures i Wied. Ann. 32, 683 (1887). 2 Ramsay and Young: Ber. d. chem. Gesell. 18, 2866 (1885); 19, 69, 2107 (1886); 20,67 (1887). 8 Compt. rend. 104, 1568 (1887). 4 Mem. Lit. Phil. Soc. Manchester, 5, 550. LIQUIDS 101 are equal at temperatures which, are at proportional distances from the boiling-points. The formula expressing the generalization of Duhring is : — . ' t' = t" - 100 f + ft = t" +f(t- 100). t' is the boiling-point of the substance under the pressure in question ; t" its boiling-point under a pressure of 76 cm. of mercury, and t and 100 the corresponding temperatures for water ; / is a con- stant factor. Duhring showed that this equation holds approximately in many cases; but that there are striking exceptions was pointed out by Winkelmann. 1 The latter, 2 in turn, proposed an expression for the relation between vapor-pressure and temperature, which is indepen- dent of the nature of the" substance ; Iput reference only can be made to it. The relation discovered by Earn say and Young 3 should, however, receive closer attention. If R is the ratio of the absolute temperatures of the two substances, corresponding to any vapor-pressure which is the same for both of them ; R' the ratio at any other pressure, which again is the same for both; t and V the temperatures of one of the bodies corresponding to the two vapor-pressures, and c a con- stant with a small plus or negative value, or may equal zero ; then R' = R + c(t' - t). When c = 0, R' = R, which means that the ratio between the absolute temperatures is a constant at all vapor-pressures. If c has a small positive or negative value this can readily be calculated. Eamsay and Young showed, by comparing a dozen or fifteen sub- stances with one another, that their formula agrees with the facts to within a comparatively small limit. They 4 tested still further the relation between the absolute temperatures of equal vapor-pressures, expressed by their equation. Using the determinations of the vapor- pressures of many esters, made by Schumann, 5 and calculating the ratios of the absolute temperatures of all of them to those of ethyl acetate at the same pressure, it was found for pressures ranging from 200 to 1300 mm., that the ratio of the absolute temperatures is a constant at all pressures. This is shown by a few results taken from the paper of Ramsay and Young. i Wied. Ann. 9, 391 (1880). * Ibid. 22, 32 (1886). 2 Ibid. 9, 208 (1880). 6 Wied. Ann. 12, 40 (1881). » Phil. Mag. 21, 33 (1886). 102 THE ELEMENTS OF PHYSICAL CHEMISTRY Pressures. 200 MM. 760 mm. 1300 MM. MEAN. Methyl formate .8706 .8720 .8715 .8714 SEthyl formate . .9323 .9352 .9344 .9340 Methyl acetate . .9431 .9440 .9420 .9430 Propyl acetate . 1.0690 1.0677 1.0678 1.0682 Methyl propionate 1.0073 1.0080 1.0073 1.0075 x Ethyl propionate 1.0614 1.0605 1.0615 1.0611 Methyl butyrate 1.0716 1.0720 1.0724 1.0720 Ethyl isobutyrate 1.0935 1.0943 1.0953 1.0944 Methyl valerate . 1.1139 1.1131 1.1135 1.1135 ^-Ethyl valerate . 1.1619 1.1634 1.1642 1.1632 From the mean ratio for each ester between its absolute tempera- ture and that of ethyl acetate at the same pressure, and from the temperatures of ethyl acetate at the three pressures, the boiling- points of the twenty-seven esters were calculated. The results are given by them in a table, together with the temperatures as deter- mined experimentally. In no case does the calculated value differ from the observed by more than 0°.7. This is, of course, a striking confirmation of the general truth of the relation pointed out in the equation of Ramsay and Young. Relations between Boiling-points and Composition and Constitu- tion. The Work of Kopp. — The relations between composition and constitution and boiling-points have been extensively investigated among the organic liquids. Kopp, 1 as early as 1842, extended his investigations of other physical properties of substances to their boiling-points, and discovered comparatively simple relations between the boiling-points of liquids and their composition. He showed that as the compound increases in complexity the boiling-point is raised. An ethyl compound boils about 19° C. higher than the corresponding methyl compound. A little later in the same year 2 he formulated his generalization, that equal differences in the composition of organic compounds correspond to equal differences in the boiling-point. This would be very remarkable if it were true, but we shall see that it is only an approximation. If the law of Kopp was rigidly true, then, isomeric compounds, since they have the same composition, must boil at the same tem- 1 Lieb. Ann. 41, 79 (1842). * Ibid. 41, 169 (1842). LIQUIDS 103 perature. Kopp pointed out in 1844 1 that this is not the case. Ethyl acetate and butyric acid are isomeric, yet the former boils 82° lower than the latter. These isomers, however, are not of similar constitution. He determined, then, the boiling-points of isomeric substances whose constitutions are similar. BOILIKG-POIHT Methyl acetate, CH s COOCH 5 .... . 56° Ethyl formate, HCOOC2H5 .... . 55° Methyl valerate, CH 3 CH 2 CH 2 CH 2 COOCH 8 . . 115° Amyl formate, HCOOC 6 H u .... . 116° Ethyl butyrate, CH 3 CH 2 CH 2 COOC 2 H 6 . 115° It would appear from these results that isomeric substances -having similar constitution have the same boiling-point, to within the limit of experimental error. In 1855 Kopp 2 published the results of an elaborate investiga- tion on the boiling-points of organic liquids. He included in this work a number of alcohols, acids, and ethereal salts. A few of his results will show that his conclusions are substantiated by the facts. Boiling-point Methyl alcohol, CH 4 65° Ethyl alcohol, C 2 H 6 78° Propyl alcohol, C s H 8 96° Butyl alcohol, C 4 H 10 O 109° Formic acid, HCOOH 105° „ Acetic acid, CH„COOH 117° Propionic acid, C 2 H 6 COOH ..... 142° < Butyric acid, C 3 H 7 COOH 156°' Ethyl formate, HCOOC 2 H 5 55% >19° Ethyl acetate, CH 3 COOC 2 H 6 74° < > 22° Ethyl propionate, C 2 H 6 COOC 2 H 6 96°/ Kopp 3 drew the general conclusion from this work that, " for homologous compounds belonging to the same series, the difference in boiling-points is, in general, proportional to the difference in composition. The difference in boiling-point, corresponding to the 1 Lieb. Ann. 50, 71 (1844). 2 Ibid. 96, 1 (1855). s Ibid. 96, 32 (1855). 104 THE ELEMENTS OF PHYSICAL CHEMISTRY difference in composition of CH 2 , is the same in many series oi compounds, and is equal to 19." Work since the Time of Kopp. — More accurate experimental work has subsequently shown that there is no law connecting the boiling-points of substances and their composition and constitution. Indeed, it would be most remarkable if any such law did exist, since the boiling-points of liquids are the temperatures, measured from the freezing-point of water, at which their vapor-pressures just over- come the atmospheric pressure. These boiling-points evidently bear no close relation to any fundamental property of the compound, and, therefore, are not, strictly speaking, comparable temperatures. While no generalization worthy of the name of law connects the boiling-points of substances with their composition and constitution, a number of relations between them have been found to exist. Ditt- mar 1 showed that the two isomeric substances, ethyl formate and methyl acetate, do not have the same vapor-tension at the same tem- perature, that of ethyl formate being the greater throughout. He gives the temperatures of equal vapor-pressures, and they are as follows : — Ethyl formate . . 20° 26° 33° 43° 53° Methyl acetate . . . 21°.7 27°. 8 34°. 7 44°. 5 54°. 4 The boiling-point of methyl acetate is, therefore, higher than that of ethyl formate. That isomeric compounds do not boil at the same temperature, but, if they have similar constitution, boil at nearly the same tem- perature, is shown by the following examples : — Boiling-point Octyl formate, C 9 Hi 8 2 198°. 1 Heptyl acetate, C 9 H 18 2 191°. 3 Amyl hutyrate, C 9 H 18 2 184°. 8 Butyl valerate, C 9 H 18 2 185°.8 Kopp supposed, as we have seen, that within a homologous series of compounds a constant difference in composition corresponds to a constant difference in boiling-point. This was found by Schor- lemmer 2 not to be true for the normal paraffine hydrocarbons and some of their derivatives, as the following results will show. b.-p. rep- resents the boiling-point, and d. the difference between the boiling- points of two successive members of a homologous series. 1 Lieb. Ann. Suppl. 6, 328 (1868). « Lieb. Ann. 161, 263 (1872). LIQUIDS 105 i.-p. d. b.-p. d. b.-p. a. CAo . i° 37° 32° 29° 25° C2H5CI . . 12°. 5 33°. 9 31°.2 28°.0 C 2 H 6 Br . . 39°.0 32°. 29°.4 28°.3 C6H 12 . 38° C 8 H 7 C1 . . 46°.4 C 8 H 7 Br . . 71°.0 CeHii . 70° C4H9CI . . 77°.6 C 4 H 9 Br . . 100°.4 CyHie . 99° C5H11CI . . 105°. 6 C 5 H n Br . . 128°. 7 CsHis . 124° b.-p. d. b.-p. d. CH 3 I . 40°. 32°.0 30°. 27°.6 25°. 8 C 2 H 6 . . . 78°.4 18°.6 19°.0 21°.0 19°. C 2 H 6 I . 72°. C s H 8 . . . 97°.0 CgHvI . 102°.0 C4H10O . . 116°.0 C4H9I . 129°. 6 C 5 H 12 . . 137°.0 C6Hni . 155°.4 C 6 H 14 . . 156°.6 It follows from these results that as the compounds become more complex, the difference between the boiling-points of two succeeding members of a homologous series becomes less. This is what we would naturally expect, since the larger the number of carbon and hydrogen atoms in the molecule the smaller the influence of a CH 2 group when introduced into the compound. This same relation is brought out by Zwicke and Franchimont, 1 though perhaps in not quite so striking a manner, in connection with the acids of the parafline series and some of their esters. Boiling-point Boiling-point of Ethyl Ether Acetic acid, Propionic acid, Butyric acid, Valeric acid, Caproic acid, CHsCOOH C 2 H 6 COOH C 8 H 7 COOH C 4 H 9 COOH C 5 H u COOH (Enanthylic acid, C 6 H 13 COOH 118°.0 140°. 6 162°. 3 184°.0 205°.0 221°.0 ^>22°.6 ^>21°.7 /21°.7 />21°.0 y i6°.o 77°.0 \21°.8 \22°.2 121°.0 / N2 x23°.0 167 °-°>20°.0 187°. The decrease in the difference between the boiling-points of suc- cessive members of homologous series of compounds with increase in complexity, was found also by Linnemann. 2 As the result of his more accurate investigations he concluded that "the difference between the boiling-points decreases, in most of the series thus far studied, with increasing number of carbon atoms, at least among the earlier members of the series." 1 Lieb. Ann. 164, 333 (1872). ■ Ibid. 162, 39 (1872). 106 THE ELEMENTS OF PHYSICAL CHEMISTRY The effect of constitution on boiling-point is clearly shown by the substituted hydrocarbons of the benzene series. If one hydro- gen of the benzene ring is substituted by a group, the resulting com- pound has a different boiling-point from its isomeric compound with two hydrogen atoms in the benzene ring substituted by two groups. When three hydrogen atoms in the benzene ring are substituted by three groups, the compound has a still different boiling-point. This is seen from the following data taken from the work of Kopp : — 5. -p. b.-p. b.-p. C 6 H 5 • C 2 H 5 133°-135° | / CHs C 6 H 4 < 139°-140° N CH S C 6 H5.C 3 H 7 151°-153° ! pTT C 6 H 4 / " 169°-160° X C 2 H 5 /CHs C 6 H 3 — CH S 165°-166° ^CHs •CgHs ■ C4H9 — [ /CH 3 C 6 H 4 < 175°-178° X C 8 H 7 /C2H5 C 6 H 4 < 178°-179° X C 2 H 6 /CHj C 6 H 8 — CH 8 i83°-i84° C2H5 By comparing the boiling-points of isomeric substances enclosed between the same horizontal lines, it at once becomes apparent that constitution has a marked influence on boiling-point in this series of hydrocarbons. The larger the number of hydrogen atoms sub- stituted by groups, the higher the boiling-point of the resulting compound. That constitution has a marked influence on boiling-point has also been pointed out by Naumann. 1 His paper deals with the hydrocarbons of the paraifine series and some of their derivatives, including some alcohols, aldehydes, ketones, and acids. A few meta- meric compounds are taken from the table given by Naumann. Normal pentane, Isopentane, CH 8 .CH 2 .CH 2 .CH S .CH 8 ^>CH.CH 2 CH 8 . . CH 8 I b.-p, 38° 30° Tetramethyl methane, CH 8 — C — CH 8 9 8 .6 I CH 8 Ber. d. ehem. Gesell 7, 173 (1874). LIQUIDS 107 i.-p. Normal butyl alcohol, CH„ . CH 2 . CH 2 . CH 2 OH . . 116° Isobutyl alcohol, ^ > CH . CH 2 OH . . . 109° Secondary butyl alcohol, CH 3 . CH 2 . CHOH . CH S . . 99° CH S I Tertiary butyl alcohol, H 8 C — C — OH 82°. 5 I CH 3 The normal compounds, or those with a chainlike structure, have the highest boiling-points. The larger the number of side chains, the lower the boiling-point of the compound. This is some- times expressed by saying, the more symmetrical the compound the lower its boiling-point. Naumann 1 attempts to explain the higher boiling-point of the normal compounds as due to their chainlike structure. The molecules constructed in this way make better con- tact than when there are side chains to the molecules, and the larger the number of side chains the poorer the contact between the molecules. The better the contact between the molecules, the higher will be the temperature required to tear the molecules apart and send them off as vapor ; consequently, the more nearly the com- pound conforms to the chain structure, the higher will be its boiling- point. In the light of our present conceptions of structure and of the •energy relations in substances, this explanation cannot be very seri- ously considered. We have, on the other hand, already seen that the greater the number of substituting groups in the benzene hydrocarbons, the higher the boiling-point. This apparent discrepancy between the two series of compounds need occasion no great surprise, if we con- sider the very different constitutions of the paraffines and benzene compounds. Of the isomeric substitution products of benzene the ortho com- pounds in general boil higher than the meta, and these, in turn, a little higher than the para compounds. This again is only an ap- proximate relation, to which many exceptions are known. Effect of Certain Atoms or Groups on the Boiling-point of Liquids. — The boiling-points of compounds are affected with some regularity by the introduction of certain atoms or groups. Thus, the introduc- tion of a chlorine atom into a methyl group raises the boiling-point of the compound about 60° to 65°. The introduction of a second or 1 Ber. d. ehem. Gesell. 7, 173 (1874; 108 THE ELEMENTS OF PHYSICAL CHEMISTRY third chlorine atom has a much less marked influence on the boiling- point. This is shown by acetic acid and its chlorine substitution products. b.-p. a. Acetic acid, CH 3 COOH Monochloracetie acid, CH 2 ClCOOH .... Dichloracetic acid, CHCl 2 COOH .... Trichloracetic acid, CCI3COOH .... 118°.0 185°.0 194°.0 198°.0 67°.0 9°.0 4°.0 A rise in boiling-point is produced when chlorine is replaced by bromine, and a still further rise when bromine is replaced by iodine. It should be observed that most of the relations pointed out between boiling-points and composition and constitution are only regularities, which hold in a large majority of cases. Exceptions to many of these are not wanting. Thus, hydrogen replaced by chlo- rine generally means that the chlorine substitution product will boil higher than the original substance, but Henry l has shown that when the hydrogen in acetonitrile is replaced by chlorine the monochlor- nitrile boils higher than the original compound. When the second and third hydrogen atoms of the nitrile are replaced by chlorine, the resulting compounds boil lower than the monochlor derivative, and the trichlornitrile boils almost as low as the original nitrile itself. b.-p. b.-p. CH3CN . CH2C1CN .... 81° 123° CHCI2CN CClsCN .... 112° 83° In dealing with these regularities in boiling-points we must re- member that they are only the first approximations to the truth. We should scarcely speak of them as generalizations, unless in a very narrow and imperfect sense, and still less should we regard them as laws of nature. We should consider them as the pioneer efforts in a direction which some day will lead to a fundamental and deep-seated generalization, which will throw much light on the inter- and intra-molecular condition of matter. Ber. d. chem. Gesell 6, 734 (1873). LIQUIDS 109 HEAT OF VAPORIZATION Heat of Vaporization. Methods of Determining. — We have seen in the preceding section that quite different temperatures are required to convert different liquids into vapor at the same pressure; the boiling-points of liquids are very different. We shall now learn that very different amounts of heat are required to convert comparable quantities of liquid into vapor. Whenever a liquid is converted into vapor, a large amount of heat disappears as such. A part of this is consumed in doing work in driving back the air, since a small volume of liquid occupies a com- paratively large volume in the form of vapor. The amount of this work can be easily calculated, knowing the pressure of the air and the volume of the vapor formed. It has been found that only a small part of the heat that disappears in vaporization is consumed in doing external work ; the larger part does internal work in the liquid, transforming it from the liquid to the gaseous condition. In measuring the heat of vaporization of a liquid, we can either measure the amount of heat required to convert a given quantity of the liquid into vapor at the same temperature as that of the liquid, or we can condense the vapor to liquid and measure the amount of heat liberated during the process of condensation, since we know that the heat liberated in condensation is exactly equal to that con- sumed in vaporization. It is far simpler to measure the heat liber- ated during condensation, and this has been done. The apparatus devised by Schiff * has some advantages over that constructed several years earlier by Berthelot. 2 If the vapor is condensed in a calorim- eter containing water at ordinary temperatures, the heat given up to the calorimeter is that required to vaporize the liquid, plus the heat consumed in raising the liquid from the temperature of the calorimeter to its own boiling-point. The latter quantity must be subtracted from the total heat as measured in the calorimeter to obtain the heat of vaporization of the liquid. Relations between Heats of Vaporization. The Law of Trouton. — To discover any relations which may exist between the heats of vaporization of different substances, we must deal with comparable quantities of substances. It is most convenient to use gram-molecular quantities, and we would then have to do with molecular heats of vaporization. An extremely interesting and probably very important relation between the molecular heats of vaporization of different sub- i Lieb. Ann. 234, 338 (1886). 2 Ann. Chim. Phys. [5], 12, 550 (1877). 110 THE ELEMENTS OP PHYSICAL CHEMISTRY stances was discovered by Trouton. 1 The molecular heats of vapori- zation are proportional to the absolute temperatures at which the liquids boil. That this relation is very nearly true is seen from the following data, taken from the work of Schiff. 2 M h is the molecular heat of vaporization, and Tthe absolute boiling temperature of the substance. Boiling-point Heat of Vapobization Mh T Ethyl formate, C 8 H 6 2 . 53°. 6 92.2 cal. 20.8 Ethyl acetate, C4H8O2 77°.0 83.1 " 20.8 Ethyl propionate, C6H10O2 98°. 7 77.1 " 21.0 Methyl butyrate, C5H 10 O 2 102°. 3 77.3 " 20.9 Methyl valerate, C 6 Hi 2 02 116°.3 70.0 " 20.9 Ethyl valerate, C7HJ4O2 . 134°.0 64.7 " 20.6 Isoamyl acetate, C7H14O2 142°. 66.4 " 20.7 Isoamyl isobutyrate, C9H18O2 169°.0 57.9 " 20.6 Benzene, CeH 6 80°.35 93.5 " 20.6 Toluene, C7H8 . 116°.8 83.6 " 20.0 Meta-xylene, C 8 Hi . 139°.9 78.3 " 20.0 Mesytilene, CgHia . 162°. 7 71.8 " 19.8 Cymene, CioHu 175°.0 66.3 " 19.8 It will be seen at once that the value of — is obtained for any compound, by multiplying its heat of vaporization by its molecular weight to obtain the molecular heat of vaporization, and dividing this by the boiling-point of the substance plus 273°. These results, which are a few taken from many, show to within what limits the law of Trouton holds good for these classes of sub- stances. Ostwald 3 has calculated, from the measurements of others, the ratio — for entirely different classes of substances : — Boiling-point Molec. Heat OF Vaporization Mil T Nitric acid, HN0 8 .... 86° 72.5 20.2 Bromine, Br2 63° 76.7 22.5 Ethylene bromide, C2H 4 Br 2 . 111° 82.3 21.5 Ethyl bromide, C 2 H e Br . 41° 67.2 21.4 Methylene chloride, CH2CI2 . 40° 64.0 20.5 Sulphur dioxide, S0 2 — 8° 59.0 20.0 Cyanogen, C 2 N 2 .... — 21° 56.3 22.4 1 See Oompt. rend. 132, 879 ; 1 "•Ml Mag. 18, 54 (1884). 2 Lieb. Ann. 234, 338 (1886). 8 Lehrb. d. allg. Chem. 1 ,355. LIQUIDS 111 The molecular heats of vaporization are expressed in units which are one hundred times as large as those in the above table. The law of Trouton is thus shown to hold closely for a number of classes of substances. While we at present do not see the full sig- nificance of this relation between heat of vaporization and absolute boiling-point of a substance, we cannot escape the conviction that it is the expression of some principle of profound significance, connect- ing the energy relations of the liquid and gaseous states of aggrega- tion. Heat of Vaporization at the Critical Point. — We have seen that the critical point is that at which all differences between the liquid and its saturated vapor disappear. It is, therefore, necessary that at the critical point the heat of vaporization should become zero. This has been verified experimentally by Mathias. 1 He devised a constant temperature method, applied it to sulphurous acid, carbon dioxide, and nitrous oxide, and showed at least in the case of carbon dioxide, that at the critical point the latent heat (heat of vaporization) is zero. This is another interesting condition which obtains at that very remarkable point, known as the critical point of a liquid. SPECIFIC HEAT OF LIQUIDS Specific Heat of Liquids. Methods of Determining. — Just as the amount of heat required to convert comparable quantities of different liquids into vapor varies for every liquid, so, also, the amount of heat consumed in raising a liquid through any given range of temperature varies from one liquid to another. The relative amounts of heat required to raise unit quantities of different sub- stances through the same range of temperature are known as the specific heats of the substances in question. Water is taken as the unit, and the specific heats of other substances compared with the specific heat of water. The amount of heat required to raise the temperature of one gram of water from 0° to 1° C. is termed a calorie. 2 The quantity of heat required to raise the temperature of one gram of any substance the same amount, expressed in calories, is the specific heat of the substance referred to water as unity. The earlier methods of determining specific heats consisted in bringing the substance whose specific heat was to be determined, at a known temperature, in contact with a substance whose specific heat was known ; the temperature of the latter being different from 1 Ann. Ohim. Phys. [6], 21, 69 (1890). 2 Other definitions of the calorie are given. These will be considered under thermochemistry. 112 THE ELEMENTS OF PHYSICAL CHEMISTRY that of the former. The resulting temperature was determined, and from these data the specific heat of the substance in question could be calculated. Since water is taken as the unit in measuring specific heats, the substance in question was usually mixed with water and the resulting temperature determined. From the nature of this method it has been termed the "method of mixtures." It is obvious that a number of corrections must be introduced, as in all calorimetric measurements, for the specific heat of the vessel, etc. Bunsen 1 devised an ice-calorimeter which has been used for measuring specific heats. From the amount of ice melted by a given quantity of any substance at a definite temperature, it is easy to calculate the specific heat of the substance. It is of course neces- sary in using this method to know the heat of fusion of ice, but this has been fairly accurately determined as 79.7 calories. The Specific Heat of Water. — Since the specific heat of water is taken as the unit, it is especially important that this quantity should be most accurately determined at different temperatures. It was found by Regnault, and by a number of investigators since his time, that the specific heat of water is not a constant for different temperatures. Very different results have been obtained from time to time by different experimenters. Some found that the specific heat of water increased with the temperature, others that there were irregularities at about 4° C, and others still that the specific heat decreased up to a certain temperature and then began to increase. Among the most accurate determinations of the specific heat of water which have ever been made, if not the most accurate, are those of Rowland. 2 In connection with his determination of the mechani- cal equivalent of heat he reinvestigated the problem and found that the specific heat of water decreases from 5° C. up to about 30° C, and then began to increase again. The results of Rowland are given in the following table, together with those more recently obtained by Liidin : 3 — Rowland's Results Ludin's Results 0° 1.0051 5° 1.0054 1.0027 10° 1.0019 1.0010 15° 1.0000 1.0000 20° 0.9979 0.9994 25° 0.9972 0.9993 30° 0.9969 0.9996 35° 0.9981 1.0003 1 Fogg. Ann. 141, 1 (1870). 2 The Mechanical Equivalent of Seat, p. 120. 8 Dissertation, Zurich, 1895. Callendar and Barnes : Brit. Ass. Hep. 1899, A 8. LIQUIDS 113 Eowland 1 says in connection with his results, which show that the specific heat of water decreases at first and then begins to in- crease: "However remarkable this fact may be, being the first instance of the decrease of the specific heat with rise of temperature, it is no more remarkable than the contraction of water to 4°." Relations between Composition and Constitution, and Specific Heats. — To determine whether any simple relations exist between the composition and constitution of substances and their specific heats, we must again deal with comparable quantities of substances. We employ gram-molecular quantities of substances ; and when we multiply the specific heat of the substance referred to one gram by the molecular weight of the substance, we obtain its molecular heat. The molecular heats of a number of homologous series of compounds have been calculated by Ostwald 2 from their specific heats as deter- mined by Reis. 3 The molecular heats of a few substances will be given to show the relations which have been observed. Moleo. Heat Moleo. Heat | Methyl alcohol, CH 4 21.0. i > 9 3 ■' Ethyl alcohol, • C 2 H 6 30. s/ >10.2 ! Propyl alcohol, C 8 H 8 40. 5< ! >10.4 1 Butyl alcohol, C 4 Hi O 50.9< 1 > 9-6 ; Amyl alcohol, C 6 H 12 60.5/ Formic acid, HCOOH 24.2. > 7.4 Acetic acid, CH 8 COOH 31.6/ >2x7.9 Butyric acid, C 8 H 7 COOH 47.4/ Benzene, C 6 H 6 33.8. > 8 Toluene, C 7 H 8 41.8< > 7 Ethylbenzene, C 8 Hi 48. 8< / 8 Mesitylene, C 9 H 12 56.8/ i Propyl chloride, C S H 7 C1 31.6 Propyl bromide, C 3 H 7 Br 32.3 Propyl iodide, C S H 7 I 34.3 These results show that for homologous series of compounds a constant difference in composition (CH 2 ), corresponds approximately to a constant difference in molecular heat. The molecular heats of the three halogens do not differ very considerably, yet there is a slight increase from the chloride to the bromide to the iodide. 1 The Mechanical Equivalent of Heat, p. 131. 2 Lehrb. d. Allg. Chem. II, p. 586. 8 Wied. Ann. 13, 447 (1881). 114 THE ELEMENTS OF PHYSICAL CHEMISTRY The effect of constitution on molecular heats is shown by the following isomeric substances : — Molec. Heat f Butyric acid, C 4 H 8 2 47.4 I Isobutyric acid, C4H 8 2 47.6 ( AUyl alcohol, C 3 H 6 38.1 I Propyl aldelyde, C 8 H 6 32.6 If the constitution of isomeric substances does not differ greatly, the molecular heats are not very different. If, however, the isomeres have constitutions which are very different, the molecular heats may differ widely from one another. The relation between composition and specific heat, which was brought out by the work of Reis, was shown by Schiff r not to apply to all classes of compounds. Indeed, a marked exception was ob- served in the case of the esters of the fatty acids. " All the esters of the fatty acids have, at the same temperatures, and, therefore, also at the same absolute temperatures, equal specific heats." He investigated some twenty-seven of these esters, and also a number of other classes of compounds, including aromatic hydrocarbons, fatty acids, and a number of alcohols. As the result of this work Schiff announced what he termed a law 2 for all the esters having the formula CbH^Oj. " Equal weights at equal absolute temperatures have equal heat capacities." " Equal volumes at equal fractions of the absolute critical tem- perature have equal heat capacity." The relations between specific heats and composition and consti- tution, like the relations between boiling-points and composition and constitution, must be regarded as only approximations. When these quantities have been more extensively and accurately measured, we may be able to arrive at some wide-reaching generalization, con- necting specific heats with the chemical nature of the substances in question. We have thus far studied some thermal properties of liquids — boiling-points, heat of vaporization, and specific heats. Certain optical properties of pure liquids will now be taken up. 1 Lieb. Ann. 234, 300 (1886). Ztschr. phys. Chem. 1, 376 (1887). 2 Lieb. Ann. 234, 331 (1886). LIQUIDS 115 THE REFRACTIVE POWER OF LIQUIDS Refraction of Light. Index of Refraction. — When a ray of light passes from one medium into another of different density, it is bent out of its course, or, as we say, refracted. For light passing from any given medium into another, there is a constant relation between the sine of the angle of incidence and the sine of the angle of refrac- tion. This ratio is termed the index of refraction of the substance. If we represent the angle of incidence by i, and the angle of refrac- tion by r, the index of refraction, n, is expressed thus : — sin i n = — — . sin r This expresses the index of refraction of the one medium with respect to the other, and is also the ratio between the velocities of monochromatic light in the two media. If we choose some medium as the standard and determine the indices of refraction of other media in terms of this standard, the results will be comparable with one another. In practice the air is chosen as the most convenient standard, since light is passed through the air and then through the medium whose refractive power is to be determined. Several methods have been devised for determining the refrac- tive power of liquids. In one 1 a hollow prism is filled with the liquid, and the amount by which the ray of light is bent out of its course in passing through the liquid is determined by means of the spectrometer. A more convenient method, especially for use with liquids, is based upon a somewhat different principle. When a ray of light passes from a more refracting to a less refracting medium, there is a limit to the angle of incidence at which refraction will take place. Beyond this angle the ray will not enter the less refracting medium at all, but will be totally reflected. The value of this angle depends upon the relative refractive powers of the two media. This prin- ciple has been made use of by Pulfrich 2 for determining the relative refractive powers of substances. The Pulfrich refractometer consists essentially of a rectangular prism of strongly refracting glass, on whose horizontal surface there is a small glass cylinder to receive 1 Pogg. Ann. 98, 91 (1856). 2 Ztschr. f. Instrumentenkunde, 8, 47 ; IS, 389. Ztschr. phys. Chem. 18, 294 (1895). 116 THE ELEMENTS OF PHYSICAL CHEMISTRY the liquid to be studied. The monochromatic light enters the liquid nearly parallel to the horizontal surface of the prism. Only those rays can enter the prism from the liquid whose angle of emergence is less than the angle of total reflection., The apparatus is provided with a telescope and graduated circle. The telescope moves in a vertical plane, until it is just on the border between light and dark, and in this way the angle of emergence is determined. The size of this angle depends upon the relative indices of refraction of the liquid and the prism. If we represent this angle by e, the index of refraction of the liquid by n, and that of the prism by N, we have, — = V$ T = sin^ e. This apparatus has a number of advantages over all other forms for determining indices of refraction. It is very simple to use, and gives accurate results ; it requires but little time to measure the refractive power of any liquid; and a small quantity of the substance suffices, since it is only necessary to cover that portion of the surface of the prism enclosed within the cup. Eeference 1 only can be made to other applications of the Pulfrich refractometer. The refractive power of liquids is affected by temperature and wave-length of light, so that these must be kept constant to obtain comparable results. Refractivity and Density. — A number of formulas have been proposed connecting the index of refraction of a substance with its density. Biot and Arago in 1806 proposed for gases the formula = const., based on the emission hypothesis of light. The d theoretical foundations for this formula failed to exist after the emission hypothesis was overthrown, and it was also shown by direct experiment to be a very rough approximation, holding only in a limited number of cases. Gladstone and Dale 2 found an empirical expression which was very much more nearly in accord with experimental results. Their equation is, — tzil = C onst. d Landolt 3 tested this formula at different temperatures and found that it held very closely for many substances. He also applied this i Le Blanc: Ztschr. phys. Chem. 10, 433 (1892). 2 Phil. Trans. (Lond.), 1858. 8 Lieb. Ann. Suppl. 4, 1 (1865). LIQUIDS 117 equation 7.7 , C 5 Hi 2 0. 43.89/ M(n-1) Ethyl formate, C S H 9 2 29.80 < Ethyl acetate, C4H8O2 36.16-. Ethyl hutyrate, C 6 Hi 2 2 51.32 < Ethyl valerate, C7H14O2 59.20- >6.36 >2 x 7.58 >7.88 Landolt concluded 2 from a large number of such data that the molecular refraction increases a nearly constant amount for the com- mon difference in composition of CH 2 . This increase is about 7.60. In a similar manner, it was shown that the molecular refraction of two compounds which differ in composition by one carbon atom, is about 5. If they differ by two hydrogen atoms, the difference between their molecular refractions is 2.6. If they differ by an oxygen atom, the difference between their molecular refractions is about 3 units, and so on. The refraction equivalents of a number of the elements were thus worked out. Landolt showed that the refraction equivalents of carbon, hydro- gen, and oxygen, in their compounds, were almost exactly the same as the refraction equivalents in the free state. From the refraction equivalents of these elements he calculated the index of refraction of a number of compounds composed of carbon, hydrogen, and oxygen, and compared the results obtained with those found directly by ex- periment. A few of his results are given. 1 Fogg. Ann. 122, 545 (1864) ; and 123, 595 (1864). 2 Wied. Ann. 123, 611 (1864). LIQUIDS 119 Take the case of ethyl alcohol C 2 H 6 0. The refraction equivalent of carbon is 5, that of hydrogen 1.3, and that of oxygen 3. The molecular refraction of ethyl alcohol would be calculated thus : — 2x5 + 6x1.3 + 1x3 = 20.8. The index of refraction of a compound, n, is calculated from the molecular refraction B, and the density D, as follows ; P being the molecular weight : — p In an analogous manner Landolt calculated the indices of refrac- tion of other substances. n Calculated n Found Methyl alcohol, CH 4 1.328 1.328 Ethyl alcohol, C 2 H 6 . 1.362 1.361 Propyl alcohol, CsHgO . 1.381 1.379 Formic acid, CH 2 2 1.361 1.369 Acetic acid, C 2 H 4 2 1.371 1.370 Propionic acid, CsH 6 02 . 1.388 1.385 Methyl acetate, C 3 H60 2 1.352 1.359 Ethyl acetate, C4H 8 2 . 1.373 1.371 Methyl butyrate, C5H10O2 1.387- 1.387 Methyl valerate, C 6 Hi 2 O a 1.392 1.393 Aldehyde, C 2 H 4 . 1.326 1.330 Acetone, CsH 6 . 1.353 1.357 The close agreement between the index of refraction of a large number of compounds, calculated as described above, and as found experimentally, led Landolt to the conclusion that the molecular re- fraction of a compound is the sum of the refraction equivalents of the elements which enter into the compound. Landolt 1 also compared the molecular refractions of a number of metameric substances. Propionic acid Methyl acetate Ethyl formate Butyric acid Ethyl acetate Valeric acid Methyl butyrate C3H6O2 C 4 H 8 2 CsHio0 2 Molecular Effraction r 28.57 . ] 29.36 1. 29.18 ' 36.22 8.17 ' 44.05 43.97 ■{! 1 Pogg. Ann. 123, 602 (1864). 120 THE ELEMENTS OF PHYSICAL CHEMISTRY The molecular refractions of metameric substances do not differ very considerably from one another. There are appreciable differ- ences in some cases, but even these are not very great. The effect of constitution on molecular refraction, while recog- nized by Landolt, was not carefully investigated by him. Effect of Constitution on Refr activity. — The first systematic study of the effect of constitution on refractivity was made by Briihl. 1 Gladstone had found that the molecular refraction of a considerable number of certain classes of substances, as calculated from their composition, differed considerably from the value found experimentally. He observed that these compounds belonged to the benzene series, and then studied a large number of benzene deriva- tives. These showed, in general, a much higher refractivity than corresponded to their composition. These abnormally high results were evidently due to the presence of the benzene ring. Briihl began the study of the effect of constitution on refractivity in 1878, and has continued his work on such problems up to the present. He found that carbon atoms united by "double union" had a greater influence on refractivity than singly united carbon. This is shown by the following results taken from the paper of Briihl. The saturated and corresponding unsaturated compound are given together. Molecular Refrac- tion Observed Molecular Refrao- tion Calculated DlFF. f Allyl alcohol, C 8 H 6 . 1 Propyl alcohol, C 3 H 8 28.00 27.09 27.80 25.22 0.2 1.87 f Propyl aldehyde, C 8 H 6 . lAcroleiine, CsH 4 25.42 25.31 25.22 22.64 0.2 2.67 f Isobutyric acid, C 4 H 8 02 . 1 Methylacrylic acid^HeC^ 35.48 35.07 35.56 32.98 0.08 2.09 There is a difference between the calculated and observed molecu- lar refraction of about 2 for the compounds containing one doubly united carbon atom ; the refractivity being calculated from the com- position. Briihl also studied compounds containing two and three doubly united carbon atoms. 2 1 Lieb. Ann. 200, 139 (1880). 2 Ibid. 200, 139 (1880). LIQUIDS 121 Compounds with Two Doubly United Carbon Atoms Molecular Refraction Observed Molecular Refraction Calculated DlFF. Valerylene, C5H8 .... Diallyl, C 6 H 10 38.7 46.0 34.6 42.1 4.1 3.9 Each double union corresponds in these substances to about 2 units. The following compounds were supposed to contain three double unions : — Molecular Refraction Observed Molecular Refraction Calculated Diff. Monochlorbenzene, CoHsCl Monobrombenzene, CeH 5 Br 42.2 50.7 55.8 49.8 36.9 45.1 50.4 43.5 5.3 5.6 5.4 6.3 Here the three double unions correspond to about 6 units in the molecular refraction. It thus seems that the presence of a double union between carbon atoms in a compound has a constant influence on its refractive power, and if there is more than one pair of doubly united carbon atoms, each double union has the same influence as if it alone were present. The effect on refractivity of carbon atoms united by triple union, as in acetylene, was also studied. A pair of carbon atoms united by triple union raises the refractivity by 1.8 to 1.9 units. Carbon united by triple union has thus a slightly smaller influence than when united by double union. Bruhl points out at the close of this important paper that refrac- tivity can be used to throw light on the constitution of compounds of carbon. If the question is to determine whether a given com- pound contains a doubly linked carbon atom, it is only necessary to determine its refractive power. If the refractivity determined ex- perimentally agrees with that calculated from the composition of the molecule, on the assumption that all the carbon atoms are united by single union, then we can conclude that there are no doubly linked carbon atoms in the molecule. If the refractivity found is about two units higher than that calculated on the above assumption, then there is one double union in the molecule ; if the refractivity found 122 THE ELEMENTS OF PHYSICAL CHEMISTRY is about four units higher than that calculated, then there are two double unions in the molecule ; and so on. Constitution of Benzene. — This method was applied by Bruhl to benzene. We have seen from results already given that the molecu- lar refraction of benzene and its derivatives, as found experimentally, is nearly six units higher than the molecular refraction calculated on the assumption that the six carbon atoms are united by single unions. Since one double union increases the molecular refraction by two units, we must conclude that there are three double unions in the benzene molecule. We are thus led by the method of refractivity to the formula of benzene proposed by Kekule : — CH CH CH This represents the molecule of benzene as containing three singly and three doubly united carbon atoms, and on the whole is probably the most generally accepted formula for benzene which we have up to the present. It should, however, be stated here that another physical chemical method has led to exactly the opposite conclusion ; viz. that in benzene we have all the carbon atoms united by single bonds. It is impossible to decide at present between these two con- clusions, but the fact that such different results are obtained by dif- ferent methods should make us cautious in accepting as final the results obtained by any one method, however reliable it apparently may be. Gladstone 1 again took up the study of refraction after Bruhl 2 had published his earlier work, and sought to obtain further evidence in reference to the refraction-equivalents of carbon, hydro- gen, oxygen, and nitrogen in organic compounds. 8 A large number of organic compounds were investigated, and the refraction-equivalents of a number of the elements determined. The refraction-equivalent of the CH 2 group was found to be 7.63. The refraction-equivalent of hydrogen is very close to 1.3. Therefore, the refraction-equivalent of carbon must be very nearly 5. In the aromatic hydrocarbons the refraction-equivalent of carbon is about 6. A still larger value was found for carbon among some of the higher members of homolo- gous series of hydrocarbons. Gladstone also worked out the refrac- i Journ. Chem. Soc. 45, 241 (1884). 2 Lieb. Ann. 200, 139 (1880); 203, 1, 255, 363 (1880); Mem. Akad. Ber. 11, 84. 8 Proc. Boy. Soc. 1881, 327. LIQUIDS 123 tion-equivalents of a number of other elements. Chlorine was found to be 9.9, bromine 15.3, and iodine 24.5. Oxygen had been shown by Briihl to have two values, — a value of 3.4 when in the carbonyl condition, and of 2.8 when oxygen is united to two other atoms. Gladstone found the value 2.9. Nitrogen was found to have two values, 4.1 and 5.1 in different compounds. The lower value was found in the nitrates, and the higher in the organic bases and amides. The higher value, however, was found in the majority of cases. This work of Gladstone shows conclusively the effect of constitu- tion on refractivity, and thus confirms the conclusions o* Briihl. In Gladstone's own words : " These optical properties seem capable of deciding with certainty whether an organic body is a saturated compound or not. They indicate also the number of carbon atoms in that condition which is generally denoted as ' doubly linked,' and they give us a clew as to the mode in which oxygen and nitrogen are combined. " In later investigations Briihl 1 pointed out even more clearly and conclusively the effect of constitution on refractivity. He laid down as the fundamental law of refraction, that the refractivity of carbon and hydrogen varies according to the way in which they are com- bined. For any given combination it is approximately constant, de- pending only slightly upon the configuration of the atoms in the different compounds. The monovalent elements have, on the other hand, nearly constant atomic refractions. Briihl takes up again the question of the constitution of benzene as determined by its refractive power. The most accurate work gives a molecular refractivity of 25.93. The molecular refractivity calculated for the formula C 6 H 6 is 21.12. The difference is 4.81. This corresponds to 3 x 1.60, which means that there are three ethylene groups in the benzene molecule, corresponding to the for- mula of Kekule. Q He then studied again the effect of the acetylene union W on re- fractivity, and found that it corresponded to 2.02. If in the forma- tion of benzene from three molecules of acetylene, the three triple unions were transformed into nine single unions, then the molecular refraction of liquid benzene should be about 6.06 smaller than that of three molecules of acetylene gas. The difference as found was only 1.19. Therefore, when acetylene passes into benzene the triple unions are not converted into single unions. 1 Lieb. Ann. 235, 1 (1886); 836, 233 (1886). Ztschr. phys. Chem. 1, 307 (1887). 124 THE ELEMENTS OP PHYSICAL CHEMISTRY Briihl found, on the other hand, that when an acetylene union passes into an ethylene union there is a decrease in the refractivity of 0.40. When three acetylene unions pass into three ethylene unions, the decrease in refractivity would, therefore, be 0.40x3=1.20; and this is exactly the difference between the refractivity of three molecules of ethylene and the molecule of benzene formed from them. We are, therefore, led to the conclusion that when three molecules of acetylene form a molecule of benzene, the acetylene unions pass over into ethylene unions, thus : — 3 HC=CH = 3-HC = CH- which is the Kekule' formula for benzene. The above line of reasoning is so clear and so satisfactorily con- firmed by experimental evidence at every point, that there would seem to be no escape from the conclusion were it not for the conflict- ing result, which, as we shall see, is furnished by another physical chemical method. Molecular Refraction in General an Additive Property. ■ — As the final result, up to the present, which has been reached by the work of Gladstone and especially of Briihl, it can be stated that the molec- ular refraction of a compound is, in general, the sum of the atomic refractions of the atoms which enter into the molecule. This is only approximately true, since, as we have seen, constitution has a marked influence in some cases on refractivity. The atomic refrac- tion is approximately constant under all conditions only for the univalent elements. Oxygen in the carbonyl condition has a greater refractive power than in the hydroxyl condition. The presence of double or triple bonds in the molecule increases its refractivity, as we have seen in ethylene, acetylene, and benzene. That constitution has a marked influence on the refractivity of other elements, espe- cially nitrogen, has been shown by the work of Briihl 1 and others, but reference only can be made to these investigations. Atomic Refractions of Some of the More Common Elements. — The atomic refractions of some of the best known elements are given in the following table. Column I is taken from the work of Brilhl, 2 and is the refractivity referred to the red hydrogen line. Column II contains the results given by Conrady, 8 and are referred to the sodium line D. i Ztschr.phys. Chem. 16, 193, 226, 497, 612 (1895); 22, 373 (1897); 25, 577 (1898). Gazz. chim. ital. 24, I (1894) ; 25, II (1895). 2 Ztschr. phys. Chem. 7, 191 (1891). « Ibid. 3, 210 (1889). LIQUIDS 125 Column I Column II Bed Hydrogen Line Sodium Line D Carbon united by single bond 2.365 2.501 Hydrogen 1.103 1.051 Hydroxyl oxygen ... . . 1.506 1.521 Oxygen united as in ether .... 1.655 1.683 2.328 2.287 Nitrogen united to carbon with one bond 2.760 6.014 5.998 8.863 8.927 13.808 14.120 Ethylene union ( = ) . . 1.836 1.707 Acetylene union ( = ) . 2.220 The atomic refractions of the elements of the first and second groups of the Periodic System have been determined by Kananni- koff. 1 ROTATION OF THE PLANE OF POLARIZED LIGHT Optically Active Substances. — It was known nearly a hundred years ago that when a beam of polarized light is passed through certain liquids, the plane of polarization is rotated or turned. This phenomenon was manifested by many substances in the crystalline condition, also by a number of carbon compounds in the liquid state and in solution. We are concerned here only with those optically active substances which are liquid at ordinary temperatures, or which are in solution. Some of the substances rotate the plane of polariza- tion to the right and are called dextro-rotatory ; others rotate to the left, and are termed lsevo-rotatory. Dextro-rotation is indicated by the plus sign (+), laevo-rotation by the minus sign (— ). The number of substances whose rotatory power can be compared has increased enormously in the last few years. Biot and Seebeck pointed out in 1815 that certain organic substances have the power to rotate the plane of polarization. Oil of turpentine, and sugar and tartaric acid in aqueous solution, have this property, as was shown at this early date. From this time to 1879 the number of optically active substances increased to 300, while to-day we know over 700 substances 2 which have the power to rotate the plane of polarized light. The reason for the enormous activity in the preparation and i Journ. prakt. Chem. [2], 31, 321 (1885). 2 For further details consult the admirable book of Landolt : Das optische Drehungsvermogen organischer Substanzen, 2d edition, 1898. 126 THE ELEMENTS OF PHYSICAL CHEMISTRY study of these optically active substances will become apparent in the next few pages. Measurement of Rotation. — The instrument used in measuring the rotation of polarized light is known as the polarimeter. A beam of white light, or better, of monochromatic light, is passed through a Nicol's prism and polarized. This is then passed through a second Nicol's prism, which is turned until the light is completely extin- guished. The position of the second prism or analyzer is then care- fully noted. A glass tube containing the liquid to be investigated is then inserted in the path of the polarized ray of light, between the two Nicols. The plane of polarization is rotated and, conse- quently, the field of the second Nicol is no longer dark. It is now necessary to rotate the second Nicol, or analyzer, through a given angle to obtain again extinction of the light. The angle through which the analyzer must be rotated is read on the circular scale, and this is the angle through which the plane of polarization has been turned by the layer of the liquid used. The rotatory power of a liquid depends chiefly upon the chemical nature of the substance, as we shall see. It evidently depends also upon the thickness of the column of liquid through which the polar- ized ray passes. It depends further upon the wave-length of light and upon the temperature. In measuring the rotatory power of a liquid all of these factors must be taken into account.- The normal temperature chosen for such work is usually 20°. It is most con- venient to use as monochromatic light that of the sodium flame. Specific and Molecular Rotation. — Biot defined the specific rota- tion of an optically active liquid as that produced by a layer a decimetre in length, or if a solution it must contain one gram of the active substance in the volume of one cubic centimetre. But the density of the liquid must be taken into account. If we represent the specific gravity of the liquid by d, the length of the column of liquid expressed in decimetres by I, the rotation to the right or left expressed in degrees by os ; the specific rotation A for a definite temperature (20°) and a definite wave-length of light (D light) is expressed thus : — A=«. Id This specific rotation is a characteristic constant for the compound in question. In order to discover relations we must deal with comparable quantities of substances ; and preferably with quantities which bear LIQUIDS 127 the same relations to one another as the molecular weights of the substances in question. If we deal with gram-molecular weights of substances, the observed rotation is known as the molecular rotation. The molecular rotation M is obtained by multiplying the specific rotation of the substance by the molecular weight m. Since the molecular rotation thus obtained is very high, it has been found con- venient to divide this value by 100. The molecular rotation would then be calculated from the specific rotation as follows : — , r ffl a M= 100 Id If we are dealing with a solution containing p grams of substance in a volume of v cubic centimetres of solution, and I is the length of the column in decimetres, the specific rotation is expressed thus : — A = ^-, lp the molecular rotation thus : — M = jm_ o^, 100 lp Optical Activity and Chemical Constitution. — The earlier work in this field had to do with' the discovery of compounds which are optically active. The discovery of any relation between optical ac- tivity and chemical composition and constitution belongs to a later period. Pasteur 1 threw much light on this problem by his discov- ery that ordinary racemic acid can be broken down into two modifi- cations, the one turning the plane of polarization to the right, the other to the left. If a solution of sodium ammonium racemate is evaporated at low temperatures, rhombic, hemihedral crystals sepa- rate, having the composition Na.NH 4 .C 4 H 4 6 + 4 H 2 0. The crys- tals are, however, not all identical. The tetrahedral faces on some of the crystals are different from those on other crystals. Indeed, the crystals divided themselves sharply into two classes, the one containing dextro-hemihedral faces, the other laevo-hemihedral faces. We have here enantiamorphism, as in the case of quartz, the one crystal being the image of the other in a mirror. The two kinds of crystals were separated mechanically, and dis- solved in water. The solution containing the crystals with the right-handed faces rotated the plane of polarized light to the right ; those with the left-handed faces rotated the plane of polarization to i Ann. Chim. Phys. [8], 24, 442 (1848) ; 28, 56 (1850) ; 31, 67 (1851). 128 THE ELEMENTS OF PHYSICAL CHEMISTRY the left. In Pasteur's own words : 1 " When I had discovered the hemihedrism of all the tartrates, I quickly studied with care the double paratartrate (racemate) of sodium and ammonium. But I saw that the little tetrahedral faces, corresponding to those of the isomorphous tartrates, were placed relative to the principal faces of the crystal, sometimes on the right, at other times on the left, on the different crystals which I have obtained. If these faces were respectively prolonged, they would give the two symmetrical tetra- hedra of which we have spoken. I carefully separated the right- handed from the left-handed hemihedral crystals. I observed separately their solutions in the polarizing apparatus of Biot, and saw with surprise and delight that the right-handed hemihedral crystals rotated the plane of polarization to the right, and that the left-handed crystals rotated to the left. . . . The rotatory power thus shows the kind of asymmetry of the crystals. The two kinds of crystals are isomorphous, and isomorphous with the correspond- ing tartrate, but the isomorphism presents itself here with a pecul- iarity thus far not exemplified ; this is the isomorphism of two asymmetric crystals, the one being the image of the other in a mirror." In a later investigation, Pasteur 2 decomposed the two salts ob- tained from racemic acid, and secured the two corresponding acids, which he termed dextro-racemic and lsevo-racemic acids. The dex- tro-racemic acid was shown to be identical with ordinary dextro-tar- taric acid, rotating the plane of polarization to the right. The laevo-racemic acid rotated the plane of polarization just as much to the left, as the dextro to the right. From racemic acid Pasteur was thus able to obtain two acids, the one rotating the plane of polariza- tion to the right, the other to the left ; the racemic acid itself being optically neutral. He was, however, not content to stop here. If racemic acid had been broken down into two optically active constit- uents, then, when these constituents were brought together in the proper proportion, racemic acid should be reformed. Pasteur mixed concentrated solutions of dextro-racemic and lsevo-racemic acids. Heat was evolved, and crystals of racemic acid separated in abund- ance. Instead of dextro-racemic, ordinary dextro-tartaric, acid could be used, since the two are identical. In this way an optically inactive substance was, for the first time, broken down into two optically active substances, which ro- tated the plane of polarized light to the same extent, but in the oppo- i Ann. Chim. Phys. [2], 24, 456. » Ibid. [3], 28, 56 (1850). LIQUIDS 129 site direction. Further, the optically inactive substance was formed again by mixing solutions of the two optically active substances. From these results Pasteur reasoned as follows : l "Are the atoms of the dextro acid grouped in the form of a right-handed spiral, or do they stand at the corners of an irregular tetrahedron, or do they exist in some other asymmetric arrangement ? We are not able to answer these questions. But there is no doubt on this point, that an asymmetric grouping of the atoms, corresponding to an object and its image in a mirror, must be present. It is just as certain that the atoms of the lsevo acid have exactly the opposite arrange- ment. We know, finally, that racemic acid is formed by the union of these two oppositely asymmetric atomic groupings." The most important advance of a general character, which was introduced by this work of Pasteur, was the clear recognition of molecular asymmetry in the structure of chemical molecules. He was not able to point out the nature of this asymmetry, since the facts known at that time in reference to the constitution of optically active substances were far too meagre to lead to any wide-reaching generalization. Theory of Van't Hoff and Le Bel. — In the period following that in which the work of Pasteur was done, much light was thrown on the constitution of chemical compounds, and especially upon the constitution of organic compounds. With this newly acquired knowl- edge Van't Hoff in Holland and Le Bel in France were able to con- nect optical activity with chemical constitution. Van't Hoff's paper in Dutch bears the date Sept. 5, 1874. Le Bel's paper 2 in French appeared in November, 1874. Since Le Bel did not go as far as Van't Hoff in advancing a definite theory, his contribution to this important subject will be taken up first. 3 Le Bel fully recognized, from the work of Pasteur, the importance of asymmetry in conditioning rotatory power. " If the asymmetry exists only in the crystalline molecule, only the crystal will be active ; if, on the contrary, it belongs to the chemical molecule, the solution of the substance will show rotatory power." Since the latter is the case, we must regard the chemical molecule as asymmetric. This was the starting-point for Le Bel. In compounds containing carbon the cause of the asymmetry is to be ascribed to the presence of a carbon atom combined with four different atoms or groups. Le Bel 1 Becherches sur la dissymetrie moleculaire, p. 25. 2 Bull. Soc. Chim. [2], 22, 337 (1874). 8 " Sur les relations qui existent entre les formules atomiques des corps orga- niques et le pouvoir rotatoire de leurs dissolutions." Ibid. K 130 THE ELEMENTS OF PHYSICAL CHEMISTRY illustrates this principle by means of optically active substances known at that time, and shows by a number of examples that opti- cally active compounds contain an asymmetric carbon atom, i.e. a carbon atom in combination with four different atoms or groups. One of the simplest examples is lactic acid, which contains an asym- metric carbon atom in combination with hydrogen, hydroxyl, methyl, and carboxyl, thus : — H I CH 3 — C — COOH I OH Le Bel pointed out at the very close of his important paper, that we never obtain by direct synthesis the dextro or the leevo acid, but always the inactive or racemic modification, which is a combination of equal parts of the two active forms. Van't Hoff 1 also pointed out that in every optically active sub- stance there is at least one carbon atom in combination with four different atoms or groups — one asymmetric carbon atom. This holds good up to the present, with the possible exception of one compound, which, according to Baeyer, is optically active and does not contain an asymmetric carbon atom. The compound in question is so complex that its constitution cannot be regarded as finally established, and it may yet be shown not to be an exception to the above generalization. Van't Hoff, however, went much farther than simply to recognize asymmetry as the cause of optical activity. He attempted to point out the geometrical configuration which is probably fundamental to carbon compounds. Take the simplest saturated compound of car- bon and hydrogen, CH 4 . This substance had been shown by the work of Henry to be symmetrical ; i.e. every hydrogen atom bears ex- actly the same relation to the molecule. By what geometrical config- uration in three dimensions could this fact be represented ? Plainly only by one, — the regular tetrahedron. The carbon atom is situated at the centre of such a tetrahedron, and the four hydrogen atoms at the four solid angles. Such an arrangement is symmetrical, and accords with all of the facts known in connection with the compound CH 4 . In this way arose the theory of "the tetrahedral carbon atom." In every optically active substance, as we have seen, there is a carbon atom in combination with four different atoms or groups. 1 La Chimie dans VEspace. Rotterdam, 1875. LIQUIDS 131 The carbon atom is situated at the centre of the tetrahedron, and the four atoms or groups in combination with it are at the four solid angles of the tetrahedron. This arrangement is, of course, asym- metric, and thus we have the theory of " the asymmetric tetrahedral carbon atom." These simple suggestions lie at the foundation of all stereochem- istry, which is one of the most interesting and important phases of organic chemistry during the last quarter of a century. We can see at once, by means of the tetrahedron, why it is necessary that all the four atoms or groups in combination with the central carbon atom should be different. If any two atoms or groups are the same, it is impossible to construct two tetrahedra which cannot be super- imposed. This can readily be seen by means of models. If, on the other hand, all four atoms or groups are different, then two tetrahedra containing these atoms or groups arranged around a central carbon atom, will always bear the relation to one another of an object and its image in a mirror. The two tetrahedra would represent enanti- omorphous forms, and if one would rotate the plane of polarization to the right, the other would rotate it to the left. The theory thus explains why it is necessary to have all four of the atoms or groups around the central carbon atom different, in order to have optical activity. The theory also explains the very important fact pointed out by Le Bel, that by synthesis we never obtain the dextro or the laevo form alone, but always a mixture of both forms. Since optical activ- ity depends only on the arrangement of the constituents in the mole- cule, from the law of probability we would have just as many molecules formed having the one configuration as the other. For every dextro-rotatory substance there would thus be an equal quan- tity of the corresponding laevo compound formed. Here, again, the theory furnishes a satisfactory explanation of facts which, without its aid, are entirely inexplicable. The presence of an asymmetric carbon atom is necessary, as we have seen, for optical activity. The converse does not hold true. We may have asymmetric carbon atoms present, and yet the com- pound be optically inactive. This fact is also satisfactorily explained by our theory. The compound may have more than one asymmetric carbon atom, as in inactive tartaric acid, 1 and the asymmetric carbon atoms may equalize each other's influence. 1 Inactive tartaric acid is a fourth modification of tartaric acid, and is to be distinguished from dextro-tartaric acid on the one hand, and from laevo on the other, and from racemic acid, a mixture of these two. 132 THE ELEMENTS OF PHYSICAL CHEMISTRY COOH.H.OH.C- C.OH.H.COOH. This compound is optically inactive and cannot be broken down into optically active substances. The influence of the one carbon atom on polarized light is exactly equal and opposite to the influence exerted by the other, hence inactivity. Again, the compound may be optically inactive because it is composed of an equimolecular mixture or a dextro and a lsevo substance. This, as we have seen, is the case with racemic acid; it is a mixture of equal parts of dextro and of lsevo tartaric acid. Indeed, we never obtain one active sub- stance directly by synthesis. The two optically opposite varieties are always formed together, and the mixture of these two, or the racemic modification, is the result. We have already seen in one case how it is possible to obtain optically active varieties from a racemic mixture ; we will now examine more closely the methods available for separat- ing racemic modifications into their optically active constituents. Separation of Optically Active Isomeres from Racemic Modifica- tions. — The synthesis of racemic modifications, or mixtures of equal quantities of dextro and lsevo forms, is comparatively simple in many cases, and a large number of such syntheses have been effected. It then remains to separate the optically active isomers from this mixture. Several methods have been used : — I. We have seen how Pasteur made use of one method, viz. that based on the different crystalline forms of salts of the two active substances. He was able to separate the crystals mechanically, and from racemic acid to obtain dextro and lsevo tartaric acid. II. A second method consists in adding to the mixture of the isomeric components an optically active substance which will com- bine with them. The two compounds formed may differ sufficiently in properties to enable them to be separated. They may differ in solubility, crystal form, vapor tension, melting-point, etc. By utiliz- ing some such differences a number of racemic forms have been separated into their constituents. The active alkaloids have proved very useful in this connection. Pasteur succeeded in separating racemic acid into dextro and lsevo tartaric acids, by means of certain active alkaloids. The separation was effected through the difference in crystal form of the two compounds with the alkaloid. The free tartaric acids were easily obtained from the compounds with the alkaloids. III. A third method of separating the constituents from a racemic modification consists in treating the mixture with certain micro- organic forms. These will often destroy one of the active modifica- LIQUIDS 133 tions in the mixture and leave the other. Thus, penicillium, allowed to act on a dilute solution of ammonium racemate, will destroy the dextro-rotatory compound and leave the lsevo-rotatory. In this way, of course, only one of the active modifications can be obtained, the other having been destroyed by the organism. By means of these methods of separating racemic mixtures into optically active constituents, and of chemical synthesis, we can pre- pare optically active substances in the laboratory, and a large number of such compounds have already been prepared. The claim of Pasteur that optically active substances can be made only through the agency of the life process, does not seem to be borne out by the facts. In his later claim, 1 in reply to a criticism of his view by Schutzenberger, he says : " To transform an inactive substance into another inactive substance which can be resolved simultaneously into a dextro substance and its corresponding laevo compound, is not at all comparable with the possibility of transforming an inactive substance into a simple active substance." Here again the view of Pasteur does not find general support. That active substances can be made in the laboratory, without the intervention of life, is just as certain as that organic compounds can be synthesized from dead matter without the intervention of the life process. The theory of Van't Hoff and Le Bel has proved most fruitful in throwing light on many cases of isomerism, which, without its aid, are entirely inexplicable. It has also suggested many new lines of work, and has probably contributed more to the advancement of organic chemistry in recent times, than any other line of thought. We need only refer to the work of such men as Wislicenus, 2 Hantzsch and Werner, V. Meyer and Auwers, and Emil Fischer, to show what a tre- mendous influence this theory of the tetrahedral carbon atom has had. The Hypothesis of Guye. — The theory of the asymmetric carbon atom as the cause of optical activity has been tested quantitatively by Guye. 3 He attempted to discover relations between the nature and magnitude of the rotation, and the nature of the atoms or groups which are combined with the carbon atom and occupy the corners of the tetrahedron. If we assume that the four valences of carbon are directed' toward the four solid angles of a regular tetrahedron, the six planes of sym- metry of the compound CB, 4 represent what Guye termed the planes of symmetry of carbon. When the carbon is symmetrical, the centre 1 Compt. rend. 81, 128 (1875). 2 Ueber die Baurnliche Anordnung der Atome in organischen Molekulen. 8 Compt. rend. 110, 714 (1890). 134 THE ELEMENTS OF PHYSICAL CHEMISTRY of gravity of the molecule •will lie in at least one of the six planes of symmetry. When the carbon is asymmetrical, the centre of gravity will not lie in any of these planes. If we represent the distances from the centre of gravity of the molecule to each of the planes of symmetry by d\, d 2 , d s , d^ d s , d e , respectively, the product of these six values is known as the product of asymmetry. This product is zero when the carbon is symmetrical, but has different values as the asymmetry differs. If these differences are regarded as positive or negative, depending on the side of each plane on which they occur, the product of asymmetry will be positive or negative, as the number of negative factors is even or odd. The hypothesis advanced by Guye is, in his own words : " The product of asymmetry can then serve as a measure of the asymmetry of the carbon, and it is but natural to suppose that the rotatory power undergoes the same variation as this product." Guye then deduces certain consequences of this hypothesis which can be tested experimentally : — I. Whenever an element or group is substituted by another, and the centre of gravity of the molecule remains on the same sides of the planes of symmetry of the carbon, the rotatory power should pre- serve the same sign. II. If by the substitution the centre of gravity of the molecule is removed farther from the planes of symmetry, the rotatory power should be increased. If, on the contrary, the centre of gravity ap- proaches more nearly the planes of symmetry, the rotatory power should decrease. III. If by the substitution the centre of gravity is replaced from one side of one of the planes of symmetry to the other, the rotatory power should undergo a change in sign. The remainder of Guye's first paper is devoted to the discussion of experiments which verified these three principles. By varying the masses of the atoms or groups in combination with carbon, he could vary the position of the centre of gravity of the molecule. By increasing the mass of the group which replaces the hydrogen of the carboxyl in some organic acid, the centre of gravity could be re- moved farther from the principal planes of symmetry. The rotatory power should be increased by this means. The following results were obtained with tartaric acid : — Rotation Methyltartrate +2.14 Ethyl tartrate + 7.66 Propyl tartrate + 12.44 Isobutyl tartrate + 19.87 LIQUIDS 135 If in dextro-tartaric acid each of the two hydroxyl hydrogen atoms is replaced by benzoyl, we have a group of mass 17 substituted by a group of mass 121. The centre of gravity will pass from one side to the other of a plane of symmetry. Consequently, dibenzoyl- tartaric acid should be laevo-rotatory. Its rotation is — 117.68. If we now replace the hydrogen of dibenzoyl tartaric acid by the groups methyl, ethyl, propyl, butyl, the centre of gravity of the mole- cule will lie on the same side of the plane of symmetry as in the acid itself. But it will approach the plane of symmetry as the substitut- ing group becomes heavier and heavier, and, consequently, the amount of the lsevo rotation should become less and less as the group which replaces the hydrogen becomes of greater mass. The facts accord with the hypothesis. Rotation Methyldibenzoyl tartrate — 88.78 Ethyldibenzoyl tartrate — 60.02 Isobutyldibenzoyl tartrate .... — 41.95 Since this hypothesis was proposed, Guye has carried out many and elaborate investigations 1 to test its validity. The result of all this work is to show that the hypothesis accords with the facts in many directions. But it is only a partial expression of the truth. It alone is not sufficient to account for optical activity. In addition to the effect of mass on optical activity, we must take into account the relative position of the four groups, their mutual action on one another, their configuration, and the chemical nature of the atoms themselves which are combined with the carbon atom. The phe- nomenon of optical activity is, then, far more complicated than would appear from the hypothesis of Guye alone. This hypothesis is un- doubtedly a step in the right direction toward the solution of the problem of optical activity in terms of molecular composition and molecular structure, but it is only a step, and by no means the last one. MAGNETIC ROTATION OF THE PLANE OF POLARIZATION Observation of Faraday. — The observation was made by Faraday 2 that many substances acquire the power of rotating the plane of polarization when placed in a magnetic field. He first worked with glass, but soon discovered that other substances possess the same i Compt. rend. Ill, 745 ; 114, 473 ; 116, 1133, 1378, 1451, 1454 ; 119, 906 ; 120, 157, 452, 632, 1274 (1890-1895). Ann. Chim. Phys. [6], 25, 145 (1892). Guye and Chavanne : Compt. rend. 116, 1454 ; 119, 906. 2 Phil. Trans. 136, 1 (1846). Pogg. Ann 68, 105 (1846). 136 THE ELEMENTS OF PHYSICAL CHEMISTRY power of becoming active under the influence of magnetic force. If the substance has a rotatory power of its own, as oil of turpentine, sugar, tartaric acid, etc., the effect of the magnetic force is to add to or subtract from their specific power, according as the natural and acquired rotatory powers have the same or different signs. Faraday found that substances having very different chemical, physical, and mechanical properties become optically active under the magnetic influence. His work included solids and liquids, acids, alkalies, and neutral substances. He worked with solutions in alcohol and in wa- ter, and of the latter class he studied some 150 examples. He found that the " exceeding diversity of substance caused no exception to the general result, for all the bodies showed the property." Investigation of De La Rive. — An investigation of the magnetic rotatory power of substances was published by De La Eive 1 in 1871. He determined the magnetic rotatory power of substances, in terms of water as unity, and found that the magnetic rotatory power does not have any relation to other physical properties. Rise in tem- perature diminished the rotatory power of liquids. The rotatory power of a mixture of two liquids is the mean of the rotatory powers of the constituents, when the two liquids do not act chemically. Work of Becquerel. — An elaborate investigation on magnetic rotatory power was carried out in 1877, by Becquerel. 2 He studied also the refractive power of substances, and discovered certain rela- tions between the two properties. For the substances of a given chemical family the magnetic rotation divided by the term n 2 (n 2 — 1), n being the index of refraction, is very nearly a constant. Becquerel studied the effect of the chemical nature of the substance on mag- netic rotatory power, and concluded that the chemical nature of substances affects directly their magnetic rotatory power, and the different elements combined in a compound exert their own inde- pendent influence. Investigations of Perkin. — The most elaborate investigations, by far, in the field of magnetic rotation, are those of Perkin. His work was begun 3 more than fifteen years ago, and has been con- tinued nearly up to the present. 4 Perkin has investigated especially the relations between chemical composition and constitution, and magnetic rotation. He took the molecular rotatory power of water as unity, and compared the rotatory power of other substances with i Ann. Chim. Phys. [4], 22, 5 (1871). 2 Ibid. [5], 12, 5 (1877). » Journ. pra/ct. Chem. [2], 31, 481 (1885) ; [2], 32, 523 (1885). * Journ. Chem. Soc. 49, 777 ; 51, 808 ; 53, 561, 695 ; 59, 981 ; 61, 287, 800 ; 63, 57 ; 65, 402, 815; 67, 255 ; 69, 1025 (1886-1896); 61, 177 (1902). LIQUIDS 137 it. Similarly, the specific rotatory power of a substance is its specific rotation referred to that of water under exactly the same conditions. A few of the results obtained by Perkin will show what rela- tions were discovered by him. Take first the influence of the CH S group, obtained by studying homologous series of compounds. Molecular Magnetic Rotation. Dipf. Formic acid Acetic acid Propionic acid . Butyric acid . Methyl bromide Ethyl bromide . Propyl bromide Methyl iodide . Ethyl iodide . Propyl iodide . 1.617 2.525 3.462 4.472 4.644 5.851 6.885 9.009 10.075 11.080 0.908 0.937 1.010 1.207 1.034 1.066 1.005 There is thus very nearly a constant difference in the molecular magnetic rotation produced by the constant difference in composition of CH 2 , where the compounds have similar constitution. This dif- ference is about 1.02. The effect of constitution on magnetic rota- tion can best be seen by studying isomeric substances. Molkg. Mag. rotation Moleo. Mag. Rotation ( Propyl alcohol . . . 1 Isopropyl alcohol . . / Propyl bromide . . 1 Isopropyl bromide . 3.768 4.019 6.885 7.003 ( Propyl chloride . . i Isopropyl chloride f Butyric acid .... «. Isobutyric acid . . . 5.056 5.159 4.472 4.479 These results show that constitution has a marked influence on magnetic rotation, and has a different influence in compounds of different composition. Perkin has attempted to throw light on a number of interesting questions by means of the magnetic rotation method, but for further details in this connection his original papers must be consulted. See Schonrock: Ztschr.phys. Chem. 11, 753 (1893); 16, 29 (1895). 138 THE ELEMENTS OF PHYSICAL CHEMISTRY Work of Rodger and Watson. — The section on magnetic rotation should not be closed without brief reference to the work of Rodger and Watson. 1 They used a stronger magnetic field and, conse- quently, had a larger rotation to measure. Their work consists chiefly in improving the apparatus to be used in studying magnetic rotation. A few results were obtained, and it is to be hoped that further work will be done with the stronger field. MAGNETIC PROPERTY Paramagnetic and Diamagnetic Bodies. — Faraday 2 found that substances in general divide themselves into two classes with re- spect to their behavior toward a magnet. Those which were attracted by the magnet, such as iron, cobalt, nickel, manganese, chromium, platinum, etc., were termed paramagnetic. Those which were repelled by the magnet, such as bismuth, tin, mercury, copper, arsenic, iridium, uranium, tungsten, etc., were called diamagnetic. The magnitude of the attractive and repellent forces was meas- ured by Pliicker. 3 He found that the magnitude of the attractive force was proportional to the number of magnetic molecules present. Work of Wiedemann. — The most accurate work which has been done on the magnetic properties of substances is that of G. Wiede- mann. 4 He measured the force by means of the torsion of a German silver wire. The specific magnetic attraction, /x, is expressed thus : — A where A is the attraction exerted, B, the mass of the substance, and G, the magnetism of the electromagnet. The molecular magnetism, M, is the specific magnetism, /n, multiplied by the molecular weight of the substance, m : — M = m/x. Wiedemann confirmed the conclusion of Pliicker, that the mag- netic attraction is proportional to the number of molecules of dis- solved salt. He also used different salts of the same metal, and found that the molecular magnetic attraction was the same for the different salts, if the magnetic metal was in the same state of oxida- tion in all of the salts. 1 Ztschr. phys. Chem. 19, 323 (1896). Phil. Trans. 186 (A), 621 (1895). 2 Phil. Trans. 1846, 1. Pogg. Ann. 69, 289 (1846). « Pogg. Ann. 74, 321 (1848). * Ibid. 126, 1 (1865) ; 135, 177 (1868). Wied. Ann. 32, 452 (1887). LIQUIDS 139 More Recent Work. — Henrichsen, working in part with Wleiigel, 1 and in part alone, 2 has carried out a number of measurements on the magnetic property of substances. He has somewhat modified the torsion method of Wiedemann, and has used a number of diamag- netic substances. According to him, molecular magnetic repulsion, at least, is an additive property; being approximately the sum of the atomic repulsions. Certain constitutive influences manifest them- selves ; the presence of doubly united carbon seemed to increase the diamagnetic property. Certain very simple relations between the atomic magnetic attrac- tions of nickel, cobalt, iron, and manganese, as shown by aqueous solutions of their compounds, have been pointed out by Jager and Stefan Meyer. 3 Their meaning is not at all apparent. Meyer 4 has published a number of papers quite recently on vari- ous phases of this subject. In his most recent communication he concludes that when contraction in volume takes place in compounds, the paramagnetism increases; when dilation occurs, diamagnetism increases. SPECIFIC GRAVITY AND VOLUME RELATIONS OF LIQUIDS Specific Gravity, Specific Volume, and Molecular Volume. — By the specific gravity of a substance is meant the mass contained in a given volume. We must choose some substance as the unit and com- pare other substances with it. Water is usually taken as the unit. 13y specific volume of a substance is understood the volume in cubic centimetres occupied by a gram of the substance. If we represent the specific gravity of a substance by s, the specific volume is equal to - ■ The molecular volume M is the specific volume multiplied by the molecular weight m of the substance : — s Methods of determining the Specific Gravity of Liquids. — A method for determining the specific gravity of a liquid consists in weighing a solid of known volume in the liquid by means of the Mohr balance, and determining the loss in the weight of the solid. This is exactly equal to the weight of liquid displaced by it. Know- ing the volume of the solid immersed in the liquid, we know the volume of the liquid displaced by the solid. A more convenient 1 Wied. Ann. 22, 121 (1884). 8 Ibid. 63, 83 (1897). 2 Ibid. 34, 180 (1888). 4 Ibid. 69, 236 (1899) ; 68, 325 (1899). 140 THE ELEMENTS OF PHYSICAL CHEMISTRY o 1 .method for determining the specific gravity of a liquid consists in weighing directly a known volume of the liquid. A number of forms of vessels have been devised for determining the specific gravity of liquids. That shown in Fig. 12 is the Ostwald modification of the Sprengel pycnometer. The liquid is drawn into the pycnometer through the capillary, c. The apparatus is then placed in a constant temperature bath and brought to the temperature desired. The liquid is brought to the mark at m by removing liquid from, or adding liquid to, c. The pycnometer is weighed empty; it is then filled with water and weighed, and finally filled with the liquid in question and reweighed. Let these weights be w l} w lt and w 3 . If the weight of the displaced air is A, and we represent the specific gravity of the liquid by S — S: ^ Fig. 12. w s — Wi + A w 2 — W} + A Work of Kopp. — Relations between the molecular volumes of certain liquids were early pointed out by Kopp. 1 He found that constant differences in composition corresponded to constant differ- ences in the molecular volumes. Thus, the molecular volume of an ethyl compound is 234 units greater than that of the corresponding methyl compound. The atomic volumes of a number of the elements were worked out by Kopp, and it was shown that molecular volumes are approximately the sum of the atomic volumes of the elements present in the molecule. Kopp's later investigations 2 confirmed, in the main, the results of his earlier work. Take homologous series of compounds : — Molecular Volume Difference Formic acid, CH 2 2 .... 41.8 63.5 85.4 106.6 130.3 85.4 107.6 125.8 149.1 21.7 21.9 21.2 23.7 22.2 18.2 23.3 1 Lieb. Ann. 41, 79 (1842). 2 Ibid. 96, 153, 303 (1855). LIQUIDS 141 A constant difference in composition corresponds to a constant dif- ference in molecular volume. The effect of constitution on molecular volume can be seen by studying isomeric substances. 1 Molecular Volume. 1 Methyl formate, C2H4O.J UO.U . 63.4 f Ethyl valerate, CjHuO.! 1 Amyl acetate, C7H14O2 .... . 173.5 . 173.4 r Propionic acid, C a H 8 C>2 .... . 85.4 ■j Ethyl formate, C s H 6 2 .... . 85.3 1 Methyl acetate, CsH 6 2 .... . 84.8 Isomeric substances have the same specific volumes. It should be observed that these determinations were made at the boiling-points of the liquids in question. Kopp 2 also found that two atoms of hydrogen and one atom of oxygen can replace one another without appreciably changing the molecular volume. Similarly, one atom of carbon and two atoms of hydrogen can replace each other without affecting the molecular volume. He calculated the atomic volume of carbon to be 11, of hydrogen 5.5, of carbonyl oxygen 12.2, and of hydroxyl oxygen 7.8. From these values Kopp calculated the molec- ular volumes of a large number of liquids, and showed that they agree very closely with the values found experimentally at the boiling-points of the substances. More Recent Work. — That constitution has an influence on molecular volume is made probable by the more recent work. Buff 3 thought that carbon had a larger atomic volume in the unsaturated than in the saturated condition. Thorpe found that isomeric sub- stances have approximately, but not exactly, the same molecular volumes at their boiling-points. The conclusion from the best work which has been done is that molecular volumes are, in general, additive, — the sum of the atomic volumes. The effect of constitution, however, manifests itself especially with carbon and oxygen and, consequently, the law of Kopp that constant differences in composition produce equal differ- ences in molecular volume is only an approximation to the truth. VISCOSITY OF LIQUIDS Methods of determining Viscosity. — The methods of determin- ing the inner friction of a liquid, or its viscosity, are based upon two principles. Either a solid body is moved in the liquid and the 1 Lieb. Ann. 96, 171 (1855). 2 Loe. cit. 172. = Lieb. Ann. Suppl. 4, 129 (1865). 142 THE ELEMENTS OF PHYSICAL CHEMISTRY resistance to the movement measured, or the liquid is moved over a solid, as through a capillary tube. The best methods are based upon the second principle. Definite volumes of liquids are allowed to flow through a capillary tube, and the time required is noted. The form of apparatus 1 consists of a bulb attached to a capillary tube, and a bulb or some other form of vessel at the other end of the capillary to receive the liquid. The volume of the first bulb is known, and the time required for this volume of the liquid to flow through the capillary is determined. Work of Thorpe and Rodger. — The most elaborate, and probably the most accurate work which has ever been done on the viscosity of liquids, is that of Thorpe and Rodger. 2 .These authors review the work which had already been done on viscosity, and then discuss their own. The aim of their investigation was to throw light on the relation between the viscosity of homogeneous liquids and their chemical nature. The method was to measure the time required by a liquid to flow through a capillary tube. The viscosity could be measured from zero up to the boiling-point of the liquid. The formula of Slotte was used for calculating viscosity : — 7/ = c (1 + bt ) u. 7] is the coefficient of viscosity in dynes per square centimetre ; c, b, and u are constants, varying with the nature of the liquid. The viscosities of some seventy liquids were measured at different tem- peratures. To discover quantitative relations between viscosity and chemical nature, some temperatures must be chosen at which the liquids are in comparable condition with respect to their viscosities. Comparisons were made at the boiling-points of the liquids, but it was found better to use temperatures at which the rate of change of the viscosity coefficient is the same for all liquids — temperatures of equal slope. Comparisons were, therefore, made at temperatures at which —2 is the same for the different liquids. In all homologous series, except the alcohols, acids, and dichlorides, the group CH 2 increases the viscosity coefficient. Its influence diminishes as the series ascends. The compound with the highest molecular weight has the highest coefficient, among corresponding compounds. An iso-com- pound has always a larger coefficient than a normal compound. 1 Ztschr.phys. Chem. 1, 285 (1887). 2 Proc. Boy. Hoc. 1894. Jour. Chem. Soe. 71, 360 (1897). Chem. News, 69, 123, 135 (1894). Ztschr. phys. Chem. 14, 361 (1894). Ibid. 19, 323 (1896). Beck: Ibid. 48, 641 (1904). LIQUIDS 143 Alcohols and acids give exceptional results. Constitution has a marked influence on the viscosity coefficient, as is shown by compar- ing saturated and unsaturated compounds. If we compare molecular viscosities at equal slope, we find that for most substances these can be calculated from the constants for the atoms in the molecule. Some of these constants are : — Viscosity Constants Hydrogen 44.5 Carbon 31.0 Hydroxyl oxygen 166.0 Carbonyl oxygen 198.0 Chlorine in monoohlorides 256.0 Bromine in monobromides 374.0 Iodine in monoiodides . 499.0 Double linkage 48.0 Ring grouping 244.0 The effect of constitution on viscosity is shown by the large value of the constant for ring-grouping, double linkage, etc., and for the different values of oxygen when in the hydroxyl and carbonyl con- dition. Water and the alcohols present marked exceptions to any relation thus far discovered between viscosity and chemical nature. SURFACE-TENSION OF LIQUIDS Surface-tension. Method of Measuring. — While gases tend to expand and increase their volume, the surface of a liquid tends to contract and occupy a smaller volume. This potential energy, present at the surface of liquids, produces a tension which is known as surface-tension. Any force which tends to increase the size of the liquid surface is opposed by the surface-tension of the liquid. There are a number of methods of measuring the surface-tension of liquids, but of these the most convenient and important from the physical chemical standpoint is the so-called capillary method. The height to which the liquid rises in a capillary tube is determined, and from this the surface-tension of the liquid is calculated as fol- lows : Let h be the height to which the liquid rises in a capillary tube of radius r, D the density of the liquid and d the density of the gas in which the experiment is carried out, and g the acceleration of gravity ; the surface-tension y is obtained from these values : — y = \ ghr (D — d) (dynes per cm.). Relations between Surface-tension and Composition. — Relations between surface-tension and composition were pointed out in 1860 144 THE ELEMENTS OF PHYSICAL CHEMISTRY by Mendeleeff, 1 but more extended investigations were published in 1864 by Wilhelmy. 2 He compared the capillarity coefficients of substances, which he termed a. This was obtained from the con- stant A 2 , by multiplying by S, the specific gravity of the liquid, and dividing by 2 : — A 2 S * = ^- Wilhelmy found that an increase in composition of CH 2 does not appreciably change the value of a : — « Methyl alcohol 2.42 Ethyl alcohol 2.32 Amyl alcohol 2.43 Addition of carbon increases the value of a : — a Alcohol, C 2 H 6 2.36 Acetone, C 8 H 6 2.45 Amylene, C 5 H l0 1.75 Xylene, C 8 H 10 2.75 Addition of oxygen increases the coefficient : — a. Acetone, C s H 6 2.45 Ethyl formate, C 8 H 6 2 2.63 Lactic acid, C 8 H 6 8 3.94 Isomeric compounds have equal coefficients only when they have similar constitution : — a / Ethyl formate, C 8 H e 2 2.63 I Methyl acetate, C 8 H 6 ? 2.58 / Ethyl butyrate, C 6 H 12 2 2.55 I Amyl formate, CeHi 2 02 2.61 An extensive investigation on the capillary constants of liquids at their boiling-points was published by Schiff 3 in 1884. He recog- nized that two liquids are really comparable only at their critical temperatures, but critical temperatures evidently could not be used to study capillarity, since this disappears at such temperatures. A study of the molecular volumes of liquids at their boiling- points has shown that this temperature represents an analogous condition, since a constant difference in composition corresponds 1 Oompt. rend. 50, 52 ; 61, 97. 2 Fogg. Ann. 121, 44 (1864). 8 Lieb. Ann. 223, 47 (1884) . An extensive bibliography is appended. LIQUIDS 145 very nearly to a constant difference in molecular volume. Says Schiff, 1 "This consideration has led me to choose the boiling-point as the temperature for comparison, and to compare the capillarity constants determined at this temperature." He first determined whether there is any relation between the molecular weights of substances and their capillary constants, by comparing the constants of substances having the same, or nearly the same, molecular weights and different constitution. Mol. Wt. Capillarity Constant Allyl alcohol, C 8 H 6 57.87 5.006 Acetone, C 3 H 6 57.87 5.189 It was found, in general, that for substances having nearly the same molecular weight, the constant was very nearly the same. Those compounds of the fatty series, having the higher boiling- point, have the larger constant. Among the aromatic compounds, that with the higher boiling- point has the smaller constant. With respect to their influence on capillarity, the elements bear to each other the following relations : — C = 2H; = 3H; Cl = 7 H. From these and similar data it was shown to be possible to calculate the capillarity constants of liquids from the chemical formulas. Schiff's later work embraced a large number of substances, and he also studied the effect of temperature on surface-tension. His later work confirmed, in the main, the conclusions from his earlier investigations, but some exceptions were discovered. A carbon atom is not always equivalent to two hydrogen atoms in its influence on surface-tension, but in some cases, as with the fatty acids, may be equivalent to three hydrogen atoms. A chlorine atom is generally equivalent to seven hydrogen atoms, but in some cases is equivalent to only six. A bromine atom is equivalent some- times to thirteen, and sometimes to eleven, hydrogen atoms ; iodine to nineteen hydrogen ; nitrogen to two and to three hydrogen ; and so on. From the above it will be seen that capillarity is considerably affected by constitution, under some conditions. Uolecular Weights of Pure Liquids determined by Means of their Surface-tension. — The determination of the molecular weight of a pure homogeneous liquid is to be sharply distinguished from the » Lieb. Ann. 223, 53 (1884). 146 THE ELEMENTS OF PHYSICAL CHEMISTRY determination of the molecular weight of one substance dissolved in another. As we shall see, we have excellent methods for solving the latter problem, but only one partially satisfactory method for the former. The work of the Hungarian physicist Eotvos 1 showed that the rate of change in surface-energy with the temperature is a con- stant. If y is the surface-tension, s the surface, and t the tempera- ture measured from the critical temperature as zero, we have — dt That the formula might be applied to different liquids, s is taken as the molecular surface. If we represent the molecular volume by Mv, and regard this as a cube, any face of the cube will be (Mv)* = s. The formula of Eotvos then becomes — y (Mv)% = ct, where t is the temperature of the experiment, calculated from the critical temperature downward. Ramsay and Shields 2 tested the above formula experimentally, using a number of liquids whose molecular volumes were known ; such as ether, methyl formate, ethyl acetate, carbon tetrachloride, benzene, chloroform, methyl alcohol, ethyl alcohol, and acetic acid. They must first determine the value of y for each of the liquids. The surface-tension y is calculated from the equation y = J rhg (p — u), where r is the radius of the capillary tube, h the height to which the liquid rises in the tube, g the acceleration of gravity, p the density of the liquid at the temperature of the experiment, and Vn D'vV The numerical value of the constant in the case of many liquids which had been shown not to be polymerized, was found to be close to 100. For polymerized liquids the constant was much larger, reaching a maximum value of 215 in the case of water. Solving the above equation for n, we have ■-(£)■. and since c = 100 for non-associated liquids, f T V100 Dj To calculate the number of atoms in the molecule of any given liquid, it is only necessary to determine experimentally the absolute temperature T at which the liquid boils, and its density D at zero degrees. The method is thus obviously very simple to carry out in the laboratory. 152 THE ELEMENTS OP PHYSICAL CHEMISTRY A few results are given below for non-polymerized or non-asso- ciated liquids : Compound n Known n Calculated Ethylene chloride 8 8 Thiophene 9 10 Furfural .... 11 12 Methyl acetate . 11 12 Ethyl acetate . 14 14 Anisol .... 16 18 Piperidine 17 18 Methyl benzoate 18 18 Triethylamine . 22 23 Carvacrol . 24 26 Decane .... 32 33 Dodecane 38 40 Tetradecane 44 46 More than one hundred non-associated liquids were brought within the scope of this work, and in no case was there a difference of more than two atoms between the number of atoms in the molecule as calculated and as given by the simplest chemical formula. A few results are given for associated liquids: Compound n Known n Calculated 6 19 7 14 8 14 9 19 10 16 11 16 12 20 14 19 16 21 Methyl alcohol Aldehyde . Acetic acid Ethyl alcohol Acetone . Pyridine . Propyl alcohol Aniline Butylamine The association as found by the surface-tension method agrees closely with that given by the method of Longinescu. The results with inorganic liquids were not as satisfactory as with organic. The large atomic weights of many of the' elements seem to be detrimental to the application of this method. It seems to hold where the atomic weights are not greater than 40. Under these conditions the results obtained by this method agree satisfactorily LIQUIDS 153 with those given by the surface-tension method. The association factor for water is nearly 5; i.e. the molecule was found to contain 14 atoms, while the simplest water molecule contains 3. The num- ber of atoms in the molecule of liquid hydrofluoric acid was found to be 9, while the number in the simplest chemical molecule is 2. Hydrogen sulphide was found to contain 5 atoms, while the simplest possible number is 3. Liquid ammonia contained 14 atoms in the molecule, while the simplest possible number is 4. Liquid hydrocyanic acid contains 18 atoms in the molecule, while the simplest molecule would contain 3. The association factor is six. This is the most highly associated of any known liquid, which, ' as we shall see, is in accord with its high dielectric constant and its high dissociating power. Although the fundamental equation which underlies Longinescu's method is, at present, empirical, yet the fact that this method gives results in accord with those obtained by the surface-tension method, which has a good physical foundation, entitles it to serious considera- tion. longinescu's Method as applied to Solids. — Longinescu has at- tempted to apply his method to the problem of the molecular weights of substances in the solid state. 1 In this case T is the absolute temperature of fusion of the solid, and D is its density. The values of the constant as found were 50 and 70. Taking its value as 70, we have / T ' \J0 2> For a large number of organic compounds the number of atoms in the molecule found by this method was the same in the solid and in the liquid state. For inorganic substances the results usually show a much larger number of atoms in the molecule in the solid state than when in the liquid condition. Thus, water in the solid state contains 29 atoms in the molecule, as compared with 14 in the liquid state. Hydrocyanic acid has 52 atoms in the solid molecule and only 18 in the liquid molecule. Ammonia has 40 atoms in the solid molecule and only 14 in the liquid. Cyanogen has 30 atoms in the solid molecule and only 8 in the liquid. Sulphuric acid, on the other hand, has 9 atoms in the solid and 10 in the liquid molecule. Potassium has 60 atoms in the solid and 132 in the liquid molecule, and sodium seems to have 56 atoms in the solid and 108 in the liquid molecule. i-Journ. de Chemiephys. 1, 296 and 391 (1903). 154 THE ELEMENTS OF PHYSICAL CHEMISTRY There is nothing with which to compare these results with solids, and they are therefore to be accepted with very great reservation. Dissociation of the Molecules of Liquids. — Longinescu has shown that if we represent by T the absolute temperature at which a liquid boils, and by M its molecular weight, T , 1000 -VM a . ■y/M holds for a large number of liquids such as the hydrocarbons, esters, etc. For polymerized liquids the value is greater than 64. In the above equation the first term is equal to 37 and the second to 27. For a large number of liquids the first term is less than 37 and the second greater than 27, showing that the two values of M obtained from the above equation of the second degree find their counterpart in the liquid. That is to say, in a liquid we may have both polymerized and dissociated molecules — the molecules that are dissociated being broken down into their eonstitutent atoms or groups. Thus, HI= H+ I. A number of lines of evidence for this view are given. This kind of dissociation is to be distinguished sharply from electrolytic dissociation, or the breaking of molecules down into ions, which does not take place in pure liquids, since they are non-conductors. DIELECTRIC CONSTANTS OF LIQUIDS The Dielectric Constants of Some of the More Common Solvents. — The dielectric constant, or specific inductive capacity of liquids, has recently acquired a very special interest from the physical chemical standpoint, due to a relation which is supposed to exist between this property and the power of liquids to break down molecules into ions. This relation will be taken up later, when- the dissociating power of different liquids is under consideration. The meaning of the term " dielectric constant of a medium " is best illustrated, perhaps, as follows : When two charges of electricity are placed at a certain distance apart and separated by a dielectric, the force with which they act upon one another is proportional to the product of the two quantities, and inversely proportional to the square of the distance between them. But it was shown by Faraday that the nature of the non-conducting medium between the two charges must be taken into account. A factor must be introduced for the nature of this medium. This factor, which is a constant for any given medium, was termed by him the specific inductive LIQUIDS 155 capacity of the medium, and has since come to be known as the dielectric constant of the medium. A number of methods have been devised for determining dielec- tric constants. We should mention especially those of Thwing, 1 Nernst, 2 and Drude. 3 The method of Drude is, on the whole, the best. It consists in measuring the length of stationary electrical waves in the medium in question. These are a function of the dielectric constant of the medium, and a very simple function. The length of the wave is inversely proportional to the square root of the dielectric constant of the medium. The dielectric constants of some of the more common solvents at 18° are given in the following table : Dielectric Constant Hydrogen dioxide 92.8 ? Water 77.0 Formic acid 63.0 Nitrobenzene 36.0 Methyl alcohol 33.7 Ethyl alcohol 25.9 Propyl alcohol 22.0 Ammonia, liquid 22.0 Amyl alcohol 16.0 Ethylene chloride 11.0 Aniline 7.3 Chloroform 5.0 Ether 4.4 Carbon disulphide ... . 2.6 Benzene .2.3 It was thought for a long time that water has the highest dielec- tric constant of any known solvent. When solutions of salts in liquid ammonia were shown to have high conductivity, it was supposed that the dielectric constant of liquid ammonia would be very high. The work of Goodwin and Thompson 4 showed, however, that such was not the case, the constant for liquid ammonia being only about 22. The effort to find a solvent with a higher dielectric constant than water was continued, and has apparently been crowned with success. 1 Ztschr. phys. Chem. 14, 286 (1894). 2 Ibid. 14, 622 (1894). * Ibid. 23, 267 (1897). * Phys. Bev. 8, 38 (1899). Turner: Ztschr. phys. Chem. 35, 385 (1900). " Dielectric Constants of Gases and Vapors." See Badeker : Ibid. 36, 305 (1901). See Palmer: Phys. Bev. 14, 38 (1902). Schlundt : Journ. Phys. Chem. 8, 122 (1904). Von Wilier : Phil. Mag. (6) 7, 655 (1904). 156 THE ELEMENTS OF PHYSICAL CHEMISTRY Calvert * has shown, from a study of the dielectric constant of an aqueous solution of hydrogen dioxide, that it is probably higher than that of water, having the value given in the table. There is thus one liquid known which probably surpasses water with respect to this property. This, however, is not proved as yet, and even if it is true is not very surprising, since hydrogen dioxide is very closely allied to water in composition, being in a certain sense water intensified. A survey of this chapter will show that there is a close relation between many of the physical properties of liquids and their com- position and constitution. Many of these relations are thus far purely empirical, their meaning and significance being entirely un- known. Yet, in most cases, such relations have been clearly estab- lished beyond question, by very elaborate and careful investigations. While at present we fail to see the real significance of most of these relations, we cannot but recognize their great importance. The in- troduction of an atom or a group of atoms, producing a constant effect on so many physical properties ; or the constant influence of a double or triple bond, are facts which must lie very close to the ulti- mate composition and constitution of matter. We feel, instinctively, that there is some generalization of the very deepest significance foreshadowed, as it were, by facts such as those considered in this chapter; and instead of these empirical generalizations being neg- lected, they should stimulate to renewed effort to discover what they really mean. 1 Ann. der Fhys. 1, 473 (1900). "Dielectric Constants." See Nernst: Wied. Ann. 57, 209 (1896). A begg : Ibid. 60, 54 (1897). Dewar and Flem- ing: Proe. Boy. Soc. 61, 1, 299, 316 (1897). Drude : Wied. Ann. 60, 527 (1897). Stark: Ibid. 60, 629 (1897). Dewar and Fleming: Proe. Boy. Soc. 61, 358 (1897). CHAPTER IV SOLIDS General Properties of Solids. — The third state of aggregation of matter is known as the solid state. We have seen that when any gas is cooled below a certain point it passes over into the liquid state. When any liquid is cooled sufficiently it passes over into a solid. It is thus possible to pass from the gaseous or liquid state to the solid. The reverse transformation is also possible, — a solid can be converted into a liquid by heat, and, as we have seen, a liquid can be transformed into a gas. Every elementary form of matter may take any of the three states of aggregation • — gas, liquid, or solid ; the state in which it exists at any given time is determined by the temperature and pressure to which it is subjected. By varying these sufficiently and in the right direction, it can be made to take either of the other forms. We have already studied the general characteristics of the gaseous and liquid states ; we shall now turn to the general properties of solids. The most striking difference between solids, and liquids and gases is that the first has a definite form and occupies a definite space. In respect to these properties, solids differ fundamentally from the other states. Another striking difference which really lies at the foundation of those just referred to, is the relative rigidity of the parts in a solid. The particles are firmly fixed, and move over one another only with the greatest difficulty, enormous pressures being required to change the form of solids. As it is said, the resistance to movement or the inner friction of solids is very great. With liquids there is some inner friction, but relatively little, while with gases the resistance to the movement of the parts is relatively quite small. Solids behave very differently from gases with respect to their power to resist pressure. The volume of gases is changed by press- ure, approximately according to the law of Boyle — volume varies inversely as pressure. The volume of solids is changed but little, even when the pressure is very great. In this respect the difference between solids and liquids is much less than between solids and gases. r-7 158 THE ELEMENTS OF PHYSICAL CHEMISTRY Liquids are compressed but little by great pressure, but the change in volume is greater than with solids. The density of solids is much greater than that of gases, and, in general, greater than that of liquids. This is just what we would expect, since the solid state represents matter in the most condensed form. It is true that some liquids are heavier than some solids, but the above statement is generally true. The change in the volume of solids produced by heat is much less than for gases. The temperature, coefficient of the latter is, as is well known, ^-j, while the volume of solids changes only a small fraction of this amount for a change of one degree in temperature. The solid state not only represents matter in its most concen- trated form, but, as we have seen, in its most resistant state ; resist- ant not only to physical agents, but also to chemical. While a substance remains a solid it is much less active chemically than when in either of the other states of aggregation. In many cases a solid will not react at all with another substance, but when it is melted reacts readily. The result is, we know much less of the chemistry of solids than of liquids and gases. The same holds true with respect to our physical chemical knowledge of solids. Partly on account of the relative inertness of solids, and partly because of a lack of efficient methods with which to study them, we know relatively little of matter in the solid state from the physical chemical stand- point. Much that is included in some works on physical chemistry with respect to solids, seems to belong either to pure physics or to the science of crystallography and mineralogy. The subject of solids can be dealt with very briefly by the physical chemist, and, consequently, this chapter is quite short. CRYSTALS Crystal Systems. — Most of the solid substances with which we are familiar tend to take certain definite geometrical forms, which are more or less characteristic of the substance. This is true whether the solid is formed from a homogeneous liquid or from solution. In the latter case, however, there is generally better opportunity for the particles to arrange themselves according to their attractive forces, and, consequently, well-defined crystals are more frequently formed from solution than from a pure liquid. In a crystal the particles are arranged iu a perfectly orderly manner, and fulfil the condition that the arrangement about any one point is the same as about any other point. SOLIDS 159 Crystals fall into a number of groups or systems, with respect to the nature of their crystallographic forms. Indeed, six such crystal- lographic systems are recognized. I. Some crystal forms are built up upon three axes which are all of the same length, and are all at right angles to one another. This system, known as the regular or isotropic system, is distinguished from the remaining systems in that all the properties of the crystals are the same in every direction. This system includes such well- known forms as the octohedron, cube, dodecahedron, etc. The regular system is distinguished from all the other crystallographic systems, in that it has the largest number of planes of symmetry. II. The tetragonal system comprises all of those forms which are built upon two axes of the same length and the third axis of a different length from the other two ; all the angles between the axes being right angles. In such crystals the axis which is longer or shorter than the other two is placed vertically, and the two axes of equal length are placed, therefore, in the horizontal plane. The sym- metry here is evidently of a lower order than in the regular system. III. A third crystallographic system is conceived as built upon three axes symmetrically arranged in a horizontal plane, all of equal length, and making right angles with a vertical axis which is of different length. It is evident that this system, called the hexagonal, is closely related to the tetragonal from a geometrical standpoint, and we shall see that crystals in the two systems resemble one another closely with respect to their physical properties. IV. The orthorhombic system has three axes all of unequal length, but all making right angles with one another. It is evident that the symmetry of the geometrical forms built upon such axes is lower than in any other system thus far considered. V. The above four systems have all the axes making right angles with one another, except the hexagonal system which has three lateral axes, and these make angles of sixty degrees with one another. There are crystallographic systems in which the axes do not make right angles with each other. The first of these — the monoclinic — has all three axes of unequal length, and one of them not making a right angle with the other two. The presence of the oblique angle has evidently reduced the degree of symmetry very nearly to its limit. Indeed, in the monoclinic system there is only one plane of symmetry remaining — the plane of the oblique and vertical axis. There is only one more step possible in decreasing the symmetry of a system, and that is realized in the sixth and last crystallographic system. 160 THE ELEMENTS OF PHYSICAL CHEMISTRY VI. In the triclinie or asymmetric system the three axes are all of unequal lengths, and are all inclined to one another. There is no right angle in this system, and, therefore, no plane of symmetry. The triclinie system stands, then, at one extreme, in which all symmetry has been lost, while the regular system represents the highest degree of symmetry. Holohedrism. Hemihedrism. Tetartohedrism. — A given crystal form may occur with all the planes present as an octahedron, a prism, a pyramid, etc. When all the planes belonging to a given form occur, we have a complete or holohedral crystal. It frequently happens, however, that only half the planes belong- ing to a given form occur. These are then extended until they meet and give a figure which is quite different from the holohedral form from which they are derived. Thus, the hemihedral form of the octahedron is the tetrahedron ; of the hexagonal pyramid the rhoin- bohedron, etc. In a similar manner only one-fourth of the planes of the holo- hedral form may occur. In this way tetartohedral forms are pro- duced, and examples of tetartohedrism are not wanting. Importance of Crystallography for Chemistry and Physical Chem- istry. — The subject of crystallography has an important chemical and physical chemical bearing. A given substance not only crystal- lizes in certain characteristic forms, but the angles between the planes are constant for the same substance. This fundamental law of crystallography is known as the law of Steno. The crystal form and size of the angles thus become important constants for any given substance, and are of the very greatest importance in identify- ing chemical compounds. Further, since different substances usually have different forms, and always different angles if they have the same form, we utilize the form of crystals to determine the purity of the substance with which we are dealing. If from a solution or molten mass more than one form of crystals separates, we are gener- ally justified in concluding that we are dealing with a mixture. In some cases, however, the same substance crystallizes in more than one form, so that the above conclusion is not always valid, but such cases are relatively not common. On the other hand, two substances may crystallize in apparently the same form ; e.g. calcium carbonate and magnesium carbonate as dolomite. In such cases, while the form appears to be the same the angles made by the faces depend upon the composition. The angles on a pure calcite crystal differ from those on dolomite, and, indeed, the angle can be used to deter- mine the amount of magnesium carbonate present in the dolomite. SOLIDS 161 We thus see from the above that while crystal form alone is not always an absolute guarantee of the purity of a substance, it is of very great aid to the chemist in determining whether he is working with a chemical individual or with a mixture. All that has been said above in reference to the application of crystallography to chemistry, applies with equal force to physical chemistry. In all physical chemical work the question of the purity of the substance is fundamental, and the crystallographic method is, as we have seen, of great assistance in this connection. The application of crystal form to a physical chemical problem of the very highest importance has already been studied. It will be remembered that Pasteur sepa- rated dextro and lsevo tartaric acids by means of certain hemihe- dral faces, which occurred on the ammonium sodium salts of these acids — one hemihedral form occurring on some crystals, the other form on other crystals. And this was the beginning of what has been developed into an entirely new branch of science ; viz. stereo- chemistry. However, in addition to all this, the form of crystals has still another interest for the physical chemist. When the physical prop- erties of crystals were studied, it was found that there are certain very close connections between these properties and the geometrical form of the crystal. To some of these relations we will now turn. PROPERTIES OP CRYSTALS. RELATIONS BETWEEN FORM AND PROPERTIES Optical Properties. — The six crystal systems which we have just considered fall into three classes with respect to their action on light. The first class includes the regular system. The substances which crystallize in this system have only the power to refract light, but no power to doubly refract it. This holds for every direction in which the light is passed through the crystal. A large number of apparent exceptions to this generalization have been observed. Many substances which crystallize ia the regular system have been found to show double polarization. This phenomenon has been sat- isfactorily explained as due to a lamellar arrangement within the crystal, or to a certain stress or strain in the crystal produced dur- ing its growth, or to a combination of individuals which form an apparently isometric crystal. Since so many crystals in the regular system show no double refraction, it is evidently not a characteristic of the system, but an accidental state which obtains under certain conditions of growth. 162 THE ELEMENTS OF PHYSICAL CHEMISTRY The second class includes the tetragonal and hexagonal systems. These have one optic axis, and hence are termed uniaxial. If a ray of light is passed through the crystal along this axis, which is parallel to the vertical axis of the crystal, i.e. the axis which differs in length from the other two, there is no double refraction. The three remaining crystallographic systems fall into the third class. There is no direction through crystals in these systems in which light passes as through an isotropic substance. They have no iso- tropic axis. There are, however, two directions through such crys- tals in which the two rays into which light is broken travel with the same velocity. These are known as the optical axes, and hence such crystals are termed biaxial. The relations between crystallographic form and optical proper- ties become perfectly clear when we regard light as a vibratory motion of the ether. We must regard the crystallographic axes as expressing the relative densities of the ether in the different direc- tions through the crystal. Thus, when all the axes are of the same length, the density of the ether is the same in all directions through the crystal. When the axes are of different lengths, the ether is unequally dense in the different directions. Applying these concep- tions to the different crystallographic systems, we are impressed by the beautiful agreement between theory and fact. In the regular or isotropic system the axes are all of equal length ; therefore, the ether is equally dense in all directions through such crystals. Light would then move in all directions through such crystals with equal velocity, and, consequently, there could be no double refraction. In the uniaxial systems (tetragonal and hexagonal) the ether is equally dense in the directions of the axes of equal length, but more or less dense in the direction of the axis of unequal length. If light is passed through such crystals in any direction except parallel to the axis of unequal length, it will encounter ether of unequal den- sities in the different directions. Consequently, the ray of light will be broken up into two rays, or, as we say, will be doubly refracted. If the ray passes through the crystal parallel to the axis of unequal density, it will encounter ether of equal density in all directions, since the axes normal to this axis are of equal length. The ray will not be broken up into two when it moves in this direction, or, as we say, is not doubly refracted. When we come to the biaxial systems, the problem is much more complicated. The three axes are all of unequal length, and, there- fore, the densities of the ether are different in the directions of the three axes. A ray of light passed through the crystal along any SOLIDS 163 crystallographic axis will necessarily be broken up into two. There are, however, two directions through such crystals, in the plane of greatest and least density, along which the two beams of light move with equal velocity. These two optic axes are placed symmetrically with respect to the directions of least and greatest density. These directions may, or may not, coincide with the crystallographic axes, depending upon the system. In the orthorhombie system these directions coincide with the crystallographic axes. In the mono- clinic system only one of these directions is coincident with the crystallographic axes, — the one perpendicular to the plane of sym- metry, — while in the triclinic system neither of these directions is coincident with the crystallographic axes. The phenomenon of polarization of light by crystals is a neces- sary consequence of the difference in density of the ether in different directions through the crystal. If the ray encounters ether of dif- ferent densities, it is broken up into two rays, whose vibrations are in planes at right angles to one another. Light whose vibrations are reduced to a single plane is said to be polarized. These two polarized rays move through the crystal with different velocities — the velocity being conditioned by the density of the ether. Know- ing the relation between crystallographic form and density of the ether in the crystal, we are able to predict with certainty in just what cases light will be polarized by passing it through any given crystal. A close relationship between the geometrical forms of crystals and their optical properties is thus evident. Indeed, the form is an index to the condition of the ether in the crystal — a geometrical expression of the relative densities of the ether in different directions through the crystal. Thermal Properties of Crystals. — The thermal properties of crystals, which will be considered here, are the expansion of crys- tals by heat and the thermal conductivity of crystals. Only crys- tals in the regular system expand equally in all directions with rise in temperature. Crystals in all of the other systems expand differ- ently in different directions. Pizeau 1 has shown that crystals in the tetragonal and hexagonal systems expand equally in two directions, and differently in the third direction. This corresponds perfectly with the geometrical form and optical properties of such crystals. The effect of temperature on crystals in the different systems can best be illustrated thus: If a sphere is cut from a crystal in the 1 Compt. rend. 66, 1005, 1072. 164 THE ELEMENTS OF PHYSICAL CHEMISTRY regular system at any given temperature, it will remain a sphere at all temperatures. If a sphere is cut from a crystal in the tetrag- onal or hexagonal systems, at any temperature, it will not be a sphere at any other temperature, since the expansion along one axis is different from that along the other two — it will become an ellip- soid of revolution. If the crystal is orthorhombic, monoclinic, or triclinic, it will expand differently in all three directions, and, consequently, the sphere will become a triaxial ellipsoid. The conductivity of heat by crystals obeys the same laws as the optical conductivity. The thermal conductivity was studied by boring small holes in plates of crystals, inserting a warm wire into the hole, and observing the melting of a layer of wax with which the plate was covered. In crystals of the regular system the figure of the melted wax was always a circle; in uniaxial crystals a circle or ellipse, depending upon whether the plate was cut perpendicular to the optic axis, or parallel to it. In biaxial crystals the figure of the melted wax was always an ellipse. 1 These facts will be seen to be perfectly analogous to the action of crystals on light, and also to their thermal expansion. Electrical Conductivity. — Our knowledge of the electrical con- ductivity of crystals we owe chiefly to G. Wiedemann. 2 Plates of crystals were covered with some non-conducting powder, such as lycopodium or minium. Above these an isolated fine point was suspended and charged positively by means of a Ley den jar. The powder was repulsed from the charged point, in the form of a circle with isometric crystals, but approximately in the form of an ellipse with other crystals. The powder renders visible the distribution of electricity over the surface of the plate of crystal, and from the figure we can see the relative electrical conductivities in different directions. Wiedemann found that electricity is conducted through crystals most rapidly in the directions in which light' moves most rapidly. The results show that the electrical properties of crystals agree also with their thermal properties. We thus have a close connection between the optical, thermal, and electrical properties of crystals, and what is of even greater inter- est, a close connection between these properties and the geometrical forms of the crystals. Other properties of crystals could be taken i S&iarmont: Ann. Ohim. Phys. [3], 31, 457 (1847); 88, 179 (1848). Pogg. Ann. 73, 191 (1848); 74, 190 (1849); 75, 50 (1849). Lang : Pogg. Ann. 135, 29 (1868). 2 Pogg. Ann. 76, 404 (1849). SOLIDS 165 up if space permitted, such as the figures produced by etching the crystals, the hardness and elasticity of crystals, etc. ; but the more important properties considered above show beyond question tnat the form which matter takes in the crystal is either conditioned by, or more probably conditions, the sta.te of strain or stress to which the ether is subjected. There is thus a striking agreement between the form of the crystal and its properties, which depend upon the condition of the ether in the crystal. CRYSTALLOGRAPHIC FORM AND CHEMICAL COMPOSITION Polymorphism. — The conclusion might be drawn from what has been stated, that a definite chemical substance always crystallizes in the same form, which is characteristic of the substance. While this is generally true, it is by no means always so. The same element or compound may crystallize in more than one form, and the forms may even have different degrees of symmetry. When the same substance crystallizes in two forms, it is called diamorphous ; when in more than two, polymorphous. Sulphur is a good example of an element which crystallizes not only in more than one form, but also with different symmetry. As found in nature it is orthorhombic; but if molten sulphur is allowed to cool under certain conditions, it crystallizes in the monoclinic system. Calcium carbonate is an example of a com- pound crystallizing in more than one system. As calcite it crystal- lizes in the hexagonal system, while as aragonite it belongs to the orthorhombic system. Other substances are known which crystallize in more than two forms, and so on. There are a number of conditions which determine the form which a given substance will take. Of these the most important is tem- perature. This is shown very well in the ease of sulphur. At the higher temperature the monoclinic form is the most stable, while at lower temperatures the orthorhombic represents the more stable con- dition. The monoclinic form passes over readily into the ortho- rhombic at lower temperatures. In connection with the effect of temperature on molecular struc- ture, reference should be made to the recent work of Cohen 1 on tin. He has found that ordinary white tin is stable only above 20°. Below this temperature it passes over slowly into a gray crystalline modifi- cation, which has very different properties from the ordinary white tin. The gray modification when heated above 20° passes rapidly i Ztschr. phys. C'hem. 30, 601 (1899) ; 33, 57 (1900) ; 35, 588 (1900). 166 THE ELEMENTS OF PHYSICAL CHEMISTRY back into the white again. While the exact crystallographic change which takes place has not yet been worked out, it is quite certain that the transformations in the case of tin are strictly analogous to those which take place with sulphur. Conditions other than temperature also affect the crystal form. The presence of even a small amount of a foreign substance may condition the form in which another substance will crystallize. Take the case of calcium carbonate, which can crystallize in either the hexagonal or orthorhombic system. If a substance is present which crystallizes in the hexagonal system, the carbonate of calcium will be much more liable to form hexagonal crystals ; but if some orthorhombic substance is present, the carbonate will more probably form orthorhombic crystals. The influence which one substance may have on the form which another will take, may even be so great as to force it to take a form in which it would never crystallize if left to its own forces. The examples of polymorphism given above all represent the condition where each of the forms can be transformed into the other by heat or some other agent. There are, however, cases known where a substance crystallizes in two forms, which have thus far not been transformed into one another. Thus, diamond and graphite have not been mutually transformed into one another, although the latter has been obtained from the former. That there is really any inherent difference between this case and those above considered, where such reciprocal transformations have been effected, no one can believe. The two or more forms in which the same kind of matter occurs, represent, as we shall see, but different conditions of energy. The one form contains more energy stored up within itself than the other, and hence the difference in properties, including the difference in crystal form. The one form is the more stable under certain conditions of temperature, etc., while another modification is the more stable under other conditions. The meaning of this will be clearer when we come to see the significance of energy relations as conditioning the properties of substances in general. Isomorphism. — It is evident from the last paragraph that the same substance may crystallize in more than one form. This raises the question as to whether different substances ever crystallize in the same form. This question was answered once for all by Mitscherlich. In an investigation J carried on in part in the laboratory of Berzelius, he showed that a number of different substances may crystallize in i Ann. Chim. Phys. [2], 14, 172 (1820). SOLIDS 167 the same form, and then completed an elaborate investigation in the same laboratory on the arseniates and phosphates. He found that these salts, although quite different chemically, crystallize in forms which are so nearly identical that it was impossible to detect with certainty any appreciable differences. As the result of this work Mitscherlich was led to the following generalization : l — " TJie same number of atoms combined in the same manner produce the same crystalline form ; and the same crystalline form is independent of the chemical nature of the atoms, and is determined only by the number and relative position of the atoms." 1 This conclusion, as is well known, went too far beyond the facts, yet it has considerable historical interest in connection with the determination of atomic weights, as we have seen. It is now well known that there are substances with the same crystalline form, whose molecules contain very different numbers of atoms. The work of Mitscherlich established the fact of isomorphism, and showed that a crystal would grow as well in a solution of an isomorphous substance as in its own. He showed that a number of single sul- phates may grow into the same crystal, also that an alum crystal may contain a number of alums. In the light of polymorphism and isomorphism, one would natu- rally ask, can crystal form be used at all as a characteristic of chemi- cal composition ? The answer is, it can. Most substances crystallize under ordinary conditions in characteristic forms, and crystal form has been of the very greatest service in identifying and testing the purity of chemical substances. MELTING-POINTS OF SOLIDS Method of Determining the Melting-point. — The method of deter- mining the melting-point of a solid, which is generally employed, is very rough. The solid is placed in a fine glass tube closed at the bot- tom, and attached to a thermometer. The whole is then immersed in sulphuric acid in a small glass bulb, and the acid warmed to the melt- ing-point of the solid. It is evident that such a method can give only approximate results, however- slowly the sulphuric acid is heated. There is nothing to protect the thermometer from the effect of radia- tion, and the warm bulb is constantly radiating heat outward on to the colder objects around it. In order that any measurement of tem- perature should be accurate, it is necessary that the bulb of the ther- mometer should be surrounded by a metallic screen, as nearly as 1 Ann. Chim. Phys. [2], 19, 419 (1821). 168 THE ELEMENTS OF PHYSICAL CHEMISTRY possible at its own temperature. In making an accurate melting- point determination, the bulb of the thermometer should be sur- rounded by a screen of platinum foil, which is also immersed in the same liquid as the thermometer in order that it may be heated to the same temperature. Since this precaution has been for the most part disregarded, the melting-point determinations, especially of or- ganic compounds, may contain some considerable error. The above method is employed when only a small amount of sub- stance is at disposal. If a larger amount is available, the whole mass may be heated above its melting-point and converted into liquid. The liquid can then be carefully cooled down to its freezing-point, which is the same as the melting-point of the solid. In this ease the liquid is almost certain to suffer undercooling, i.e. to cool below its freezing-point before solidification begins. This will often take place even when the entire mass of the liquid is vigorously stirred. Under- cooling can be prevented by adding a small fragment of the solid substance. When the liquid has cooled a trifle below its freezing- point, it is only necessary to add a small particle of the solid, when all undercooling will be removed by the separation of more of the solid substance, which will warm the remainder of the liquid up to its true freezing-point. It is only necessary to read the temperature of the liquid containing some of the solid phase of the substance, on an accurate thermometer, at standard pressure, and we have the true melting-point of the substance. An almost infinitesimal quantity of the solid phase is sufficient to cause an undercooled liquid to freeze. In this connection refer- ence only can be made to a recent paper by Ostwald, 1 which records some very surprising results bearing upon this point. Relations between the Melting-points of Substances. — Certain regularities between the melting-points of the elements have already been pointed out. We will consider here some relations which have been discovered between the melting-points of com- pounds. The bromine compounds z melt higher than the correspond- ing chlorine compounds, and the nitro compounds higher than the bromine compounds. Of the disubstitution products of benzene the para compounds, in general, melt higher than the ortho or meta. A relation which is far more interesting than the above has been pointed out by Baeyer. 8 In studying the oxalic acid series Baeyer 1 Ztschr. phys. Ohem. 22, 289 (1897). 2 Peterson, Ber. d. chem. Gesell. 7, 68 (1874). 8 Ibid. 10, 1286 (1877). SOLIDS 169 noticed that those compounds which have an even number of carbon atoms melt higher than those with an odd number. Succinic acid, C4H e 04 Pyrotartaric acid, C6H e 04 Adipic acid,C6H 10 O4 Pimelic acid,C 7 H 12 04 Suberic acid, C 8 H 14 04 Azelaic acid, C 9 H 16 4 Sebasic acid, Ci Hi 8 O4 Brassylic acid, CuH 20 O4 Melting-point 180° 97° M48° 103 d 140° 106° 127° 108° A similar regularity was observed with the normal members of the formic acid series : — Melting-point tfELTING-POINT Acetic acid, C2H4O2 + 17° Cglli60 2 - + 16° Propionic acid, C S H 6 02 lower than — 21° CgHigC^ + 12° 1 Butyric acid, C4H 8 2 0° CioH 2 o0 2 ' + 30° Valeric acid, C5H10O2 lower than — 16° < C16H3202 > + 62° Caproic acid, C 6 Hi 2 2 -2° CirH340 2 + 59°.9 J CEnanthylic acid, C7Hi 4 2 - 10°. 5 C18H3602 69°.2 In both series, the members with an odd number of carbon atoms have lower melting-points than their two adjoining members with an even number of carbon atoms. The meaning of this regularity is entirely unknown. Quite recently Bay ley 1 has shown that the ratio between the melting-points and boiling-points of a number of hydrocarbons of the paraffine, ethylene, and acetylene hydrocarbons is nearly a constant. It may vary from 1.5 to 2 within a given series, but usually much less. The author attempts to connect the constitution of the com- pound with the value of this ratio. Melting-point a Criterion of Purity. — Of all the methods avail- able for identifying a substance and testing its purity, no one is so frequently made use of by the chemist as the melting-point method. The temperature at which a substance melts is a characteristic con- stant for the substance, and this is often used as one means of iden- tifying it. Further, if the substance is pure it will melt sharply at one temperature. If the melting-point is not sharp, a part of the substance melting at one temperature and the remainder not until a higher temperature is reached, we must conclude that the compound 1 Chem. News, 81, 1 (1900). 170 THE ELEMENTS OF PHYSICAL CHEMISTRY is not pure, and that we are dealing with a mixture. The presence of a very small amount of a foreign substance affects the melting- point quite considerably, usually producing a lowering of this point, so that a sharp melting-point means a high degree of purity. LATENT HEAT OF FUSION Latent Heat, and Molecular Latent Heat of Fusion. — When a solid is heated up to a certain temperature it begins to melt. If more heat is added at this temperature, the solid continues to melt, but the temperature does not rise until all of the solid has passed over into the liquid condition. During the process of melting, a large amount of heat is consumed and disappears as such. This was early termed " latent heat," and the name still persists. The amount of heat required to melt one gram of a substance at a fixed temperature is termed the latent heat of fusion of the substance at the temperature in question. This quantity multiplied by the molec- ular weight of the substance gives the molecular heat of fusion. When the melted substance solidifies, exactly the same amount of heat is given out as was consumed in melting it. The latent heat of fusion of a solid is perfectly analogous to the latent heat of vaporization of a liquid. It will be remembered that when a liquid is heated to the boiling-point, and more heat is added, the temperature does not rise, but the liquid passes over into vapor. The heat required to convert a liquid into vapor is usually very large ; indeed, the latent heat of vaporization is much greater than the latent heat of fusion. The large amount of heat consumed in passing from the solid to the liquid state, and from the liquid to the gaseous condition, does internal work driving the molecules farther apart, and producing in general a molecular rearrangement. Determination of Latent Heat of Fusion. — The method of meas- uring the latent heat of fusion consists not in measuring the amount of heat which must be added in order to fuse a given quantity of any substance, but in measuring the heat liberated by a given quan- tity of a molten substance at its melting-point when it solidifies. This heat of solidification is exactly equal to the latent heat of fusion. The latent heat of fusion of liquids, like their latent heat of vaporization, is of importance in physical chemistry, as we shall see, because of certain theoretical relations which have been worked out between this quantity and the lowering of the freezing-point of a solvent by a dissolved substance. The latent heat of fusion of SOLIDS 171 a- few of the more common solvents is given in the following table : — Latent Heat of Fusion Ice Benzene / 1 1. 1 cai. 29.1 cal. Nitrobenzene 22.3 cal. Formic acid 58.4 cal. Acetic acid 43.7 cal. SPECIFIC HEAT OF SOLIDS Law of Dulong and Petit. — Although a portion of the material belonging to this section has necessarily been anticipated in the dis- cussion of methods for determining atomic weights, the subject will now be taken up a little more systematically. A relation between the specific heats of solid elementary substances and their atomic weights was discovered as early as 1819 by Dulong and Petit. 1 A few examples from their paper will make this relation clear : — Specific Heat Atomic Weight Product 0.0293 12.95 12.43 11.16 6.75 4.03 3.957 3.392 2.011 3794 Gold 0.0298 3704 0.0314 0.0557 0.3740 0.3759 0.0927 0.3736 0.1100 0.3755 0.3731 0.3780 These atomic weights are referred to oxygen as unity. The value of the " product " must be multiplied by 16 to obtain the value assigned to it to-day. The product of the specific heat by the atomic weight is known as the atomic heat ; and this is very nearly a constant for the different elements. Work of Regnault. — The law of Dulong and Petit was thoroughly tested some twenty years later by Regnault, 2 who worked with a large number of elementary substances. He found that the law is in the main true, but the atomic heats are not the same for the dif- » Ann. Chim. Phys. [2], 10, 395 (1819). a Ibid. [2], 73, 5 (1840). 172 THE ELEMENTS OF PHYSICAL CHEMISTRY ferent elements ; they are only approximately a constant. The sub- sequent work of Regnault on the specific heats 'of the elements brought out a number of interesting facts. He showed that the atomic weights of a number of the elements must be only half 1 the values previously assigned to them, in order that the law of Dulong and Petit might apply to these substances. He, however, found cer- tain elements to which the law of Dulong and Petit did not apply at all. The specific heat of different kinds of carbon 2 was determined, and found to vary greatly with the nature of the material. The lowest value, 0.146, was found with the diamond, and the highest, 0.260, with animal charcoal. Values ranging all the way between these two extremes were found with graphite, anthracite, coke, and wood charcoal. This was evidently at variance with the law under consideration, and especially so since the highest value found was far too low to accord with the law. Regnault 3 discovered the same discrepancy in the cases of sili- con and boron. Their specific heats were far too low to give the nearly constant value of the atomic heat, when it was multiplied by the atomic weight of the element. Work of Kopp. — The work of Kopp, 4 published nearly twenty- five years later than that of Regnault, added greatly to our knowl- edge of the specific heat of solids. It is impossible to enter into the details of this tremendous piece of work ; only a few of the conclu- sions reached can be pointed out. The law of Dulong and Petit was found to hold approximately — the atomic heats of the ele- ments being nearly constant. The elements carbon, boron, and sili- con present exceptions to this law, as Regnault had found. If the molecular heat of many compounds is divided by the number of atoms in the molecule, the quotient is approximately 6.4., i.e. the same as the atomic heat of the elements. The molecular heat is thus approximately the sum of the atomic heats of the atoms which are present in the molecule. Kopp 5 drew the following general conclusions from his work : First, every element in the solid condition at a sufficient distance from its melting-point has a definite specific or atomic heat. This may vary somewhat with the temperature and density of the sub- 1 Ann. Chim. Phys. [3], 26, 261 (1849) ; 46, 257 (1856); 63, 5 (1861). Com.pt rend. 55, 887. 2 Dumas and Stas: Ann. Chim. Phys. [3], 1, 202 (1840). « Ann. Chim. Phys. [3], 1, 129 (1841). * Lieb. Ann. Suppl. 3, 1, 289 (1864-1865). 6 Ibid. 8, 289 (1864-1865). SOLIDS 173 stance, but not very greatly. Second, every element has the same specific and atomic heat in the free condition and in combination. Work of Weber. — The elements carbon, boron, and silicon pre- sented, as we have seen, unmistakable exceptions to the law of Du- long and Petit. Weber 1 undertook to study the specific heat of these elements at different temperatures. He observed, from the work of others, that the higher the temperature the greater the specific heat found. He determined to work at higher temperatures, and found that the specific heat of carbon remained practically constant with rise in temperature, after a dull red heat was reached. Also that the specific heats of graphite and diamond became identical above 600°, and remained the same however high the temperature to which both were heated. The specific heat of carbon between 600° and 1000°, multiplied by the atomic weight of carbon (12), gave 5.4 to 5.6 as the atomic heat of carbon. The true specific heat of carbon at 2000° must be at least 0.5, so that at this temperature the atomic heat of carbon would be 6, which brings it in line with the law of Dulong and Petit. Similar results were obtained for boron and silicon ; the specific heats of these elements increased with rise in temperature to such an extent, that we are justified in concluding that the law of Dulong and Petit holds also for these elements at more elevated tempera- tures. In closing this chapter on solids, we leave what we have called the Older Physical Chemistry. This refers not so much to the question of years as to the nature of the problems dealt with, and the methods employed in solving them. Some of the work discussed in the preceding chapters was done in the last few years, and some investigations which will be referred to in subsequent chapters were carried out early in the century. It is, however, true in general that most of the work thus far considered belongs to the period previous to 1885, and also true that a very large proportion of what follows was done subsequent to that date. But the distinction which we wish to draw is far more funda- mental than that of years. The physical chemistry of to-day differs not only in degree from that of twenty-five years ago, but in kind. What was studied and taught at that time under this head bears no close relation whatsoever to the work which is being done at present by the modern physical chemist. We have already seen what are i Pogg. Ann. 154, 367 (1875). 174 THE ELEMENTS OF PHYSICAL CHEMISTRY the most characteristic features of the older physical chemistry. It ■was essentially the study of the physical properties of chemical sub- stances, and the conclusions reached, as has been pointed out, were for the most part purely empirical. That they are, however, impor- tant in themselves, and especially important in what they have led to, and promise to give us in the future, no one who is familiar with the facts can deny. This phase of our subject has been dealt with at considerable length, partly because there is a marked tendency at present to dis- regard or ignore the work of the earlier physical chemists, and to think that physical chemistry really began about fifteen years ago. It is true that much of the older work has been temporarily obscured by the brilliancy of the newer results, but the work of men like Kopp, Bunsen, Kegnault, and Stas, will ever lie at the foundation of modern science. Having studied much of the work of the older period, we must now turn to the new physical chemistry. In the following chapter we shall show how the newer period was inaugurated. How a dis- covery was made about fifteen years ago, which has grown into an entirely new branch of science, a branch which already has a large literature of its own, which is being taught and studied in most of the leading universities in the world, and for which alone a number of laboratories are already equipped. The rapid growth of the science has been only commensurate with the importance of the results obtained. Modern physical chemistry has revolutionized chemical thought in many directions, it has thrown light on a num- ber of important physical problems, and has already made its way into physiology and other branches of biology, and is now finding its way into the geological sciences. We shall now see what are some of the more important develop- ments of the new science. CHAPTER V SOLUTIONS Kinds of Solutions. — We have dealt thus far with matter in the pure condition. A pure substance, either elementary or compound, was prepared and its properties studied. The substance might be in the gaseous, the liquid, or the solid state ; or it might exist in all three states under different conditions. We are, however, not limited to the study of matter in the pure form. One element or compound can be mixed with another element or compound, and the properties of the mixture investigated. It is not even necessary to stop here. Three or more substances might be mixed and such mixtures studied. Further, the substances which are mixed might be of the same or of different states of aggregation. Mixtures which are homogeneous, and from which the constituents cannot be separated mechanically, are termed solutions. It is obvious that a number of different kinds of solutions are possible. We know matter in three distinct states of aggregation, — solid, liquid, and gas. Since matter in every state can be mixed with matter in every other state, at least theoretically, we can have nine different classes of solutions. These are : — I. Solution of gas in gas. II. Solution of liquid in gas. III. Solution of solid in gas. IV. Solution of gas in liquid. V. Solution of liquid in liquid. VI. Solution of solid in liquid. VII. Solution of gas in solid. VIII. Solution of liquid in solid. IX. Solution of solid in solid. It may be stated in advance that well-defined examples of all of these classes of solutions are known. Our study of solutions con- sists, then, essentially in a study of the properties of these nine classes of mixtures. 176 176 THE ELEMENTS OF PHYSICAL CHEMISTRY SOLUTIONS IN GASES Solutions of Gases in Gases. — When different gases are brought together they either act chemically upon one another, as hydrochloric acid gas and ammonia, or they simply mix with one another, as hydrogen and nitrogen. It is to the latter class only, where no chemical action takes place, that the term " solution of one gas in another " is applied. When one gas dissolves in another, the condi- tion is always fulfilled that any quantity of the one can dissolve in any quantity of the other. When any gas dissolves in another with- out acting chemically upon it, it is always soluble to an unlimited extent, and this is a characteristic of the kind of solutions with which we are now dealing. The pressure exerted by a mixture of gases is the sum of the pressures of the constituents. This was early discovered by Dalton. 1 If we represent the pressures exerted by the constituents by p 1( p 2 , • • ■ and the volume of the mixture by V, we have — PV=V( Pl + Pl +•••)• This law of the summation of gas-pressures holds when the gases are not too concentrated, i.e. when the pressures are not great. At higher pressures many exceptions have been discovered to this gen- eralization. Indeed, this would be expected, since, when the gas- particles are comparatively numerous in a given space, their effect upon one another would come prominently into play. It may, how- ever, be said in general that the properties of mixtures of dilute gases are approximately the sum of the properties of the con- stituents. Solutions of Liquids in Gases. — Liquids in general have the power to dissolve in gases, or, as we usually say, a liquid can send off vapor into a space containing a gas. Ordinary evaporation in the presence of the atmosphere is a phenomenon of the kind we are describing. The law of the solution of a liquid in a gas was also discovered by Dalton. 2 The vapor-pressure of the vapor of a liquid in the presence of a gas is the same as in a vacuum. A number of supposed exceptions to this law have been pointed out by Regnault 3 and others, but the recent work of Galitzine * on water, ethyl chloride, and ether shows that the vapor-pressure of these substances in a vacuum is very nearly the same as in the air. Some of the apparent 1 Gilb. Ann. 12, 385 (1802). 8 Mem. Ac. 8c. 26, 679. 2 Ibid. 12, 393 ; 15, 21 (1802-1803). 4 Dissertation, Strassburg (1890). SOLUTIONS 177 exceptions to this law are probably due in part to a solution of the gas in the liquid with which it is in contact. This, as we shall see, lowers the vapor-tension of the liquid, and, consequently, affects the solubility of the liquid in the gas in question. Solutions of Solids in Gases. — There are solids known which pass over into vapor in the presence of a gas without first becoming liquid. Thus, iodine vaporizes at an elevated temperature in the presence of the atmosphere or other gases. Such mixtures are as truly solutions of solids in gases, as those which we have been considering are solutions of gases or liquids in gases. About all that is known of solutions of solids in gases is that the solubility increases with rise in temperature. This is usually expressed by saying that the vapor-tension increases with rise in temperature. SOLUTIONS IN LIQUIDS Solutions of Gases in Liquids. — In dealing with solutions in liquids as solvent, we must distinguish between the cases where chemical action takes place between the dissolved substance and the solvent, and where there is no chemical action. The latter consti- tute the true solutions in liquids. All gases are absorbed to some extent by all liquids, the amount of gas absorbed varying greatly with the nature of the gas and also with that of the liquid. A given gas is absorbed by a given liquid to a very different extent under different conditions. It is well known that the greater the pressure to which the gas is subjected, the larger the amount dissolved. A very simple relation was dis- covered by Henry ' connecting the solubility of a gas with the press- ure, and which has come to be known as Henry's law. The amount of a gas dissolved by a liquid is proportional to the pressure to which the gas is subjected. Henry tested his law for several gases at pressures ranging from one to three atmospheres, and found that it held quite closely. It has since been subjected to more careful test by Bunsen and others, 2 with the result that the law has been shown to agree very closely with the results of the best experiments. Exceptions to the law of Henry are, however, not wanting. If the gas is very soluble in the liquid, the law does not hold. This was found by Eoscoe and Dittmar 3 to be the case with ammonia in i Phil. Trans. (1803). Gilb. Ann. 20, 147 (1805). 9 Khanikof and Louguinine : Ann. Chim. Phys. [4], 11, 412 (1867). * Lieb. Ann. 112, 349 (1859). 178 THE ELEMENTS OF PHYSICAL CHEMISTRY water ; and similar results were obtained by Watts. 1 When the gas is very soluble in the liquid, the solution formed is concentrated. We have just seen that the law of Henry does not apply to such solutions. We shall see that practically all of the relations which have been found to hold for dilute solutions fail to hold in concen- trated solutions. That Henry's law should not apply to concentrated solutions should, therefore, not be a matter of any surprise. Solutions of Liquids in Liquids. — In dealing with solutions of liquids in liquids we must distinguish sharply between two cases. First, where the liquids are infinitely soluble in each other, or, as we say, where they are miscible in all proportions, as alcohol and water. This case suggests the solution of one gas in another. Here, as we have seen, we always have infinite solubility, — gases mixing with one another in all proportions. Second, where the liquids are miscible to only a limited extent, as water and ether. Here we encounter a new condition, which we shall frequently meet with hereafter in dealing with solutions, i.e. limited solubility. The prop- erties of these two classes of liquid solutions, as we shall see, are quite different. In addition to the above cases, there are liquids which are practically insoluble in one another ; hence, mixtures of such liquids cannot be regarded in any true sense as solutions, since the constituents can be readily separated mechanically. There is, however, no liquid which is absolutely insoluble in any other liquid, so that the last distinction is not a sharp one. First Class. — The properties of mixtures of liquids which mix in all proportions are not the sum of the properties of the constituents. When such liquids are mixed, there is a change in volume. Usually the volume decreases on mixing, but in some instances it increases. Changes in temperature accompany the mixing of liquids. In some cases heat is evolved ; in others it is absorbed. No relation has thus far been discovered between the volume changes and thermal changes of such mixtures. Sometimes heat is evolved when there is con- traction, in other cases when there is expansion in volume. The properties of liquid mixtures, however, are often not widely different from the sum of the properties of the constituents. In such cases, where the properties of the mixture are nearly " addi- tive," they can be approximately calculated from those of the con- stituents. If the volumes of the two liquids before they are mixed are i' x and v 2) the volume of the mixture v is approximately — V = Vi + v 2 . 1 Lieb. Ann. Suppl. 5, 227 (1865). SOLUTIONS 179 One other example will suffice to illustrate this point. Take the power of liquids to refract light. If we represent the weight of the mixture by W, the index of refraction by JV, and the density .by D ; and the corresponding values of the constituents by w^ w 2 , w 3) •■-, «!, n 2 , n s , ■••, d v d 2 , d 3 , ■■•, the following formula was deduced by Landolt : 1 — tjr N — 1 w, — 1 , n» — 1 , n a — 1 , D d r d 2 d a This formula was tested for a number of mixtures by Landolt, and found to hold. Much more recently, Schiitt 2 studied the refractive power of mixtures of ethylene bromide and propyl alcohol. The index of refraction for the sodium line was represented by n for the mixture, by Wj and n 2 for the constituents ; the density of the mix- ture is d, that of the constituents dx and d 2 . The percentage by weight of the one constituent is p, that of the other 100 — p: — n — 1 _ n x — 1 p , n 2 — 1 100 — p d d, 100 d 2 100 Schiitt tested this formula for a number of different lines in the spectrum, and found that the difference between the value calculated for the mixture and that found experimentally was about one per cent, and the difference was always on the same side. He then showed how the refractivity of one of the constituents could be cal- culated from that of the mixture, knowing the refractive power of the other constituent, and the percentage composition of the mixture. We see from the above example that with mixtures such as we are now considering, the properties are never strictly "additive." They are, at best, only approximately so, and in many cases differ very considerably from the sum of the properties of the constituents. Second Glass. — A large number of liquids are known which dis- solve one another to only a limited extent. The case of ether and water has already been mentioned. It is not a simple matter to calculate the properties of such mixtures from those of the constitu- ents. One property of such mixtures, however, is especially interest- ing ; i.e. the effect of temperature on the composition of the mixture. The work of Alexeew 3 has shown that salicylic acid, which melts at 156°, becomes liquid under boiling water, and when heated with water in a closed tube a little above 100°, this liquid mixes with 1 Lieb. Ann. Suppl. 4, 1 (1865). * Ztsehr.phys. Chem. 9, 349 (1892). 3 Jowrn. prakt. Chem. 183, 518 (1882); Bull. Soc. Ohim. 38, 145 (1882). 180 THE ELEMENTS OF PHYSICAL CHEMISTRY water in all proportions. The liquid beneath the water is not molten salicylic acid, but a solution of water in salicylic acid. In the case of liquids which mix to only a limited extent, we always have two solutions formed — that of A in B, and that of B in A — if there is more of the one constituent present than will saturate the other. In the above case we have a solution of salicylic acid in water, and a solution of water -in salicylic acid. These two become miscible in all proportions at a certain elevated temperature, as we have just seen. This has been found to be a general property of liquids which mix to only a limited extent. The two solutions merge into one at a temperature more or less elevated, but which can usually be real- ized experimentally. These facts are shown very clearly by the following curves, 1 the abscissas representing temperatures, the ordi- £ 60 " 50 \l \2 \3 H 5 10 20 SO 40 GO GO 70 80 00 100 110 120 130 140 150 160 170 temeeratubes Fig. 14. nates per cent of dissolved substance in 100 parts of solution. „ These curves represent aqueous solutions of phenol (1), salicylic acid (2) benzoic acid (3), aniline phenolate (4), and aniline (5). At the lower temperatures we have in each case two distinct solutions represented by the two arms of each curve. The lower arm represents the solution of the substance in water, there being relatively little substance and much water present in this solution, as is shown by the small value of the ordinate of this branch of the curve. The upper arm repre- sents the solution of water in the substance in question, the latter being present in very large per cent, as shown by the large value of the ordinate. As the temperature rises in each case, the two arms of the curve approach, and at a certain temperature which is defi- nite for each substance, the two arms meet. This means that at this i Alex<5ew: Bull. Soc. Ohim. 38, 146 (1882). SOLUTIONS 181 temperature the two solutions — that of A in B and that of B in A — become identical, and that the two substances can mix in all proportions. The second class of solutions of liquids ill liquids, i.e. those which mix to only a limited extent, can, then, be regarded as a special con- dition of the first class, which mix in all proportions. The condition is, that ordinary temperatures are below that at which such liquids would mix in all proportions. When solutions of liquids which belong to the second class are heated up to a certain temperature, they become miscible in all proportions, and, consequently, pass over into solutions of the first class. Vapor-pressure, Boiling-point, and Distillation of Liquid Mix- tures. — I. If the liquids do not mix to any appreciable extent, each exerts its own vapor-pressure independent of the other liquids which may be present. The vapor-pressure is, then, the sum of the vapor- pressures of the liquids which are brought in contact with one another. This has been verified experimentally by Regnault. 1 A few of his results are given in the following table : — Temperature Water Carbon Bisulphide Sum Vapor-pressure of Mixture 12°.07 26°. 87 10.5 mm. 26.3 mm. 216.7 mm. 388.7 mm. 227.2 mm. 415.0 mm. 225.9 412.3 The differences here are less than one per cent, the sum of the sepa- rate pressures being slightly greater than the vapor-pressure of the mixture. This is just what we would expect, since each liquid is slightly soluble in the other, and, as we shall see, would therefore slightly lower the vapor-pressure of the other liquid. Similar results were obtained by Regnault for other pairs of liquids which dissolve one another to only a slight extent. Such mixtures as the above would necessarily boil lower than the lowest boiling constituent, since the vapor-pressures of the several constituents summate, and would overcome the pressure of the atmosphere at a temperature lower than that at which the lowest boiling constituent alone would overcome it. The vapors of such mixtures would contain all of the constitu- ents, and in the same proportions as the relative vapor-pressures of the liquids present. When such mixtures are distilled, the distillate would contain all of the liquids present. The quantity of each would 1 Pogg. Ann. 93, 537 (1854). 182 THE ELEMENTS OF PHYSICAL CHEMISTRY depend upon the relative vapor-pressures at the temperature of dis- tillation. Some exceptions to this simple rule have been discovered. II. If the liquids are partly miscible, the vapor-pressure of the mixture is less than the sum of the vapor-pressures of the constitu- ents at the same temperature. This, again, is what we would expect, since each liquid present would depress the vapor-tension of the other. In these cases it is not possible to say offhand just what the boiling-point would be. It generally lies below the boiling-point of the lowest boiling constituent, but it can be coincident with it, or even higher than this temperature. The position of the boiling- point of the mixture with respect to that of the constituents would be conditioned largely by the degree of solubility of each liquid in the other. If the liquids readily dissolved one another, there would be a considerable depression of the vapor-tension of each by the other, and, consequently, the mixture would boil higher ; if, on the other hand, the liquids were only slightly soluble in each other, there would be relatively little depression of the vapor-tensions, and the mixture would boil lower ; in this case, lower than the lowest boiling constituent. When such mixtures are distilled, the product contains all of the constituents. The composition of the product remains constant as long as there are two layers present, since each solution has its own definite vapor-pressure at a given temperature. The effect of distil- lation would be to diminish the lower boiling solution more rapidly than the higher boiling. While there were two solu- t^ss^s tions present the boiling-point would remain constant, and would change only when one of the layers disappeared. Konowalow 1 has studied the products of distillation of such mixtures, and has plotted his results in curves. The ' ' t-6o°o abscissa represents percentage of alcohol ; the ordinate, va- T-71°0 T-4170 por-pressure. The following Fla 15 Peecentage i SO butyi, Alcohol. curves represent the results for a mixture of water and isobutyl alcohol. Konowalow measured the vapor-pressures of the mixtures at dif- 1 Wied. Ann. 14, 34 (1881). SOLUTIONS 183 ferent temperatures. The results in the above table of curves were obtained between 41° and 88°. 75. While the alcohol present was not sufficient to saturate the water, the vapor-pressure of the solu- tion increased with increase in alcohol. This is shown by the rise in the curve. When the water became saturated with the alcohol, the vapor-pressure became constant and independent of the excess of alcohol present. Such a mixture has a constant boiling-point, and the distillate a constant composition. When the excess of alco- hol present becomes so large that all the remaining water present can dissolve in it, the vapor-pressure again changes with the compo- sition, as is shown by the fall in the curve. The vapor-pressure finally falls to the value for pure alcohol. If the mixture represented by any point on the straight line is distilled, the composition of the vapor and the boiling-point will remain constant. But if a mixture represented by any point on either the rising or falling arm of the curve is distilled, the com- position of the vapor and the boiling-point will change gradually, until the liquid which is present in relatively large quantity will remain behind in nearly pure condition. III. If the liquids are soluble in one another in all proportions - , the vapor-pressure of the mixture is always less than the sum of the vapor-pressures of the constituents at the same temperature. This follows of necessity from the fact that a dissolved substance lowers the vapor-pressure of the solvent. The composition of the vapor given off from such mixtures bears no close relation to the compo- sition of the mixture. The vapor contains a preponderating amount of the most volatile constituent. Upon this fact rests the possibility of separating such mixtures by fractional distillation.. It is difficult to say at once where such mixtures will boil with respect to the boiling-points of the constituents. We have seen that the vapor-pressure of such a mixture is never equal to the sum of the vapor-pressures of the constituents. It may lie between the sum and the higher or lower vapor-pressure of the constituents; or it may even fall below the pressure of the constituent which has the lowest vapor-pressure. The boiling-point of such mixtures would, of course, vary inversely as the vapor-pressures, and, consequently, no general relation between the boiling-points of such mixtures and those of the constituents can be established. When such mixtures are distilled, that constituent which has the highest vapor-pressure (lowest boiling-point) tends to pass over in largest quantity. By repeating the distillation, it is, therefore, pos- sible to obtain the lowest boiling constituent in nearly pure con- 184 THE ELEMENTS OF PHYSICAL CHEMISTRY Fig. 16. percentage methyl alcohol Water and Methyl Alcohol. dition. Konowalow J studied the composition of the vapor and the- vapor-pressure at different temperatures, of mixtures of liquids which mix in all proportions. The following curves were plotted from his results : — ' The curves for methyl alcohol and water, and ethyl alcohol and water, show that as the amounts of alcohol increase, the vapor-pressure increases. The curves show no sign of any maximum or minimum of vapor-pressure, and since the tendency is for that sij^Bstance to pass over first which has the greatest vapor-pressure, the lowest boiling substance will pass over in nearly pure condition, since, as is seen at once from the curves, the vapor-tension increases as this sub- stance becomes greater and greater. Mixtures such as methyl alcohol and water, and ethyl alcohol and water, can then be separated by fractional distillation. All mixtures whose vapor-tension curves are of this type (Figs. 16 and 17), i.e. do not have maxima or mini- ma, can be separated more or less completely by fractional distillation. Mixtures with Constant Boil- ing-point. — Konowalow 2 also studied mixtures of water and propyl alcohol, and water and formic acid. His results are plotted in the following curves : — The curves for mixtures of water and propyl alcohol at different temperatures all show a maximum of vapor-tension, when there is about 70 per cent of the alcohol present. This mixture, containing about 30 per cent of water, has a greater vapor-pressure than any percentage ethyl alcohol Fig. 17. Water and Ethyl Alcohol. Wied. Ann. 14, 34 (1881). 2 Loc. nil. SOLUTIONS 185 Fig. 18. Percentage Propyl Alcohol. othei; mixture of these two substances. This mixture will, then, have the lowest boiling-point of any possible mixture of water and o propyl alcohol ; and if we distil any mixture of these substances, the distillate will tend more and more to the composition of this mixture. If we repeat the distillation several times, we shall obtain finally, not pure water or pure propyl alcohol as the distillate, but the mixture having the maximum vapor- tension', and, consequently, the lowest boiling-point. The curves for formic acid and water, instead of showing a maximum of yapor-tension show a minimum. This minimum exists when the mixture contains about 75 per cent. of formic acid. A mixture of this composition has, then, a lower vapor-tension than any other mixture of water and formic acid, and, consequently, a higher boiling-point. If any mix- ture of these two substances is distilled, the composition of the residue will approach more and more nearly to that of the mixture having the lowest vapor-ten- sion, and by repeated dis- tillation we can finally obtain a residue in the flask which corresponds very closely to this composition. It is obvious that mixtures which show a maximum or minimum vapor-tension can- not be separated into their constituents by fractional dis- tillation. Instead of obtain- ing the pure substances, a mixture will be obtained, in the one case in the distillate having a maximum vapor-tension, in the other in the residue having a minimum vapor-tension. Such mixtures with constant boiling-points have long been known, and were once supposed to be definite chemical compounds. A mix- ture of 20.2 per cent of hydrochloric acid and water has a constant Fig. 19. Percentage Formic Acid. 186 THE ELEMENTS OF PHYSICAL CHEMISTRY boiling-point, 110°, at the pressure of the atmosphere, and can be distilled without change in composition. Similarly, a mixture con- taining 68 per cent of nitric acid in water has a constant boiling- point, and many others are known. Roscoe 1 has proved that these mixtures are not definite chemi- cal compounds, by showing that the composition of the distillate changed when the distillation was effected under different pressures. Thus, when a mixture of hydrochloric acid and water was distilled under a pressure of two atmospheres, the mixture which had a con- stant boiling-point contained 19 per cent of the acid, instead of 20.2 per cent as when the distillation was carried on under a pressure of one atmosphere. There is, then, not the slightest reason for regarding these mix- tures with constant boiling-points as chemical compounds. Solutions of Solids in Liquids. — Whenever a solid is brought into the presence of a liquid, some of the solid dissolves. This is per- fectly general ; for, as we shall see, even metallic platinum dissolves to a slight extent in water. When we consider the number of solids and liquids known, it is evident that the number of such solutions is almost infinite. Indeed, we have become so accustomed to solutions of this class, that when the term " solution " is used, we think first of the solution of a solid in a liquid solvent. The most striking char- acteristic, perhaps, of solutions of solids in liquids is that there is a limit to the solubility of every solid in any liquid. We know of no solid which dissolves to an unlimited extent in any liquid. The degree of solubility, however, varies greatly. Some of the more resistant metals, like gold, platinum, etc., are so nearly insoluble in neutral liquids, that the most refined chemical methods are incapable of detecting their presence in the solvent, and only the most refined physical and physical chemical methods can show that they have any solubility whatever. The solubility of some compounds, on the other hand, is very great indeed. We should mention especially the strontium and calcium salts of permanganic acid. These have recently been prepared in quantity by Morse and Black, 2 using the beautiful method of preparing permanganic acid devised by Morse and Olsen, 3 and their solubility in water determined. One part by weight of water at 18° dissolves 2.9 parts of strontium per- manganate and 3.31 parts of calcium permanganate. Yet even in such extreme cases as these, a limit is reached, and beyond this it is impossible to go. That point at which a liquid cannot take up more 1 Lieb. Ann. 116, 203 (1860). 2 Dissertation, Johns Hopkins Univ. (1900). *Amer. Chem. Journ. 23, 431 (1900). SOLUTIONS 187 of the solid at a given temperature is known as the point of satura- tion, and such a solution is known as a saturated solution. There are two general methods of preparing saturated solutions. The substance, say a salt, is brought in contact with the solvent and the two shaken together at a constant temperature, until the liquid will take up no more of the salt. This is theoretically very simple, but it is found in practice that the time required to fully saturate a solution in this way is in some cases very great indeed. Another method which has been employed is based upon the fact that the solubility of many substances increases with rise in temperature. If it is desired to saturate a solvent at a given tem- perature, it is heated to a somewhat higher temperature and shaken with the substance to be dissolved. The amount which is readily dissolved at the higher temperature is more than sufficient to satu- rate the solution at the lower temperature. When the solution is cooled down to the desired temperature, any excess of the dissolved substance will separate out in the presence of some undissolved sub- stance, and the solution will be saturated at the required tempera- ture. While the results obtained by the first method are generally a little too low, due to the incomplete saturation of the solution, those obtained by the second are generally a little too high, since all of the excess of substance in solution may not separate unless the solution is vigorously stirred, and brought freely in contact with some of the undissolved substance. In studying saturated solu- tions it is best to use both methods, and take the mean between the results of the two. Just as we may have solutions which can take up more of the dissolved substance and are, therefore, unsaturated, so we may have solutions which contain more of the dissolved substance than corre- sponds to a state of stable equilibrium. Such solutions which are in a state of unstable equilibrium are termed supersaturated. If a supersaturated solution is shaken with some of the undissolved sub- stance, the excess of substance in solution will be deposited, and the supersaturated will become a saturated solution. We thus have a ready means of distinguishing between these three conditions of solutions. If the solution can take up more of the dissolved sub- stance at a given temperature, it is unsaturated at that temperature. If, when brought in contact with some of the undissolved substance it neither dissolves more of the substance nor deposits any of that already in solution, it is a saturated solution. If in contact with some of the undissolved substance it deposits some of the substance already in solution, it is a supersaturated solution. Supersaturated 188 THE ELEMENTS OF PHYSICAL CHEMISTRY solutions are formed most readily by salts which crystallize with water of crystallization. A number of anhydrous salts can also form supersaturated solutions. The general effect of temperature on solubility has been indicated. The solubility of most substances in most solvents increases with rise in temperature. This, however, is not always true. In some cases solubility decreases with rise in temperature. The best exam- ples are found among the salts of the organic acids, and of these we should mention especially the calcium salts. When a saturated solution of a calcium salt, say of citric acid, is heated to a higher temperature than that at which it was saturated, some of the salt in solution is deposited as a precipitate. When the solution cools again the precipitate redissolves. Similar results are obtained with salts of other metals and other acids. The decrease in solubility with rise in temperature is well illustrated by some of the cyanides. Much work has been done on the properties of solutions in liquids as solvents, and some of the most important results in physical chemistry have been obtained in this field. We shall now take up at some length the more important of these investigations, and show the bearing of some of the results obtained, and conclusions which have been reached. OSMOTIC PRESSURE Osmotic Pressure. — If a solution of a substance in a solvent is placed in a vessel, and over this solution the pure solvent is poured, we shall find after a time that the substance is not all contained in that part of the solvent in which it was originally present, but a part of it has passed into the layer of the pure solvent which was poured upon the solution. This shows that there is some force analogous to a pressure, driving the dissolved substance from one region to another, from the more concentrated to the less concen- trated solution. This pressure has been termed osmotic pressure. Demonstration of Osmotic Pressure. — The existence of this press- ure was early recognized. Abbe" Nollet demonstrated its existence about the middle of the eighteenth century. A glass tube closed at the bottom with animal parchment was filled with ordinary alcohol, and the tube then immersed in water. Water could pass in through this parchment, but alcohol could not pass out. The contents of such a tube gradually increased in volume, showing to the eye the existence of osmotic pressure. During the first three-fourths of the last century osmotic pressure was demonstrated by filling an animal bladder with an aqueous solution of alcohol and immersing the SOLUTIONS 189 bladder in water. The water passed into the bladder and the alco- hol could not pass out in any quantity. Hence, the bladder became distended and finally burst. It will be observed that in all of these experiments recourse was had to animal membranes. A discovery was subsequently made which has entirely done away with the use of natural membranes in demonstrating osmotic pressure. These membranes, which have the property of allowing the sol- vent to pass through them, and of preventing the dissolved substance from passing, are known as semipermeable. It was M. Traube * who first prepared such semi-permeable membranes artificially. He found that certain precipitates, deposited in a suitable manner, have the property of allowing the solvent to pass through them, but hold back the dissolved substance. These precipitates include copper ferrocyanide, and a number of similar gelatinous substances. A good method of demonstrating osmotic pressure, now that we can prepare artificial membranes, is the following. A glass tube about 2 cm. in diameter and 8 to 10 cm. long, is tightly closed at the bottom with vegetable parchment. This is soaked in water for some hours so as to drive out air-bubbles. The top of the glass tube is tightly closed with a rubber stopper, through which is passed a fine capillary tube about a metre in length. The end of the capillary should just pass through the cork, but must not protrude beyond its lower sur- face. The large glass tube is now immersed in a beaker which is sufficiently deep to receive the entire tube. The tube is then firmly clamped in a vertical position. The beaker is filled with a three per cent solution of copper sulphate. The cork is then removed from the tube, and the latter completely filled with a three per cent solution of potassium ferrocyanide, to which enough potassium nitrate has been added to make from a one to a two per cent solution. The tube is then closed as tightly as possible with the cork through which the capillary passes, care being taken that no air-bubble remains beneath the cork. The apparatus is then set in a quiet place for some days. After a day or two, if the experiment is successful, the liquid will begin to rise in the capillary, and may reach a height of from 40 to 50 cm. The experience of the writer has been that not all such experi- ments succeed. Indeed, the number which give a good demonstra- tion of osmotic pressure is only about one-third of the total attempts which he has made. The frequent failure is doubtless due in part to the nature of the parchment used. The method by which the semi-permeable membrane is formed in 1 Archivf. Anat. und Physiol., p. 87 (1867). 190 THE ELEMENTS OF PHYSICAL CHEMISTRY this case is almost self-evident. The copper sulphate from below passes into the parchment, and the potassium ferrocyanide from above also enters the parchment. The two meet right in the walls of the vegetable parchment. At the surface of contact they form the gelatinous precipitate of copper ferrocyanide in the walls of the parchment. The precipitate, deposited in this manner, has the property of semi-permeability — it allows the water to pass through and prevents the dissolved substances from passing. Since osmotic pressure always acts so that water passes from the more dilute to the more concentrated solution, the flow of water in this case is from the copper sulphate on the outside to the potassium ferrocyanide and potassium nitrate on the inside. The liquid rises in the capillary due to the inflow of water through the semi-permeable membrane. Morse's Method of preparing Semi-permeable Membranes. — The measuring of osmotic pressure has now become a fairly simple matter, due to a method devised in this laboratory by Morse, and developed by Morse and Horn. 1 They state the object they had in mind in the following words : — " It occurred to the authors that if a solution of a copper salt and one of potassium ferrocyanide are separated by a porous wall which is filled with water, and a current is passed from an electrode in the former to another electrode in the latter solution, the copper and the ferrocyanogen ions must meet in the interior of the wall and sepa- rate as copper ferrocyanide at all points of meeting, so that in the end there should be built up a continuous membrane well supported on either side by the material of the wall. The results of our experi- ments in this direction appear to have justified the expectation." In order to remove the air contained in the walls of the cup they made use " of the strong endosmose which appears when a current is passed through a porous wall separating two portions of a dilute solu- tion in which the two electrodes are immersed." A dilute boiled solution of potassium sulphate was used for this purpose. " On pass- ing the current between the electrodes in the direction of the one within the cup, the liquid in the cup rises with a rapidity which increases with the dilution of the solution, and with the intensity of the current. The water, in passing through the wall, appears to sweep out the air in an effective manner." Having removed the air by means of endosmosis, the membrane was formed by filling the cup with a tenth-normal solution of potassium ferrocyanide, and immersing it in a tenth-normal solution of copper sulphate. One electrode of platinum was inserted into the cup, and the i Arner. Chem. Jour. 26, 80 (1901). SOLUTIONS 191 other of sheet copper completely surrounded the cup. The current was passed from the copper to the platinum electrode. As soon as the copper ions, moving with the current, come in contact with the Fe(CN) 6 ions moving against the current, a precipitate of copper ferro- cyanide was formed within the wall 1 of the cup. This gradually became more compact, as was shown by the fact that the resistance offered to the passage of the current rapidly increased. The advantage of driving the ions into the wall by means of the current is that the membrane can be formed much more compactly than by simply allowing them to pass into the wall by diffusion. With such a cell it is possible to demonstrate osmotic pressure in a most satisfactory manner. When the cell is filled with a normal solution of cane sugar, closed with a cork through which a capillary manometer passes, and immersed in pure water, the liquid will rise in the capillary at the rate of more than a foot an hour, and in one day a pressure of thirty feet of the sugar solution is easily secured. This so far surpasses all other demonstrations of osmotic pressure thus far devised, that they become insignificant by comparison. The demonstration of osmotic pressure on the lecture table by means of this method has become as simple a matter as many of the daily experiments in inorganic and organic chemistry. This method promises much for the quantitative study of osmotic pressure. The ease with which the cells can be prepared, and the great resistance offered by the membranes formed by the electrical method, bid fair to open up new possibilities in connection with the direct measurement of osmotic pressure. 2 Morse, Frazer, and their coworkers have measured the osmotic pressure of a number of solu- tions of cane sugar and glucose. Work along this line is now in progress and some of the results obtained are given in a later section. Measurement of Osmotic Pressure. — The most accurate quantita- tive method of measuring osmotic pressure until recently, was devised and used by W. Pfeffer. 3 He made use of the artificial membranes which had been discovered by Traube, and deposited them upon a support which was sufficiently resistant to enable them to withstand considerable pressure. An account of the apparatus used by Pfeffer and the method which he employed will be given in his own words : * "I obtained the first favorable results by proceed- 1 In very hard-burned cups the membrane forms on the inner surface of the cup. 2 Amer. Ohem. Jour. 34, 1 (1906); 36, 1 (1906). 8 Osmotische Untersuchungen. Leipzig, 1877. i Ibid. pp. 4-6, 7-8, 20. Scientific Memoirs Series, IV, 4-5. Edited by Prof. J. S. Ames. (Published by Amer. Book Co.) 192 THE ELEMENTS OF PHYSICAL CHEMISTRY ing as follows : I took [unglazedj porcelain cells, such as are used for electric batteries, and, after suitably closing them, I first injected them carefully with water, and then placed them in a solution of copper sulphate, which, either im- mediately or after a short time, I introduced into the interior of a solu- tion of potassium ferrocyanide. The two membrane-formers now pene- trate diosmotically the porcelain wall separating them, and form, where they meet, a precipitated membrane of copper ferrocyanide. This ap- pears, by virtue of its reddish brown color, as a very fine line in the white porcelain which remains color- less at all other places, since the membrane, once formed, prevents the substances which formed it from passing through. "In Fig. 1 the apparatus ready for use, with the manometer (m) for measuring the pressure, is shown, at approximately one-half the nat- ural size. "The porcelain cell z and the glass pieces v and t, inserted in posi- tion, are shown in median longitu- dinal section. The porcelain cells which I used were on the average, approximately 46 mm. high, were about 16 mm. internal diameter, and the walls were from 1\ to 2 mm. thick. The narrow glass tube v, called the connecting-piece, was fastened into the porcelain cell with fused sealing-wax, and the closing-piece t was set into the other end of this tube in the same manner. The shape and purpose of this are shown in the figure." To give some idea of the great number of details which must be followed out in order to prepare a good cell for measuring osmotic pressure the following paragraphs are quoted from Pfeffer's mono- graph : — Fig. 20. SOLUTIONS 193 "All 1 porcelain cells were treated first with dilute potassium hydroxide, and then with dilute hydrochloric acid (about 3 per cent), and after being well washed were again completely dried before they were closed, as already described. Substances which are soluble in these reagents, such as oxides and iron, which under certain conditions can do harm, would thus be removed. " After the apparatus was closed the precipitated membrane was formed either in the wall or upon the surface, according to the prin- ciple already indicated. In order that this should be done success- fully, a number of precautionary measures are necessary, and these will now be discussed. Since I experimented chiefly with mem- branes of copper ferrocyanide, which were deposited upon the inner surface of porcelain cells, I will fix attention especially upon this case. " The porcelain cells were first completely injected with water under the air-pump, and then placed for at least some hours in a solution containing 3 per cent of copper sulphate, and the interior was also filled with this solution. The interior of the porcelain cell was then rinsed out once quickly with water, well dried as quickly as possible by introducing strips of filter paper, and after the outside had dried off somewhat, it was allowed to stand some time in the air until it just felt moist. Then a- 3 per cent solution of potassium ferrocyanide was poured into the cell, and this immediately reintro- duced into the solution of copper sulphate. " After the cell had stood for from twenty-four to forty-eight hours undisturbed, it was completely filled with the solution of potassium ferrocyanide and closed as shown in Fig. 1. A certain excess of pressure of the contents of the cell now gradually mani- fested itself, since the solution of potassium ferrocyanide had a greater osmotic pressure than the solution of copper sulphate. After another twenty-four to forty-eight hours the apparatus was again opened, and generally a solution introduced which contained 3 per cent of potassium ferrocyanide and 1\ per cent of potassium nitrate, and which showed an excess of osmotic pressure of somewhat more than three atmospheres.'' If all of these details are carefully observed and suitable fine- grained porcelain cells are chosen, the preparation of good semi-per- meable membranes offers no serious difficulty. Pfeffer states that he prepared twenty such cells almost without a failure. The measurements of osmotic pressure were made by means of these porcelain cells lined with the precipitate which formed the semi-permeable membrane. After the manometer was attached to 1 Scientific Memoirs Series, IV, 6-7. Edited by Ames (Amer. Book Co.). o 194 THE ELEMENTS OF PHYSICAL CHEMISTRY the cell, the latter was filled with the solution whose osmotic pressure was to be measured. The cell was then tightly- closed and fastened to a glass rod as seen in figure. The whole cell, including the manometer, was intro- duced into a bath as shown in the figure. The bath was filled with pure water, and the osmotic pressure of the solution against pure water measured on the mercury- manometer. Special precau- tions were taken to keep the temperature of the whole apparatus constant, since, as we shall see, there is a large temperature coefficient of osmotic pressure. The tem- perature of the experiment was accurately determined by means of carefully stand- ardized thermometers. Some of Ffeffer's Results. — Pfeffer measured the os- motic pressure of solutions of a number of substances at different concentrations. With cane sugar he obtained the following results for dilutions ranging from one to six per cent, keeping the temperature as nearly- constant as possible. The temperature for the series ranged from 13°.5 to 14°.7. Fig. 21. c = CONCENTRATION IN PER p P Cent by Weight 1 Osmotic Pressure C 1 per cent 53.5 cm. 53.5 2 per cent 101.6 cm. 50.8 4 per cent 208.2 cm. 52.0 6 per cent 307.5 cm. 51.2 Osmotiscke Untersuchungen (1877), p. 110. SOLUTIONS 195 From these results it would appear that osmotic pressure is'propor. p tional to the concentration of the solution, since — = a constant, or C very nearly a constant. The deviation from a constant is so slight that it is evidently due to experimental error. The following results were obtained with potassium nitrate : — C = Concentration in Per Cent by Weight 1 p Osmotic Presbure P C 0.80 per cent 1.43 per cent 3.3 per cent 130.4 cm. 218.5 cm. 436.8 cm. 163.0 152.8 132.4 The ratio of pressure to concentration decreases as the concentration increases in this case. These results are, however, not very accurate, since the membrane used by Pfeffer was not entirely impervious to potassium nitrate. Pfeffer also studied the effect of temperature on osmotic pressure. He took a given solution and measured its osmotic pressure at different temperatures, and in this way worked out the temperature coefficient of osmotic pressure. The following results were obtained with a one per cent solution of cane sugar : — Temperature 6°. 8 13°.2 14°.2 22°.0 36°.0 Osmotic Pressure 50.5 cm. 52.1 cm. 53.1 cm. 54.8 cm. 56.7 cm. It is obvious from these results that the osmotic pressure of such a solution increases with rise in temperature. Similar results were obtained with sodium tartrate : — Temperature 13°.3 36°. 6 Osmotic Pressure 147.6 cm. 156.4 cm. Effect of the Mature of the Membrane on Osmotic Pressure. — The effect of the nature of the semi-permeable membrane on the magni- tude of the osmotic pressure was also investigated by Pfeffer. 2 In addition to copper ferrocyanide, he used membranes of Prussian blue and calcium phosphate. It will be observed that all of these sub- Osmotische Untersuchungen, p. 113. : Ibid. p. 116. 196 THE ELEMENTS OF PHYSICAL CHEMISTRY stances are gelatinous precipitates like copper ferrocyanide. Pfeffer found an osmotic pressure of only 38.7 cm. for a one per cent solu- tion of cane sugar when Prussian blue was used as the membrane, and only 36.1 cm. when calcium phosphate was employed. From these results it would seem at first sight that the nature of the membrane had an influence on the magnitude of the osmotic pressure. The real explanation of these differences is, however, quite different. The membranes of Berlin blue and calcium phosphate were not sufficiently resistant to withstand the pressure, consequently they would leak, and the true value of the maximum pressure was never shown by the manometer. This conclusion was made very probable by the behavior of these membranes during the experiments. Of all the membranes tried by Pfeffer, only copper ferrocyanide was capable of withstanding the pressure, and only those results which were obtained with this membrane can be regarded as the true expressions of the osmotic pressures of the solutions employed. Further, Ostwald * has devised an ingenious method for proving theoretically that the osmotic pressure of a solution is independent of the nature of the membrane used in measuring it. Given the cylinder, Fig. 22. Introduce two semi-permeable membranes, M x and M 2 , as shown in the drawing. The space between the membranes contains the solu- tion, the two spaces, A and B, the pure solvent. Let us first suppose that the osmotic pressure at M x is greater than at M 2 . Let us call the first pressure p v and the second pressure p 2 . The solvent will pass in through both membranes M M Fig. 22. until the pressure p* is reached. Then the solvent will cease to flow in through A M 2 , but will continue to enter through Mi. As soon as the pressure in the solution be- tween the membranes exceeds p 2 , the solvent will flow out through the membrane M 2 , and will continue to flow in through M v Since the pressure could, then, never rise to p„ the solvent will continue to flow in through M x forever, and to flow out through M 2 . We would thus have perpetual motion, which is impossible. Suppose we assume, on the other hand, that p 2 is greater than p x , by an exactly similar line of reasoning it is shown that we would then have a continual flow of the solvent through the cylinder from right to left — the reverse of 1 Lehrb. d. Allg. Chem. I, p. 662. SOLUTIONS 197 the first direction. Again, we would have perpetual motion, which is impossible. Therefore, since p 1 cannot be greater nor less than jo 2 , it must be equal to it. In a word, the osmotic pressure of a solution is independent of the nature of the membrane used in measuring it. It is, of course, assumed in this discussion that the dissolved substance is such as would not act chemically upon the membrane. If there was any chemical action, the membrane would be destroyed at once and the experiment ruined. The quantitative measurements of the absolute osmotic pressure of solutions made by Pfeffer are the best up to the present. Indeed, very little has been done along this line since Pfeffer ended his work. We should, however, mention in this connection the work of Adie. 1 Measurement of the Relative Osmotic Pressures of Solutions. — While but little work has been done recently on the absolute osmotic pressures of solutions, probably on account of the difficulties involved in such work, much has been done on the relative osmotic pressures exerted by different substances. A number of new methods have been devised for measuring relative osmotic pressures, and some of these, together with the results obtained, we shall now consider. Method employing Vegetable Cells. — The method is based upon the preparation of solutions of different substances, each of which will have the same osmotic pressure as the contents of cells of certain plants ; and, therefore, the same osmotic pressure as one another. The difficulty is to determine just when the solution around the cell has the same osmotic pressure as the contents of the cell itself. This has been accomplished by the Dutch botanist De Vries, 2 to whom the method with which we shall now deal is due. He found three plants which fulfil the conditions necessary to success, — Trades- cantia discolor, Curcuma rubricaulis, and Begonia manicata. The cells of these plants are four to six sided. The cell-walls are strong and resistant, and do not change their size or shape when the cell is im- mersed in solutions of other substances. These walls are easily permeable to water and aqueous solutions. The cell-walls are lined on the inside with a very thin, colorless membrane, which is filled with the colored contents of the cell. This membrane is semi-perme- able, allowing water to pass, but holding back the dissolved sub- stance. The contents of the cell is an aqueous solution of glucose, potassium and calcium malate, coloring matter, etc., having an osmotic pressure of from four to six atmospheres. The semi-perme- 1 Chem. IVeivs, 63, 123 (1891). Proc. Chem. Soc. 344 (1891). 2 Ztschr. phys. Chem. 2, 415 (1888); 3, 103 (1889). 198 THE ELEMENTS OF PHYSICAL CHEMISTRY able membrane lining the cell- wall distends when the contents of the cell increases in volume, and contracts when the volume of the contents diminishes. The method of determining the relative osmotic pressure of the contents of the cell and of the solution in which it is placed will be readily understood from the foregoing description of the cell. Thin tangential sections are taken from the middle rib on the under side of the leaf of Tradescantia 1 containing a few hundred living cells. This section is placed under the microscope, and the cells surrounded by the solution whose osmotic pressure it is desired to compare with that of the contents of the cells. In such a preparation, all of the cells have the same osmotic pressure, since any differences would have equalized themselves in the plant. It is then only necessary to compare the osmotic pressure of the solution with that of any one of the cells present. A B ,. C Fig. 23. When the cell' is immersed in a solution having the same osmotic pressure as the contents of the cell, the cell has the normal appear- . ance as shown in A in the figure. When the cell is immersed in a solution having a smaller osmotic pressure than its own con- tents, it will also have the appearance of A, in the figure. Water will pass from the solution through the semi-permeable membrane into the cell, and tend to distend it. But the resistant cell-wall will prevent any appreciable distention, and, consequently, the cell will appear about as a normal cell. If, on the other hand, the cell is immersed in a solution having greater osmotic pressure than its own contents, water will pass from the cell through the membrane out into the solution. The cell contents, having lost water, will contract 1 Cells are taken from other places in different plants. SOLUTIONS 199 as shown in B and C in the figure ; the semi-permeable membrane will also contract and follow the cell contents, and this contraction can readily be seen since the cell contents are colored. By starting with a solution whose osmotic pressure is greater than that of the cell, shown by the contracting of the cell contents when the cell is sur- rounded by the solution, and continually diluting it, noting its action on the cell at every stage of dilution, a solution is finally reached in which the cell will just preserve its normal form. The solution then has the same osmotic pressure as the contents of the cell. The solu- tion can then be analyzed and its strength determined. In an exactly similar manner solutions of other substances can be prepared, each having the same osmotic pressure as the contents of the cell, and these solutions analyzed and their strengths determined. Since each of these solutions has the same osmotic pressure as the contents of the cell, they have the same osmotic pressure. This method can, of course, be applied only to those substances which do not act chemi- cally on the delicate membranes which surround such plant cells. This method has been called by De Vries the plasmolytic. He 1 de- termined the concentrations of quite a large number of substances which were isosmotic with the cell contents. These isosmotic or isotonic concentrations were expressed in gram-molecular quantities, and their reciprocal values were termed the isotonic coefficients of the substances. These isotonic coefficients show at once the relative osmotic pressures of solutions of equal molecular concentration. The isotonic coefficient of potassium nitrate is taken as 3. A few of De Vries' results are given for future reference. Substance Formula Isotonic Coefficient Glycerol CsHg08 1.78 Invert sugar CeHjsOe 1.81 Cane sugar . C12H22O11 1.88 Malic acid . C 4 H 6 6 1.98 Tartaric acid C4H6U6 2.02 Citric acid . CeHgC^ 2.02 Potassium nitrate KN0 8 3.00 Sodium chloride . NaCl 3.05 Potassium acetate C2H3O2K. 3.00 Calcium chloride . CaCl 2 4.33 Magnesium chloride MgCl 2 4.33 Potassium citrate . C 8 H 6 7 K 5.01 1 Ztschr.phys. Chem. 2, 427 (1888) ; 3, 103 (1889). 200 THE ELEMENTS OF PHYSICAL CHEMISTRY An examination of these results shows certain relations which we shall learn are very important. The neutral organic substances and the weak organic acids have isotonic coefficients which are about con- stant, and which have the value of approximately 2. The salts have much higher coefficients — ranging from 3 to 5. The meaning of these facts will appear in due time. Method employing Animal Cells. — We have seen above how vege- table cells can be used to measure relative osmotic pressures. We can use certain cells of animals for the same purpose. Hamburger : has used the red blood corpuscles of the deer and frog. If to defibri- nated deer's blood a solution of potassium nitrate, 1.04 per cent, is added, the red blood corpuscles will settle completely to the bottom and will be covered by a clear, almost colorless liquid. If the solu- tion of potassium nitrate has a concentration of 0.96 per cent, or less, the separation into the two layers is not complete. The corpuscles do not settle to the bottom completely, and, consequently, the super- natant liquid is somewhat colored — the more deeply colored the more dilute the solution of potassium nitrate added. By proceeding carefully, a solution of potassium nitrate can be found in which the red corpuscles will just settle to the bottom. Similarly, solutions of other substances can be prepared of such a concentration that the red blood corpuscles will just settle and leave a clear liquid above them. Such solutions have the same osmotic pressure; and from these data it is evident that the isotonic coefficients of substances can be calculated, as from the results obtained by De Vries using vege- table cells. Without giving the results of Hamburger in detail, it may be stated that the isotonic coefficients which he found, agree with those obtained by De Vries to within the limits of error of the two methods. Reference only can be made to the work of others, 2 in which red blood corpuscles were used. Method in which Bacteria are used. — We have seen how both vegetable and animal cells can be used to determine relative osmotic pressure. We shall now see that cells which are neither the one nor the other, or perhaps both, can also be used in this connection. Wladimiroff s has used certain forms of bacteria, such as Bacterium Zopfii, Bacillus subtilis, Bacillus Typhi abdominalis, Spirillum rvforum, etc. The movements of the bacteria were found to be very different in solutions of the same substance of different concentra- 1 Ztschr. phys. Chem. 6, 319 (1890). 2 W. Loeb : Ibid. 14, 424 (1894). H. Koppe : Ibid. 16, 261 (1895). S. G. Hedin: Ibid. 17, 164 ; 21, 272 (1895 and 1896). 3 Ibid. 7,529(1891). SOLUTIONS 201 tions. If we start with a very dilute solution and continually increase its strength, the movements of the bacteria become slower and slower. Solutions of different substances were prepared of such strengths that they had the same influence on a given kind of bac- teria, and then their relative concentrations determined. The con- clusions reached by Wladimiroff were, that although certain neutral salts seem to have a poisonous action on some bacteria, and certain salts could enter the protoplasm of other bacteria, yet most of the relations investigated between salts and bacteria agreed with the laws of osmosis as established by entirely different methods. Method of Tammann. — It still remains to describe a method which differs fundamentally from the three just considered. In these three methods the semi-permeable membrane was of living substance. The semi-permeable membrane in the optical method is an inorganic pre- cipitate and, indeed, the same precipitate as was used by Pfeffer in preparing his porcelain cells. If a drop of a solution of potassium f errocyanide is allowed to fall into a solution of copper sulphate, the drop becomes completely surrounded with a precipitate of copper ferrocyanide, and this precipitate, as we have seen, forms the very best semi-permeable membrane. We would have, then, a drop of a solution of potassium ferrocyanide surrounded by a semi-permeable membrane, and this in contact with a solution of copper sulphate. If the solution of potassium ferrocyanide is more dilute than that of copper sulphate, water will pass out into the copper sulphate, dilute it just around the drop, and, consequently, produce a current of the more dilute solution upward from the drop. If, on the contrary, the contents of the drop are more concentrated than the solution of copper sulphate, water will pass from the copper sulphate through the membrane into the solution of potassium ferrocyanide. The solution of copper sulphate just around the drop will thus become more concentrated, and because of its greater specific gravity, will sink to the bottom. It is, then, only necessary to observe whether the current rises or falls from the drop, to determine the relative concentrations of the two solutions. In these observations a refrac- tometer is used, slight currents being detected by the different refrac- tivities. It is, of course, possible to prepare the two solutions of such concentrations that water will pass neither the one way nor the other. The two solutions would then have the same osmotic pressure. It is thus quite possible to prepare solutions of ferrocyanides which are isosmotic with copper and zinc salts. The work of Tammann, 1 i Wied. Ann. 34, 299 (1888). 202 THE ELEMENTS OF PHYSICAL CHEMISTRY who devised this method, was limited to these substances. It has, however, been extended more recently to a third substance added to the other two, provided the third substance does not act chemically upon either of the others. This method is obviously sub- ject to narrower limitations than any of those previously considered; the methods involving the use of living membranes being applicable to all substances which do not act upon the cells and destroy them. A careful study of the best methods available for measuring osmotic pressure will undoubtedly leave the impression that this is a quantity with which it is difficult to deal experimentally. While it is possible to prepare good cells according to the method worked out by Pfeffer, yet much time and experience are necessary to secure fair results. And further, the best that has been accomplished up to the present is to measure the osmotic pressure of comparatively dilute solutions. Pfeffer's work was limited to a six per cent solu- tion of cane sugar, — less than one-fifth normal, — and no one has since been able to work at greater concentrations. To determine the absolute osmotic pressure of more concentrated solutions, 1 it is evi- dent that some indirect method must be applied, since thus far it has been scarcely possible to prepare membranes which shall be able to withstand, without rupture, a pressure of many atmospheres. It should be stated again that the method of Morse, already described, promises much in this direction. Eelations have, however, been established between the osmotic pressure of solutions and certain other properties which can be readily dealt with experimentally. As we shall see, by measuring certain other quantities we can easily calculate the osmotic pressure of solu- tions which are far too concentrated, and whose osmotic pressures are far too great to measure directly. These matters will be further discussed in the proper places. RELATIONS BETWEEN OSMOTIC PRESSURE AND GAS- PRESSURE Pfeffer carried out the measurements already referred to, and doubtless saw their physiological significance, but he did not point out any relations between osmotic pressure and gas-pressure. This, like so many other brilliant discoveries, was reserved for Van't Hoff. In his epoch-making paper, 1 which has contributed more toward the development of the new physical chemistry than any other one 1 Ztschr.phys. Chem. 1, 481 (1887). Scientific Memoirs Series, IV, p. 13. SOLUTIONS 203 article, he points out a number of surprisingly simple relations, and some of these will now be taken up. Boyle's Law for Osmotic Pressure. — The law of Boyle for gases states that the pressure of a gas varies directly as the concentration of the gas. We have seen from Pfeffer's results, that the osmotic pressure of a solution varies directly with the concentration. This p is shown by the fact that — is a constant, to within the limits of \j experimental error. This relation for the osmotic pressure of solu- tions certainly suggests the relation for gases expressed by the law of Boyle. Van't Hoff also points out that the work of De Vries leads to the same conclusion. De Vries took solutions of potassium nitrate, potassium sulphate, and cane sugar, and determined the concentra- tions which were isosmotic or isotonic with the contents of a given cell. He then used cells of other plants and determined the isos- motic concentrations of these substances. Four such isotonic series were worked out. The results are given below, the concentrations being expressed in gram-molecules per litre, the unit being potas- sium nitrate. Series KNO, K 2 SO, C w H 2I O u I 1 0.75 II 1 0.77 1.54 III 1 0.77 1.54 IV 1 — 1.54 The relation between the concentrations which have the same osmotic pressure is constant, independent of the actual value of the concentrations. This is but another expression of the law of Boyle as applied to the osmotic pressure of solutions. Gay-Iussac's Law for Osmotic Pressure. — According to the law of Gay-Lussac the pressure of a gas increases with the temperature, at the rate of -^ts f° r every rise of one degree centigrade. Pfeffer's results show that the osmotic pressure of a solution increases with rise in temperature, and the rate of increase is very nearly -^-^ for every degree. Pfeffer did not make an extensive study of the tem- perature coefficient of osmotic pressure, but as far as his results go they lead to the conclusion stated above. If we examine the effect of temperature on osmotic pressure, as shown on page 186, we shall see that this conclusion is, in general, confirmed. 204 THE ELEMENTS OF PHYSICAL CHEMISTRY If the law of Gay-Lussac applies to the osmotic pressure of solutions, then solutions which are isosmotic at one temperature must remain isosmotic at other temperatures, since they would have the same temperature coefficient of osmotic pressure. This has been tested by the methods for determining relative osmotic pressures. Hamburger, using the method already referred to as involving red blood corpuscles, found that solutions of potassium nitrate, sodium chloride, and cane sugar, which were isosmotic at 0°, were also isos- motic at 34°. There is, however, a still more striking experimental verification of the applicability of the law of Gay-Lussac to Solutions. If a tube is filled with a gas and all parts of the tube kept at the same temper- ature, the concentration of the gas will be the same in every part of the tube. If, on the other hand, one portion of the tube is kept warmer than the others, the gas will so distribute itself through- out the tube that the pressure will remain the same in all parts of the tube. Since the pressure of a gas increases with the temperature, each particle will exert a greater pressure in the warmer region, and, consequently, there will be fewer particles required in the warmer portion of the tube to exert the same pressure as exists in the colder portion. In a word, the gas would tend to become more concentrated in the colder portion, and more dilute in the warmer portion of the tube. 1 If the osmotic pressure of solutions obeys the laws of gas"-press- ure, a phenomenon similar to the above should be observed with solutions, and such is the fact. If the two parts of a perfectly homo- geneous solution are kept at different temperatures for any consider- able length of time, the solution becomes more concentrated in the region which is colder. This has come to be known from its discov- erer as the principle of Soret. 2 This principle is of the very greatest importance in testing the law of Gay-Lussac for osmotic pressure. If this law holds, then the colder portion of the solution should become more concentrated by yts ^ or every difference of one degree in temperature. This could be easily tested by experiment. The experiments were carried out by Soret by placing the solutions in vertical tubes, in such a manner that the upper portions of the tubes were warmed to a constant temperature, and the lower portions cooled to a constant temperature. The earlier experiments of Soret gave a 1 It should, of course, be remembered that the condition described for a gas Js somewhat ideal. The gas particles, due to their rapid movement, would mix, but the principle which it is desired to illustrate holds good. a Ann. Chim. Phys. [6], 22, 293 (1881). SOLUTIONS 205 difference in concentration which was not quite as great as that calculated from the law of Gay-Lussac. His later experiments, in which the solutions were allowed to stand at constant temperatures for a longer time, gave differences which, while a little too low, yet accorded very nearly with the theory. A slight difference between calculated and experimental values creates no surprise when we con- sider that the solutions must stand for months at the constant tem- peratures in order that equilibrium may be reached, and some mixing of the parts due to agitation or jarring is, therefore, unavoidable. The agreement is, however, so close that it is now quite certain that the principle of Soret furnishes the best proof of the applicability of the law of Gay-Lussac to the osmotic pressure of solutions. Avogadro's Law applied to the Osmotic Pressure of Solutions. — The applicability of the laws of Boyle and Gay-Lussac to the osmotic pressure of solutions, shows that this quantity is analogous to gas- pressure. It, however, leaves the question as to the relative magni-. tudes of the two pressures entirely unanswered. The one might be very large and the other very small, and still the two laws which we have just considered apply to both. We now come to the question, is there any close relation between the magnitudes of the two press- ures exerted under comparable conditions ? The law of Avogadro, applied to gases, states that in equal volumes of all gases at the same temperature and pressure, there are the same number of ultimate parts. If the law of Avogadro applied to solutions it would be stated thus, in equal volumes of solutions which, at the same temperature have the same osmotic press- ure, there are contained the same number of dissolved particles. The simplest way in which this law can be tested for solutions is to see what relation exists between the gas-pressure of a gas particle and the osmotic pressure of a dissolved particle under the same conditions of temperature and concentration. Let us compare the gas-pressure of hydrogen gas and the osmotic pressure of cane sugar in water. Given a one per cent solution of cane sugar ; such a solution would contain one gram of sugar in 100.6 cc. of water, and the osmotic pressure of such a solution can be calculated from Pfeffer's results. Hydrogen gas, having the same number of parts in a given volume, would have the following pressure : The molecular weight of cane sugar is 342, that of hydrogen 2. The hydrogen gas must, therefore, contain ^f^ grams in 100.6 cm., which is the same as 0.0581 grams per litre. Hydrogen gas at 0°, and at a pressure of one atmosphere, weighs per litre 0.08995 grams ; the above concentration of hydrogen gas will, therefore, exert a gas-pressure of ^e QQ - = 0.646 atmos- phere at 0°. °- 08 " 5 206 THE ELEMENTS OF PHYSICAL CHEMISTRY It is now only necessary to compare the osmotic pressure exerted by the cane sugar with this gas-pressure, to see if any simple rela- tions exist between the two. The following table of results is taken from the paper by Van'fc Hoff : 1 — Temperature Osmotic Pressure of Cane Sugar Gas-prebsure op Hydrogen Gas 6° .8 13°.7 15°.5 36°.0 0.664 0.691 0.684 0.746 0.665 0.681 0.686 0.735 The remarkable fact is established by these results that the osmotic pressure of a solution of cane sugar is exactly equal to the gas-pressure of a gas having the same number of parts in a given volume, temperature being the same in both cases. Under the same conditions, then, a dissolved particle exerts the same osmotic press- ure as a gas particle exerts gas-pressure. Causes of Gas-pressure and of Osmotic Pressure. — That there should be an equality between these two pressures is very surpris- ing, if we consider the great difference between the phenomena with which we are dealing. Gas-pressure is explained in terms of the kinetic theory of gases, as due to the particles of gas bombarding "against the walls of the confining vessel. It should be stated that we do not know what is the cause of osmotic pressure. A great number of explanations and theories have been offered to account for osmotic pressure, but in the opinion of the writer no one of them is at all satisfactory. Some have attempted to account for osmotic pressure by the attraction of water by the dissolved substance, but this is only a renaming of the phenomenon, and in no sense an explanation of it. Others have suggested that water passes through the semi-permeable membrane from the more dilute to the more con- centrated solution, because of the screening action of the dissolved particles. These cannot pass through the membrane, and, therefore, screen it from the blows of the solvent. Since the greater screening influence is exerted on the side containing the larger number of dis- solved particles, we have the flow of the solvent from the more dilute to the more concentrated solution. A careful analysis of this explanation shows that it is not sufficient. The screening influence of the dissolved particles would be just as great below, keeping the Ztschr.phys. Chem. 1, 493 (1887). SOLUTIONS 207 water which has passed through the membrane from rising, as it is above, since the membrane is quite permeable to water. There is a strong tendency at present to refer osmotic phenomena to surface- tension, and this is probably the key to the solution of the problem. 1 Exceptions to the Applicability of the Gas Laws to Osmotic Press- ure. — We have just seen that the three best known laws of gas- pressure apply to the osmotic pressure of solutions of substances like cane sugar. We might conclude from this that the laws of gas- pressure always apply to the osmotic pressure of solutions of all substances. Such is not the case. Van't Hoff 1 pointed out that there are not only exceptions to this generalization, but a great many exceptions. Indeed, the substances which present exceptions are quite as numerous as those which conform to the rule. The osmotic pressure of most salts, of all the strong acids, and all the strong bases, is much greater for all concentrations than would be expected from the osmotic pressure of solutions of substances like cane sugar for the same concentrations. The osmotic pressures of these three classes of substances are always greater than would be expected from the laws of gas-pressure applied to the osmotic pressure of solutions. The general expression for the laws of Boyle and Gay-Lussac is, as we have seen (page 45) — pv = BT. t This applies directly to the osmotic pressure of solutions of sub- stances like cane sugar. But in order that it may apply to solutions of salts, acids, and bases, a coefficient must be introduced, which, for these substances, is always greater than unity. This coefficient was called by Van't Hoff i, and it has come to be known as the Van't Hoff i. The above expression when applied to acids, bases, and salts becomes— pv =iRT. While these exceptions were clearly recognized by Van't Hoff, he was unable to explain them, or to offer any satisfactory theory to account for them. In this case, as in so many others, the exceptions are as interesting and important as the cases which conform to rule. We shall see that these exceptions led to a theory which is one of the most im- portant in modern chemical science, and which, together with the relations between gas-pressure and osmotic pressure just considered, constitutes the corner-stone of modern physical chemistry. 1 See Lovelace : Amer. Chem. Journ. 39, 546 (1908). 208 THE ELEMENTS OF PHYSICAL CHEMISTRY The paper which we have just considered is of such fundamental importance that it is difficult to lay too much stress upon it. As the subject develops we shall see its bearing at every turn, and shall learn to regard it as, indeed, epoeh-making in the highest sense, — as a monumental contribution to science in the last part of the nineteenth century. It is always of interest to follow the line of thought which leads to any great discovery. The steps by which Van't Hoff was brought in contact with the work of Pfeffer on osmotic pressure, and was led to the study of dilute solutions from this standpoint, were developed in full by Van't Hoff in a lecture before the German Chemical Society in 1894, and which appeared in the Berichte, Vol. 27, 6. A brief account of this lecture was given by the present writer in his Tlieory of Electrolytic Dissociation, p. 77. ORIGIN OF THE THEORY OF ELECTROLYTIC DISSOCIATION The Problem as it was left by Van't Hoff. — Van't Hoff saw clearly, as we have stated, that a large class of compounds shows an osmotic pressure which conforms to the gas laws, and yet a very large class gives an osmotic pressure which is always too great. Van't Hoff's own words in this connection will be given : * "If we are still considering ' ideal solutions,' a class of phenomena must be dealt with which, from the now clearly demonstrated analogy be- tween solutions and gases, are to be classed with the earlier so-called deviations from Avogadro's law. As the pressure of the vapor of ammonium chloride, for example, was too great in terms of this law, so, also, in a large number of cases, the osmotic pressure is abnor- mally large, and in the first case, as was afterwards shown, there is a breaking down into hydrochloric acid and ammonia, so also with solutions we would naturally conjecture that in such cases a similar decomposition had taken place. Yet it must be conceded that anomalies of this kind existing in solutions are much more numer- ous, and appear with substances which it is difficult to assume break down in the usual way. Examples in aqueous solutions are most of the salts, the strong acids, and the strong bases. ... It may then have appeared daring to give Avogadro's law for solutions such a prominent place, and I should not have done so had not Arrhenius pointed out to me, by letter, the probability that salts and analogous substances when in solution break down into ions." 1 Ztschr. phys. Chem. 1, 500 (1887). Scientific Memoirs Series, IV, 34. Edited by Ames (Amer. Book Co.). SOLUTIONS 209 The last sentence furnishes the connecting link between the gen- eralization reached by Van't Hoff and the discovery of the theory of electrolytic dissociation. The latter we owe to the Swedish physicist Arrhenius, to whose work we shall now turn. Work of Arrhenius. — A paper bearing the title On the Dissocia- tion of Substances Dissolved in Water appeared in the same volume of the Zeitschrift fur physikalische Chemie 1 as the paper by Van't Hoff, which we have just considered. Arrhenius was impressed by the generalizations reached by Van't Hoff connecting gas-pressure and osmotic pressure, and especially by the large number of excep- tions to these generalizations. Eeferring to the equality of gas- pressure and osmotic pressure under the same conditions, Arrhenius says : 2 " Van't Hoff has proved this law in a manner which scarcely leaves any doubt as to its absolute correctness. But a difficulty which still remains to be overcome is that the law in question holds only for ' most substances,' a very considerable number of the aque- ous solutions investigated furnishing exceptions, and in the sense that they exert a much greater osmotic pressure than would be required from the law referred to." Arrhenius stated the problem in the above words. We will now follow the line of thought which led him to its solution. 2 " If a gas shows such a deviation from the law of Avogadro, it is explained by assuming that the gas is in a state of dissociation. The conduct of bromine and iodine, at higher temperatures, is a very well-known example. We regard these substances under such con- ditions as broken down into simple atoms. " The same expedient may, of course, be made use of to explain the exceptions to Van't Hoff's law ; but it has not been put forward up to the present, probably on account of the newness of the subject and the many exceptions known, and the vigorous objections which would be raised from the chemical side to such an explanation." Arrhenius then puts forward' the assumption of the dissociation of certain substances dissolved in water to explain the exceptions to Van't Hoff's generalization. Osmotic pressure is, as we have seen, proportional to the concentration of the solution. This is the same as to say that osmotic pressure is proportional to the number of dissolved particles. If a substance exerts an abnormally great osmotic pressure, there must be more parts present in the solution than we would expect from the concentration. But acids, 1 Ztschr. phys. Chem. 1, 631 (1881). Scientific Memoirs Series, IV, p. 47. 2 Scientific Memoirs Series, IV, 47-48. Edited by Ames (Amer. Book Co.). p 210 THE ELEMENTS OF PHYSICAL CHEMISTRY bases, and salts, represented by hydrochloric acid, potassium hydrox- ide, and potassium chloride, are the substances which show the ab- normally great osmotic pressure. How is it possible to conceive of substances such as these breaking down into any larger number of parts than would correspond to their molecules ? This is the problem which must be solved, and Arrhenius has solved it, as we believe, satisfactorily. He went back to the theory proposed by Clausius to account for the facts which were known in connection with the phenomenon of electrolysis. The theory of Clausius will be developed later at some length. Suffice it to say here that it was found that an infinitely weak current will decom- pose water to which a little acid is added, liberating hydrogen at one pole and oxygen at the other. If the aqueous solution of the acid contained only molecules, in order that we might have elec- trolysis the current must be capable of decomposing the molecules. The fact is that a current far too weak to decompose a molecule of water will effect electrolysis. Therefore, some of the molecules present in the solution, either those of the water or of the acid, must be already broken down before the current is passed. Clausius did not claim that the molecules are broken down into their constitu- ent atoms. Such a theory would be absurd. His theory was that the molecules are broken down into parts, which he called ions (a term first used by Faraday), and each ion is charged with electricity, either positively or negatively. An ion may be a charged atom or a charged group of atoms. The theory that molecules are broken down into ions by a solv- ent like water was proposed, then, by Clausius in 1856. A similar theory was advanced by the chemist Williamson in 1851, as the result of his work on the synthesis of ordinary ether from alcohol and 'sulphuric acid. This, also, will be considered in detail in the proper place. The theory of Clausius differed from that of Williamson, in that the former assumed that there are only a few molecules broken down into ions, while Williamson thought that most of the molecules present are in a state of decomposition. It should be observed that both of these theories are purely qualita- tive suggestions. The one thought that only a few molecules in solution are broken down into ions, the other, that we have to do mainly with ions ; but neither suggested any method by which we could determine the actual amount of the dissociation in any case. The new feature which was introduced by Arrhenius was to point out a method for determining just what per cent of the mole- cules is broken down into ions. He thus converted a purely qualita- tive suggestion into a quantitative theory, which could be tested SOLUTIONS 211 experimentally. The methods for measuring the amount of dis- sociation in solution, which were worked out by Arrhenius, will be considered in the proper places. It would be premature to dis- cuss them here, since they fall naturally in line in the subsequent chapters. The Theory of Electrolytic Dissociation. — The theory of electro- lytic dissociation, as we have it to-day, states that when acids, bases, and salts are dissolved in water, they break down or dissociate into ions. Examples of the three classes are the following : — HC1 = H + CI, KOH = K + OH, KC1 = K + CI. Each compound dissociates into a positively charged part called a cation, and a negatively charged part an anion. These ions may be charged atoms as the above cations, or groups of atoms as the anion OH. The cations are usually simple atoms charged with posi- tive electricity. The cation of all acids is hydrogen ; the nature of the anion varies with the nature of the acid. It may be chlorine, bromine, the N0 3 group, S0 4 , etc. The anion of bases is the group (OH) ; the cation varies with the nature of the base. It may be potassium, barium, ammonium, etc. The anions and cations of salts both vary with the nature of the salt. They depend upon the nature of the acid and the base which have combined to form the salt. It was stated that hydrogen is the cation into which all acids dissociate. It may be added that this is the characteristic ion of all acids, and whenever it is present we have acid properties. Further, we never have acid properties unless there are hydrogen ions present. The same may be said of the hydroxyl ions into which bases dis- sociate. This is the characteristic ion of bases. The evidence bearing upon the theory of electrolytic dissociation, and the objections which have been urged to it, will be presented as the subject develops. One misconception which has arisen so often must, however, be anticipated in advance. It has been repeatedly urged that the theory claims that a com- pound like potassium chloride dissociates into potassium and chlo- rine, and since neither potassium nor chlorine can remain in the "Osmotic Pressure of Concentrated Solutions," Ewan: Ztschr. phys. Chem. 31, 22 (1899). "Experiments bearing on the Theory of Electrolytic JJissocia- tion," Noyes and Blanchard : Ibid. 36, 1 (1901). J s 212 THE ELEMENTS OP PHYSICAL CHEMISTRY presence of water under ordinary conditions without acting upon it, the theory is self-evidently wrong. This objection, like so many others, is based upon an imperfect understanding of the theory. No one has ever claimed that a compound like potassium chloride dis- sociates in the presence of water yielding atomic or molecular potas- sium, having the properties of ordinary potassium. The products of dissociation are a potassium ion and a chlorine ion, and the potassium ion is a potassium atom charged with a unit of positive electricity. There is no reason whatever for supposing any close agreement between the general properties of a potassium atom and those of a potassium atom charged with electricity. About the only property which we would expect to remain unchanged is that of mass, and the mass of an atom is not changed by charging it. The properties of atoms are doubtless very closely connected with the energy relations which obtain in or upon the atom. When we change these as fundamentally as by adding an electrical charge, we would expect fundamental changes in properties ; and such are the facts. It can be safely stated that whatever may be the ultimate fate of the theory of electrolytic dissociation, it will never suffer seriously from any such objection as that just referred to. Evidence furnished for the Existence of Free Ions in Solution. — The most direct evidence for the existence of free, electrically charged particles or ions in aqueous solutions of salts, is, perhaps, furnished by the fact that when a tube containing such a solution is rapidly rotated in a centrifugal machine, there is found to be pro- duced an electromotive force between the outer and inner ends of the rotating solution ; showing that there is an accumulation of opposite electricities at the two ends of the tube. The sign of the electric charge at the outer end corresponds in general to that of the denser ion. Thus, a solution of potassium iodide becomes negatively charged at the outer end, apparently because the iodine ion is denser than the potassium ion, and is thrown outwards to a greater extent by the centrifugal force. On the other hand, a silver nitrate solution would become positively charged at the outer end because of the greater density of the silver ion. With an ordinary centrifugal machine the magnitude of this effect is small, but still large enough to be detected with suitable electric instruments; thus, with a solution of potassium iodide in a tube 20 cm. long, which is rotating at the rate of 4000 revolutions per minute, the electromotive force has been found by R. C. Tolman to be about 2.8 millivolts. 1 The effect increases 1 Private communication from A. A. Noyes to the author, the work being done in the Research Laboratory of Phys. Chem. of the Mass. Inst. Tech. See also des Coudres: Weid. Ann. 49, 284 (1893) ; 57, 232 (1896). SOLUTIONS 213 rapidly with the length of tlfe tube and the rate of rotation; and a very powerful centrifugal machine is now being constructed for the accurate study of this phenomenon. Another effect of centrifugalizing salt solutions, which can be predicted theoretically, 1 and which it is claimed has been realized, 2 may also be here mentioned. Since with most salts, both the ions and also the undissociated molecules are probably denser than the aqueous medium, all of these are thrown outwards by the centrifugal force, so that the solution will increase in concentration at the outer end until the tendency to diffuse in the opposite direction, arising from the concentration-difference, becomes great enough to balance the centrifugal tendency. This concentration-change, unlike the electrical effect, can be produced only gradually, owing to the slow- ness of diffusion processes. The Effect of Osmotic Pressure partly overcome by Centrifugal Force. — That the effect of osmotic pressure in maintaining homo- geneity in a solution can be partly overcome mechanically, has been shown by the work of van Calcar and Lobry de Bruyn. 3 They placed at first a one per cent solution of potassium sulphocyanate in a centrifuge, which was rotated for about five hours. At the end of this time tests were made, and it was found that the solution in the exterior of the vessel was more concentrated than in the interior. A similar experiment with a number of other substances led to a similar result, the solution becoming more concentrated towards the periphery. The homogeneity of the solution was thus destroyed mechanically by means of centrifugal force. Since any given solution is main- tained in a homogeneous condition by diffusion, and since diffusion is caused by osmotic pressure, it follows that the effect of osmotic pressure is partly overcome by centrifugal force. The authors then placed a saturated solution of some salt in the centrifuge, to see whether it could not be made to crystallize around the exterior by rapid rotation. They placed a saturated solution of sodium sulphate in the centrifuge, and rotated it for five hours at 2400 turns per minute. They state that about f of \ 1 Gouy and Chaperon : Ann. Chim. Phys. (6) 12, 384 (1887) ; des Coudres : Weid. Ann. 55, 213 (1895). 2 Lobry de Bruyn and van Calcar: Bee. Trav. Chim. 23, 218 (1894). It should be stated, however, that the effects which these investigators claim to have found are much larger, and were much more rapidly obtained, than would be predicted theoretically. s Bec. Trav. Chim., Pays-Bas, 23, 218 (1904). 214 THE ELEMENTS OF PHYSICAL CHEMISTRY the total amount of salt in solution -was thus made to separate in the solid condition. The magnitude of the result is so large as to arouse the suspicion that they were really dealing with a supersaturated solution* of this salt, which, as is well known, is very easily obtained. See Bredig : Ztschr. phys. Chem. 17, 459 (1895). RECENT MEASUREMENTS OF OSMOTIC PRESSURE Work of Morse, Frazer, and Students. — The recent measure- ments of osmotic pressure by Morse and his coworkers were made possible by the discovery by Morse of a new method for making semi-permeable membranes. Instead of allowing the two membrane- formers — copper sulphate and potassium ferro-cyanide — to diffuse into the porous cup, the one from the outside and the other from the inside, as Pfeffer had done; the cation of the copper sulphate and the anion of the ferrocyanide were driven into the walls of the cup by means of the electric current. 1 The semi-permeable membranes thus prepared were very much more resistant to pressure than the membranes made by diffusion alone. Having found a means of preparing strongly resistant semi- permeable membranes, the next problem was to make a form of un- glazed porcelain cell, which should meet the various requirements for measuring osmotic pressure. 2 Cups made by a number of potters were tested as to their fitness for the work, and were found to be defective. Subsequent examination of these cups showed that they were made of too coarse-grained material, and contained pores or holes that were too large. When the membranes were deposited in the walls of such cups, these large pores proved to be sources of weakness, and the membranes thus deposited would not withstand without rupture any great pressure. It was necessary to make the porcelain cups in the laboratory from very fine-grained clay. The deposition of the membrane is de- scribed by Morse and Frazer in the following words : 3 " The interior electrode (the cathode) is a narrow platinum cylinder about 40 mm. in length. The exterior electrode is a cylinder of copper. The solution of potassium ferrocyanide, which is placed within the cell, and that of the copper sulphate which surrounds it, are both of 0.1 1 Morse and Horn : Amer. Chem. Joum. 26, 80 (1901). "Ibid. 28, 1 (1902). 8 Ibid. 34, 16 (1905). SOLUTIONS 215 normal concentration. The former is renewed every 5 or 10 minutes, by admitting through the separating funnel a volume of the fresh solution which is about equal to the capacity of the cell. The object of the frequent renewal of the solution of potassium ferrocyanide is to prevent an accumulation of alkali within the cell, the presence of which appears to have an injurious effect upon the membrane. A pressure of 110 volts is well adapted to the deposition of the mem- brane in any cell which is fit for quantitative measurements, and we have used approximately this voltage in all of our experiments. We have come to regard, in a general way, 100,000 ohms or more as a proper resistance for a membrane, though good measurements have been obtained with cells in which the resistance of the membrane did not exceed 30,000 ohms. " Whatever the character of the results on the first trial may have been, the cell is taken down, washed, and soaked for several hours in distilled water. It is then resubjected to the membrane-forming process, again washed, and immediately thereafter it is filled and set up with a view to securing the measurement of osmotic pressure. However well the first membrane may have behaved, the second one usually surpasses it, and it is not ordinarily necessary to repeat the treatment described above more than once before undertaking the measurement of pressure. The above applies to solutions of cane sugar. In the case of glucose 1 it was necessary to remake the membrane a number of times." It would lead us too far to discuss the details in connection with the calibration of the mamometer, the closing of the cells, the ther- mostat for constant temperature, etc. The measurements of osmotic pressure have thus far been limited to solutions of cane sugar and glucose. Some of the results obtained are given below — these values being the average of a much larger number of measurements. 2 Column I is the concentration in terms of a gram-molecular weight of the dissolved substance in 1000 grams of the solvent. Column II is the osmotic pressure in atmospheres at 0°. Column III is the osmotic pressure from 4° to 5°. Column IV is the osmotic pressure at 10°. Column V is the osmotic pressure at 15° and column VI the osmotic pressure at 25°. 2 1 Amer. Chem. Journ. 36, 1 (1906). 2 These results have not yet been published in full, but have been kindly handed to the author by Professor Morse. 216 THE ELEMENTS OF PHYSICAL CHEMISTRY Osmotic Pressure of Cane Sugar I II III IV V VI Pressures Pressures Pressures Pressures Pressures 0° 4°-5° 10° 15° 25° 0.1 2.42 2.40 2.44 2.48 2.56 0.2 4.79 4.75 4.82 4.91 5.10 0.3 7.11 7.07 7.19 7.33 7.57 0.4 9.35 9.43 9.58 9.78 10.12 0.5 11.75 11.82 12.00 12.29 12.73 0.6 14.12 14.43 14.54 14.86 15.42 0.7 16.68 16.79 17.09 17.39 18.02 0.8 19.15 19.31 19.75 20.09 20.73 0.9 21.89 22.15 22.28 22.94 23.66 1.0 24.45 24.53 25.06 25.42 26.33 Total Pressures 131.71 132.68 134.75 137.49 142.24 Mean Ratio of -i Osmotic to > 1.074 1.065 1.061 1.064 1.064 Gas-presBure > Mean Ratios ov Osmotic to Gas-pressure Mean Eatios Concen- tration Eatios, 0° Ratios, 4°-5° Ratios, 10° Eatios, 15° Ratios, 25° of Series at 10°, 15°, and 25° 0.1 1.085 1.060 1.056 1.053 1.053 1.054 0.2 1.074 1.045 1.043 1.045 1.048 1.045 0.3 1.064 1.041 1.038 1.040 1.038 1.039 0.4 1.049 1.042 1.037 1.040 1.041 1.039 0.5 1.055 1.043 1.040 1.046 1.048 1.045 0.6 1.056 1.059 1.050 1.055 1.058 1.054 0.7 1.070 1.060 1.058 1.058 1.059 1.058 0.8 1.074 1.067 1.069 1.069 1.066 1.068 0.9 1.091 1.081 1.073 1.085 1.082 1.080 1.0 1.097 1.084 1.085 1.083 1.084 1.084 • SOLUTIONS Osmotic Pressure of Glucose 217 Concen- tration Tempera- ture Osmotic Pressure Gas- pressure Molecular Osmotic Pressure Molecular Gas- prossure Ratio of Osmotic to Gas- pressure 0.1 10°.20 2.39 2.31 23.90 23.10 1.034 0.2 10°.40 - 4.78 4.63 23.90 23.15 1.032 0.3 10 c .00 7.11 6.92 23.70 23.07 1.027 0.4 10°.15 9.54 9.24 23.85 23.10 1.032 0.5 10°.20 11.91 11.55 23.83 23.11 1.031 0.6 10°.10 14.30 13.85 23.83 23.08 1.032 0.7 10°.00 16.70 16.16 23.86 23.09 1.033 0.8 10°.00 19.05 18.46 23.81 23.08 1.032 0.9 10°.10 21.39 20.78 23.71 23.09 1.030 1.0 10°.00 23.79 23.08 23.79 23.08 1.031 The constant nature of the ratios between the total osmotic pres- sures found, and the theoretical gas-pressure when the gas occupies the volume of the pure solvent, speaks for the great accuracy of these difficult measurements. The same fact is brought out in the second table, where the indi- vidual ratios are given for the different temperatures. While the ratio is in no case unity, yet it is remarkably constant for all of the temperatures when we consider the experimental difficulties encoun- tered. The last three series being the most recent, are the most accurate. These results show that the law of Gay-Lussac for gas-pressure applies to the osmotic pressure of sugar solutions. It has been found by Morse 1 and his coworkers that a large num- ber of gelatinous substances show considerable osmotic activity when deposited in the walls of porcelain cups. Among these are aluminium and ferric hydroxides ; ferric, uranyl, and cupric phosphates ; uranyl, stannous, cadmium, zinc, and nickel f errocyanides ; and cobalt, nickel, ferrous, copper, zinc, cadmium, and manganese cobalticyanides. Some of these may prove to be useful in measuring osmotic pressure. Recent Measurements of Osmotic Pressure — Work of the Earl of Berkeley and Hartley. — The Earl of Berkeley and E. G. J. Hartley 2 have recently measured the osmotic pressure of very concentrated solutions of cane sugar, dextrose, and mannite. 1 Amer. Chem. Journ. 29, 173 (1903). 2 Proc. Boy. Soc. 73, 436 (1904) ; Trans. Boy. Soc, A 206, 481 (1906). 218 THE ELEMENTS OF PHYSICAL CHEMISTRY The method which they employed is to bring a counter pressure to bear on the solution, which shall just be sufficient to prevent water from passing through the semi-permeable membrane into the solu- tion. This pressure would then be equal to the osmotic pressure of the solution. Their method can best be understood by examining the sketch of their apparatus (Fig. 24). Their own description of the apparatus is given. Fio. 24. "The Osmotic Apparatus. — The apparatus used is shown in Tig. 24. AB is a porcelain tube, 1 15 cm. long, 2 cm. external and 1.2 cm. internal diameter; the vertical ends are glazed. This tube carries the semi-permeable membrane as close to the outer surface as possible. GO is a gun-metal cage against the ends of which the der- matine rings DD are compressed, when the two parts E and F of the outer gun-metal vessel are screwed together. The ends of this cage have shallow radial grooves cut out of them, so as to prevent the dermatine rings from rotating and rubbing the membrane during 1 The porcelain tubes are similar in all respects to those described in our preliminary communication. SOLUTIONS 219 the operation of screwing E and F home. The length of the cage is such that, when finally set up, the dermatine rings just overlap the ends of the porcelain tubes. " The outer gun-metal vessel (capacity about 250 en. cm.) contains the solution which, when a pressure is applied to it, forces the dermatine rings against the bevelled faces OO, and thus causes a tight joint to be made with the porcelain tube. The joint between E and F is made good by another dermatine ring X, which is com pressed between the metal ring I and the nuts JJ. "The ends of AB are closed by pieces of thick- walled rubber tubing KK, through which the brass tubes LL are passed ; a water- tight joint between LL and the inside of the porcelain tube is obtained by compressing the rubber between the metal washers MM and the nuts NN. 1 The brass tubes are joined by rubber tubing, one to a glass tap and the other to an open glass capillary — the latter, which we shall call the water gauge, was graduated in millimeters and calibrated; one centimeter of the bore contains 0.00312 cu. cm. The outer ends of E and F have threads cut on them to receive the brass rings 00, which in their turn are perforated by screw-holes to receive the thumb-screws PP, by means of which, together with a rubber washer, a tight joint is made between the flanges QQ of the curved metal tubes FT" and the ends of E and F. The uses of these tubes will be explained later. "The perforation R is for filling the apparatus with solution, and also for connecting to the pressure apparatus, while S serves to empty the vessel. The method of making a pressure-tight joint, shown at R, originated, we believe, at the Cambridge Scientific In- strument Co. It may be useful to call attention to it, as we have experienced no trouble, although the joint has been made and remade over a thousand times. It is scarcely necessary to describe the joint, as the diagram illustrates it sufficiently. The only point to empha- size is that the thread on the steel pressure tube T should be of a smaller pitch than that on the outside of the nut. "The Semi-permeable Membranes. — The membranes were depos- ited on the surface of the porcelain tubes by the following means. The porcelain tube is placed in a copper sulphate solution (50 grams in a litre) in a desiccator and the air exhausted, until no more bubbles come off from the tube — this takes place only after several days — the tube is withdrawn, wiped inside and outside with a clean linen duster, and allowed to dry for f hour. The ends are then *It seems advisable to point out that the rubber tubing KK is unaffected by the pressure put upon the solutloD. 220 THE ELEMENTS OF PHYSICAL CHEMISTRY closed by rubber plugs, perforated for the passage of glass rods; then, holding the tube horizontal and spinning it rapidly between the fingers, it is plunged into a solution of potassium ferrocyanide (42 grams in a litre). By this means an even deposit of copper ferrocyanide, very close to the outer surface of the porcelain, is ob- tained. The tube is allowed to soak in the ferrocyanide, after which it is set up for electrolysis. The same solutions and of the same strength are used ; the tube is plugged at one end, and at the other is fitted with a perforated plug and thistle funnel, through which a copper electrode dips into the copper sulphate solution, while a platinum electrode is immersed in the ferrocyanide surrounding the porcelain tube. It was found best to place the platinum electrode in a porous pot suspended in the ferrocyanide solution, in order to prevent the alkali from attacking the membrane, and the solution in the pot was frequently changed during the experiment. "Remaking the Membranes Under Pressure. — All the tubes which, judging by their resistances, seemed promising, were also remade electrolytically under pressure. The object aimed at was to break down the weak places in the membrane while the current was passing, so that any small holes would be filled up at once by the interaction of the copper and ferrocyanide ions. It is probable that the pressure alone causes a considerable part of the improvement by forcing the membrane into the pores of the porcelain." The Results. — The following are the values for the equilibrium pressures at 0° C. of the various solutions — there being a pressure of one atmosphere on the solvent. Cane Sugar Grams in A Litre Osmotic Pressure e 180.1 13.95 300.2 26.77 420.3 43.97 640.4 67.51 660.5 100.78 750.6 Dextrose 133.74 99.8 13.21 199.5 29.17 319.2 53.19 448.6 87.87 548.6 Galactose 121.18 250 35.5 380 62.8 500 95.8 SOLUTIONS 221 Mannite E S is E e •§3 u Concentration Grams in a Litre 100 110 125 Galactose. Osmotic Pressure in Atmospheres 13.1 14.6 16.7 Cane Susar. ISO 75 So 25 WO EQ U k. j= 120 Q. o> O E <: .5 90 10 U fc. tf Eaoult used twelve volatile liquids as solvents, and dissolved in these a number of substances as slightly volatile as possible, such as cane sugar, glucose, urea, naphthalene, anthracene, ethyl benzoate, aniline, nitrobenzene, henzoic acid, etc. He found the following re- markable relation : " If 2 we divide the molecular lowering of vapor- pressure, C, in a given volatile liquid, by the molecular weight of (j the liquid, M\ the quotient, — , which represents the relative lower- ing of pressure produced by one molecule of non-volatile substance in one hundred molecules of solvent, is a constant." 1 Compt. rend. 104, 1430 (1887). 2 Scientific Memoirs Series, IV, 127. Edited by Ames (Amer. Book Co.). SOLUTIONS 261 Solvent M" C c M' Water 18 0.186 0.0102 Phosphorus trichloride 137.5 1.49 0.0108 Carbon bisulphide . 76.0 0.80 0.0105 Tetrachlormethane . 154.0 1.62 0.0105 Chloroform 119.5 1.30 0.0109 Amylene . 70.0 0.74 0.0106 Benzene . 78.0 0.83 0.0106 Methyl iodide . 142.0 1.49 0.0105 Ethyl bromide . 109.0 1.18 0.0109 Ether 74.0 0.71 0.0096 Acetone . 58.0 0.59 0.0101 Methyl alcohol 32.0 0.33 0.0103 Although the values of M' and O vary as greatly as in the above Q table, the ratio, — , , is practically constant, and has the value 0.0105. Eaoult states his law as follows : 1 " One molecule of a nan-saline, nonvolatile substance, dissolved in one hundred molecules of any vola- tile liquid, lowers the vapor-pressure of this liquid by a nearly constant fraction of its value — approximately 0.0105." This law, it will be recognized at once, is strictly analogous to that discovered by Eaoult for the lowering of the freezing-point of solvents. It will be shown a little later that the two classes of phenomena are very closely connected. Determination of Molecular Weights from the Lowering of Vapor- tension. — The possibility of determining the molecular weights of dissolved substances by measuring the lowering of the vapor-tension of solvents produced by them, was clearly pointed out by Eaoult. 2 The law of Eaoult can be formulated thus : — f-f'_ r « / ^N+n in which n is the number of molecules of the dissolved substance, i Ztschr. phys. Chem. 2, 372 (1888). Tammann : Acad. St. Petersburg Mem. 35, No. 9 (1887). See Kahlbaum : Ztschr. phys. Chem. 13, 14 (1894); 26, 577 (1898). Gahl: Ibid. 33, 178 (1900). Zawidski : Ibid. 35, 129 (1900). Noyes : Ibid. 35, 707 (1900). Ramsay and Steele: Ibid. 44, 348 (1903). Lowenstein : Ibid. 54, 707 (1906). 2 Scientific Memoirs Series, IV, 127. Edited by Ames (Amer. Book Co.). 262 THE ELEMENTS OP PHYSICAL CHEMISTRY N the number of molecules of the solvent, and C a constant. Since C is practically unity, the above expression becomes : — f-f = n . / F+n If we represent the molecular weight of the substance by M, and w the weight of substance used by w, n — -=j- Making N= 1 and sub- stituting this value of n in the above expression, we have — /-/' _ w f ~ M+ w Knowing w,f, and /', we can calculate M, the molecular weight of the substance in question. This method of determining molecular weights has never found extensive application in the laboratory, partly on account of the comparative difficulty involved in measur- ing vapor-pressure, and chiefly because it was quickly supplanted by a method which can be carried out far more accurately and rapidly in practice. Furthermore, certain serious sources of error in the measurement of vapor-tension have been pointed out by Tammann. 1 If there is present as an impurity in the solvent any more volatile substance, it will affect the vapor-pressure very considerably. And, again, if the solution is not kept actively stirred, the layer at the surface will become more concentrated, due to the evaporation of the solvent from this portion of the solution. The vapor-tension will, then, be that of the more concentrated solution, and, consequently, lower than the true vapor-tension of the solution. The Work of Beckmann. — Beckmann 2 began his work by im- proving the method for measuring vapor-tension, but soon abandoned the vapor-tension method altogether as a means of determining molecular weights. Instead of determining the relative vapor-ten- sions of solvent and solution at a given temperature, he determined the temperatures at which both solvent and solution have the same vapor-pressure. It was found to be especially convenient to deter- mine the temperatures at which the vapor-pressures of the liquids are just equal to the pressure of the atmosphere. In a word, to determine the boiling-points of the pure solvent and of the solution, since the boiling-points are temperatures of equal vapor-pressure. 1 Wied. Ann. 33, 683 (1887). See Smits : Ztschr. phys. Chem. 51, 33 (1905). 2 Ztschr. phys. Chem. 4, 544 (1889). SOLUTIONS 263 We have seen that the vapor-tension of a solvent is greater than that of a solution at the same temperature. The boiling- point of the solvent is, therefore, lower than that of the solution. The method as carried out by Beckmann consists in determin- ing the rise in the boiling-point of a solvent produced by a dis- solved, non-volatile substance. The apparatus first devised 1 by Beckmann for determining the boiling-points of solvents and solutions has been so greatly im- proved that it is now of hardly more than historical interest. The best form 2 which has ever been suggested by Beckmann is shown in Fig. 38. The glass tube A contains the liquid whose boiling-point is to be determined. Into this liquid the thermometer dips, as shown in the figure. In the bottom of the tube are placed glass beads, garnets, or platinum scraps, so as to secure a more uniform rate of boiling. A con- denser is attached to the tube A, as shown in the figure. This tube is surrounded by a double- walled glass jacket B, into which is introduced some of the same liquid whose boiling-point is to be determined in A. This is also provided with a return condenser, Fig. 38. The liquid in B is boiled 1 Ztschr. phys. Chem. 4, 544 (1889). 2 Ibid. 8, 226 (1891). See Ibid. 39, 385, and 40, 129. See Koloff : Ibid. 11, 7 (1893). Schall: Ibid. 12, 145 (1893). Beckmann, Fuchs, and Gernhardt: Ibid. 18, 473 (1895). Beckmann: Ibid. 21, 239 (1896). Beckmann: Ibid. 22, 609(1897). Meyerhoffer: Ibid. 22, 619(1897). Bigelow: Amer. Chem. Journ. 22, 280 (1899). McCoy: Ibid. 23, 355 (1900). Batteli and Stefanini : Ann. Chim. Fhys. (7) 20, 64 (1900). Eiiber: Ber. d. chem. Gesell. 34, 1060 (1901). Beckmann: Ztschr. phys. Chem. 39, 129,385 (1902); 40, 129 (1902). Beck- mann: Ibid. 44, 161 (1903). Beckmann: Ibid. 46, 853 (1903). Beckmann: 76^.51,329(1905). Beckmann: Ibid. 53, 129 (1905). Geib: Dissertation, Leipzig (1906). Beckmann: Ibid. 57, 129, 58, 543, 60, 385 (1907). 264 THE ELEMENTS OF PHYSICAL CHEMISTRY at the same time as the liquid in A, so that the innermost vessel is surrounded by a layer of liquid having the same boiling-point. The whole apparatus rests upon an asbestos box, and heat is supplied by a flame placed beneath. Beckmann has devised a number of modifications 1 of this apparatus, but in the opinion of the writer none of them represents any marked improvement on the form just described. Carrying out a Molecular Weight Determination with the Beck- mann Apparatus. — The pure solvent is poured into the tube A, the filling-material (beads or garnets) introduced, and the thermometer inserted so that when the cork is forced into the top of tube A the bulb of the thermometer is entirely covered by the liquid, but does not touch the glass beads. The mercury in the Beckmann ther- mometer is so adjusted that the top of the column comes to rest between the divisions 0° and 1° when the solvent boils. The vessel A is then carefully cleaned and dried, and after introducing the filling-material a weighed amount of the solvent is poured in. The thermometer is inserted and the condenser attached. Some of the pure solvent is poured into the vapor-jacket, and boiled simulta- neously with that in the tube A. The position of the mercury is carefully noted on the thermometer, after the solvent has boiled about twenty minutes, and the barometer is also very carefully read. The flame is now removed and the solvent allowed to cool. The substance whose molecular weight is to be determined is pressed into tablets, weighed, and introduced into the solvent. The boiling is renewed after all the substance has dissolved, and the temperature at which the solution boils carefully noted on the ther- mometer. The barometer is read again, and if any change has occurred, the proper correction 2 is introduced into the readings on the thermometer. Care must always be taken to tap the thermome- ter before making a reading. The difference between the boiling- point of the solvent and that of the solution is the rise in boiling-point produced by the dissolved substance. The calculation of the molecular weight of the dissolved sub- stance from the rise in boiling-point is very simple. The rise in boiling-point is directly proportional to the lowering of the vapor- pressure, and, therefore, depends upon the relative number of mole- i Ztschr. phys. Ohem. 15, 656 (1894) ; 17, 107 (1895) ; 18, 492 (1895) ; 18, 661 (1895) ; 21, 245 (1896). 2 For details see Biltz: Practical Methods for Determining Molecular Weights, translated by Jones and King ; also Jones : Freezing-point, Boiling- point, and Conductivity Methods (Chem. Pub. Co.). SOLUTIONS 265 cules of the solvent and of the dissolved substance. If we represent the unknown molecular weight by M, the weight of the substance used by w, the weight of the solvent by W, and the rise in the boiling-point of the solvent by B, we have — M= C100w BW ' The value C is a constant for every solvent, and is the molecular rise in the boiling-point of the solvent produced by a completely undissociated substance. It can be either determined experimentally, or can be calculated by a method which will be described later. Molecular weights, as determined by the boiling-point method, usu- ally are the simplest possible, though there are many exceptions to this generalization. Improvements in the Boiling-point Apparatus of Beckmann. — A number of modifications of the Beckmann apparatus have been pro- posed, in addition to those suggested by Beckmann himself. Hite 1 introduced one glass tube into another, and placed the thermometer in the innermost tube, in order that the cold, recondensed solvent might not come in contact with the thermometer before it had been reheated. He also, by means of a glass cap into which notches had been filed, caused the steam to rise in very fine bubbles through the liquid just around the bulb of the thermometer. He thought that in this way he could secure a better stirring of the liquid just around the thermometer. The apparatus of Hite is undoubtedly an im- provement on any which had been proposed up to that time. In an attempt to improve the Hite apparatus, Jones 2 devised and used the following form (Fig. 39). Into the glass tube A, some glass beads or garnets are introduced. To the side tube A, the condenser is attached. Into the beads a cylinder of platinum P is inserted by placing the finger upon the top of the cylinder and gently shaking the whole apparatus. The liquid whose boiling-point is to be deter- mined is introduced into A until the bulb of the thermometer, placed as shown in the figure, is covered. The liquid must not come within a centimetre, or a centimetre and a half, of the top of the platinum cylinder. The tube A is surrounded by a thick jacket of asbestos J, and rests on an asbestos board in which a circular hole is cut, and over which a piece of wire gauze is laid. Heat is supplied by means of a very small flame B, placed beneath the apparatus and protected by a metallic screen as shown in the drawing. The essential difference between this apparatus and other forms 1 Amer. Chem. Journ. 17, 507 (1895). "Ibid. 19, 581 (1897). 266 THE ELEMENTS OF PHYSICAL CHEMISTRY is the platinum cylinder which is introduced into the boiling liquid. The object of this cylin- der is twofold. It prevents the cooled recondensed solvent from coming in contact with the thermometer before it is reheated to the boiling-point. It reduces the effect of radiation to a mini- mum. Jf the bulb of the ther- mometer is surrounded only by the boiling liquid, or even if a layer of asbestos is wrapped around the glass tube, heat will be radiated out from the hot bulb on to colder objects in the neigh- borhood. The temperature of the bulb will always tend to be a little lower than that of the boiling liquid in which it is immersed. By surrounding the bulb with a piece of metal as nearly as possible at the same temperature as the bulb itself, the effect of radiation is reduced to a minimum. The apparatus is exceedingly simple, and when applied to the determination of molecular weights of dissolved substances, was found to give good results with both low-boiling and high- boiling solvents. 1 Another ap- plication of this method will be considered a little later. The Apparatus of Landsberger as modified by Walker and Lumsden. — The apparatus of Landsberger 2 is based upon a 1 " Elevation of the Boiling-points of Aqueous Solutions of Electrolytes." See Johnston : Trans. Boy. Soc, Edinburgh, 45, Part I, p. 193. Amer. Chem. Journ. 19, 590 (1897). a Ber. d. chem. Gesell. 31, 458 (1893). Fig. 39. SOLUTIONS 267 somewhat different principle, especially with respect to the method of heating the liquid. The solvent or solution is heated to the boiling-point by means of the vapor of the pure solvent. The ap- paratus, as modified by Walker and Lumsden, 1 is shown in Fig. 40. A flask >!fconWis the boiling solvent. The vapor is led through th/tube B irfbo^jthe tube JV, which contains the solution. This is surrounded by a larger tube E, which is connected with a condenser C. The vapor escapes from N through the hole H, and there is conse- quently a layer of vapor between N and E. The lower end of R contains a number of per- forations through which the vapor escapes. The bulb N prevents the liquid from spat- tering through the opening H. The pure sol- vent is poured into N until the bulb of the thermometer is just covered. The pure solvent in F is boiled after introducing some fragments of unglazed porcelain, and the vapor quickly boils the liquid around the thermometer. After this point is determined on the thermometer the tube is emptied, and a quantity of solution containing a known amount of dissolved substance in a given volume is added. The boiling-p»int of the solution is deter- mined in the same manner as that of the solvent. The solution is continually changing concentration due to the condensation of vapor 1 Journ. Ctem. Soc. 502 (1898). See Sakurai : Ibid. 61, 989 (1892). 268 THE ELEMENTS OF PHYSICAL CHEMISTRY from the vessel F. After the boiling-point of the solution is deter- mined, the inner tube, with thermometer and delivery tube, are weighed. Knowing the weight of this part of the apparatus empty, and the weight of the substance, we know the weight of the solvent. If a number of determinations are desired, using the same quantity of substance, the passage of the vapor is interrupted from time to time, the boiling temperature read, and the amount of solvent present determined. In such cases the volume of the solvent is read off, the tube N being graduated for this purpose. In reading the volume the thermometer and delivery tube are removed in each case from the solution. The object of heating the solution by means of its own vapor is to prevent any superheating, such as may take place when a flame is applied directly to the solution. The method as devised by Landsberger, and as modified by Walker and Lumsden, yielded good results in their hands when applied to the problem of molecular weight determinations. Measurement of Dissociation by Means of the Boiling-point Method. — We have already seen how the freezing-point method can be applied to the measurement of electrolytic dissociation in solvents which freeze near the ordinary temperatures. There are, however, many of our most common solvents which do not freeze at tempera- tures to which that method is applicable, such as the alcohols, acetones, esters, etc. In many such cases we have absolutely no method for measuring the dissociation in these solvents, unless the boiling-point method could be applied. Jones and King 1 attempted to apply the_ boiling-point method to this problem, using the apparatus which had been designed by Jones. They measured the dissociation of one or two salts in ethyl alcohol, and showed that concordant results could be obtained. The problem was subsequently studied far more extensively by Jones, 2 using his own apparatus. He used as solvents methyl and ethyl alcohols, and as dissolved substances, potassium, sodium, and ammonium bromides and iodides, potassium and sodium acetates, and calcium nitrate. The results obtained agreed satisfactorily with one another to within a per cent or two, and made it very probable that electrolytic dissociation could be measured by this boiling-point method to within a very few per cent. The relative dissociating power of different solvents is, as we shall see, of more than the average interest, especially on account of certain theoretical questions which are involved. The dissociation 1 Amer. Chem. Journ. 19, 753 (1897). 2 Ztschr. phys. Chem. 31, 114 (1899) (Jubelband zu Van't Hoff). SOLUTIONS 269 of the above-named salts in water, and in ethyl and methyl alcohols, is given in the following table. The results with the alcohols are taken from the measurements of Jones, using the boiling-point method. Substance Dilution Noemal Dissociation in Water Dissociation in Methyl Alcohol Dissociation in Ethyl Alcohol KI .... 0.1 88% 52% 25% Nal 0.1 84 60 33 NH 4 I .... 0.1 — 50 — KBr .... 0.1 86 50 — NaBr .... 0.1 86 60 24 NH 4 Br .... 0.2 — 49 21 CH3COOK . 0.1 83 36 16 CH 8 COONa . 0.1 — 38 14 Ca(NO s ) 2 . 0.1 — 15 5 The interpolations by which the above values were obtained could be made only approximately, therefore the values of the disso- ciation are given only in whole numbers. It will be observed that the dissociation in methyl alcohol is more than half of that in water, while the dissociation in ethyl alcohol is less than one-third of that in water. Further relations between the dissociating power of different solvents will be discussed under electrochemistry. The Vapor-pressure of Amalgams. — The molecular weights of metals dissolved in mercury were determined by the amount which they lowered the freezing-point of the mercury. Their molecular weights have also been determined from their depression of the vapor-tension of mercury. The following results are taken from the work of Ramsay : * — Metal Molecular Weight Found Atomic Weight Lithium Sodium . Calcium Barium . Magnesium Zinc Gallium Manganese Silver . 7.10 21.6-15.1 19.1 75.7 24.0-21.5 70.1-65.4 69.7 55.5 112.4 7.02 23.04 40.1 137.0 24.3 65.4 69.9 55.0 107.9 1 Journ. Ohem. Soc. 55, 521 (1889). See Haber: Ztschr. phys. Chem. 41, 399 (1902). 270 THE ELEMENTS OF PHYSICAL CHEMISTRY The molecular weights of most of the metals investigated by Ramsay, when dissolved in mercury, are the same as the atomic weights, showing that the molecule under these conditions consists of one atom. The cases of calcium and barium are exceptions ; their molecular weights being one-half their atomic weights. This would show that what we are accustomed to call the atom of these ele- ments is capable of subdivision, and is broken down in the presence of mercury into two parts. The conclusion that the atom of calcium can be broken down was reached by Humphreys and Mohler, 1 from a study of the dis- placement of certain spectrum lines of calcium under pressure. They discovered a simple relation between the atomic volumes of the elements and the amount by which their lines are displaced when the vapor is subjected to pressure. In order that the relation should hold for calcium, it was necessary to assume that the atom had broken down into smaller parts. That two such independent lines of research should lead to the same general conclusion is cer- tainly suggestive. Relation between Lowering of Vapor-tension and Osmotic Pres- sure. — De Vries 2 has shown experimentally that a proportionality exists between the isotonic coefficients of a number of substances and the molecular lowering of vapor-tension. (Lowering of vapor- tension and rise in boiling-point are, of course, proportional.) The following results are taken from the work of De Vries : — Isotonio Lowering of Substance Coefficients Vapor-tension MULTIPLIED BY 100 multiplied by 1000 198 178 202 197 NaNOs . 300 296 NaCl 305 330 NH4CI . 300 313 K 2 C 2 4 . 393, 372 K2C4H4U6 399 388 KgCeHgO? 601 499 The proportionality between lowering of vapor-tension or rise in boiling-point and osmotic pressure, as established by experiment, is at once apparent. 1 Astro-Physical Journal, 3, 135 (1896). 2 Ztschr. phys. Chem. 2, 427 (1888). SOLUTIONS 271 i =3H / Fig. 41. Demonstration of the Relation between Lowering of Vapor-ten- sion (Rise in Boiling-point) and Osmotic Pressure. — The relation between osmotic pressure and lowering of vapor-pressure has been derived in a simple manner by Arrhenius. 1 The line of r e a s oning is as follows : — Given a vessel of the form shown in the figure, closed at the bottom by a semi-permeable wall. The vessel is filled with a solution S, and dips into another vessel containing the pure solvent D. The apparatus is covered with a bell-jar, and exhausted. Equilibrium will exist when the pressure of the column of liquid from the surface of the solvent up to h, is equal to the osmotic pressure. When equilibrium is estab- lished, the vapor-pressure of the solution at h must be just equal to the pressure of the vapor of the solvent at this point. If it were less, liquid would condense in h; if more, it would distil out of h, and there would not be equilib- rium, since liquid would flow either out or in through the membrane. If /' is the tension of the vapor of the solution at h, f the vapor-tension of the solvent, h the height of the column of liquid, and d the density of the vapor, we have — f'=f-hd. The Value of d. — Let v be the volume of a gram-molecule of the vapor of the solvent D, and / the pressure of this vapor : — fv = BT, RT /" If M is the molecular weight of the solvent, — d=—, v M_RT d~ /" The Value of h. — Let us have a very dilute solution, in which n gram-molecules of substance are contained in g grams of solvent. From Van't Hoff's law of osmotic pressure we would have — PV=RTx.n, in which P is the osmotic pressure of the solution, and V its volume. 1 Ztsehr.phys. Chern. 3, 115 (1889). V = - d = Mf RT 272 THE ELEMENTS OF PHYSICAL CHEMISTRY Let s be the specific gravity of both solution and solvent (they are practically the same for very dilute solutions) : — P = h xs; s Substituting, PV=nRT= J ^ = hg; nRT Jig = nRT. .\7i = if nRT Mf Substituting the values h = and d = -=^ into the equation f'=f— hd, we have — /' =/- nRT X 9 Mf RT =/- nMf ~9~' /-/' nM / 9 J which is essentially Raoult's fundamental equation for the lowering of the vapor-pressure of a solvent by a dissolved substance. Raoult's equation, which has been amply verified by experiment, is usually written — f N' where N is the number of gram-molecules of the solvent. It is evi- dent that iV=-|^when the two equations become identical. Relation between Rise in Boiling-point and Lowering of Freezing- point. — Eaoult has shown experimentally that the lowerings of the freezing-point produced by some eighteen salts stand in the same relation to one another as the rise in boiling-point produced by these same substances. The same relation has been repeatedly estab- lished by subsequent experiments. That there is a relation between the two is demonstrated theoreti- cally, by the fact that the formula which is used to calculate the freezing-point constant of a solvent can also be employed to calcu- late the boiling-point constant. The formula deduced (p. 255) for the 2 T 2 freezing-point constant, C= 1f ,„ r , gives us the boiling-point constant Acetone . . . 17.1 Aniline . . . 32.0 Ether . . . . 21.6 Benzene . 26.1 Ethyl alcohol . . 11.7 Chloroform . 35.9 Acetic acid . 25.3 SOLUTIONS 273 if we represent by T the absolute temperature at which the solvent boils, and by L the latent heat of vaporization of the solvent. The boiling-point constants for a few of the more common solvents are given below : — Methyl alcohol ... 8.4 Carbon bisulphide . .23.5 Water 5.1 The relations between osmotic pressure, freezing-point lowering, and rise in boiling-point have been then thoroughly established ex- perimentally, and also demonstrated theoretically. The relation between each and the other two has been taken up and pointed out. Each of these properties depends only on the number of parts of the dissolved substance with respect to those of the solvent; it is a function of numbers. It does not matter whether the dissolved particle is a molecule or an ion, it has the same influence on all of these properties. These three properties of solutions are among the most important from a physical chemical standpoint, and each has an interest pecul- iarly its own. But the fact that the three are so closely related increases our interest in each, and makes a study of them more im- portant scientifically, since through such relations we arrive at wide- reaching generalizations — the highest aim of scientific investigation. DIFFUSION What is Diffusion? — When a solution of a colored compound, like copper sulphate, is placed in a glass cylinder and covered with water, the color is seen to rise gradually in the cylinder, and finally extends throughout its entire length. If the liquid is analyzed after a time, it will be found that the copper sulphate has passed into all parts of the cylinder. This is found to be a perfectly general prop- erty of dissolved substances. They always tend to distribute them- selves throughout the entire solvent until all parts of the solution become homogeneous. This applies not simply to solutions bordering on the pure solvent, but also to one solution in contact with another. If the two solutions are of the same substance, the dissolved sub- stance will always pass from the more concentrated to the more dilute solution, until homogeneity is established. If the two solu- tions are of different substances, each will distribute itself throughout the entire mass of the solvent present until each has become perfectly homogeneous. This phenomenon is known as diffusion. It is not easy to overestimate the importance of this property cf 274 THE ELEMENTS OF PHYSICAL CHEMISTRY dissolved substances, especially from the standpoint of the analytical chemist. If it was not for the power of dissolved substances to dif- fuse throughout the entire solvent present, it would be impossible to keep a solution homogeneous for any appreciable length of time. If the dissolved substance was heavier than the solvent, it would collect at the bottom of the solution ; if lighter, it would collect at the top. In any case heterogeneity would result — the solution having differ- ent concentrations in different parts. Under such conditions stand- ard solutions could not be preserved for any appreciable time. Since diffusion exists we can preserve a homogeneous solution for any length of time, provided only that we keep all parts at the same tem- perature. The importance of this property is at once evident; we shall now study it quantitatively. Experiments of Graham. — The first experiments of any consider- able importance on diffusion were those of Graham. 1 He did away with the use of any separating membrane, and used simply wide- mouthed vessels into which the solution was introduced. The vessel was then completely covered with water, allowed to stand, and the amount of substance which passed out by diffusion determined after a time. He found that the rates at which different substances dif- fuse varied greatly with the nature of the substance. Acids in gen- eral diffused more rapidly than salts, and the different salts varied greatly as to their diffusibility. Graham found that the constituents of some double salts, like the alums, could be partly separated by means of diffusion. He showed that the quantity of substance which diffuses in a given time is roughly proportional to the concentration of the solution originally employed. Fick's Law of Diffusion. — The first to arrive at any broad gen- eralization in connection with the phenomenon of diffusion was Eick, and his law is probably the most important which has ever been dis- covered in connection with this phenomenon. Fick stated his law thus : 2 " The amount of salt which diffuses through a given cross-section is proportional to the difference in concentration of two cross-sections lying infinitely near to one another, or is proportional to the difference in concentration." Weber's Method of Measuring Diffusion. — After Fick had pro- posed his law a number of attempts were made to determine its accuracy. Weber 3 devised for this purpose a method which, for simplicity and accuracy, far exceeded all those which had been pre- 1 Phil. Trans. 1850, 1, 805 ; 1851, 483. Lieb. Ann. 77, 56, and 129 (1851) ; 80, 197 (1851). 2 Pogg. Ann. 94, 69 (1855). *Wied. Ann. 7, 469, and 536 (1879). SOLUTIONS 275 viously used. This method was based upon a principle which will be considered in detail under electrochemistry. A brief description of the principle must suffice in this place. If two plates of the same metal are immersed in solutions of a salt of that metal having dif- ferent concentrations, and the plates connected, we have an element with a definite electromotive force. The electromotive force of such an element depends upon the difference in the concentration of the two solutions, and upon this fact is based the possibility of measuring diffusion by such a method. A cylindrical vessel was closed at the bottom by an amalgamated plate of zinc. Upon this was poured a concentrated solution of a zinc salt. A more dilute solution of the same zinc salt was poured upon the more concentrated, and on the surface of the more dilute solution was placed a second plate of zinc. The two zinc plates were the electrodes, and the electromotive force of this couple at any instant depends upon the difference in concentration of the two solutions at that particular moment. The two solutions being placed in contact, diffusion of the zinc salt continually took place from the more concentrated to the more dilute solution. The dif- ference in concentration became continually less, and, consequently, the electromotive force of the element became gradually smaller. When the two solutions had, by diffusion, become of the same con- centration, the electromotive force would of course entirely disappear. Testing the Law of Fick. — If we apply Pick's law to this method, we obtain the following expression when the time is long : — H is the height of the vessel used in the experiment, t is the time of the experiment, and A is a constant. IT 2 . If the law of Fick is true, the expression —Jc is a constant, independent of the time during which the experiment has lasted. Weber tested this point experimentally and obtained the following values : — ^ Days ^p* 4- 5 0.2032 5- 6 0.2066 6- 7 0.2045 7- 8 0.2027 8- 9 0.2027 9-10 0.2049 10-11 0.2049 These results confirm at once the correctness of the law of Fick. 276 THE ELEMENTS OF PHYSICAL CHEMISTRY The law has been further tested by a number of different experi- menters, using different methods. Scheffer 1 covered the solution ■with pure water, and determined the amount of substance which diffused upward into the water. He determined also the influence of concentration on the value of the diffusion constant fc. The fol- lowing results are taken from his paper, — n is the number of mole- cules of water to one molecule of substance, t is the temperature : — t lb h Sulphuric acid 11°.3 71.3 1.12 Sulphuric acid . 7°.5 686.0 1.03 Nitric acid 9°.0 7.3 2.00 Nitric acid 9°.5 73.5 1.77 Nitric acid 9°.0 426.0 1.74 Hydrochloric acid 11°.5 7.5 2.74 Hydrochloric acid 11°.0 108.0 1.84 Ammonia 4°.5 15.9 1.06 Ammonia 4°.5 84.5 1.06 Sodium hydroxide 8°.0 329.0 1.05 Sodium hydroxide 8°.0 329.0 1.04 Calcium chloride 8°.5 19.1 0.70 Calcium chloride 10°.0 27.6 0.71 With the exception of hydrochloric acid, the constant varies only slightly with the concentration, as would follow from the law of Fick. Stefan 2 showed from the law of Fick as applied to a long vessel, that the quantity a, which diffused through a given area q, should be expressed thus : — fkt a = cq-^-. This was tested experimentally by Voigtlander, 8 who worked with solutions in solid agar-agar jelly. It had already been shown by Graham,* and it was subsequently confirmed by Voigtlander, that the rate of diffusion was essentially the same in the jelly as in water. The advantages in using jelly instead of water in studying diffusion are obvious. The effect of jarring the solution would be lessened, and there would be far less mixing of the solution due to currents pro- duced by unequal heating of different parts of the mass. By work- ing with jelly solutions it was, then, possible to carry out diffusion 1 Ber. d. chem. Gesell. 15, 788 ; 16, 1903 (1882-1883). Ztschr. phys. Chem. 2, 390 (1888). 2 Wien. Akad. Ber. 79, 161 (1879). « Ztschr. phys. Chem. 3, 316 (1889). 4 Phil. Trans. 1861, p. 183. SOLUTIONS 277 experiments extending over a much greater period of time than had been practicable with aqueous solutions. Voigtlander 1 worked with a 0.72 per cent solution of sulphuric acid. He allowed this to diffuse into a cylinder containing agar-agar, and determined the amount a, which diffused through a square centimetre in a given time t. All the values of a were calculated on the basis of 60 minutes, hence the value 60 in the following constant. Time Amount Diffused a „v'60 a 5 minutes 0.30 1.04 40 minutes 0.86 1.05 120 minutes 1.48 1.05 300 minutes 2.44 1.09 900 minutes 4.30 1.11 1020 minutes 4.61 1.10 2880 minutes 7.05 1.02 These, and other similar results obtained by Voigtlander, agree with the formula deduced by Stefan, and confirm the law of Fick. Voigtlander 2 also determined a number of diffusion constants of acids, bases, and salts; and the temperature coefficients between 0°-20°, and 20°-40°. The law of Fick has also been tested and confirmed repeatedly by subsequent work, so that it can now be regarded as a well-estab- lished law of nature. The Cause of Diffusion. — What is the cause of diffusion ? What force operates to drive the dissolved substance into all parts of the solvent until the whole becomes homogeneous ? To obtain an answer to this question we must go back to the fundamental law of diffu- sion — the law of Fick. Diffusion depends upon difference in con- centration, and upon this alone, temperature being constant. This suggests at once the law of Boyle for the osmotic pressure of solutions. Osmotic pressure is proportional to concentration ; i.e. it depends upon the difference in concentration of the solution and pure solvent, or of one solution and another. Since diffusion depends upon difference in concentration, and osmotic pressure depends upon difference in concentration, the question arises, is not osmotic press- ure the cause of diffusion ? i Ztsehr.phys. Chem. 3, 321 (1889). 2 Ibid. 3, 332 (1889). 278 THE ELEMENTS OF PHYSICAL CHEMISTRY We shall see that this is very probably the case. In the first place, Boyle's law for osmotic pressure is strictly analogous to the law of Fick for diffusion. Again, the law of G-ay-Lussac for osmotic pressure holds for the temperature coefficient of diffusion, as we have already seen. The principle of Soret is but an expression of this fact. It will be remembered that the change in concentration of a homogeneous solution, produced by keeping the different parts at different temperatures, is about ^ ¥ of the original concentration for every difference of one degree in temperature. Here, then, we have two fundamental laws of osmotic pressure applying to diffusion. Diffusion in solutions takes place very slowly, as we saw when discussing the principle of Soret, while diffusion in gases quickly establishes equilibrium. This is just what we should expect, even if osmotic pressure is exactly equal to gas-pressure under the same conditions. Equilibrium is established quickly in gases because there is comparatively little inner friction and the particles can move freely. The friction in solutions is much greater, due to the presence of the solvent, and, consequently, the dissolved particles move through the solvent much more slowly than the gas particles through space. Inner friction is, then, the chief cause for the long time required for diffusion to establish equilibrium. To summarize, we can say that osmotic pressure and diffusion obey the same laws, and the former is either the cause of the latter, or they both have a common cause. Since we know of no such com- mon cause we are justified in ascribing diffusion to osmotic pressure, and in regarding the latter as the cause of the former. If ernst's Theory connecting Diffusion and Osmotic Pressure. — The relation between diffusion and osmotic pressure was brought out very clearly by Nernst 1 in his well-known paper on the " Theory of Dif- fusion." Van't Hoff had just shown the close analogy which exists between the osmotic pressure of dissolved substances and the gas- pressure of gases. Diffusion in gases was known to be due to the same cause as gas-pressure, i.e. in terms of the kinetic theory, to the movements of the gas particles; and the gas particles would move from a region of higher to that of lower pressure until equilibrium was established. Nernst saw clearly that there was a close analogy between diffusion in gases and diffusion of dissolved substances, the chief difference being in the time required to establish equilibrium. On the basis of these analogies Nernst made the following calcula- tions, which will be given in his own words for non-electrolytes, since this is much simpler than for electrolytes : — 1 Ztschr. phys. Chem. 2, 613 (1888). SOLUTIONS 279 " Given, for the sake of simplicity, a diffusion cylinder of con- stant cross-section, and let us assume that the concentration in every cross-section is the same. If there is an osmotic pressure p at the place x, in the layer qdx there exists a pressure on the substance in solution of — qdp. If c is the concentration, i.e. the number of gram-molecules of the substance in question contained in a cubic centimetre, the force which at the place x acts on every gram- molecule is — ^LE = _ _ P. if we designate by K the force which must act on a gram-molecule in solution, in order to move it with the velocity of one centimetre per second, we have — c qzdp the amount of substance in gram-molecules which wanders through the cross-section q in time z, if two layers about one centimetre apart show a difference of one in concentration. In the cases where the dissolved substance does not polymerize with increasing concentra- tion, the osmotic pressure is proportional to the concentration, i.e. p =p c, where p is the pressure in a solution of unit concentration, and we obtain — S^-lpf. (1) K dx v ' Since, however, in such great dilutions that the friction of the mole- cules of the dissolved substance against the molecules of the solvent is great with respect to their friction against one another, iT is inde- pendent of the concentration ; the elementary law of Fick for diffu- sion is at once derivable from the last expression. This law should hold rigidly for dilute solutions. At greater concentrations, on the other hand, deviations can arise, for the two following reasons; First, the force K can change with the concentration ; second, the proportionality between p and c can cease to exist." From the law of Fick the amount of salt S, which passes through the cross-section q of the diffusion cylinder in time z, if at x in the en- tire cross-section there is a concentration c (at x + dx this is c 4- do) is, S=-Wqz% (2) where k' is the diffusion coefficient for a given substance in a definite solvent. 280 THE ELEMENTS OF PHYSICAL CHEMISTRY From (1) and (2) we have : — V =J(cm. 2 sec." 1 ). In calculating diffusion coefficients the units are the centimetre and day. If we designate this by fc, we have — ft = ^8.64xl0 4 (since there are 8.64 X 10 4 seconds in a day). The pressure p is obtained from the volume occupied by a gram- molecular weight of a gas at 0°, and one atmosphere of pressure, i.e. the volume occupied by 2 grams of hydrogen or 32 grams of oxygen under a pressure of one atmosphere. According to the work of Eegnault this volume is 22,380 cm. for hydrogen, and 22,320 cm. for oxygen. If we take the mean 22,350, we have the following: To compress a gram-molecular weight of a gas at t° to a volume of one centimetre would require a pressure in atmospheres of — 22,350 (l + at)=p . Since an atmosphere is equal to 1.033 kg., p = 22,350 x 1.033 (1 + 0.0367 t) kg- = 23,080 (1 + 0.0367 cm' Substituting this value of p in the above equation and solving for K, we have — K=^. 1.99 x 10 9 (1 + 0.0367 t) kg. To ascertain the absolute value of K for any given substance, it is necessary to know the value of the diffusion constant k. This has been determined for a number of substances by Scheffer. 1 From these determinations Nernst calculated the value of iT for the follow- ing substances : — t k K Urea .... Chloral hydrate . Maimite 7°. 5 9°.0 10°.0 0.81 0.55 0.38 2.5 x 10 9 kg. 3.8 x 10 9 kg. 5.5 x 10 9 kg. 1 Ztachr. phys. Ghem. 2, 401 (1888). SOLUTIONS 281 Prom the calculations of k made by Stefan 1 on the basis of Graham's measurements, Nernst calculated the values of K for a number of substances. t * E Caramel Albumin . Cane Sugar 10° 13° 9° 0.047 0.063 0.312 44 x 10 9 33 x 10 9 6.7 x 10 9 The enormous magnitude of these numbers is, of course, surpris- ing. Thus, the force necessary to drive a gram-molecular weight of cane sugar through water with a velocity of one centimetre per second is 6700 million kilograms. Nernst raised the question as to whether this enormous resistance is closely connected with the weight, the constitution, and configuration of the molecules. With- out attempting to answer it, he pointed out that the resistance undoubtedly increases with increase in molecular weight. This is clearly seen in the above table, where those substances which have the larger molecular weights have the larger values of K. Ostwald 2 explains the enormous magnitudes of the above values as due to the very great number of molecules present in the solution — the molecular state representing matter in such a highly divided condition. As he states, the amount of force necessary to throw a stone through the air with a very considerable velocity is not great. If dow the stone is powdered, the force required to project the dust with the same velocity is very great indeed. If then we consider this process of subdivision to continue until the molecules them- selves are reached, the force required to hurl them through the air with the same velocity as was given the stone, would be enormous. If, finally, instead of through the air we hurl these infinitesimal particles through a highly resisting medium such as water, it is quite conceivable that the resistance encountered would be of the order of magnitude given above. Whether this is the expression of the whole truth, or not, it is certainly helpful in forming a con- ception of the possible cause of this very high resistance. Nernst has also worked out a theory of diffusion for electrolytes, 3 but since this involves conceptions with which it would be prema- ture to deal in this place, reference only can"be made to it. 1 Wiener Sitzungsberichte, 79, 161 (1879). 2 Lehrb. d. Allg. Ghem. I, p. 698. See Wiedeburg: Ztschr. phys. Chem. 10, 509 (1892). » Ztschr. phys. Chem. 2, 617 (1888). 282 THE ELEMENTS OF PHYSICAL CHEMISTRY Crystalloictr-and Colloids. — The section on diffusion should not be closed without brief reference to a distinction between the velocities with which substances diffuse, which was pointed out by Graham. 1 If we compare the velocity with which an acid diffuses with that of albumin, we find that the two stand in the ratio of about 50 to 1. There are many substances which, like albumin, diffuse very slowly in the presence of water. These are chiefly amorphous substances, while those which diffuse rapidly are gen- erally crystalline. The latter are termed crystalloids, the former colloids. These two classes of substances, when in solution, affect the properties of the solvent very differently. Crystalloids, as we have seen, dissolve with temperature changes. They lower the freezing- point of the solvent, and also its vapor-tension. They exert an osmotic pressure. Colloids, on the other hand, affect the properties of the solvent to only a slight extent. If they lower the freezing- point or vapor-tension of the solvent, it is only to a very slight extent. These two classes of substances can, in general, be easily sepa- rated from one another. If a solution containing both crystalloids and colloids is brought in contact with a colloidal membrane such as parchment paper, and water is placed on the other side of the mem- brane, the crystalloids will pass through the membrane, while the colloids will be prevented from doing so. This was termed by Gra- ham dialysis, and the apparatus for effecting such separations a diaiyzer. Colloidal Solutions. — Solutions of certain substances do not obey the laws of ordinary solutions, yet have, as we have seen, at least some of the properties of true solutions. Such substances are starch, albumen, gelatine, agar-agar, the gums, etc. Solutions of these substances show osmotic pressure, they lower the freezing-point and vapor-tension of the solvent, and diffuse, though very slowly. They, however, do not possess these properties to any great degree. They show only small osmotic pressure, and small lowering of the freezing-point, and diffuse very slowly indeed. While they possess the properties of ordinary solutions, they pos- sess them to such a slight degree that the difference can scarcely be accounted for simply on the basis of the greater masses of the mole- cules, or that the molecules are aggregated. Colloidal Suspensions. — A large number of apparent solutions that resemble true solutions even less closely than colloidal solutions do, are known as colloidal suspensions. Several methods of preparing iLieb. Ann. 121, 1 (1862). SOLUTIONS 283 Fig. 42. these colloidal suspensions have been worked out and applied. Colloidal suspensions of a number of the metals have been pre- pared by the electrical method devised by Bredig. Colloidal Suspensions of the Metals. — Some unusually interesting results have recently been obtained in connection with colloidal sus- pensions. It has been found possible to prepare colloidal suspensions not only of the neutral, amorphous, organic substances, but of the metals themselves- A number of years ago Carey Lea 1 showed how metallic silver could be obtained in suspension in water — the sus- pension having the same properties as that of a colloid ; and quite recently Bredig and Von Berneck 2 have worked up a more or less gen- eral method 3 for obtain- ing the most insoluble metals in the form of col- loidal suspensions. The method will be described as applied in the case of metallic platinum. Two platinum wires (a and b, Pig. 42), of about one millimetre diameter, are dipped into pure water, and brought close together. A current of from 8-12 amperes and 30-40 volts is passed through the wires. This forms an electric arc under the water. The metal is torn off from the cathode in a very fine state of division, and the water quickly becomes dark brown in color. After the suspension has acquired the concentration desired, it is filtered through a folded filter to remove any larger particles of platinum which may have been torn off. When a drop of this liquid is placed under the best microscope it looks perfectly homogeneous, which shows the very fine state of division of the platinum. In- deed, the platinum particles must be smaller than the wave-length of light. Bredig and Von Berneck found that this liquid has quite remark- able properties. It decomposes hydrogen dioxide like organic fer- ments, and resembles the latter in many other particulars. A gram atomic weight of platinum in 70,000,0000 1. of water decomposes hydrogen dioxide appreciably, thus resembling organic ferments i Amer. Journ. Science, 37, 476 (1889) ; 38, 47, 129, 237 (1889). 2 Ztschr. phys. Chem. 31, 258 (1899). 3 Ztschr. f. angew. Chem. 1898, 951. Ztschr. Elektrochem. 4, 514 (1897). Zsigmondy: Ztschr. phys. Chem. 33, 63 (1900). Bredig' s Apparatus for prb paring Colloidal Solutions. 284 THE ELEMENTS OP PHYSICAL CHEMISTRY where a very small quantity can effect a large amount of decom- position. An even more striking analogy between the action of the colloidal platinum and organic ferments is to be found in the effect of certain poisons upon both of them. A very small amount of certain substances will entirely destroy the activity of organic ferments. Exactly the same was found to be the case with the col- loidal suspension of platinum. A gram-molecular weight of hydrocy- anic acid in 1,000,000 1. of water diminished quite appreciably the activity of the colloidal platinum towards hydrogen dioxide; and a gram-molecular weight of hydrogen sulphide in 345,000 1. of water greatly diminished the activity of the platinum. A gram- molecular weight of hydrogen sulphide in 34,500 1. almost destroyed the activity of the platinum. However close the relation between these colloidal suspensions of the metals and organic ferments may be shown to be, this recent work has given an entirely new interest to the subject of colloidal suspensions in general. Other Methods of preparing Colloidal Suspensions. — Another method which is of great importance, on account both of the results which it fields and its theoretical significance, is the following: Two chemical compounds which react in the presence of an electro- lyte and give a precipitate, will nearly always give a colloidal sus- pension if no electrolyte is present. Thus, hydrogen sulphide reacts with arsenious chloride and forms a precipitate of arsenious sul- phide, hydrochloric acid being formed in the reaction. When hydrogen sulphide is passed into a solution of arsenic trioxide, arsenious sulphide is formed, but is not precipitated. It remains in the water in the form of a colloidal suspension. It should be noted that in this reaction no strongly dissociated electrolyte is present. Water is formed as one of the products of the reaction, and hydrogen sulphide is a very weakly dissociated compound. The meaning and importance of the above facts will be brought out later. Another method of preparing colloidal suspensions, especially of the metals, has been worked out and applied by Gutbier. 1 It con- sists in reducing the salts of the metals by hydrazine hydrate. Col- loidal suspensions thus prepared seem to be more stable than those obtained by the electrical method. Properties of Colloidal Suspensions. — Colloidal suspensions seem to be little more than very finely divided solid matter in the pres- ence of the solvent. Such particles can be removed by filtration i Journ. prakt. Chem. 71, 452 (1905). Cotton and Mouton : Ann. Chim. Phys. (8) 11, 145 (1907). SOLUTIONS 285 through animal membrane. In the case of a number of colloidal suspensions, when prepared by certain methods, the solid particles can actually be seen by the most improved and powerful microscopes. This is especially true of colloidal suspensions of arsenious sulphide and of metallic gold. It has not yet been definitely settled whether these colloidal sus- pensions manifest any of the properties of true solutions, even to a slight degree. It is somewhat doubtful whether they even show osmotic pressure, and, consequently, undergo diffusion. Certain properties of these colloidal suspensions have, however, been worked out, and these are important and interesting. There seems to be satisfactory evidence for the conclusion that the colloidal particles are charged electrically. This is furnished in part by the migration of the colloidal particles through the solu- tion under the influence of the current. Colloidal ferric hydroxide moves with the current towards the cathode, while colloidal arsenious sulphide moves against the current towards the anode. The ferric hydroxide is, therefore, charged positively, and the arsenious sul- phide negatively. The above property seems to be a general one for colloidal suspensions ; the hydroxides of the metals moving towards the cathode, while other colloidal suspensions, including the metal sulphides and such metals as gold and platinum, move towards the anode. Further, it has been shown by Hardy 1 that egg-albumen migrates towards the anode in an alkaline solution, but towards the cathode in an acid solution. Two theories have been proposed to account for. the electrifica- tion of the colloidal particles. According to one view the particles acquire a charge of one sign, and the surrounding water a charge of the other sign. A more probable theory is that from every colloidal aggregate there splits off either a positive or negative ion, and that the residue of the aggregate carries the opposite charge. The hydroxides would split off an ordinary hydroxy! ion, and the residue be charged posi- tively ; silicic acid would split off a hydrogen ion, etc., and the col- loidal residue be charged negatively, etc. Egg-albumen can combine with both acids and bases, and form salts. In the presence of an acid it would yield the anion of the acid, and the colloidal residue would be charged positively. In the presence of a base it would yield the cation of the base, and the residue be charged negatively. i Ztschr. phys. Chem. 33, 387 (1900). Beckhold : Ibid. 60, 257 (1907). 286 THE ELEMENTS OF PHYSICAL CHEMISTRY This theory seems to account fairly satisfactorily for the facts. Coagulation of Colloidal Suspensions. — Colloidal suspensions are not coagulated at all by non-electrolytes. They are coagulated by electrolytes, if the electrolytes are strongly dissociated into ions, and are present in sufficient quantity. 1 Almost any strongly dissociated electrolyte will produce the coagulation. If to colloidal arsenious sulphide, hydrochloric acid, ammonium chloride, magnesium sulphate, etc., are added, the arsenious sulphide is precipitated at once. The addition of cane sugar or alcohol, on the other hand, does not cause a coagulation of the arsenious sulphide. The above fact is extremely important. It is highly probable that all precipitation takes place around ions — the ion or charged particle serving as the nucleus around which the coagulation takes place. In ordinary reactions we have the solid matter coagulated and precipitated, and not remaining as a colloidal suspension, simply because we have ions present. It is obvious that this is a fact of the profound- est significance both for qualitative and quantitative analysis. The suspension of the colloidal particles is probably closely associated with the electrical charges which they carry. When two colloidal suspensions having the same kind of charge are mixed, no precipitation results. However, when two such suspensions having opposite electrical charges are mixed, there is a coagulation of both colloids ; and by using suitable quantities, both colloids can be com- pletely coagulated. Thus, when arsenious sulphide and ferric hydroxide, both in the state of colloidal suspension, are mixed, coagulation results and both are precipitated. When a colloidal suspension is coagulated by an ion of an electro- lyte, the following facts have been established : If the ion has the same kind of charge as the colloid, it does not matter whether it carries one such charge or more than one, as far as the coagulation of the colloid is concerned. If the ion has an electrical charge of opposite sign to that of the colloid, then much less of a polyvalent ion is required to effect the coagulation, than of a univalent ion. These facts are all in accord with the above suggestion. Explanation of the Coagulation of Colloids by Ions. — The action of ions in coagulating colloidal suspensions is made clear by the work of Burton. 2 There is a marked difference in potential between the particle in a colloidal suspension and the water. This dimin- ishes the surface-tension between the two, and there is nothing to i Whitney and Ober : Ztschr. phys. Chem. 39, 630 (1902). 2 Phil. Mag. 12, 472 (1906). SOLUTIONS 287 draw the fine particles together into larger particles and produce a precipitation. When an electrolyte is added to the colloidal suspension, the colloidal particles attract the ions with the charge opposite to their own, and the difference in potential between the colloidal particles and the water becomes less and less. As this difference becomes less, the surface-tension between the particles and water becomes greater. When this surface-tension has become sufficiently great, the colloidal particles are drawn together so as to expose less surface for a given mass, and we have a clotting or precipitation of the colloidal suspension. Experimental work, carried out in the laboratory of J. J. Thom- son, and which it would lead us too far to discuss in detail, confirms the above explanation. COLOR OF SOLUTIONS Color of Solutions of Non-electrolytes. — If we are dealing with non-electrolytes, i.e. substances which exist in solution entirely as molecules, it is obvious that the color of such solutions is the color of the dissolved molecules, provided, of course, that the solvent is colorless. The color of such solutions resolves itself then into the question of the color of the molecules themselves. Our knowledge " Condition and Properties of Colloids." Zacharias: Ztschr.phys. Chem. 39, 468 (1902). Winssinger: Bull. Acad. Belg. (3) 15, Nr. 2 (1888). Van Bemmelen : Bee. Pays Bas, 7, 37 (1888). Krafft : Ber. d. chem. Gesell. 29, 1334 (1896). Barus : Amer. Journ. Science, 6, 285 (1898). Krafft : Ber. d. chem. Gesell. 32, 1596 (1899). Stark: Wied. Ann. 68, 618 (1899). Whetham : Phil. Mag. (5) 48, 474 (1899). Levi: Gazz. chim. ital. 30, II, 64 (1900). Donnan : Ztschr. phys. Chem. 37, 735 (1901). Flemming : Ibid. 41, 427 (1902). Freundlich : Ibid. 44, 129 (1903). Billitzer: Ibid. 45, 307 (1903). Donnan: Ibid. 46, 197 (1903). Hardy : Proc. Cam. Phil. Soc. 12, 201 (1903). Miiller : Ztschr. anorg. Chem. 36, 340 (1903). Bechhold : Ztschr. phys. Chem. 48, 385 (1904). Paal and Amberger : Ber. d. chem. Gesell. 37, 124 (1904). Duclaux: Compt. rend. 138, 144, 809 (1904). Billitzer: Ztschr.phys. Chem., 51, 129 (1906). A. A. Noyes, Lecture, Journ. Amer. Chem. Soc. 27, 85 (1905). 288 THE ELEMENTS OF PHYSICAL CHEMISTRY in this field is not yet sufficient to enable us to deal with this prob- lem satisfactorily ; yet it is quite certain that the color of molecules is due primarily to the nature of the chemical atoms which enter into the molecules. That constitution also has an influence is made clear by many facts which are known. The problem, however, which is of special interest here, deals not with the color of molecules but with the color of ions ; i.e. with the color of solutions of dissociated substances. Color of Solutions of Electrolytes. — The problem of the color of solutions of electrolytes is simpler, and of more interest from our standpoint at present, than the problem with non-electrolytes. If the electrolyte is completely dissociated, i.e. completely broken down into ions, it is obvious that the color of such solutions is not due to the color of molecules, since there are no molecules present. The color of such solutions is due to the ions present, and to these alone. Some of the consequences of this conclusion from the theory of electrolytic dissociation are very interesting. If we have a number of compounds containing say colorless anions combined with the same colored cation, the solutions of all of these substances should have the same color. Thus, take the salts of cobalt with colorless acids, the chloride, sulphate, nitrate, acetate, etc., dilute solutions of all of these salts should have the same color, and that the color of the cobalt ion, since such solutions are completely dissociated and the anion in each case is colorless. Here the facts confirm the theory. All such salts have exactly the same color in dilute solutions. Conversely, if we have colorless cations combined with a colored anion, the solutions of the compounds formed should have the same color. This problem has been very thoroughly investigated by Ostwald. 1 He prepared solutions of a number of salts of perman- ganic acid with colorless cations, such as potassium, sodium, ammo- nium, lithium, barium, magnesium, aluminium, zinc, cadmium, etc., and then studied the absorption spectra. If our theory is correct, solutions of all of these substances should have the same color, which is to say that they should all have the same absorption bands. These bands were both carefully measured and photographed by Ostwald. These salts show five absorption bands in the yellow and green, and four of these were measured for thirteen salts of perman- ganic acid. The results of Ostwald's measurements are given in the following table : — 1 Ztschr. phys. Chem. 9, 579 (1892). SOLUTIONS 289 PERMANGANATES. ABSOBPTION BANDS i II m IV Hydrogen .... 2601 ± 0.5 2698 ±0.8 2804 ±0.7 2913 ± 1.7 Potassium . 2600 ±1.3 2697 ±0.1 2803 ±0.9 2913 ± 1.1 Sodium 2602 ± 1.2 2698 ± 0.8 2803 ±0.7 2913 ± 0.8 Ammonium 2601 ± 1.3 2698 ±1.4 2802 ±0.1 2913 ± 0.1 Lithium 2602 ±0.2 2700 ±0.2 2804 ±0.8 2914 ± 1.7 Barium 2600 ±0.9 2699 ±0.8 2804 ± 0.6 2914 ± 1.3 Magnesium 2602 ±0.8 2700 ±0.6 2802 ±0.7 2912 ±1.8 Aluminium . 2603 ±0.4 2699 ±0.9 2804 ±0.9 2914 ±0.7 Zinc . 2602 ±0.5 2699 ±0.7 2802 ± 1.2 2912 ±1.1 Cobalt 2601 ±0.2 2698 ±0.1 2803 ±0.9 2912 ± 1.7 Nickel 2603 ±0.5 2700 ± 0.7 2804 ±0.7 2913 ± 1.8 Cadmium . 2600 ±0.1 2700 ±0.2 2803 ±0.8 2913 ± 1.4 Copper .... 2602 ± 1.2 2699 ±0.1 2803 ±0.9 2913 ± 0.8 Ostwald concluded from these results that the absorption spectra of all the thirteen salts are exactly the same, to within the limit or error of measurement. The spectra of ten of these salts were photographed, the one directly over the other, and the results are given in the accom- panying figure. The agreement between the position and char- acter of the bands is so striking, that there is no room for doubt that these salts show the same absorption bands. In addition to the permangan- ates Ostwald studied a number of classes of substances. The absorp- tion spectra of ten salts of fluo- rescein were also photographed. The bands here agree as closely in position and nature as with the permanganates. Salts of eosin yellow, eosin blue, iodoeosin, ro- zolic acid, diazoresorcin, etc., with colorless cations were made, and the absorption bands of each class of compounds compared. Then salts of colored bases with color- less acids were prepared and studied Fig. 43. These included especially 290 THE ELEMENTS OF PHYSICAL CHEMISTRY p-rosaniline and aniline violet. The results with p-rosaniline are given below. The absorption band which was measured is in the yellow-green. P-Rosaniline, Dilution 5600 l. 1. Levulinio acid . . . 2715 ±0.8 11. Hyposulphuric acid . 2715 ±1.1 2. Acetic acid .... 2715 ±1.4 12. Trichlorlactic acid . 2715 ±0.7 3. Chloric acid . . . 2716 ±0.4 13. Glycolic acid . . . 2714 ±1.3 4. Benzoic acid . . . 2714 ±1.4 14. Phthalanilic acid . . 2716 ±1.3 5. Hydrochloric acid . 2714 ±1.1 15,. Perchloric acid . . 2715 ±1.2 6. Sulpbanilic acid . . 2715 ±1.2 16. Salicylic acid . . . 2715 ±1.5 7. Nitric acid .... 2715 ±0.5 17. Monochloracetic acid 2715 ±1.5 8. Phthalamodoacetic acid 9. Butyric acid . . . 2715 ±1.4 18. Lactic acid .... 2715 ±1.0 2715 ±1.3 19. O nitrobenzoic acid . 2715 ±1.3 10. Phenylpropiolic acid . 2715 ±0.9 20. Sulphuric acid . . . 2715 ±0.9 These results were also photographed, and the absorption bands of these twenty salts are shown in Fig. 44. The figures have the same significance in the plates as in the tables. Ostwald's work included about 300 compounds, in some of which the cation was colored, while others contained a colored anion. He concluded frbm this elaborate investigation, that salts with one and the same colored ion, in dilute solutions, always have the same spectra. If both ions were colored, the color of the solution would be the sum of the colors of the two ions. The color of completely dissociated solutions is, therefore, an additive property. Change in Color with Change in Electrical Charge. — An ion having the same chemical composition does not always have the same color. Take the ion Mn0 4 . If it is formed by the dissociation of potas- sium permanganate, KMn0 4 (KMn0 4 = K + Mn0 4 ), it is purplish red, and gives the characteristic color to a solution of this salt. If it is formed from potassium manganate, K 2 Mn0 4 = K + K + Mn0 4 , it is green. In the first case it carries one negative charge, in the second case two ; and this difference in electrical condition produces a change in color from purple to green. Again, to take a simpler example : The iron ion in the ferrous condition is green, as is seen in solutions of ferrous salts; while the iron ion in the ferric condition is yellow, as is seen in solutions of ferric salts. An almost unlimited number of examples of changes SOLUTIONS 291 in the color of ions with change in the electrical charge which they carry, might be given. One other point should be mentioned in this connection. An ele- ment in the form of an ion may have its own definite characteristic color. When this element is combined with other elements to form Fig. 44. a complex ion, the color of the complex may have no simple relation to that of the element when present alone as an ion. The cobalt ion is red. When combined with cyanogen to form a complex anion it is colorless. Thus the compound K 3 Co(CN) 6 dissociates into K + K + K + Co(CN) 6 , See Schutze : Ztschr. phys. Chem. 9, 109 (1892). Carrari : Gazz. chim. ital. 27, 11, 455 (1897). Pfluger : Drude's Ann. 12, 430 (1903). Utescher : Dissertation, Gottingen (1905). Fox : Dissertation, Jena (1906). 292 THE ELEMENTS OF PHYSICAL CHEMISTRY and the solution of this compound is colorless. Here, also, many examples are available. Theory of Indicators. — We have just seen that molecules may be colored, giving the characteristic color to solutions of undissociated substances; and that ions also may be colored, giving the color to completely dissociated solutions. A molecule may have the same color as the ions into which it dissociates, or it may have a different color. A colorless molecule may dissociate into ions, one or more of which is colored ; and a colored molecule may dissociate into color- less ions. Upon these facts is based the use of indicators in quantitative analysis. An indicator is a compound which shows a change of color when the solution passes from the acid to the basic condition, and vice versa. An indicator is always either a weak acid or a weak base, which, on dissociation, yields an ion which has a different color from the molecule itself. Indicators fall then, naturally, into two classes, — acidic indicators and basic indicators. As an example of an acidic indicator, we will take first phenolphthalein. This is a weak acid, which means that in the presence of water it is very slightly dissociated, if it is dissociated at all. The molecules of phenol- phthalein are colorless, as is shown by the fact that an aqueous or alcoholic solution of this substance is colorless. If a solution of a strbng base is added to phenolphthalein, the salt of that base is formed. This salt, like most salts, is readily dissociated in the presence of water. The salt of phenolphthalein dissociates into the cation of the base and the complex organic anion; e*j.g. the sodium salt dissociates into the cation sodium and the complex organic anion , and it is this latter which gives the characteristic color of this indicator. In using this indicator, a small quantity is brought into the pres- ence of the acid, which is to be titrated against a strong base. The indicator, in the presence of pure water, is almost completely undis- sociated. In the presence of the strong acid which contains many free hydrogen ions, it would be dissociated even less than in pure water, as we shall learn. An alkali is added and the strong acid is all neutralized. The moment an excess of alkali is present, it forms a salt with the phenolphthalein. This salt dissociates at once, and the colored anion gives its characteristic color to the solution. Phenolphthalein cannot be used with weak acids nor weak bases. If the acid is so weak that its salts, even with strong bases, are hydrol- yzed, i.e. broken down by water into the free acid and the free base, the free base would begin to react with the phenolphthalein long SOLUTIONS 293 before enough base had been added to completely neutralize the acid. The result would be the appearance of a faint color on the addition of a little alkali, and this color would increase in intensity as more and more alkali was added. There would, then, be no sharp change in color when all the acid had been neutralized, and the indicator would be practically worthless in such cases. Thus, carbonic and phosphoric acids and the phenols cannot be titrated with phenol- phthalein as an indicator. If a weak base is used, such as ammonia, there will also be a certain amount of hydrolysis of the salt. This will leave some free base present, which will react with the phe- nolphthalein and give rise to a gradual change in color. But even if the ammonium salt of the acid which is being titrated is not hydrolyzed by water, ammonia cannot be used with phenolphthalein. Ammonia is a weak base, and phenolphthalein is a weak acid, and the salt of the two would itself be hydrolyzed by water. The indi- cator would, therefore, not act sharply when ammonia was used as a. base. It is well known that the facts agree very satisfactorily with the theory. Phenolphthalein cannot be used as an indicator with either weak acids or weak bases. A somewhat different view as to the action of phenolphthalein as an indicator is held by Stieglitz 1 and others. According to them it is not the anion of phenolphthalein itself which gives the color, but when phenolphthalein is treated with a base it undergoes a tau- tomeric change, giving a salt of an acid with a quinone structure. This salt is dissociated into a sodium cation and an anion with a quinone structure which is colored. This conception should not be looked upon as opposed to the view of Ostwald. It really supplements the latter, going farther than Oswald attempted to go. The fundamental principle of the Oswald explanation remains unchanged — that the action of indi- cators is due to the formation of a salt of an acid or a base, and this then undergoes dissociation, yielding a colored anion or cation. Whether the color of phenolphthalein is due to the anion of phenolphthalein as such, or to a transformation product of this sub- stance, is interesting and important, but is subordinate to the funda- mental question as to the general principle involved in the action of indicators. Another example of an acid indicator whose molecules are nearly 1 Journ. Amer. Chem. Soc. 25, 1112 (1903). Rohland : Ber. d. deutsch. chem. Gesell. 40, 2172 (1907). Meyer : Ibid. 40, 2430 ; Hantzsch : Ibid. 40, 3017 (1907). 294 THE ELEMENTS OF PHYSICAL CHEMISTRY colorless and whose anion is colored, is p-nitrophenol. In alcoholic solution, in which the substance is almost undissociated, it is nearly colorless. Water dissociates it slightly, and consequently the aqueous solution is slightly colored. If an alkali is added, the salt of this weak acid is formed, and this dissociates into the metallic cation and into the anion C 6 H 4 (!N'0 2 )0, which is deep yellow in color. The action of this substance as an indicator will be understood at once from the above description of the action of ph enolphthalei'n. Para-nitrophenol may also be used to illustrate the driving back of the dissociation of a substance by adding another sub- stance with a common ion. Para-nitrophenol is a weak acid and only slightly dissociated. It is, however, sufficiently dis- sociated to yield enough anions to give a slightly yellow color to the solution. If a strong acid is added to an aqueous solution of para-nitro- phenol, the dissociation of the latter is driven back, due to the addi- tion of the common hydrogen ion, and the aqueous solution becomes colorless. Litmus is an example of an acid indicator whose molecules are colored, but whose anion has a different color. The molecules of the weak litmus acid are red. When an alkali is added, the salt is formed, and this dissociates, giving the free litmus anion, which is deep blue. Litmus, like phenolphthalem, cannot be used satisfac- torily with weak bases. These would form salts with the litmus, which would be hydrolyzed and prevent a sharp color reaction ; or their salts, with any but the strongest acids, would undergo some hydrolysis and prevent a sharp appearance of color. In order that litmus should be used in titrating weak acids, only the strongest bases can be employed. An acid indicator which can, however, be used with weak bases is methyl orange. This is a considerably stronger acid than the indi- cators which we have already considered. The molecules of the free acid are red, the anions yellow. In the presence of a strong acid we have, therefore, the characteristic red color ; while in the presence of a base the salt is formed, and this dissociates, yielding the yellow anion. This indicator can be used with weak bases, provided they are titrated with strong acids. In these cases there is but slight hydrolysis of the salts formed, and also but slight hydrolysis of the salt formed by the methyl orange and the weak base, since the indi- cator is a fairly strong acid. In the above discussion of acid indicators it will be seen that SOLUTIONS 295 weak acids must always be titrated with strong bases, and a weakly acid indicator may be employed. Weak bases, on the other hand, must be titrated with strong acids, and a strongly acid indicator must be employed. Basic indicators are but little used in practice. As an example of this class we may take cyanine. This is a weak base, and therefore but little dissociated. The molecules are deep blue in color. In the presence of an acid a salt is formed, which dissociates into the anion of the acid and the cation of the base. This very complex cation is colorless; consequently the indicator is blue in the presence of a base, and colorless in the presence of an acid. The examples considered above suffice to illustrate the different types of indicators, and to show how satisfactorily their action is explained in terms of the theory of electrolytic dissociation. 1 A Color Demonstration of the Dissociating Action of Water. — Jones and Allen 2 have worked out a color demonstration of the dissociating action of water, which is based upon the principle of indicators just considered. If to an alcoholic solution of phenolphthaleifn a few drops of aqueous ammonia are added, there is no sign of the red color of the indicator. If water is now added to the alcoholic solution, the red color appears. When potassium or sodium hydroxide is substituted for ammonia, the red color appears at once, without the addition of water. There is thus a marked difference between potassium or sodium hydroxide, and ammonium hydroxide. It would be difficult to interpret these facts without the aid of the theory of electrolytic dissociation. In the light of this theory they are perfectly intelligible. When a few drops of aqueous ammonia are added to several cubic centimetres of alcohol, little or no dissociation of the ammonium hydroxide is effected. The addition of water dissociates the base, the degree of dissociation depending upon the amount of water pres- ent with respect to alcohol. The presence of the ions NH 4 and OH would cause the phenolphthaleifn to dissociate into — C< +H. / X! 6 H 4 OH The complex anion gives its characteristic color to the solution in i Bottger : Ztschr. phys. Ohem. 24, 253 (1897). Salm : Ibid. 57, 471 (1906). 2 Amer. Ohem. Journ. 18, 377 (1896). 296 THE ELEMENTS OF PHYSICAL CHEMISTRY which it is present. The hydrogen and hydroxyl ions would then combine and form water. It is possible that the actual course of the reaction is somewhat different from that just described. It may be that the ammonium first combines with the phenolphthalein in the alcoholic solution. The addition of water would then dissociate this compound, giving the colored anion referred to above. The dissociation theory furnishes this explanation. It remains to determine whether the explanation is true. If it is, then a solution formed by adding a little aqueous ammo- nia to a considerable volume of alcohol, should show little or no dissociation, and the amount of the dissociation should increase with the addition of water. Solutions of potassium or sodium hydroxide, in mixtures of alcohol and water, should be more dissociated than corresponding solutions of ammonium hydroxide. Indeed, a solution of sodium or potassium hydroxide in alcohol alone should manifest some dissociation, since, as stated above, it gives the color reaction with phenolphthalein. All of these points were tested experimentally by the conduc- tivity method, with the result that the theory of electrolytic disso- ciation was confirmed at every point. This experiment furnishes a satisfactory lecture demonstration of the dissociating action of water. A few drops of an alcoholic solution of phenolphthalein are placed in a glass cylinder and diluted to, say, 50 c.c. by the addition of alcohol. A few drops of an aqueous solution of ammonia are then added. A red color may appear where the aqueous ammonia first comes in contact with the alcoholic phenolphthalein, but this will disappear instantly on shaking the cylinder, leaving the solution with a yellowish tint, possibly due to the formation of the ammonium salt of phenolphthalein. Water is then gradually added to the cylinder, when the red color will appear, at first faint, then stronger, as the amount of water increases. When ' the red color has become intense, add a considerable volume of alcohol, and the entire color will disappear, leaving the solution slightly yellow again. Fluorescence and Dissociation. — Closely connected with the color of solutions is the fluorescence shown by certain substances in solu- tion. When a substance like fluorescein is brought into the presence of water, it dissolves to only a slight extent, and the solution formed is only slightly fluorescent. If to fluorescein in the presence of water a little alkali is added, an intense fluorescence appears at once. This is satisfactorily interpreted in terms of the dissociation SOLUTIONS 297 theory. Fluorescein is a weak acid only slightly soluble in water, and very slightly dissociated by it. Being an acid, it would disso- ciate into a hydrogen cation and a complex organic anion. The hydrogen cation is evidently not fluorescent, since all acids yield hydrogen cations as one of the products of dissociation, and solutions of acids in general are not fluorescent. The fluorescence of fluorescein must, then, be due to the complex organic anion formed as the product of dissociation of the fluorescein molecule. If this is the true explanation of the fluorescence of this sub- stance, then, if we could increase the dissociation of fluorescein by any means, we should increase the fluorescence, since we would increase the number of fluorescent ions present in the solution. This can be accomplished by adding an alkali, which forms a salt with the fluorescein. This, like all other salts, dissociates readily in the presence of water, and we have a large number of fluorescent ions formed; hence the increase in fluorescence on addition of an alkali. It is sometimes stated that in this and similar cases we have the alkali salt formed, and it is this salt which is fluorescent as such. It should be stated here, that it has been shown that under such conditions there is not a trace of the alkali salt of fluorescein pres- ent in the solution, if the solution is very dilute. It can be shown by any of the well-established methods for measuring dissociation, that all of the salt present is broken down into ions and that there are no molecules in the solution. If there are no molecules present in the solution but only ions, it is obvious that the fluorescence can be due only to the ions. The earlier explanation that the phenomenon observed here, and also the phenomena observed with indicators, were due to the forma- tion of alkali salts, and that these persisted as such in the solutions, giving the characteristic properties, has given way in the light of the discoveries of modern physical chemistry. We now know that in all such cases we are dealing not with molecules as such, but with the ions into which they dissociate. Amphoteric Electrolytes. — Certain electrolytes in aqueous so- lution show at the same time acid and basic properties. These are termed amphoteric electrolytes} As they show both acid and basic properties, their solutions must contain both hydrogen and hydroxyl ions. These substances must then dissociate according to both the following schemes : i Bredig : Ztschr. Electrochem., 6, 33 (1900). 298 THE ELEMENTS OF PHYSICAL CHEMISTRY EOH = Rb + H; KOH = B + OH. We have here, as Bredig points out, a kind of " electrolytic tau- -tomerism," which manifests itself quite frequently. There are quite a number of amphoteric organic compounds. Diazonium hydroxide, C 6 H 5 ■ N 2 • OH, described by Hantzsch and Davidson, 1 forms salts with both hydrochloric acid and sodium hydroxide. Ox- imes having the formula B ■ NOH form salts with both acids and bases. Aminoaeetic acid is also an example of an amphoteric electrolyte. In inorganic chemistry there are also a number of compounds that can form salts either with acids or bases. Zinc hydroxide 2 and aluminium hydroxide 3 are good examples of such substances. In physiological chemistry there are a large number of ampho- teric substances. We need mention only leucine, taurine, tyrosine, asparagine, sarcosine, anthranilic acid, etc. These substances prob- ably play a prominent role in biochemistry. The dissociation of amphoteric electrolytes has been studied by Winkelblech 4 and Walker, 5 and found to be in accordance with the law of mass action. OTHER PROPERTIES OP SOLUTIONS Properties of Solutions of Non-electrolytes. — In dealing with the properties, in general, of solutions, we must clearly distinguish between solutions of undissociated and of dissociated substances. If we are dealing with the former class, the dissolved substances exist only in the molecular condition, and it is obvious that all of the properties are the properties of the dissolved molecules plus those of the solvent. If we are dealing with aqueous solutions, the properties of water being so well known, we can easily determine what are the properties of the dissolved substance. See R. Meyer : Ztschr. pkys. Ghem. 24, 468 (1897). Bredig and Winkelblech : Ztschr. Electrochem. 6, 33 (1899). Hantzsch: Ber. d. chem. Gesell. 37, 1076 (1904). Lundgn : Ztschr. phys. Chem., 84,532 (1906). Hantzsch: Ibid. 56, 67 (1906). Walker : Ibid. 56, 575 (1906). Johnston : Ibid. 57, 557 (1907). dimming : Ibid, 57, 574 (1907). Walker : Ibid. 57, 600 (1907). 1 Ber. d. chem Gesell. 31, 1612 (1898). 2 Elements of Inorganic Chemistry, H. C. Jones, p. 389. 8 Ibid. p. 409. 4 Zeit. phys. Chem. 36, 546 (1901). 6 Proc. Boy. Soc. 73, 155 (1904). SOLUTIONS 299 Properties of Solutions of Electrolytes. — If we are dealing with electrolytes, the problem is very different. The molecules are more or less broken down into ions, and at very high dilutions all the molecules are dissociated into ions. The properties of such solutions are obviously not the properties of molecules, since there are no molecules present, but the properties of the ions, which are the only units present in the solution. In terms of the theory of electrolytic dissociation, the properties of completely dissociated solutions are the sum of the properties of all the ions present in the solution — are additive. We have seen that this is true in the case of color ; we shall see in a moment how it applies to other physical properties. Meanwhile, a word in reference to the chemical properties of com- pletely dissociated solutions. Chemical Properties of Completely Dissociated Solutions. — The chemical properties of solutions which contain only ions must be the chemical properties of the ions present. Some surprising facts, however, come out when we study the chemical properties of ions. An element in the ionic state has certain definite characteristic properties. These properties bear no close relation to those of the same element in the atomic or molecular condition. Take the ele- ment which has often been cited in this connection — chlorine. One of the most characteristic reactions of the ion chlorine is the forma- tion of silver chloride by combining with the ion silver. Chlorine in the molecular condition, as in the form of gas, or even when freshly dissolved in water, does not precipitate a solution of silver nitrate. Further, chlorine in compounds like CH 3 C1, C 2 H 5 C1, etc., is not precipitated by silver nitrate, because these compounds are not dissociated by water, and the chlorine is, therefore, not in the ionic condition. Again, chlorine may even exist in the ionic condition and not be precipitated by silver nitrate, if it is in combination with other elements, forming a complex ion. Thus, the chlorine in potassium ■chlorate is not precipitated by silver nitrate, although the chlorine forms part of an ion. Potassium chlorate dissociates thus : — KClOs = K + C10 3 . The chlorine is present in combination with oxygen, forming an anion, but it has lost its most characteristic property, due to the presence of the oxygen. Another example will illustrate the same point. The most char- acteristic reaction of the ion S0 4 is its power to combine with the 300 THE ELEMENTS OF PHYSICAL CHEMISTRY ++ = ion Ba and form barium sulphate. If the ion S0 4 is in combination with a complex group, it may not precipitate barium sulphate at all. Thus, if sulphuric acid and alcohol are warmed together there is formed the compound tt s y S0 4 , ethyl-sulphuric acid. This, like all acids, dissociates into a hydrogen cation, and the remainder of the compound forms the anion — in this case C 2 H 5 S0 4 . When a solution of ethyl-sulphuric acid is treated with barium chloride, no precipitate is formed. These examples suffice to show with what care we must judge of the chemical properties of substances under different conditions, knowing their properties under any one set of conditions. Physical Properties of Completely Dissociated Solutions. — That the physical properties of completely dissociated solutions are, in gen- eral, additive, will be seen from a brief account of some of the work which has been done on solutions of salts. Only a few physical properties will be considered. The densities of solutions of a number of salts have been studied by J. Traube. When a salt is added to water, there is produced a change in volume. If the salt is completely dissociated by the water, this change must be the sum of the changes produced by all the ions present. If we represent by d the density of a solution containing a gram- molecular weight of salt having a molecular weight M, in g grams of water, and the density of pure water by d , we have an increase in volume Av : — d d The following changes in volume will show the additive nature of this property : — DlFP. KC1 26.7 9.0 NaCl 17.7 (8.4) (9.0) KBr 35.1 8.4 NaBr 26.7 (10.3) (9.4) KI 45.4 9.3 Nal 36.1 The differences between the halogens are practically constant whether they are combined with potassium or sodium. Similarly, the differences between the alkalies are constant, regardless of the nature of the halogen with which they are combined. The change in volume in neutralization has given some interesting SOLUTIONS 301 results in the hands of Ostwald. 1 He measured the volume changes produced by neutralizing potassium, sodium, and ammonium hydrox- ides ■with a large number of acids. The solutions contained a gram- equivalent of the substance in a kilogram. The changes in volume are expressed in cubic centimetres. KOH DlPF. NaOH DlPF. NH,OH DlFF. Nitric acid 20.05 (0.53) 0.28 19.77 (0.53) 26.21 -6.44 (0.13) 26.49 Hydrochloric acid . . 19.52 (0.42) 0.28 19.24 (0.43) 25.81 -6.57 (0.13) 26.09 Hydrobromic acid . . 19.63 (10.53) 0.29 19.34) (10.49) 25.91 -6.57 (9.82) 26.20 Acetic acid .... 9.52 (11.78) 0.24 9.28 (11.64) 25.54 -16.26 (11.30) 25.78 Lactic acid .... 8.27 (8.15) 0.14 8.13 (8.29) 25.87 -17.74 (7.91) 26.01 Sulphuric acid . . . 11.90 (11.82) 0.42 11.48 (11.84) 25.83 -14.35 (11.19) 26.25 Succinic acid .... 8.23 (10.64) 0.30 7.93 (10.53) 25.56 -17.63 (10.52) 25.86 Tartaric acid .... 9.41 0.17 9.24 26.20 -16.96 26.37 The differences all refer back to nitric acid as the standard. They are the same for two different bases when neutralized with the same acid, regardless of the nature of the acid ; as is shown by the practi- cally constant value of the " differences " in each vertical column. The differences are also the same when any given acid is neutral- ized by a number of bases, independent of the nature of the base ; as is shown by the constant value of the bracketed numbers in hori- zontal rows. The minus values for ammonia mean contraction in volume ; the positive values in the other two cases mean that there is an expan- sion in volume. The refractive power of strongly dissociated solutions has been studied especially by Gladstone 2 and Le Blanc. 3 The former showed that the refraction equivalents of two salts of different metals was independent of the nature of the acid with which the metals were combined. And the converse was also true: that the refraction 1 Jour.prakt. Chem. [2], 18, 353 (1878). 2 Phil. Trans. 1868. Kanonnikoff: Jour, prakt. Chem. [2], 31, 321 (1885). 3 Ztschr.phys. Chem. 4, 553 (1889). 302 THE ELEMENTS OF PHYSICAL CHEMISTRY equivalents of two salts of different acids was independent of the nature of the base with which the acids were combined. In a word, we have in ref ractivity a distinctly additive property — the ref rac- tivity being the sum of two constants, one depending upon the acid and the other upon the base. Optical activity, or the power of salt solutions to rotate the plane of polarized light, was shown by Landolt 1 to be an additive property. Completely dissociated solutions of salts containing an optically ac- tive ion showed the same rotatory power, if the concentrations are the same. This was confirmed by the work of Oudeman. 2 He found also that alkaloids show the same rotatory power for equal concen- trations, independent of the nature of the optically inactive acid with which they are combined; and further, that optically active acids show the same rotatory power, independent of the nature of the inactive base combined with them. In a similar manner it has been shown by Becquerel, Perkin, 3 and especially by Jahn, 4 that the magnetic rotatory power of com- pletely dissociated solutions is an additive property. A number of other properties of completely dissociated solutions have been shown to be additive; such as surface-tension, inner friction, heat expansion, lowering of freeezing-point, lowering of vapor-tension, etc. But those considered above are quite sufficient to show that the properties of completely dissociated solutions are, in general, additive, — the sum of two constants, — the one depending upon the anion, the other upon the cation. Additive Properties and the Theory of Electrolytic Dissociation. — The agreement between this large mass of facts and the theory of electrolytic dissociation is a strong argument in favor of the general correctness of the theory. The importance of this line of argument for the theory was early recognized, and was pointed out clearly and at some length by Arrhenius 5 when he proposed the theory of elec- trolytic dissociation. He then took up a number of the properties which we have considered in this section, and, in addition, other physical properties of solutions which it would be premature to con- sider in this place. These facts not only fall in with the theory of electrolytic disso- ciation, but it is difficult to see at present how they can be interpreted in terms of any other theory. The fact that the physical properties "Critical Temperatures of Solutions." See Centnerszwer : Ibid. 46, 438 (1903); 49, 199 (1904) ; and Centnerszwer and Zoppi : Ibid. 54, 689 (1906). '! Ber. d. cliem. Gesell. 6, 1073 (1873). 2 Beibl. Wied. Ann. 9, 636 (1885). * Wied. Ann. 43, 280 (1891). 8 Jour. Chem. Soc. 55, 680 (1889). 6 Ztschr. phys. Ghem. 1, 631 (1887). SOLUTIONS 303 of dilute solutions of electrolytes are additive, — i.e. the sum of two constants, — would certainly indicate that the two parts of the com- pound enjoyed an independent existence in the solution ; or at least an existence so nearly independent that each had but little influence on the other. This is at once apparent when we consider that the properties of each part of the compound manifest themselves as if it alone were present. But independent existence of the ions is but another name for the theory of dissociation. Hydrolytie Dissociation. — We have now become familiar with what is meant by electrolytic dissociation, or the breaking down of molecules of electrolytes into ions by such solvents as water. It now remains to consider another type of dissociation, by which the molecule is not broken down into ions, but into two or more molecules, which are different from the original molecule. It has long been known that an aqueous solution of potassium carbonate reacts alkaline. This has been explained as due to the fact that carbonic acid is a weak acid, and the strong basic property of the potassium predominates. In the light of what we now know about bases, this is obviously no explanation at all of the phe- nomenon in question. Potassium a? such has no basic property. The above is an example of a fairly large number of cases where salts of weak acids do react basic, and salts of weak bases with strong acids show an acid reaction. The explanation of such re- actions is to be found in the breaking down of the molecule in question by water, in the sense of the following equation : — K 2 C0 3 + 2 H 2 = 2 KOH + H 2 C0 3 . The water then acts upon the potassium hydroxide, producing potassium ions, and hydroxyl ions which react basic, while the carbonic acid is very slightly dissociated by water. This kind of breaking down of molecules by the addition of water is known as hydrolytie dissociation. Hydrolytie dissociation takes place when- ever we have a salt of a weak acid, or a weak base, in the presence of water; and still more when both the acid and base are weak. The number of examples of hydrolysis is therefore very large. In many cases the hydrolysis is only partial, but in a large number of reactions in chemistry it may be practically complete. Thus, if a solution of a carbonate is added to a soluble salt of aluminium, iron, etc., the carbonate of the aluminium or iron is completely hydrolyzed, and the hydroxide is precipitated. In these cases both the acid and base are weak, and the hydrolysis is practically complete. Shields 1 studied the hydrolysis of a number of salts of strong i Ztschr.phys. Chem. 12, 167 (1893). 304 THE ELEMENTS OF PHYSICAL CHEMISTRY bases with weak acids, such as sodium carbonate, sodium acetate, potassium cyanide, potassium phenolate, etc. The amount of the hydroxy! ions formed was determined by allowing them to saponify ethyl acetate. He established the relation, for salts that are not very much hydrolyzed, that the mass of the free alkali in the solution is approximately proportional to the square root of the concentration. Hydrolysis at Elevated Temperatures. — The investigations of Noyes 1 and his coworkers, Kato, Sosman, and Kanolt, have led to very interesting results. They have studied especially ammonium acetate and sodium acetate, using the change in conductivity to calculate the amount of the hydrolysis. They have also calculated the dissociation of pure water over a wide range in temperature. Their results for ammonium acetate in one-hundredth normal solution are given in the following table. Column I gives the per- centage hydrolysis of the ammonium acetate, and column II the concentration of the hydrogen ion in pure water in equivalents per litre. Hydrolysis of a Hundredth-Normal Solution of Ammonium Acetate and the Ionization of Water Temperature Hydrolysis of the Salt Hydrogen Ion Concentration in Pure Water t 100 h CbXIO 0° 0.30 18° 0.35 0.68 25° — 0.91 100° 4.8 6.9 156° 18.3 14.9 218° 62.7 21.5 306° 91.5 13.0 It will be seen from the above data, that the hydrolysis of at least a salt like ammonium acetate is very much greater at more elevated than at ordinary temperatures. A rapid increase in hydrolysis with rise in temperature was also observed in the case of other salts. It will also be noted that the dissociation of water in- creases very rapidly between 0° and 100°. Between 100° and 218° the dissociation of water continues to increase, but much more slowly than over the lower range in temperature ; while between 218° and 1 Carnegie Institution of Washington, Monograph No. 63. SOLUTIONS 305 306° the dissociation of water actually decreases, passing through, a maximum which apparently lies between 250° and 275°. Of all the substances investigated, water is the only one whose dissociation increases with rising temperature. The explanation offered by Kalmus, working in Noyes' laboratory, is that water at low temperatures contains only a few molecules of H 2 0, most of the molecules being polymerised; with rising temperatures these molec- ular complexes break down into the simple molecules H 2 0. The number of H 2 molecules in water is thus rapidly increasing with rise in temperature. It could well be that while the percentage of H 2 molecules actually dissociated into ions, like other substances decreased with rise in temperature, the concentration of the ions in pure water would increase until a large part of the polymerised water molecules had broken down into the simpler molecules, i.e. until a compara- tively elevated temperature had been reached. 1 SOLUTIONS IN SOLIDS Solutions of Gases in Solids. — Many solids have the property of dissolving gases in large quantities. Thus, charcoal dissolves large volumes of carbon dioxide, palladium dissolves hydrogen, etc. Our knowledge of such solutions is almost limited to the fact that they exist. It is known, however, that the greater the pressure to which the gas is subjected, the larger the quantity which will be absorbed by the solid. In speaking of solutions of gases in solids we mean, as in all other cases of true solution, those in which there See Rose : Pogg. Ann. 83, 132, 417 (1851). Foussereau: Ann. Chim. Phys. (6) 11, 383 (1887); 12, 553 (1887). Arrhenius: Ztschr. phys. Chem. 5, 1 (1890); 13, 407 (1894). Bredig: Ztschr. phys. Chem. 13, 214 (1894). Noyes and Hall: Ibid. 18, 240 (1895). Walker: Proc. Boy. Sue. Edinb. 18, 255 (1894); Ibid. 77, 5 (1900); Ztschr. phys. Chem. 4, 319 (1889); 32, 137 (1900). Spring: Bee. Pays Bas, 16, 237 (1897). Walker and Appleyard: Journ. Chem. Soc. 69, 134 (1896). Ley: Ztschr. phys. Chem. 30, 193 (1899) ; Ber. d. chem. Gesell. 30, 2192 (1897); 32, 2192 (1899). Jakowkin: Ztschr. phys. Chem. 29, 613 (1899). Remsen and Reid : Amer. Chem. Journ, 21, 281 (1899). Foster : Phys. Bev. 9, 41 (1899). Euler : Ztschr. phys. Chem. 32, 348 (1900). Bruner: Ibid. Z2, 133 (1900). Kohlrausch : Ibid. 33, 257 (1900). Madsen : Ibid. 36, 290 (1901). Richards and Bonnet : Ztschr. phys. Chem. 47, 29 (1904). Stieglitz and Derby : Amer. Chem. Journ. 31, 449 (1904). Rohland : Ztschr. phys. Chem. 56, 319 (1906). Rath: Dissertation, Bonn (1906). Lantelme: Dissertation, Giessen (1906). Riioker: Dissertation, Giessen (1906). Birn- baum: Dissertation, Giessen (1906). 1 The above account of the work on hydrolysis at elevated temperatures has been communicated privately by Noyes to the author. 306 THE ELEMENTS OF PHYSICAL CHEMISTRY is no chemical action between the gas and the solvent. The fact that gases can form solutions in solids is often utilized to remove the gas from regions where it is not desired. The solubility of a gas in a solid may be very great, indeed, as in the case above mentioned of carbon dioxide in charcoal. Solutions of Liquids in Solids. — It is well known that solids have the general property of taking up many liquids in greater or less quantities. The great difficulty in obtaining solids free from water might be taken as an example. Our knowledge of the properties of such solutions is really limited to their existence. This is due to the fact that such solutions have been very little studied, owing in part to the difficulties involved in dealing with them. In solutions of liquids in solids it is difficult to say just when chemical action between the two ceases, and true solution begins. Our lack of knowledge in this field is also partly due to the fact that the concep- tions of modern physical chemistry are so new that sufficient time has not yet elapsed to push the studies, in terms of these concep- tions, into remote fields. That there is much which can be learned in reference to solutions of liquids in solids, will probably be shown in the not very distant future. Solutions of Solids iu Solids. — Here our knowledge is much more satisfactory than in either of the cases which we have just consid- ered. Indeed, a study of this subject will show how interesting facts become when some one has pointed out their meaning and impor- tance. Little or nothing was heard of solid solutions until Van't Hoff 1 published his now well-known paper about eleven years ago. When electrolytes are dissolved in water, they give abnormally large depressions of the freezing-point of the solvent. To account for this and allied phenomena, the theory of electrolytic dissociation was proposed. When some other substances are dissolved in solvents other than water, they give abnormally small depressions of the freez- ing-point. This could be explained by assuming the presence of complex molecules of the substance dissolved. If this assumption is true, then, as the dilution is increased, the complex molecules should gradually break down into single molecules, and for very dilute solutions the molecular lowering found, for such substances should agree with the theoretical value. But the largest value obtained experimentally for the molecular depression was consider- ably smaller than the calculated. 2 This led Van't Hoff to suspect 1 "TJeber feste Losungen und Molekulargewichtsbestimmung an festen KSr- pern," Ztschr. phys. Chem. 5, 322 (1890). 2 Eykman : Ztschr. phys. Chem. 4, 497 (1889). SOLUTIONS 301 that when certain solutions are frozen, the solid which separates is not the pure solvent, but a mixture of the solvent and tlie dissolved substance forming a solid solution. The facts known at that time which bore on this point were then considered by Van't Hoff in the paper above cited. If a solid solution is a solid, homogeneous complex of several substances, in which the properties can^change without destroying the homogeneity, then examples are known. In isomorphous mix- tures, as the alums, there is miscibility in all proportions, corre- sponding to completely miscible liquids. Another example is the formation of " mixed crystals," which are to be distinguished from double salts, and by their chemical composition show no isomorphism. Ammonium chloride forms such crystals with the "ous " chlorides of iron, manganese, nickel, etc. Ferric chloride is taken up by am- monium, calcium, lithium, etc., chlorides. When enough ferric chloride is present, the first two form also a double salt, which can be distinguished from the mixed crystal. Further, there are many colored minerals known in which the ground mass is colorless. Yet, optical investigations have shown them to be completely homogene- ous. There are many amorphous, solid solutions, as the glasses and hyaline minerals. Spring 1 has furnished the following interesting example, showing the mutual solubility of solids. When an equimolecular mixture of barium sulphate and sodium carbonate are pressed together, a double decomposition, amounting to even 80 per cent, takes place. That an equilibrium should be established, is conceivable only on the assumption that with the solids we have a partial miscibility. Properties of Solid Solutions. — If solid solutions are a reality, then we would expect to find at least some of the properties of gaseous and liquid solutions manifested to a greater or less degree. Such is the case. The diffusion of a solid through a solid has been demonstrated. When barium sulphate and sodium carbonate were pressed together, and the pressure removed, the transformation con- tinued, and in seven days amounted to from 73 to 80 per cent. Diffusion must have come into play here ; slow, it is true, but this would be anticipated, since a gas diffuses through a gas far more rapidly than a liquid through a liquid. A more striking example of diffusion in solids where no chemical action comes into play, is the penetration of hot porcelain by carbon. Marsden 2 proved that when a porcelain crucible is heated in graphite, 1 Bull. Soc. Chim. 44, 166 (1885). 2 Proc. Edirib. Soc. 10, 712. 308 THE ELEMENTS OF PHYSICAL CHEMISTRY the carbon completely penetrates the porcelain. Further, zinc objects covered with a thin layer of copper become gradually white, due, as analysis has shown, to a gradual increase of zinc in the copper. This illustrates the diffusion of solid in solid at ordinary tempera- tures. Van't Hoff has thus furnished examples illustrating beyond question the diffusion of solid through solid. Other examples of the diffusion of one metal through another have been furnished by Spring. 1 But, perhaps, the most striking example of the diffusion of one metal through another has been recently furnished by Roberts- Austen. 2 Disks of gold were clamped to the bases of lead cylinders, and allowed to remain standing for four years. The bases of the lead cylinders were carefully smoothed and the disks of gold espe- cially cleaned. These were then placed in a vault, whose temperature was practically constant at 18° C. At the end of four years it was found that the disks of gold had adhered to the lead. Slices were cut from the lead cylinders at right angles to the axes of the cylin- ders, and these were then assayed for gold. It was found that the gold had penetrated about 8 millimetres into the lead ; the gold being more concentrated in that portion of the lead disk which was in contact with the gold plate, as we would expect. In liquids we seek the cause of diffusion in osmotic pressure. May not the diffu- sion of solid through solid be of like origin ? From the nature of solid solutions it seems to be impossible to determine this directly. The work of Colson, 3 however, on the diffusion of carbon in iron has made it probable that a proportionality exists between the amount of diffusion and the concentration, as with liquid solutions whose osmotic pressure obeys Boyle's law. The simplest connection between Boyle's law and the other laws of osmotic pressure is the law of Henry. If this applies to solid solutions, gases must be dissolved by solids in proportion to the gaseous pressure. Take the case of the absorption of hydrogen gas by palladium.* When the hydrogen is kept at 225 mm. pressure and 100°, the palladium will take up a quantity corresponding to the compound Pd 2 H. No further absorption of the gas will take place unless the pressure is increased. After the compound Pd 2 H is formed, further absorption of the hydrogen results in the formation 1 Bapport Congres International de Physique, I, 412, Paris, 1900. 2 Proc. Boy. Soc. 67, 101 (1900). See Bodlander : If. Jahrb. f. Min. Beilageband, 12, 52 (1898). Bruni : Bend. Accad. Line, 1902, II, 187. * Compt. rend. 93, 1074. * Troost and Hautefeuille : Ibid. 1874, 686. SOLUTIONS 309 of a solid solution. For our consideration only the hydrogen which forms a solid solution comes into play. Let P represent the pressure of the gas, and let V represent the volume of the gas absorbed. If we divide the pressure by the total volume absorbed, minus that volume which was taken up to form the compound Pd 2 H (in this case 600), we have : — P p r P P F-600 r-6oo 809 1428 6.8 lib 715 4.1 743 909 6.4 743 493 3.5 700 598 6.0 718 361 3.0 672 454 6.3 684 247 3.0 642 353 8.4 Palladium which had been fused. Palladium sponge The value of is, in each ease, as near a constant as could V- 600 ' be expected from the nature of the experiments. Since Henry's law holds, then, for solid solutious as well as for liquid, we have here also the osmotic pressure equal to the gas-pressure for the same concentration and temperature. Another well-known fact in connection with a liquid solution is that its vapor-tension is less than that of the solvent. In solid solu- tions there is also a diminution of the maximum tension of the solvent. Lead dithionate, 1 which decrepitates very easily, showing consider- able tension, has this tension markedly diminished by forming with it an isomorphous mixture containing a small amount of the calcium or strontium salt. The same holds for iron alum, whose tension is diminished by the formation of an isomorphous mixture with aluminium alum. This diminution in tension is not due simply to the addition of a constituent which has a smaller tension, since the tension of the mixture is less than that of either constituent. 2 This decrease in the tension of solid solutions manifests itself in the decrease of solu- tion-tension, causing a decrease in solubility. When saturated solu- tions of ammonium iron, and ammonium aluminium alums are brought together, an isomorphous mixture of both salts separates, showing a decrease in solution-tension or solubility, when the solid solution is formed. Such are some of the properties of solid solutions, and some of the analogies between these and liquid solutions. i Von Hauer : Verhand. d. k. k. geol. Beichsanstalt, 1877, 163. 2 Lehmann : Molekularphysik, 2, p. 57. 310 THE ELEMENTS OF PHYSICAL CHEMISTRY Molecular Weights of Solids. — To determine the molecular weights of substances in the liquid condition we rely chiefly upon liquid solutions. May not solid solutions furnish us with methods for determining the molecular weights of substances in the solid state ? There are two possibilities ; the one having to do with the tension of the dissolved body ; the other with that of the solvent. If we are dealing with the tension of the dissolved body, the problem reduces itself to determining whether there is proportion- ality between the gas-pressure and the concentration of the solid solution formed — whether in any given case Henry's law holds. If it does, the dissolved gas has the same molecular weight as the free gas. Thus, hydrogen dissolved in palladium hydride, forming a solid solution, has a molecular weight corresponding to H 2 . Were it H 3 or H, the values of y_ mQ wou ld have been much farther removed from a constant. The second method deals experimentally with the relation between the composition of the solid solution, and the liquid solution from which it was formed. If the dissolved body has the same molecular weight in both solutions, this relation must be constant. To deter- mine the molecular weight of, say, thiophene in the solid condition, prepare two solutions of known concentration of thiophene in benzene. When these are frozen, a solid solution of thiophene in benzene will separate in each case. If an analysis of the solid shows a constant proportionality between the amount of thiophene in the solid and liquid solutions, the thiophene has the same molecular weight in the solid as in the liquid form. Thiophene in Benzene Per Cent P Depression Found Normal Depression Difference D D P 0.847 2.10 2.84 3.63 0°. 34 0°- 82 1°.085 l c .385 0°.536 1°.325 1°.790 2°. 290 0°.195 0°.505 0°.705 0°.905 0.230 0.240 0.248 0.249 Under normal depression is the lowering which would have been produced had no solid solution been formed. Since the composition of the crystals which separated was not determined, the molecular weight of solid thiophene could not be calculated. The fact, how- Speranski: Ztschr. phys. Chem. 46, 70 (1903); 51, 45 (1905). SOLUTIONS 311 ever, that — is a constant, makes it probable that the percentage of thiophene in the solids which separated, was proportional to that in the solutions. If so, thiophene would have the same molecular weight in the solid as in the liquid solutions. Compounds which can form Solid Solutions with One Another. — Since the first fundamental paper appeared on solid solutions, by Van't Hoff, the study of such solutions has been devoted to two general problems: The relation between the chemical consitution of those compounds which can form solid solutions with one another, and the determination of the molecular weight of solids in solid solutions. Most of our knowledge on the first-mentioned problem we owe to Ciamician and his colaborers, Garelli and Ferratini. 1 The object of this work was to test the chemical relations between substances which are necessary, in order that a solid solution may be formed when a solution of one in the other was frozen. It was already known that phenol, pyrrol, thiophene, pyridine, and piperidine, dis- solved in benzene, gave abnormally small depressions of the freez- ing-point. This would indicate that solid solutions are formed only between those substances which have similar chemical constitution ; but the data were too meagre to establish finally any such relation. The paper first cited deals only with cyclic compounds : the solvents used being benzene, naphthalene, phenanthrene, and diphenyl. To determine whether a solid solution was formed, the freezing-point method was used. Whenever a solid solution of the dissolved sub- stance and the solvent separated, the freezing-point lowering would be abnormally small. It was shown that the following substances form solid solutions with the solvent indicated just above in italics : — Benzene. Thiophene, pyrrol, pyridine, pyrroline, and piperidine. Naphthalene. Indol, indine, quinoline, isoquinoline, and tetrahydroquinoline. Phenanthrene. Carbazol, anthracene, acridine, and hydrocarbazol. Diphenyl. Dipyridyl and tetrahydrodiphenyl. Indol and indine in benzene give normal freezing-point lower- ings; the same holds for carbazol or anthracene in benzene or naphtha- i Ztschr. phys. Chem. 13, 1 (1894); 18, 51 (1895); 44, 505. 312 THE ELEMENTS OF PHYSICAL CHEMISTRY lene — these substances forming solid solutions with phenanthrene. That these abnormally small depressions of the freezing-point were due to the formation of solid solutions was established in a number of cases by direct experiment. From these results it would seem that only those substances are capable of forming solid solutions with one another which have a cyclic structure of the same order; benzene being an example of the first order, naphthalene of the second, and anthracene of the third. That the chemical character of a compound, other than its cyclic structure, can have little to do with its power of forming solid solu- tions, is shown by the fact that compounds as different as pyrrol and pyridine manifest the same general cryoscopie behavior with benzene. It will be seen from the foregoing that the formation of solid solu- tions consists in the dissolved substance and the solvent crystallizing out of the solution together. This being the case, it is not impos- sible that the relation between the crystallographic forms of the two substances may play a prominent part in determining what sub- stances can form solid solutions with one another. Certain relations have already been pointed out 1 between the crystallographic con- stants of those substances which can form solid solutions. Here, however, partly on account of crystallographic difficulties, the data at hand are far too few for purposes of generalization. A second paper, 2 dealing with this part of the subject, furnishes further data which substantiate essentially the conclusions arrived at in the first. It may, then, be stated that in the ring compounds agreement in cyclic order seems to be necessary in order that solid solutions may be formed. It, however, does not follow, and it is not true, that solid solutions are formed whenever such an agreement exists. Work of Kiister on the Molecular Weights of Solids. — Con- siderable work on the second problem — the molecular weights of substances in solid solutions — has been done recently by Kiister. 3 He studied at first the division of a given compound between two solvents which are practically insoluble in one another ; the one being a liquid, the other a solid. The solvents chosen were water and pure caoutchouc. To these, in the presence of each other, ether was added and the quantity taken by each solvent determined. If the molecular weight of ether in the water was the same as in caoutchouc, when more and more ether was added to the solvents the quantity taken up by a given volume of the one, divided by the 1 Ciamician: Ztso.hr. phys. Ohem. 13, 6 (1894). 2 Garelli : Ibid. 18, 51 (1895); 21, 113 (1896); 38, 380, 501. 8 Ztschr. phys. Ohem. 13, 445 (1894) ; 17, 357 (1895). SOLUTIONS 313 quantity taken up by the same volume of the other, would be a con- stant. That this is true has been shown experimentally ! by quan- titative determinations of the division of a substance between two solvents, and is analogous to the law of Henry for gases. The experimental problem for Kuster was, then, the addition of varying amounts of ether to a given volume of water and a known weight of caoutchouc in the presence of each other, and the deter- mination of the amount of ether taken in every case by each solvent. The same point would of course be reached by keeping the amount of ether constant, and changing the relative amounts of the two solvents. Both methods were employed. The total amount of ether used in any experiment was known. The amount which was taken by the water was determined by the lowering of the freezing-point of the water produced by the ether. The difference between these two quantities was the ether which had been taken up by the caout- chouc. Care was taken to construct a freezing-point apparatus which would prevent loss of ether by evaporation. The time re- quired for equilibrium to be established between the ether and the two solvents was duly regarded, and was shown not to exceed three hours. In the first series of experiments weighed amounts of caoutchouc were added to a known volume of water and of ether, and the freezing- points of the aqueous solutions of ether determined after equilibrium had been established in each case. Fifty cubic centimetres of water were used and 5 c.c. of ether. The results of this series are given below : — Caout- Aw Vw Cw Ak Tk- Ok Ck y/Ck chouc c.c. CO. c.c. c.c. c.c. CO. Cw Chi) 1 17.606 -1.265 3.41 53.41 6.38 1.59 20.62 7.71 1.21 0.435 2 10.188 -1.380 3.72 53.72 6.92 1.28 12.29 10.41 1.55 0.466 3 5.924 -1.510 4.07 54.07 7.52 0.93 7.33 12.69 1.69 0.473 4 2.724 -1.660 4.47 54.47 8.21 0.53 3.57 14.85 1.81 0.469 In the preceding table : — E is the freezing temperature of the aqueous solution of ether ; Aw is the number of cubic centimetres of ether in the aqueous solution, calculated from the value of E ; Vw is the volume of the aqueous solution ; i Jakowkin : Ibid. 18, 585 (1895). 314 THE ELEMENTS OF PHYSICAL CHEMISTRY Cw is the volume concentration of the ether in the aqueous solution, _ 100 Aw . Vw ' Ak is the ether in the caoutchouc, = 5 — Aw ; Vk is the volume of the caoutchouc solution of ether ; Ck is the volume concentration of the ether in the caoutchouc, = 100—. Vk Ck The value of -77— is not constant, but, as is seen in the table, increases as the amount of caoutchouc present decreases ; showing that the molecular weight of the ether dissolved in the caoutchouc is greater than that of the ether in the water. Ether dissolved in water gives a normal molecular depression of the freezing-point, and has, therefore, the simplest molecular weight, which corresponds to the formula C 4 H 10 O. The ether molecule in the caoutchouc must consist of more than one chemical molecule. Since the values of are very nearly constant, the molecular Cw weight of ether in caoutchouc must, in part at least, be double the simplest molecular weight ; l for, as we shall learn, the square root sign in this connection has that significance. In a second series of experiments the amount of water and of caoutchouc were kept constant, and the amount of ether changed. ■Ck The value of . — increased with increase in the concentration of the Cw ether, showing that more double molecules exist in the caoutchouc when the concentration of the ether is increased, as would be expected. In the most dilute solution of ether employed, it is calculated that only one-tenth of the ether in the caoutchouc exists as double molecules ; while in the most concentrated solution of ether, about one-half of the molecules are double. The effect of temperature on the division of ether between water and caoutchouc was also investigated. It was found that the water takes relatively more of the ether, the lower the temperature. The number of double molecules of ether in the caoutchouc, for a given amount of ether, is about three times as great at 0° as at 21° ; show- ing an increase in the number of simple molecules with increase in temperature, as would be expected. 1 Ztschr. phys. Chern. 8, 112 (1891). SOLUTIONS 315 The Molecular Weight of a Pure Homogeneous Solid. — The work described up to this point has shown, according to Kiister, that ether dissolved in caoutchouc consists partly of single and partly of double molecules ; the number of double molecules increasing as the concentration of the ether increases, and as the temperature is lowered. This tells us, however, absolutely nothing as to the molec- ular weight of pure ether in the solid condition. The second investigation 1 of Kiister aims at a solution of the problem of the molecular weight of a pure substance when in the solid solution. In his original paper on solid solutions Van't Hoff included isomorphous mixtures. In these substances Kuster con- cludes that the physical molecules of the solvent and of the dissolved substance must have like structure, and be composed of a like num- ber of chemical molecules. If we could ascertain the molecular weight of one of the substances in the isomorphous mixture, we would, therefore, know the molecular weight of the other, which we can regard as the solvent. The division of one constituent of the isomorphous mixture between the other (which we will regard as a solid solvent) and a liquid solvent, would, as seen above, throw light on the molecular weight of the constituent of the mixture first mentioned. It was difficult to find an isomorphous mixture which would fulfil the con- dition that only one constituent should be soluble in the liquid solv- ent. Kuster, however, secured such in a mixture of naphthalene and y8-naphthol. These compounds form a complete series of iso- morphous mixtures with one another. Further, the /J-naphthol was soluble in water, which was used as the liquid solvent, while the naphthalene was practically insoluble. The experimental work con- sisted, then, in determining the division of the /3-naphthol between the water and the naphthalene. Isomorphous mixtures of /?-naphthol and naphthalene of known composition were added in turn to meas- ured volumes of water, and shaken with it until the water became saturated with the /J-naphthol. The amount of /3-naphthol present in the water in each case was then determined. If we represent the concentration of /J-naphthol in the water by Km, and the concentration of that which remains in the mixture by Km, we have — -\/Km _ p Kw ~~ The values found experimentally vary from 11.8 to 20.8. 1 Ztschr. phys. Chem. 17, 357 (1895). See Ibid. 50, 65 (1905); 51, 222 (1905). 316 THE ELEMENTS OF PHYSICAL CHEMISTRY The author concludes, as with ether in caoutchouc, and for the same reason, that the /8-naphthol in the isomorphous mixture has twice the molecular weight of that in the water. The molecular weight of j8-naphthol in water has been shown to correspond to the simple formula C 10 H 8 O. /3-naphthol in naphthalene has, then, the double molecular weight (C 10 H 8 O) 2 . /3-naphthol forms isomorphous mixtures with naphthalene; there- fore, the molecules of crystallized naphthalene and also of j8-naphthol are to be expressed by the double formulas, (C 10 H 8 ) 2 and (C 10 H 8 O) 2 . There are certain assumptions involved in this process of reason- ing, so that the conclusion while interesting cannot be accepted as final. We have studied examples of solutions of matter in every state of aggregation, in matter of the same and every other state. We shall now turn from the study of matter as such, to the study of other changes which always take place to some extent when sub- stances react chemically. Thus, thermal changes always accompany chemical reaction. Again, if the reaction takes place under certain conditions marked electrical changes result. It was early recognized that energy transformations of some kind frequently accompany the transformations of matter ; but the atten- tion of the earlier chemists was confined almost entirely to the study of the material changes which were effected by chemical reaction. The nature of the substances which enter into the reaction, and especially the nature of the products formed, furnished the chief problems for the chemist in the first half of the nineteenth century. During the latter half of the century, however, more and more atten- tion was paid to the energy changes; especially to the amount of heat which is set free when substances react; and this continued until the new physical chemistry, in the last fifteen years of the century, showed the tremendous importance of these energy trans- formations. Indeed, we know now that it is almost impossible to overestimate their importance, since they are probably the cause of all chemical activity. Substances react chemically because of differ- ences in the quantity and intensity of the intrinsic energy present in them. In studying energy changes we are then dealing with the real cause of reactions, and from the standpoint of the science of chemistry these are far more important than the material transfor- See Vaubel : Joum. prakt. Chem. 1904, 545. SOLUTIONS 317 mations which accompany them. The fundamental problems of chemistry will never be solved by a study of the material changes alone, since these are relatively the less important side of chemical phenomena ; but only through elaborate investigation of the energy relations which obtain in systems before reactions, and in the prod- ucts of the reaction. The remainder of our subject has to do largely with energy changes. The transformations of intrinsic energy into heat constitute the subject-matter of Thermochemistry. Electrochemistry deals with the transformation of intrinsic en- ergy into electrical, and of electrical into intrinsic. The relations between intrinsic energy and light furnish the material of Photochemistry. 1 We can also study the velocities with which chemical reactions take place, and the conditions of equilibrium in such reactions. These furnish the subject-matter of Chemical Dynamics and Chemical Equilibrium. We may also measure the relative Chemical Activities of different substances. We shall take up first the subject of thermochemistry. 1 These subjects are taken up in the above order, since in terms of our pre- vailing theories we deal first with heat, then with electricity, and finally with light. CHAPTER VI THERMOCHEMISTRY DEVELOPMENT OF THERMOCHEMISTRY Earlier Observations; Law of Lavoisier and Laplace. — It was very early observed that chemical reactions are accompanied by thermal changes. Sometimes heat is absorbed, but much more frequently it is given out. The qualitative observations were fol- lowed by quantitative measurements as early as the time of Eobert Boyle. The first valuable measurements of the heat of reaction were made by Lavoisier and Laplace. 1 They measured the amounts of heat liberated in many chemical reactions, and also studied the thermal changes which take place within the living body. They arrived at the first important generalization in the field of thermo- chemistry. The amount of heat which is required to decompose a compound into its constituents is exactly equal to that which was evolved when the com- pound was formed from these constituents? The Work of Hess. — Modern thermochemistry may be said to date from the time of Hess. 8 He discovered a fact whose impor- tance' for thermochemical study it is difficult to overestimate. Many chemical processes do not take place in one stage, but in several ; and it was often difficult, not to say impossible, to deal with such from the thermochemical standpoint. Hess showed that the lieat evolved in a chemical process is the same whether it takes place in one or in several stages. This principle, known as the " Constancy of the heat sum," made it possible to deal with a large number of reactions which otherwise would lie entirely out of the scope of ther- mochemical measurements. Take, for example, the burning of sulphur in oxygen. If we know the heat evolved when sulphur is burned in oxygen to form sulphur dioxide and the heat evolved when sulphur dioxide is burned to sulphur trioxide, we would know 1 (Euvres de Lavoisier, II, 283. "Ibid. II, 287. 3 Pogy. Ann. 50, 385 (1840). Klassik. d. exakt. Wissen. 9. 318 THERMOCHEMISTRY 319 at once the amount of heat which would be evolved when sulphur was burned directly to sulphur trioxide, — it would be the sum of the above quantities. On the other hand, if we knew the heat evolved when sulphur is burned to the trioxide, and the heat evolved when the dioxide is oxidized to the trioxide, we would know the heat which would be set free when sulphur was burned to the dioxide, — it would be the difference between the above two quan- tities. This simple example will suffice to illustrate the application of the principle in thermochemistry. It is almost constantly used in dealing with the more complex reactions, especially in the field of organic chemistry. Indeed, without the aid of it, our knowledge of the thermochemistry of organic reactions would be very limited. Hess made a second very important contribution to thermo- chemistry. When solutions of neutral salts are mixed there is no thermal change, and Hess expressed this fact in his Law of the Thermo- neutrality of Salt Solutions. We shall see that this law is extremely interesting in the light of the theory of electrolytic dissociation, which furnishes for the first time a satisfactory explanation of it. Indeed, we shall learn how the law is a necessary consequence of this theory. Hess attempted to explain the law of the thermo-neutrality of salt solutions, on the assumption that the heat evolved in salt formation depends only on the nature of the acid and not at all on the nature of the base. This assumption was erroneous and, there- fore, the explanation based upon it. So important is the work of Hess that he is regarded as the father of all modern thermochemistry. Work of Favre and Silbermann. — The experimental work of ITavre and Silbermann 1 is of the very greatest importance for the development of thermochemistry. There are few physical measure- ments more difficult than the determination of the amount of heat. The determination of temperature alone is not always a simple matter, but this is but the first stage in determining the quantity of heat. To determine the amount of heat, we must allow this to warm some substance like water, and must know the rise in tempera- ture produced and the amount of water used. The experimental solution to a thermochemical problem, therefore, involves several steps. When the heat is liberated in the reaction, it must be taken up by some substance whose specific heat is known — say water. i Ann. Chim. Phys. [3], 34, 357 ; 36, 1 ; 37, 406 (1852-1853). 320 THE ELEMENTS OF PHYSICAL CHEMISTRY The water must be enclosed in some form of vessel, and this vessel has a different specific heat from that of the water. Further, the vessel and water, as quickly as they become warmed above the temperature of surrounding objects, begin to radiate heat outward upon the colder objects. There is thus a continual loss of heat taking place during the experiment. Again, the liquid must be kept stirred during the experiment to secure uniform temperature throughout. The stirring produces heat, and the stirrer has a differ- ent specific heat from that of the water. The specific heat of the water itself must be determined at different temperatures, etc. These are just a few of a very large number of factors which have to be reckoned with in all thermochemical measurements. The work of Favre and Silbermann had to do chiefly with the improvement of the experimental method for making calorimetric measurements. They devised a form of calorimeter which lies at the basis of all the forms which have been used since their time. They made a large number of thermochemical measurements, and showed that the heat of neutralization depends, not only on the acid as Hess had supposed, and not only on the base as Andrews l thought, but that it depends upon both. The investigations of Favre and Silbermann are nearly as important experimentally as those of Hess are theoretically for the development of modern thermochemistry. Investigations of Julius Thomsen. — Thermochemistry in recent times has centred around two men; and our most reliable results were obtained by these men and their pupils. One of these is Julius Thomsen in Copenhagen. Thomsen's investigations 2 extend from the fifties up to the present. His collected works, 8 published in four volumes, contain the most important thermochemical data on record. Thomsen recognized that all chemical reactions are accompanied by thermal changes, and undertook to measure the magnitude of these changes in a very large number of cases. He improved thermo- chemical methods far beyond any of his predecessors, and the methods which he employed have been subsequently improved only in cer- tain minor points. The work of Thomsen will constantly reappear throughout the entire chapter on thermochemistry. Berthelot's Investigations and Deductions. — It was stated that in recent times two men have led the work in thermochemistry. The one, a Dane, has just been mentioned ; the work of the other, a Frenchman, — Berthelot, — will now be considered. The work of 1 Pogg. Ann. 54, 208 ; 59, 428 ; 66, 31 (1841-1845). 2 Ibid. 88, 349 (1853); 90, 261 ; 91, 83 (1854); 92, 34 (1853). 8 Therrnochemische Untersuchungen. 4 volumes (1882). THERMOCHEMISTRY 321 Berthelot was begun somewhat later than that of Thomsen ; his first publication having appeared in 1865. 1 It was not until considerably later 2 that Berthelot began his experimental work, which has con- tinued with more or less regularity up to the present. Berthelot improved a number of forms of apparatus, and devised new methods of work, which greatly extended our knowledge in this field. The Berthelot bomb, in which combustions were effected in oxygen under high pressure, made it possible to study, thermochemically, a large number of heats of combustion of organic substances, which could not have been dealt with under ordinary conditions. The work of Berthelot, like that of Thomsen, will constantly appear throughout this chapter. The three fundamental principles or generalizations at which he arrived should, however, be mentioned in this place. I. The thermal change in a chemical reaction, if no external work is done, depends only on the condition of the system at the beginning and end of the reaction, and not on the intermediate conditions. II. The heat evolved in a chemical process is a measure of the corresponding chemical and physical work. III. " Every chemical transformation which takes place without the addition of energy from without, tends to form that substance or system of substances, the production of which is accompanied by the evolution of the maximum amount of heat." 3 This third principle, which has come to be known as the law of maximum work, but which should be known as the law of maximum heat evolution, has also been stated by Berthelot 4 as follows : — " Every chemical change which is accomplished without a pre- liminary action, or the addition of external energy, necessarily occurs if it is accompanied by disengagement of heat." The third principle when stated in this form is known as the "principle of the necessity of reactions." We shall learn that the third principle of Berthelot is far from a rigid generalization. It holds in a large majority of cases, but there are so many exceptions known that it cannot be regarded as a law of nature. However, when we consider the vast number of cases to which the principle does apply, we see in it the germ of some great truth, which has not yet been fully understood and expressed. With this preliminary historical introduction, we shall turn to the subject of thermochemistry proper. i Ann. Chim. Phys. [4], 6, 290 (1865). " Mec. Chim. I, 29. 2 Ibid. [4], 28, 94 (1873). * Loo. cit. 322 THE ELEMENTS OF PHYSICAL CHEMISTRY CONSERVATION OF ENERGY APPLIED TO THERMO- CHEMISTRY Mass unchanged in Chemical Eeactions. — One of the facts funda- mental to the whole science of chemistry is the conservation of mass. When chemical reaction takes place, the substances change most of their properties. A liquid may become a gas or a solid, a solid a liquid or a gas. A poisonous substance like chlorine may combine with a metal like sodium, forming a compound which is not only not injurious to the body, but nutritious ; and so on through the entire list of properties except that of mass. Some of the most accurate experimental work which has ever been carried out had for its object the solution of the problem — is mass unchanged in chemical action ? The epoch-making work of Stas on the atomic weights of some of the elements showed very slight differences between the sum of the masses of the products of a reaction, and the sum of the masses of the constituents which enter into the reaction. In no case, however, were these differences larger than the possible experimental errors. In recent time, as we have already seen (p. 2), an investiga- tion was carried out by Landolt 1 to determine whether the weight of the products of a reaction is exactly equal to the weight of the constituents before the reaction — weight being our means of meas- uring mass. The result showed that slight ■ differences existed between the weight of the products of a reaction, and the weight of the constituents before the reaction; but these differences were always so small that no final conclusion could be drawn from them. The conservation of mass, then, stands out as the one property of matter which always remains unchanged, regardless of the number and kind of chemical transformations through which the matter is passed. The importance of this great law of nature for the science of chemistry it is absolutely impossible to overestimate. If there was a change in mass in chemical reaction, all quantitative work would be impossible, and chemistry would be reduced to mere quali- tative observations. The science of chemistry rests, fundamentally, upon the law of the conservation of mass. Another law of equal im- portance we shall now consider. Energy unchanged in Chemical Reactions. — In chemical reactions two great changes take place. 1 Ztschr. phys. Chem. 12, 1 (1893). THERMOCHEMISTRY 323 1. A change in all the properties of the substances which react, except mass. 2. A change in the form of energy in the reacting substances. While the form of energy changes, the question arises, is there any loss or gain in energy in chemical reactions ? The law of the conservation of energy, which is one of our best established laws of nature, comes to our aid. This law is stated by Maxwell * as fol- lows : " The total energy of any material system is a quantity which can neither be increased nor diminished by any action between the parts of the system, though it may be transformed into any of the forms of which energy is susceptible." The total energy is, then, the same after the reaction as before. Before the reaction the total energy was in the form of chemical or in- trinsic energy. After the reaction a part still remains in the form of intrinsic energy, a part is transformed into heat, and if there is a change in volume, as almost always occurs, a part is spent in doing external work. If we represent the change in the intrinsic energy by dE, the heat evolved or absorbed by d6, and the external work done by d W, we have — dE = dd + d W. The law of the conservation of energy is as fundamental to the science of thermochemistry as the law of the conservation of mass is to the science of pure chemistry. If energy were either created or destroyed in chemical reactions, we could, it is true, measure the amount of heat liberated in chemical reactions ; but such measure- ments would have relatively little value; indeed, about the same value as quantitative determinations in pure chemistry if the law of the conservation of mass did not apply. The law of the conserva- tion of energy, which is the first principle of thermodynamics, is, then, the foundation of the science of thermochemistry. Same Amount of Heat liberated under the Same Conditions. — The same chemical reaction under the same conditions always liberates the same amount of heat. In order to obtain this result the reaction must take place under exactly the same conditions. Thus, the heat liberated when a given quantity of metal, say zinc, dissolves in a certain solution of an acid, is a constant. But in order that this amount of heat may be obtained, the metal and acid must be at a definite temperature, and the solution of the acid must have a cer- tain definite concentration. If the acid varies in concentration, the 1 Matter and Motion, art. 74. 324 THE ELEMENTS OF PHYSICAL CHEMISTRY products formed may be different, and, consequently, a different amount of intrinsic energy may be converted into heat. Again, we may have what is apparently the same chemical reaction taking place under different conditions, and giving rise to very different amounts of heat. Take, for example, the solution of zinc in sulphuric acid. When a given weight of zinc is dissolved in sulphuric acid of a cer- tain concentration, a definite amount of heat is liberated. . If the zinc is connected with some other element so as to form a battery, and then allowed to dissolve in sulphuric acid of the same concen- tration, a very different amount of heat will be liberated! The change in intrinsic energy, dE, is the same, but in the second case a part has been converted into electrical energy, and, therefore, the amount which remains to be converted into heat is less. If we represent the second condition in terms of the general en- ergy equation, we must introduce another term for the electrical energy into which a part of the intrinsic energy has been transformed. Let us call this dE e . We should then have — dE = dO + dE e +dW. The difference between the intrinsic energy of two systems is equal to the heat liberated, plus the electrical energy, plus the work done. Importance of Thermochemical Measurements. — The importance of thermochemical measurements will appear at once from what has preceded. We have no means of measuring directly the intrinsic en- ergy contained in a substance. The best we can do is to measure the difference in intrinsic energy between a system and another system into which this can be transformed. The best method of measuring this difference is to transform the one system into the other by chemical means, when the excess of the intrinsic energy in the one over that in the other will be transformed into heat ; and if there is a change in volume, also into work. By measuring the amount of heat set free, and the external work done, we know at once the difference between the intrinsic energies of the two systems. Unless there is a gas formed or used up in the reaction, the external work done is very small, and can usually be neglected. The heat liberated is, then, a measure of the difference between the intrinsic energies of the substances which react, and the intrinsic energy of the products of the reaction. Thus, the heat liberated is a measure of the difference between the intrinsic energy of hydrogen plus that of chlorine, and the intrinsic energy of the hydrochloric acid formed. Thermochemical measurements, then, are our best means, and in many cases our only means, of determining the difference between THERMOCHEMISTRY 325 the intrinsic energies of two systems, one of which can be transformed into the other. This alone should suffice to show the importance of such work. The "Heat Tone" of a Reaction. — The term "heat tone" of a reaction is so frequently used that it should be clearly explained in this connection. The heat tone of a reaction is the sum of the heat developed in the reaction and the external work expressed as heat which is done. Since we have reactions which evolve heat and are termed exothermic, and also reactions in which heat is absorbed and are termed endothermic, the heat tone may be positive or negative. The work done may be positive as when a gas is formed, or it may be negative as when a gas is used up ; so that both of the factors of heat tone may be positive, or both may be negative, or one positive and the other negative. Since the heat evolved is so large with respect to the work done, the sign of this factor essentially condi- tions the sign of the heat tone. THERMOCHEMICAL METHODS The problem in thermochemical measurements is to determine the amount of heat which is liberated in chemical reactions. In order to do this the heat which is set free is allowed to warm a known quantity of some liquid whose specific heat is known. The rise in temperature is then measured by means of an accurate ther- mometer. The liquid which is best adapted to such work is water, and the water calorimeter is almost exclusively used at present. The Water Calorimeter. — In all forms of the water calorimeter the heat which is liberated in the reaction is taken up by a known quantity of water. The reaction must, therefore, take place in some vessel surrounded by the water of the calorimeter. A platinum vessel is usually employed, holding from one-half to one litre. This is surrounded by a known quantity of water, which is placed in an outer vessel of silver or some other metal. This outer vessel is then surrounded by poorly conducting material so as to diminish the loss of heat by radiation. The substances which are to react either in the pure state or in solution are brought to the same temperature and then introduced into the innermost vessel. The temperature of the water is determined before and after the reaction, and from the rise in temperature, the quantity of water present, and its specific heat, the amount of heat liberated in the reaction is determined at once. A great many forms have been given to the water calorimeter for special purposes. The most important of the early forms, as 326 THE ELEMENTS OF PHYSICAL CHEMISTRY has already been stated, was that devised by Favre and Silbermann. 1 For a number of modifications consult the works of Berthelot 2 and Thomsen. 3 One form will be described in some detail below, just to give a clear idea of the instrument as used in practice. The form chosen is one which was designed and used by Ber- thelot * especially for reactions in solution, such as the neutralization of acids and bases. (The apparatus is shown in Fig. 45.) The platinum vessel A, holding about 600 c.c, is surrounded by a vessel Fig. 45. of thin copper, which, in turn, is closely surrounded by a silver vessel B. The whole is introduced into a double-walled vessel of sheet iron C containing water between the walls. This water is agitated by means of the stirrer D, and its temperature read on the i Ann. Chim. Phys. [3], 34, 357 (1852) ; [3] 36, 1 (1852). 2 JSssai de Mecanique Chimique. 8 Thermochemische Untersuchungen. 4 Essai de Mkcanique Chimique, I, p. 140. THERMOCHEMISTRY 327 thermometer E. The whole apparatus is then surrounded by some non-conducting material, such as felt, and is kept in a room as nearly as possible at constant temperature. If the liquids are such as would react on platinum, the inner- most vessel should be made of very hard glass. The liquid in the calorimeter proper (.4) is stirred thoroughly by means of a platinum or glass stirrer, which is moved backward and forward in the liquid. The thermometers employed must, of course, be very carefully calibrated and standardized against some standard instrument. The Explosion Bomb. — In order that a reaction can be studied thermochemically, it must fulfil the following conditions : First, it must take place at ordinary temperatures ; second, it must proceed rapidly to the end. A large number of reactions, which, under ordinary circumstances, do not fulfil the above conditions, can be made to fulfil them. Thus, many processes of combustion do not take place at ordinary temperatures at all in the air, and even at elevated temperatures require considerable time for their completion. Many such reactions can, however, be made to proceed rapidly to the end in a very brief period of time, if they take place in the presence of oxygen under increased pressure. For this purpose, an apparatus has been devised in which combustions can readily be effected at ordinary temperatures. The combustion or explosion bomb, as it is termed, while bearing certain relations to a form of apparatus early devised by Andrews, 1 we really owe to Berthelot. 2 The form of bomb which is used at present is seen in the accom- panying figure (Fig. 46). This is the form with which so much good work has been done by Stohmann 8 and his assistants in Leipzig; Stohmann himself having worked with Berthelot in Paris. The walls of the bomb are of steel, and are sufficiently thick to withstand very great pressure. The bomb was lined on the inside with platinum. But since this required more than a thousand grams of platinum, it is obvious that some cheaper material would be very desirable. The lining used by Stohmann is enamel, which is not acted upon by many chemical substances. Upon the vessel 6, is placed a weighed amount of the substance whose heat of combus- tion is to be determined. An iron wire of known length rests upon 1 Fogg. Ann. 75, 27 (1848). 2 Ann. Chim. Phys. [5], 23, 160 (1881) ; [6], 10, 433 (1887). 3 Journ. prakt. Chem. 39, 503 (1889). 328 THE ELEMENTS OF PHYSICAL CHEMISTRY the substance, and through this wire an electric current can be passed. The iron burns readily in the oxygen when once heated by the current, and ignites the substance. The bomb is filled with oxygen under a pressure of about 25 atmospheres, from a cylinder containing oxygen under a higher pressure, and then closed by tightly screwing down the top. The whole bomb is then immersed in the water of a suitably arranged calorimeter. The current is passed through the wire, which burns in the oxygen and ignites the substance ; and the combustion of the tablet of the substance is quickly completed. The heat liberated is measured in the water calorimeter in the usual manner. A large number of corrections have to be introduced into all such measurements. Thus, the heat which is liberated when the iron wire burns, must be taken into account. Further, the bomb is filled with air at the outset, and the nitro- gen of this air is oxidized to nitric acid. This reaction liberates heat, and the amount must be ascertained and the correction applied. Fig THERMOCHEMISTRY 329 In addition, there are all the ordinary corrections of calorimetry, and many further details which must be learned by practice with the apparatus. By. means of this apparatus the heats of combustion of a large number of substances have been studied, and our thermochemical knowledge greatly extended in the field of organic chemistry. THERMOCHEMICAL UNITS AND SYMBOLS Units used in Thermochemistry. — The unit of heat in thermo- chemical measurements is the calorie. The calorie has been defined as the quantity of heat required to raise one cubic centimetre of water one degree in temperature. This definition would be exact if it had not been shown that the specific heat of water varies with the tem- perature. The work of Rowland and others has made it certain that the amount of heat required to raise the temperature of 1 c.c. of water from 0° to 1°, is not the same as the amount necessary to raise the temperature of the same quantity of water from 20° to 21°, or from 50° to 51°. In our definition of calorie we must, therefore, specify the temperature ; and the temperature usually chosen is the ordinary temperature, 16° to 18°. The difference of a degree is not a matter of any very great importance, since the specific heat of water changes very slightly over this range in temperature. It has also been suggested that we define a calorie as T ^ lr of the amount of heat required to raise 1 c.c. of water from 0° to 100°, and the suggestion is undoubtedly valuable. The calorie most frequently used in thermochemical measure- ments refers to 18°, and it is in terms of this unit that thermochemi- cal results are usually expressed. It is written " cal." Ostwald has suggested a larger unit which is one hundred times the smaller, and is written K. K = 100 cal. There is also a still larger unit which is frequently used, and which is one thousand times the smallest unit. It is written " Cal." We have, then, the following relations between the three units : — K = 100 cals. ; Cal = 10 K = 1000 cals. Thermochemical Symbols. — The methods of expressing the re- sults of thermochemical measurements are simple. The symbols of the substances which react mean gram-atomic weights of the sub- stances. Thus — H 2 + O = H 2 + 68,360 cals. 330 THE ELEMENTS OF PHYSICAL CHEMISTRY means that when 2 g. of hydrogen unite with 16 g. of oxygen, form- ing 18 g. of water at ordinary temperatures, there are 68,360 cal- ories of heat liberated. These same facts are sometimes expressed thus : — [H„ Q] = 68,360 +. The plus sigu means that heat is liberated or that the reaction is exothermic. A minus sign would mean that the reaction is endo- thermic, or that heat is absorbed. If we interpret this in terms of our energy conceptions, it means that the intrinsic energy of 2 g. of hydrogen, plus the intrinsic energy of 16 g. of oxygen, exceed the intrinsic energy of 18 g. of water by ■68,360 calories. The same principle holds when compounds react. Thus — NH 3 + HC1 = NH 4 C1 + 41,900 cals. means that when 36.45 g. of hydrochloric acid combine with 17.07 g. of ammonia, 41,900 calories of heat are liberated. This is also written : — [NH 3 ,HC1]= 41,900. If we wish to represent that the reaction takes place in solution, the presence of the large quantity of water is represented by the sym- bol aq. Thus — KOH aq + HC1 aq = KC1 aq + 13,700 cals. means that when a gram-molecular weight of caustic potash in solu- tion in water reacts with a gram-molecular weight of hydrochloric acid in aqueous solution, there is formed a gram-molecular weight of potassium chloride in aqueous solution, and 13,700 calories of heat are liberated. If we wish to represent the heat set free when a substance dis- solves in water, the symbol aq is written after the formula of the substance : HC1, aq = 17,320 means that 17,320 calories of heat are liberated when a gram-molecular weight of hydrochloric acid gas is dissolved in water. If we wish to represent both chemical action and solution, we write as follows : — H + CI -(- aq = HC1 + aq + 39,300 cals. And this means that when 1 g. of hydrogen combines with 35.4 g. of chlorine in the presence of water which absorbs the hydrochloric acid formed, the heat set free due to combination and solution is 39,300 calories. THERMOCHEMISTRY 331 If a compound is broken down into its constituents, this fact is expressed by placing the minus sign before the formula of the sub- stance : — - HC1 = - 22,000 cals. And this means that when a gram-molecular weight of hydrochloric acid is decomposed into hydrogen and chlorine, 22,000 calories of heat are absorbed. If we wish to represent the state of aggregation of the substances which react and the products formed, this can be done as follows: The gaseous condition is represented by italics, the liquid by ordi- nary type, and the solid by extra heavy type. _H" 2 = water- vapor ; H 2 = liquid water ; H 2 = ice. .HjAooo - HAop = 9670 cals. This means that when a gram-molecular weight of water-vapor at 100° is condensed to water at 100°, so many calories of heat are set free. The application to other cases is self-evident. SOME RESULTS WITH THE ELEMENTS It would be impossible within the scope of this work to give an account of any considerable proportion of the thermochemical results which have been obtained. A few of the more interesting results with certain elements and compounds will, however, be very briefly referred to. We shall take up first some rather striking results which were secured with certain elements. Oxygen. — Oxygen is known to exist in two modifications, — ordi- nary oxygen and ozone. The difference between these two is usually referred to the number of atoms contained in the molecule, — oxygen containing two atoms, ozone three. The chemical properties of these two forms of oxygen are very different, ozone being the more active chemically. This would lead us to suspect that the molecule of ozone contains more energy than the molecule of oxygen. This has been tested by thermochemical methods. Hollmann burned the same substance in oxygen and in ozone. The end products were the same in both cases. Therefore, any difference in the amounts of heat liberated must have been the thermal equivalent of the excess of intrinsic energy in the one form of oxygen over that in the other. He found that more heat was liber- 332 THE ELEMENTS OF PHYSICAL CHEMISTRY ated when the substance was burned in ozone, and concluded that the difference in intrinsic energy of the two modifications of oxygen was to be expressed by the following equation : — 2 3 = 3 2 + 2 x 17,100 cals. More recent determinations have shown larger differences between the intrinsic energies of the two modifications of oxygen. Thus, Ber- thelot 1 oxidized arsenious to arsenic acid, on the one hand by oxygen, on the other by ozone, and concluded from the results that — 2 3 = 3 2 + 2 x 29,600 cals. The still more recent work of Van der Meulen, in which ozone was decomposed by platinum black, gave the result — 2 3 = 3 2 + 2 x 36,200 cals. These results show conclusively that a difference exists between the intrinsic energy of the molecule of oxygen and that of ozone, and that the molecule of ozone contains the greater amount of energy. The differences in the chemical properties of these two modifications of oxygen is, undoubtedly, very closely associated with this differ- ence in the amounts of energy stored up in their molecules. We shall see that similar relations exist with other elements which occur in more than one modification. Sulphur. — Sulphur exists in two crystalline modifications. The more common form is orthorhombic, and is obtained when ordinary amorphous sulphur is dissolved in carbon bisulphide and the solu- tion evaporated. When, on the other hand, ordinary sulphur is melted and allowed to cool rapidly, we obtain monoclinic crystals. The monoclinic form is much less stable than the orthorhombic at ordinary temperatures, and readily passes over into the latter. It, therefore, seems to be the analogue of ozone, and orthorhombic sulphur of ordinary oxygen, since ozone readily passes over into ordinary oxygen. We should, then, expect that the molecule of monoclinic sulphur would contain more intrinsic energy than that of orthorhombic sulphur. This was tested by Favre and Silbermann. 2 When orthorhombic sulphur was burned, 71,000 calories of heat were liberated. When monoclinic sulphur was burned, 73,300 calories were set free. The difference, 2300 calories, is the thermal equiva- lent of the difference in the intrinsic energy of the two modifications. 1 Ann. Chim. Phys. [6], 10, 162 (1876). 'Ibid. [3],. 84, 443 (1852}. THERMOCHEMISTRY 333 Carbon. — Carbon exists in a number of modifications, — ordinary- amorphous carbon, graphite, diamond, etc. The same question arises here as has already been considered in the cases of oxygen and sulphur : is there a different amount of energy contained in the molecules of these different forms of carbon ? This has been answered by Favre and Silbermann, 1 who determined the heats of combustion of the different modifications of carbon, and found : — For charcoal 96,980 cals. For retort carbon . 96,530 cals. For graphite 93,360 cals. For diamond I 93,240 cals. 1 94,550 cals. Of the different modifications of carbon, charcoal contains the great- est amount of energy, and the crystallized modifications, graphite and diamond, the least. The same general results obtained with other elements appear here in the case of carbon. Phosphorus. — A fourth non-metallic element which exists in more than one form is phosphorus — yellow or ordinary phosphorus and the red modification. These contain different amounts of energy in their molecules, as is shown by the different amounts of heat set free when they are burned to the same end product. When yellow phosphorus is transformed into red there are about 27,300 calories of heat liberated. This is approximately the thermal equivalent of the difference between the intrinsic energies of the two modifications. Much work has been done on the thermochemistry of other inor- ganic elements, and also an enormous amount on the thermal rela- tions of the metallic elements ; but for the results obtained, reference must be had to some of the larger works, 2 which deal more in detail with thermochemical results. NEUTRALIZATION OF ACIDS AND BASES Heat of Neutralization. — When solutions of acids and bases are brought together, heat is liberated. Quantitative measurements of the amounts of heat set free, brought out a simple and very impor- tant relation. This can best be seen from the following results for strong acids and bases. Gram-molecular weights of different acids were brought together with a gram-molecular weight of a given base, both the acid and base being present in very dilute solution. The 1 Ann. Chim. Phys. [3], 34, 408 (1852). 2 Ostwald : Lehrb. d. Allg. Chem. II. Thomsen : Thermochemische Unter- suchungen. Berthelot : Essai de Mecanique Chimique. 334 THE ELEMENTS OF PHYSICAL CHEMISTRY amounts of heat set free by a number of acids when neutralized with the base sodium hydroxide, were : — Heat of Neutbalization Hydrochloric acid and sodium hydroxide .... 13,700 cals. Hydrobromic acid and sodium hydroxide .... 13,700 cals. Nitric acid and sodium hydroxide 13,700 cals. Hydriodic acid and sodium hydroxide .... 13,800 cals. Chloric acid and sodium hydroxide 13,760 cals. Bromic acid and sodium hydroxide 13,780 cals. Iodic acid and sodium hydroxide 13,810 cals. The remarkable fact comes out that the heat of neutralization of these strong acids with a given base, sodium hydroxide, is a constant. This suggests a further question very closely correlated to the above. Suppose we neutralize a given acid with a number of bases, will the heat liberated be a constant, and if so, will this bear any close relation to the above constant where the base was the same and the acid changed ? This can be answered by the following results, in which hydrochloric acid was neutralized by a number of bases : — Heat op Neutralization . 13,700 cals. . 13,700 cals. . 13,800 cals. . 13,900 cals. Hydrochloric acid and lithium hydroxide . Hydrochloric acid and potassium hydroxide Hydrochloric acid and barium hydroxide . Hydrochloric acid and calcium hydroxide . The heat of neutralization of a given acid with a number of bases is also a constant, provided the acid and bases are present in very dilute solution. But what is even more surprising, the constant in this case has the same value as in the preceding case where the base was unchanged, and the nature of the acid varied. These facts when they were first discovered were very perplexing. Indeed, no satisfactory explanation of them could be furnished, and it was not until the theory of electrolytic dissociation was proposed that we could account for them at all. Explanation of the Constant Heat of Neutralization of Strong Acids and Strong Bases. — It is one of the crowning glories of the theory of electrolytic dissociation, that it not only explains all of the facts in connection with the neutralization of strong acids and bases in dilute aqueous solution; but these facts are a necessary consequence of the theory. Take, as an example, hydrochloric acid and sodium hydroxide. In a very dilute aqueous solution of hydrochloric acid all the mole- cules are dissociated into hydrogen and chlorine ions thus : — HC1 = H + CI. THERMOCHEMISTRY 335 Similarly, in dilute aqueous solution, the molecules of sodium hydrox- ide are completely broken down into ions : — NaOH = Na + OH. When the dilute aqueous solutions of the base and acid are brought together, the following reaction takes place : — Na+ OH + H + CI = Na + CI + H 2 0. The cation of the base, sodium, and the anion of the acid, chlorine, remain in solution as ions after the process of neutralization in exactly the same condition as before neutralization took place. The anion of the base-hydroxyl and the cation of the acid-hydrogen combine and form a molecule of water. ■ ' It may be urged that the sodium and chlorine ions combine, since sodium chloride is formed as the result of the neutralization. The salt is formed if the solution is evaporated; i.e. if the solution is concentrated. But it can be shown by several separate and inde- pendent methods, that a dilute solution of sodium chloride contains only ions and no molecules. The sodium and chlorine, then, remain as ions. The hydrogen and hydroxyl combine and form a molecule of water. This is proved by the fact that water is always formed as the result of the process of neutralization; and further, it has been shown by a half-dozen different methods 1 that hydrogen and hydroxyl ions cannot remain in the presence of one another uncom- bined to any appreciable extent. This is the same as to say that water is practically undissociated. Since hydroxyl is the anion of every base, and hydrogen the cation of every acid, the process of neutralization of any strong acid with any strong base in dilute solution, consists in the union of the hydroxyl ion of the base with the hydrogen ion of the acid, forming a molecule of water. The process of neutralization of any acid by any base is, there- fore, exactly the same as the process of neutralization of any other acid by any other base. The total heat that is liberated when a gram- equivalent of a completely dissociated acid acts on a gram-equivalent of a completely dissociated base, is the heat set free by the union of a lOstwald: Ztsckr. phys. Chem. 11, 521 (1893). Wijs : Ibid. 11, 492; 12, 514 (1893). Arrhenius : Ibid. 11, 827 (1893). Bredig : Ibid. 11, 830 (1893). Nernst : Ibid. 14, 155 (1894). Kohlrausch and Heydweiller : Ibid. 14, 317(1894). 336 THE ELEMENTS OF PHYSICAL CHEMISTRY gram-equivalent of hydroxy! ions with a gram-equivalent of hydrogen ions. Thus : — H aq + OH aq = 13,700 cals. Since all processes of neutralization of completely dissociated acids and bases are the same, the heat of neutralization of all such acids and bases must be a constant, and must be the heat of combination of a gram- equivalent of hydroxyl and hydrogen ions. Neutralization of Weak Acids and Bases. — If either the acid or base is what we term weak, the heat of neutralization is not 13,700 calories, but differs from this value. Thus, take the following exam- ples : — Heat of Neutralization Formic acid and sodium hydroxide .... 13,400 cals. / Acetic acid and sodium hydroxide . Dichloracetic acid and sodium hydroxide Valeric acid and sodium hydroxide Phosphoric acid and sodium hydroxide . 13,300 cals. 14,830 cals. 14,000 cals. 14,830 cals. In these cases the acids are weak and the base is strong; neverthe- less, there are considerable differences between the heats of neutral- ization and the constant 13,700 calories. Similar results were obtained when weak bases were neutralized with a strong acid. If, however, both acid and base are weak, the heat of neutralization differs still more from the constant 13,700 calories. A few examples of this condition are given below: — Heat of Neutralization Formic acid and ammonium hydroxide .... 11,900 cals. Acetic acid and ammonium hydroxide .... 11,900 cals. Valeric acid and ammonium hydroxide .... 12,700 cals. When the weak base ammonia is neutralized by the weak organic acids, the heat of neutralization differs very widely from the con- stant 13,700. Explanation of the Results with Weak Acids and Bases. — If the acid or base is weak, we shall learn that it is only little dissociated by water, even in dilute solutions. When only a part of the acid or base is dissociated, the process of neutralization could proceed only until all the dissociated substance had reacted ; were it not for the fact that as soon as the ions already present begin to react, more ions would be formed from the undissociated molecules, or, in a word, the process of dissociation would continue as the reaction continued until all the molecules had dissociated. When molecules dissociate into ions, heat is either evolved or THERMOCHEMISTRY 337 consumed. The thermal change which accompanies the dissocia- tion of the undissociated molecules, either increases or diminishes the amount of heat set free due to neutralization alone. If the heat of dissociation is positive, it adds itself to the heat of neutralization ; if negative, it diminishes the heat of neutralization. Thus, the heat which is liberated when a weak acid acts on a weak base, may be either greater or less than the constant 13,700 calories — greater when the heat of dissociation is positive, less when it is negative. It could be equal to the constant only when the heat of dissociation is zero. The facts, then, agree with the theory, not only when the acid and base are completely dissociated, but when the dissociation is not complete. We could predict from the theory of electrolytic disso- ciation that the heats of neutralization of weak acids and bases would not be a constant, with the same certainty that we could pre- dict the constant value of the heats of neutralization of completely dissociated acids and bases. The apparent exceptions presented by the weak acids and bases furnish as strong confirmation of the theory as the cases which conform to rule. Explanation of the Law of the Thermoneutrality of Solutions of Salts. — The theory of electrolytic dissociation furnishes us with the first rational explanation of the law of the thermoneutrality of salt solutions. This law, which it will be remembered was discov- ered by Hess, states that when dilute solutions of salts are mixed there is little or no change in the heat tone. This is a necessary consequence of our theory. Take two salts, sodium chloride and potassium bromide. In dilute aqueous solutions these exist entirely as ions : — + _ NaCl = Na + CI ; KBr =K +Br. When the solutions of these salts are mixed, all of the parts remain in solution as ions. There is no chemical action whatso- ever, every constituent remaining in the same condition after as before mixing. There is, then, absolutely no reason to expect any thermal change, and none results. We can now begin to see the importance and wide-reaching sig- nificance of the theory of electrolytic dissociation. This theory furnishes us with the explanation of the constant heat of neutrali- zation of acids and bases, and of the law of the thermoneutrality of salts ; and this is but the beginning. We shall see as our subject develops, that it has thrown an entirely new light on a great num- 338 THE ELEMENTS OF PHYSICAL CHEMISTRY ber of chemical, physical, and biological problems which, without its aid, were simply empirically established facts, whose meaning was entirely shrouded in darkness. We shall see that this theory is fundamental, if we hope to raise chemistry from empiricism to the rank of an exact science. Thermochemical Method of Determining the Relative Strengths of Acids and Bases. — One important application of the heat of neutral- ization must be considered here. We have seen that when a very dilute solution of any strong acid acts on a very dilute solution of any strong base, the heat liberated is a constant, independent of the nature of the acid and the nature of the base. This applies only to very dilute solutions. If the solutions are more concentrated, the heat liberated on neutralizing an acid with a base depends on the nature of the acid and also on the nature of the base. This fact has been utilized to determine the relative strength of acids and bases, and in the following way. Given the problem to determine the relative strengths of hydro- chloric and sulphuric acids. An equivalent of each acid is neutral- ized by an equivalent of some base, say sodium hydroxide ; and the amount of heat set free in each case, determined. To one equivalent of hydrochloric acid and one equivalent of sulphuric acid, under the same conditions as above, and in the pres- ence of each other, one equivalent of the base is added. If all the base went to the hydrochloric acid, the heat liberated would be the same as that set free when the base acted on hydrochloric acid alone. If all the base went to the sulphuric acid, the heat liberated would be equal to the heat of neutralization of the sulphuric acid by the base, under the same conditions. If the base went part to the hydrochloric acid and part to the sulphuric, the amount of heat set free would lie between the above two values. The latter condition is the one which always obtains. The amount of heat set free falls between the amounts liberated with each acid separately, and, consequently, a part of the base goes to each acid. Knowing the amount of heat liberated with each acid separately, and the amount of heat set free when the acids are treated in the presence of each other with one-half enough base to neutralize them, we know at once the way in which the acids divide the base between them ; and this is the expression of the relative strengths of the acids. The above line of reasoning is given for the sake of simplicity and clearness. In actual practice the mode of procedure is some- what different, though the principle is the same. One acid is allowed THERMOCHEMISTRY 339 to act on a salt of the other acid, and the final distribution of the base between the two acids determined by the amount of heat set free. This method of solving the problem is relatively complex. Take the action of nitric acid on, say, sodium sulphate. It is neces- sary to know the heat liberated when nitric acid is neutralized by the base, when sulphuric acid is neutralized by the base, the heat evolved when sulphuric acid acts on sodium sulphate, when nitric acid acts on sodium nitrate, and also whether there is heat evolved when the two acids are brought together. Given all of the above data, it is possible to determine, approxi- mately, the relative strengths of nitric and sulphuric acids. It is, however, obvious that this method of determining the strengths of acids is very complicated, and further, when we consider the rela- tively large errors in all thermochemical measurements, the results obtained in this way could not be more than approximations. The above method of determining the relative strengths of acids is not used at all at present, since, as we shall soon learn, we have far more accurate and very simple methods for solving such problems. The thermochemical method has been briefly considered here for the sake of completeness, and because it acquired considerable prominence at a somewhat earlier period. The thermochemical method of determining the relative strength of bases is exactly the same in principle as that described above for acids. Given two bases whose relative strengths are to be deter- mined. An equivalent of each base is neutralized with a given acid, and the amount of heat measured. Then one equivalent of the acid is added to one equivalent of the two bases in the presence of each other, and the amount of heat determined. From the relations of these three quantities the division of the acid between the two bases is ascertained. Here, again, in practice one base is allowed to act on the salt of the other base with the acid, and the division of the acid between the two bases determined by thermal methods. The method here is just as complex as when applied to the relative strengths of acids, and has been entirely supplanted by more refined methods for determining the relative strengths of bases. SOME RESULTS WITH ORGANIC COMPOUNDS Heat of Formation. — By heat of formation of a compound we mean the amount of heat which is set free or absorbed when the compound is formed by a direct combination of the constituent ele- ments. In order that the term "heat of formation" may have a 340 THE ELEMENTS OF PHYSICAL CHEMISTRY quantitative significance, we must deal with definite amounts of sub- stances ; and in order that the heats of formation of different sub- stances may be comparable, we must deal with comparable amounts of substances. We choose for sake of convenience gram-molecular weights of substances, and determine heats of formation in terms of these quantities. The heat of formation of a compound is, then, the amount of heat set free or absorbed when a gram-molecular weight of the compound is formed from its elements. The heat of combination of a compound may be determined in many cases directly, by allowing the elements to combine and meas- uring the heat set free ; but in many cases this is not possible. A large number of substances cannot be formed directly from the ele- ments. In such cases an indirect method of determining the heat of formation must be employed. The indirect method most com- monly used is to burn the elements in oxygen ; then burn the com- pound in oxygen, and measure in each case the amount of heat set free. Since the products of the combustion of the elements are the same as the products of the combustion of the compound containing these elements, any difference in the amounts of heat set free in the two cases is the heat of formation of the compound. Take the case of methane. It would be impossible to determine directly the heat of formation of methane. This can, however, be determined very easily by burning carbon in oxygen, by burning hydrogen in oxygen, and finally by burning the methane in oxy- gen. Any difference between the heat of combustion of the com- pound and the sum of the heats of combustion of the elements is the heat of formation of the compound. The following results were obtained in this case : — Heat liberated by burning 12 g. C in oxygen .... 96,960 cals. Heat liberated by burning 4 g. H in oxygen 136,720 cals. Sum = 233,680 eals. Heat liberated by burning 16 g. methane in oxygen . . 211,930 eals. The difference between the two values, 21,750 calories, is the heat of formation of methane. In a manner exactly similar to the above, the heats of formation of a large number of compounds have been worked out. Indeed, there are comparatively few compounds formed directly from the elements with sufficient ease to enable their heats of formation to be measured directly. The above indirect method of measuring heat of formation is therefore applied in a large majority of cases. THERMOCHEMISTRY 341 Heat of Combustion. — By heat of combustion of a compound is meant the heat which is evolved when a compound is completely burned in oxygen. The carbon under these conditions is completely oxidized to carbon dioxide, the hydrogen to water, the nitrogen to nitric acid, and the sulphur to sulphur trioxide. The heat of com- bustion of organic compounds is a very important quantity to deter- mine, since it is the only means, in many cases, of determining the heat of formation of the substance. As we have just seen, it is only necessary to determine the heat of combustion of the elements which enter into a compound, and the heat of combustion of the compound itself, and then to subtract the one from the other, in order to arrive at the heat of formation of the compound from its elements. Indeed, the most important quantity by far in the field of organic chemistry, from the thermochemical standpoint, is the heat of com- bustion. In order that this should be determined, it is necessary that the combustion should proceed to the end at once, and that all the constituents should be completely oxidized. For this purpose the combustion bomb, which has been already described, was devised and used. In an atmosphere of relatively concentrated oxygen, i.e. oxygen under high pressure, most organic compounds are completely oxidized ; and by means of the explosion method the heats of com- bustion of an enormous number of organic substances have been ascertained by Berthelot, 1 Thomsen, 2 Stohmann, and Langbein, 3 and others. A few of the more interesting of these results are given below. Saturated or Methane Hydrocarbons. — The heats of combustion of a number of members of this series have been measured by Thom- sen and others. The results for a few hydrocarbons are given below : — Hydrocarbons Heat of Combustion Differences Methane, CH4 211.9 Cals. S> 158.5 Cals. Ethane, CaHe 370.4 Cals. <> 158.8 Cals. Propane, C 3 H 8 529.2 Cals. <> 158.0 Cals. Butane, C4H10 687.2 Cals. / / 159.9 Cals. Pentane, C 6 Hi 2 847.1 Cals. 1 Essai de Mecanique Chimique. 2 Thermochemische Untersuchungen. 8 Journ. prakt. Chem. 1885-1895. 342 THE ELEMENTS OF PHYSICAL CHEMISTRY A constant difference in composition of CH 2 corresponds to very nearly a constant difference in the heat of combustion. This amounts to about 159 Calories. The effect of constitution in this series of hydrocarbons is practi- cally zero, — a normal compound having the same heat of combus- tion as an isocompound of the same composition. The Unsaturated (Ethylene and Acetylene) Hydrocarbons. — The results with the unsaturated hydrocarbons are very similar to those with the saturated. Ethylene Hydrocarbons Heat of Combustion Difference Ethylene, C 2 H 4 ... Propylene, CsH 6 Amylene, CsHio . . . . 333.4 Cals. . 492.7 Cals. / 650.6 Cals. / 807.6 Cals. ' 159.3 Cals. 157.9 Cals. 157.0 Cals. Acetylene Hydrocarbons Heat of Combustion Difference Acetylene, C 2 H 2 Allylene, C 8 H 4 . . 310.1 Cals. v 467.6 Cals. ' 157.5 Cals. The constant difference in composition of CH 2 has a constant influence on the heat of combustion, whether the compound contains a larger or smaller number of carbon atoms. A fact brought out by the above results, of more than ordinary interest, is that the constant difference in composition of CH 2 pro- duces the same difference in the heat of combustion, whether we are dealing with saturated hydrocarbons or with either of the series of unsaturated hydrocarbons. The meaning of this fact is not at pres- ent clear, but it is certainly important from the standpoint of the constitution of these substances. Alcohols. — The alcohols differ from the corresponding hydro- carbons in that they contain one atom of oxygen more than the latter. They thus represent the first stage of oxidation of the hydrocarbons. The heat of combustion of the alcohols is less than that of the hydrocarbons, as we would expect, since they are already partly oxidized. A few results are given : — THERMOCHEMISTRY 343 Alcohols Heat of Combustion Difference Methyl alcohol, CH4O .... Ethyl alcohol, C 2 H 6 .... Propyl alcohol, C s H 8 .... Isobatyl alcohol, C 4 Hi O .... 182.2 Cals. x 340.5 Cals. / 498.6 Cals. / 658.5 Cals. / 158.3 Cals. 158.1 Cals. 159.9 Cals. We observe the same relation here as with the hydrocarbons. A constant difference in composition between succeeding members of the homologous series corresponds to a constant difference in the heat of combustion. As we have stated, the hydrocarbons differ from the correspond- ing alcohols in that the latter contain an oxygen atom. We should, therefore, expect a nearly constant difference between the heat of combustion of the hydrocarbon and the alcohol. Tacts substantiate this conclusion. Heat of combustion of CH 4 - CH 4 = 29.7 Cals. Heat of combustion of C 2 H 6 — C 2 H 6 = 29.9 Gals. Heat of combustion of C 3 H 8 — C 3 H 8 = 30.6 Cals. Heat of combustion of C 4 H 10 - C 4 H 10 O = 28.7 Cals. Results similar to the above were obtained with other oxidation products of the hydrocarbons. In some cases the effect of consti- tution was more pronounced than in others, but, on the whole, noth- ing essentially new would be brought out by going farther into details in this direction. One further class of paraffine derivatives must, however, be considered. Halogen Substitution Products of the Paraffines. — Take first the chlorine derivatives of the paraffines. A constant difference in com- position corresponds to a constant difference in the heat of combus- tion. Heat of Combustion Difference Methyl chloride, CH S C1 Ethyl chloride, C 2 H 6 C1 . Propyl chloride, C 3 H,C1 Isobutyl chloride, C 4 H 9 C1 164.8 Cals. 321.9 Cals. 480.2 Cals. 637.9 Cals. 157.1 158.3 157.7 344 THE ELEMENTS OP PHYSICAL CHEMISTRY Results of a similar character were obtained with other halogen derivatives of the paraffines. An interesting relation between the heats of formation of the chlorides, bromides, and iodides of the paraffines has been pointed out by Ostwald. 1 He gives the following table of results, cal- culated from the heats of combustion of the compounds and of the elements : — Heat of Formation Heat of Formation DlFF. CH3C1 22.0 Cals. CH s Br 14.2 Cals. 7.8 Cals. C 2 H 6 C1 29.6 Cals. CsHJBr 21.8 Cals. 7.8 Cals. C3H7CI 36.0 Cals. C 3 H 7 Br 29.1 Cals. 6.9 Cals. CH 3 I 2.8 Cals. 19.2 Cals. C 2 H 6 I 9.9 Cals. 19.7 Cals. There is a constant difference between the heats of formation of the bromides and chlorides, and the iodides and chlorides. This difference is independent of the size of the group combined with the halogen, i.e. whether it is methyl, ethyl, propyl, etc. Results of this kind are certainly very closely connected with the fundamental problems of the combination of matter. The Thermochemistry of Benzene. — The thermochemical results which have been obtained with benzene are especially interesting, as showing a new application of the results of such measurements. The problem of the constitution of benzene has been, and is still, one of the fundamental problems of organic chemistry. The mole- cule contains six carbon atoms and six hydrogen atoms, and the fun- damental question is the way in which the carbon atoms are united. Two possibilities be- tween which it has been found difficult to decide hc ch are the following : — In I the carbon atoms are united alternately by single and double union. ^ r, CH There are three double 1 II and three single bonds in CH % HC I HC CH \r»S 'CH CH CH the molecule. In II all the carbon atoms are united by single bonds. There are nine single bonds in the molecule. The first formula is the 1 Lehrb. d. Allg. Chem. II, p. 390. THERMOCHEMISTRY 345 well-known hexagon of Kekule - ; the second, the prism formula of La- denburg. The attempt has been made to decide between these formu- las by thermochemical methods. Thomsen found * that when carbon is united with carbon by double linkage (C=C) the heat of combus- tion is different from that of carbon united to carbon by single linkage (C — C). He worked out, approximately, the heat of com- bustion of carbon under these two conditions, and also the heat of combustion of six hydrogen atoms. He then determined the heat of combustion of benzene, and found the value 788 Cals. When the heat of combustion of the six hydrogen atoms was subtracted from this quantity, the remainder was found to correspond to the condi- tion of six carbon atoms united by single union. In a word, there are nine single unions in benzene, or the prism formula of Laden- burg represents the structure of the benzene molecule. We must not, however, accept this conclusion as in any way final. We have seen that exactly the opposite result was reached by Briihl from a study of the refractivity of benzene. He concluded from his work, that there are three single and three double bonds in the benzene molecule. It must also be remembered that no one method is capable of settling such a problem, to the exclusion of the results of all other methods. A great many purely chemical methods have been brought to bear on the problem of the constitution of benzene, with the gen- eral result that the hexagonal formula of Kekule seems to account for the facts rather better than any other which has been proposed. There is this objection, however, to the formula of Kekule, that it represents the benzene molecule as occupying only two dimensions in space. It should be stated in this connection that a number of facts have been pointed out, especially by Ladenburg, which seem to indicate the general correctness of the prism formula. It is thus obvious that the question of the constitution of benzene is still an open one. Effect of Constitution on Heat of Combustion. — Certain striking relations between the heats of combustion of compounds and their differences in composition have been pointed out. We must not, how- ever, draw the conclusion that heat of combustion is conditioned only by the composition of the molecule. The constitution of the molecule, or the way in which its constituents are united, has a marked influence, in many cases other than benzene, on the heat of combustion. To determine the effect of constitution on heat of combustion, it is necessary to compare substances having the same 1 Thermochemische Untersuchungen. 346 THE ELEMENTS OF PHYSICAL CHEMISTRY composition, but different constitution. Such, are, of course, the well-known isomeric compounds. If we compare isomeric com- pounds having nearly the same constitution, we shall find compara- tively slight differences in the heats of combustion. This is shown by the following example : — Heat of Combustion Methyl acetate, CH 3 C00CH S .... 395 Cals. Ethyl formate, HCOOC 2 H 6 390 Cals. If the isomeric compounds differ still more in constitution, the difference in the heats of combustion will be still greater. Take the compounds : — Heat of Combustion Methyl formate, HCOOCHs 252 Cals. Acetic acid, CH 8 COOH 210 Cals. When the difference in constitution is very great, there may be a very large difference between the heats of combustion, as in the case given below : — Heat of Combustion Benzene, C 6 H 8 788.0 Cals. Dipropargyl, C 6 H 6 883.2 Cals. No very important generalization connecting constitution and thermal relations has been reached. The data at hand are far too meagre, and the phenomena dealt with perhaps too complex, to admit at present of any wide-reaching conclusion. It is, however, quite clear from the above examples, that constitution has a marked influence on heat of combustion ; and this is the point upon which it is desired to lay stress in this place. The energy contained in a molecule is, then, not conditioned solely by the number and kind of atoms present, but also by the way in which they are combined with one another. This is proved by the fact that the heats of combustion of isomeric substances differ ; and since the end products in such cases are the same, the molecules of isomeric substances must contain different amounts of energy. 1 1 For the most recent reliable measurements in thermochemistry see — Stohmann and Kleber : Journ. prakt. Chem. (2) 43, 538 (1891). Stohmann and Langbein : Ibid. 45, 305 (1892) ; 46, 530 (1893). Stohmann : Ibid. 48, 447 (1893); 49, 99, 483 (1894). Stohmann and Schmidt: Ibid. 50, 385 (1894). Stohmann and Langbein : Ibid. 50, 388 (1894). Stohmann and Schmidt: Ibid. 52, 59 (1895). Stohmann and Schmidt : Ibid. 53, 345 (1896). Stohmann and Hausmann: Ibid. 55, 263 (1897). J. Thomsen : Ibid. 71, 164 (1905); Ztschr. anorg. Chem. 40, 185 (1904). CHAPTER VII ELECTROCHEMISTRY' DEVELOPMENT OF ELECTROCHEMISTRY Earlier Observations. — The discovery of simple electrical phe- nomena preceded, by a long time, the recognition of the relation between electricity and other manifestations of energy. It was not until about the middle of the eighteenth century that Beccaria 1 showed that metals like zinc could be obtained from their oxides by means of the electric spark. In this reaction the chemical attraction between the zinc and the oxygen was overcome by means of elec- tricity, and it appeared probable that some relation existed between the two. The observation of Van Marum that metal wires when heated by the current in an atmosphere of nitrogen were not converted into the oxide, as they were in the presence of oxygen, was of special importance as bearing upon the theory of combustion in vogue at that time. A burning body was supposed to give off a substance having negative weight, called phlogiston. What we now call an oxide was then termed a " calc." The calc differed from the metal in that it contained less phlogiston. If this was the true explanation of combustion, then there was no reason why a heated metal should not form a calc in nitrogen as well as in oxygen, since neither of these gases took part in combus- tion. The fact that no calc was formed in the presence of nitrogen was a strong argument against the theory of phlogiston, as a satis- factory and sufficient explanation of the phenomenon of combustion. Galvani's Discovery. — It was not until the last decade of the eighteenth century that the wife of Galvani discovered by accident that when the crural nerve in the hind leg of a frog was touched with a scalpel, it was thrown into contraction by an electric dis- charge in the room. Galvani's investigations in this field brought out the fact that when both muscle and nerve were connected with 1 Geschichte Elek. (Priestly), Berlin, 1772. 347 348 THE ELEMENTS OF PHYSICAL CHEMISTRY metallic conductors, especially when these were of different metals, the contractions could be produced without the presence of an elec- tric discharge. He asked himself whence the source of this elec- tricity, and concluded that it must exist in the animal body. This was the origin of his theory of " animal electricity.'' Volta's Discovery of the Primary Battery. — That strong con- tractions in the muscle were produced only when different metals were used, showed to Volta 1 the insufficiency of the explanation offered by Galvani to account for the source of the electricity. Volta 1 pointed out clearly that in order that such contractions should be produced it was necessary that two different metals, or conductors of the first class, should be brought in contact, and at the same time their opposite ends should be brought in contact, with a conductor of the second class. There were thus two possible sources of the electricity ; either at the contact of the two different metals with each other, or at the contact of the metals with the con- ductors of the second class, i.e. the liquids present in the animal itself. He concluded that the chief source was at the contact of the two metallic surfaces. Volta thus distinguished between conduc- tors of the first and second classes ; placing in the first those sub- stances which conduct like the metals, in the second those which conduct like aqueous solutions. The Voltaic Pile. — The recognition of chemical action as the cause of galvanic action led to the construction of the voltaic pile. Volta constructed his pile of zinc and silver, placed alternately over one another, and moistened these with a salt solution held by some porous material. The strength of such a pile depended upon the number of couples. The discovery of the voltaic pile or battery marks an epoch in the development of electrochemistry. This placed in the hands of the investigator an unlimited supply of elec- tricity, which made it possible to carry on systematic investigations which had hitherto been impossible. From this time electrochem- istry developed by enormous strides — one important discovery quickly following another. The Electrolysis of Water. — The source of the electricity in the voltaic pile being due to the chemical action in the couple, they had to do here with a clear case of the transformation of chemical energy into electrical. The next step which naturally would have been taken was to determine whether it was possible to effect chemical decom- position by means of the current from such a pile. This was done 1 Phil. Trans. 1793, I, p. 10. Grens 1 Journ. d. Phys. 3, 479 (1796). ELECTROCHEMISTRY 349 by Nicholson and Carlisle 1 at the beginning of the nineteenth century. By means of the current they decomposed water into oxygen and hy- drogen, the gases being liberated on the two poles of their couples. This was an imnputant step, since it showed clearly the transforma- tion of electrical energy into chemical, and made it strongly prob- able that there is a close relation between the two. Work of Davy. — At this time Humphry Davy 2 began his ■epoch-making experiments with the electric pile, which finally re- sulted in the separation of the alkali metals from their oxides. The •decomposition of these oxides directly by the current was strong evidence in favor of some close relation between chemical attraction and electrical attraction. As the result of his electrochemical stud- ies he was led to the electrochemical theory which bears his name. According to this theory, the atoms of different substances acquire , •different electrical charges by contact, and these attract one another , because of the different charges upon them. The differences between the charges may be so small that the attraction between them will not be sufficient to cause the atoms to leave their former ' positions, or they may be great enough to effect such a rearrange- 1 ment. In the latter case, a chemical compound is formed. The chemical attraction of atoms depends, then, only upon the ■ •electrical attraction between the opposite charges which have accu-i mulated upon them, due to their contact with one another. A large number of atoms, each with a small attractive power, may overcome -a greater attraction between a smaller number of atoms. This accounts for the effect of mass in chemical action, which we shall learn is very great indeed. Electrolysis, according to this theory, consists in equalizing the ! charges upon the atoms. The negatively charged atom receives posi- ; tive electricity from the positive pole, to which it is attracted and \ becomes electrically neutral. The positively charged atom is at- 4 tracted to, and electrically neutralized at, the negative pole. The ! •compound is thus necessarily broken down, since the force which held its constituents together no longer exists. The Electrochemical Theory of Berzelius. — The theory of Davy never acquired any prominence, and soon gave place to that of Ber- ■zelius, which differed from it fundamentally. According to Davy ran atom as such is electrically zero, and becomes charged positive or 1 Nicholson's Journ. 4, 179 (1800). 2 Ibid. 4, 275, 326. Gilb. Ann. 7, 114 (i$01); 28, 1, 161 (1808). Bakerian Zect. Boy. Soc. (1806). 350 THE ELEMENTS OF PHYSICAL CHEMISTRY negative by contact with another atom, which takes a charge of the opposite sign. Berzelius l claimed that every atom is charged with j both kinds of electricity. These exist upon the atom in polar ar- I rangement, and the electrical nature of the atom depends upon which i kind of electricity is present in excess. One kind is usually present i in large excess, giving the atom a decidedly positive or negative character. One " pole " is usually much stronger than the other, so that the atom reacts as if it were " unipolar." Chemical attraction is but the electrical attraction of these oppositely charged atoms, and the intensity of the former is conditioned by the magnitude of the charges upon the atoms. A negatively charged atom is attracted to, and combines with, one carrying a positive charge. The magni- tude of these opposite charges may not be the same, the compound formed being electrically positive or negative, depending upon which kind of electricity is present in excess. Two compounds, the one charged positive and the other negative, may thus in turn combine, forming a still more complex compound. In this way Berzelius was able to account for the more complex substances, such as the so- called double compounds. Objections to the Theory of Berzelius. — The theory as put forward by Berzelius did not long enjoy freedom from adverse criticism. Indeed, it seemed to carry with it, of necessity, a questionable conse- quence. If chemical union is due to the electrical attraction of oppositely charged atoms, which come together and more or less equalize their charges, then, as soon as the equalization is effected, the cause for the union no longer exists, and the constituents of the compound must fall apart. As soon, however, as any decomposition took place, the products of the decomposition would again become oppositely charged, would, therefore, attract one another and reunite. There would thus result a continual decomposition and reunion, and a chemical compound would always seem to be in a state of unstable equilibrium. The theory, however, was soon called upon to meet what was supposed to be a very serious objection. If chemical union depends only upon the electrical charges upon the atoms, then, the proper- ties of the compound formed would be a function of the electrical charges upon the atoms in the compound. It was found to be possi- ble to substitute the three hydrogen atoms in the methyl group of acetic acid by three chlorine atoms, without seriously changing the properties of the compound. Berzelius could not satisfactorily ex- 1 Gilb. Ann. 27, 270 (1807). Afh. i Fysik. Kemi oeh Miner, Stockholm, 1806. ELECTROCHEMISTRY 351 plain this fact. The three hydrogen atoms each carried a positive charge, while the three chlorine atoms each carried a negative charge. That three positive charges could be replaced in a compound by three negative charges, without fundamentally changing the nature of the compound, was, for a long time, an insuperable objection to the electrochemical theory of Berzelius. Indeed, this argument was regarded until very recently as practically overthrowing the theory. Thomson overthrows this Objection. — The above objection to the theory of Berzelius persisted nearly to the end of the nineteenth century. It has, however, been recently removed by the work of J. J. Thomson, 1 which will be referred to in this place as it bears so directly upon a theory whose importance is now very great indeed. Thomson has shown experimentally that the same element may be charged now positive, now negative, depending upon conditions. He electrolyzed hydrogen gas, 2 and found that positive hydrogen went to one pole and negative to the other. The spectra of the hydrogen around the two poles was studied and found to be quite different. The molecule of hydrogen gas is, then, very probably made up of a positive and a negative hydrogen ion. We must not, therefore, conclude that because hydrogen is some- times positively charged it is always so. Thomson's own words in connection with the bearing of his work on the theory of Berzelius are given below : — " In many organic compounds, atoms of an electropositive element hydrogen are replaced by atoms of an electronegative element chlo- rine, without altering the type of the compound. Thus, for example, we can replace the 4 hydrogen atoms in CH 4 by CI atoms, getting, successively, the compounds CH S C1, CH 2 C1 2 , CHC1 3 , and CC1 4 . It seemed of interest to investigate what was the nature of the charge of electricity on the chlorine atoms in these compounds. The point is of some historical interest, as the possibility of substituting an electronegative element in a compound for an electropositive one, was one of the chief objections against the electrochemical theory of Berzelius. When the vapor of chloroform was placed in the tube, it was found that both the H and CI lines were bright on the nega- tive side of the plate, while they were absent from the positive side, and that any increase in the brightness of the H lines was accom- panied by an increase in the brightness of those due to CI. . . . The appearance of the H and CI spectra on the same side of the plate was also observed in methylene chloride and in ethylene chloride. Even 1 Nature, 52, 453 (1895). 2 Ibid. 52, 451 (1895). 352 THE ELEMENTS OF PHYSICAL CHEMISTRY when all the H in CH 4 was replaced by CI, as in carbon tetrachloride CC1 4 , the CI spectra still clung to the negative side of the plate. " The same point was tested with SiCl 4 , and the CI spectra was brightest on the negative side of the plate. " From these experiments it would appear that the CI atoms, in the chlorine derivatives of methane, are charged with electricity of the same sign as the H atoms they displace." This work leaves the classical argument against the theory of Berzelius without foundation, since the hydrogen atoms in acetic acid are replaced by chlorine atoms which carry the same kind of charge as the hydrogen which they replace. Therefore, the proper- ties of trichloracetic acid should resemble closely those of acetic acid if the theory of Berzelius is true, and such is the fact. The Law of Faraday. — The period immediately following the one just considered, from an electrochemical standpoint, was not very fertile until we come to the investigations of Faraday. 1 Upon these investigations it is difficult to lay too much stress. Faraday showed the identity of electricity from different sources, whether produced by friction or by chemical action. He also studied the relation between the amount of chemical decomposition effected by a current in passing through a conductor of the second class, and the amount of electricity which flowed through the conductor. He found that the two were proportional to one another, and from this announced the first part of his law : — The amount of chemical decomposition effected by the passage of the current is proportional to the amount of electricity which flows through the conductor. This is one of the few laws of nature which seems to hold rigidly under all known conditions. There is no well-established exception to this law. Faraday determined also the amounts of different elements which are separated from their compounds, by passing the same current through solutions of these compounds. For example, the same current was passed through solutions of, say, copper sulphate, zinc chloride, and silver nitrate, and the amounts of copper, zinc, and silver deposited determined by weighing the electrodes before and after the experiment. A generalization of very wide significance was reached, which is the second part of the law of Faraday : TJie amounts of the different elements which are separated by the same quantity of electricity bear the same relation to one another as the t 1 Hxpr. Researches, III, Ser. No. 373 (1832). ELECTROCHEMISTRY 353 equivalents of these elements. The atoms of all univalent elements carry exactly the same quantity of electricity, of bivalent elements twice as much, of trivalent three times as much, and so on. In a word, all univalent atoms carry the same amount of electricity, and all polyvalent atoms a simple, rational, multiple of the amount carried by univalent atoms — the multiple being the valence of the atom. After Faraday proposed his law, confusion arose between the terms "quantity of electricity" and "electrical energy,' 7 and some confusion might still exist if we are not careful to consider the wide difference which exists between the meaning of these terms. Elec^ trical energy, like every other manifestation of energy, can be factored into a capacity factor and an intensity factor. The capacity, factor of electrical energy is the quantity of electricity, the intensit; factor the potential. These bear the following relation to electric: energy: — capacity factor x intensity factor = electrical energy, or quantity x potential = electrical energy. J The law of Faraday says that when equal quantities of electricity are passed through conductors of the second class, chemically equiv- alent quantities of the different elements are separated from their compounds. It says nothing whatever about the potential required to effect the decompositions, and, consequently, nothing about the electrical energy required in the different cases. Indeed, it is self- evident that this would be very different in different cases. Electrolysis. — The power of the electric current to effect the decomposition of chemical compounds was brought into special prominence by the work of Faraday. The decomposition of com- pounds by the current, he termed electrolysis. Some of the most important advances which were made at this period are along the line which we are now considering. Theories were proposed to account for the facts then known, which we recognize at the present day as containing the essence of one of the widest reaching general- izations in modern chemical science. When the two poles of a voltaic cell were immersed in acidulated water, hydrogen was liberated upon the one pole, and oxygen upon the other. Between the two poles there was a layer of water par- ticles, which apparently underwent no decomposition. The question arose, Do the hydrogen and oxygen set free come from the same or from different particles of water ? It was not a simple matter to decide this point. A superficial glance at what took place would probably leave the impression that they came from different particles 2 A 354 THE ELEMENTS OF PHYSICAL CHEMISTRY of water; yet it might be true that the water molecules which underwent decomposition were those which were halfway between the poles, and that the hydrogen moved from this point in one direction, and the oxygen in the other. Humphry Davy undertook to decide this question experimentally. He placed each pole of a voltaic cell in a vessel containing water, and connected the two vessels by placing a finger of one hand in the one vessel, and a finger of the other hand in the other vessel. He insulated his body from the earth by standing on aTsibber plate. The electrolysis took place, and the gases separated from the electrodes just as if the vessels had been connected directly. According to Davy, in such an arrangement it is difficult to see how the hydrogen and oxygen liberated at the poles could come from the same molecule of water. It was, therefore, probable, that in the ordinary electrolysis of water, the hydrogen and oxygen came from different molecules of water. Theory of Grotthuss. — The first to account at all satisfactorily for electrolysis was Grotthuss, 1 at the early date of 1805. At the + + ~ SB SB SB Fig. 36. moment when the hydrogen and oxygen separate, the one becomes positive and the other negative. The positively charged hydrogen is attracted to the negative pole and repelled from the positive pole. The negatively charged oxygen is attracted to the positive and repelled from the negative pole. This clear and concise idea of Grotthuss is represented graphically in the accompanying figure (36). 1 Ann. de Chim. [1], 88, 54 (1806). ELECTROCHEMISTRY 355 The atoms marked positive represent hydrogen ; those marked negative, oxygen. Before the current is passed, each oxygen atom is combined with a certain definite hydrogen atom, forming water. When the current is passed, the hydrogen atom nearest the negative pole gives up its positive charge to that pole, — becomes electrically neutral, and separates as hydrogen gas. (See Fig. 37.) The oxygen atom which was originally in combination with this hydrogen is now free, and combines with the hydrogen of the next molecule of water. This sets another oxygen atom free, which combines with the next hydrogen, and so on until the positive pole is reached, when the last oxygen atom in the chain not having any hydrogen + H SSSB0E Fig. 37. with which to combine, takes up positive electricity from the positive pole, becomes electrically neutral, and escapes as gaseous oxygen. The gases which escape only on the electrodes come from different molecules of water, as was made very probable by the experiment of Davy. The molecules between the electrodes are, during the electrolysis, constantly interchanging their con- stituents. The distinctive feature of the theory of Grotthuss is that before electrolysis, each hydrogen atom is combined with a definite oxygen atom, from which it does not part company. The current must first decompose the water molecules before any electrolysis can take place. This theory accounted for the facts known at that time, and it remained as the established theory of electrolysis until after the middle of the nineteenth century. 356 THE ELEMENTS OF PHYSICAL CHEMISTRY Theory of Williamson. — A theory as to the condition of things in solution was proposed by Williamson l in 1851. This theory was the outcome of his work on the preparation of ordinary ether by the action of sulphuric acid on ethyl alcohol. The reaction which gave ether as the product was recognized as proceeding in the following stages : — I. S0 2 < q§ + HOC 2 H 6 = S0 2 < °°°K' + H 2 ; ii. so 2 < °°»p» + HOC 2 H 5 = S0 2 < oh + §]£ > 0. The first stage of the reaction consists in the replacement of a hydrogen atom of the sulphuric acid by the ethyl group, with the elimination of a molecule of water. The second consists in the replacement of the ethyl group in ethyl sulphuric acid, by the hydroxyl hydrogen atom from the alco- hol. The reaction which takes place as represented in I is reversed in II, the final result being the removal of a molecule of water from two molecules of alcohol, and the formation of a molecule of ordinary ether. From this Williamson concluded "that in an aggregate of the molecules of every compound, a constant interchange between the elements contained in them is taking place." Williamson z concluded his paper with the following very signifi- cant words : " In recent years chemists have added to the atomic theory an uncertain, and, as I believe, an unsubstantiated hypothesis, that the atoms are in a condition of rest. I reject this hypothesis , and found my views on the broader basis, the movement of the atoms." J Theory of Clausius. — Clausius s did not think it necessary or even justifiable to go as far as Williamson, and assume that there is a constant interchange of parts in a solution, and that no one part- molecule remains attached to another for any appreciable time. On the other hand, he saw that the theory of Grotthuss was not capable of accounting for facts which had come to light since it had been_ proposed. The current, according to Grotthuss, must first decompose J the molecules before it can effect any electrolysis. In reference to this point Clausius 4 says: "In order to separate the once combined^ part-molecules, the attractions which they exert upon one another must be overcome. To accomplish this, a force of definite strength is necessary, and one is therefore led to the conclusion that as long as the force in the conductor does not possess this strength, no de- i Lieb. Ann. 77, 37 (1851). 8 Pogg. Ann. 101, 338 (1857). 2 Ibid. 77, 48 (1851). * Ibid. 101, 346 (1857). ELECTROCHEMISTRY 357 composition of the molecules can take place. But, on the contrary, when the force has acquired this strength, very many molecules must be decomposed at the same time, in that they are all under the effect of the same force, and have almost exactly the same position to one another. If the conductor conducts only by electrolysis, we may draw the following conclusion in reference to the current : As long as the driving force in the conductor is below a certain limit no current will pass, but when it has reached this limit a very strong current suddenly exists. " This conclusion is in direct opposition to the facts. The small- est force produces a current by alternate decomposition and reunion, and the intensity of the current increases according to Ohm's law, — proportional to the force. Therefore, the assumption that the part- molecules of an electrolyte are combined rigidly to form whole molecules, and that they have definite, regular, arrangement is erroneous." .The assumption, then, that the natural condition of a solution of an electrolyte is one of static equilibrium, in which every positive part-molecule is combined rigidly with a negative, was abandoned by Clausius as untenable and his own theory proposed in its place. According to Clausius, an electrolytic solution consists mainly of whole molecules of the electrolyte, but in addition, there are some part-molecules. A positive part-molecule may, during the move- ments to which it is subjected, come into a position with respect to the negative part of another molecule, which is more favorable for union with this, than with its own negative companion. It would then part company with the latter and join the former. This would leave, then, a positive and a negative part-molecule free to move about through the solution and combine with other part- molecules, or break down whole molecules already existing as such in the solution. These movements and decompositions take place with the same irregularity as the heat movements which produce them. The two part-molecules resulting from the breaking down of a whole molecule, may combine directly with one another, or may be prevented from doing so by the movements due to heat. The amount of such decomposition in a solution would depend upon the nature of the solution and upon the temperature. Allow an electric force to act upon a solution containing a mix- ture of whole and part-molecules. The part-molecules will no longer move about equally in all directions, as they would if subjected to the action of heat alone, but more positive parts will move in the direction of the negative pole, and negative parts toward the positive 1 Free Ions, Ostwald and Nernst: Ztst.hr. phys. Chem. 3, 120 (1889). 358 THE ELEMENTS OF PHYSICAL CHEMISTRY pole, than, in any other direction. This directing influence of the current will also facilitate the breaking down of the whole molecules into part-molecules. This assumption of a partial breaking down of the molecules in a solution of an electrolyte, before any current is passed, accounted satisfactorily for the fact which could not be explained by the theory of Grotthuss — viz., that an infinitely weak current could effect electrolysis of water containing a little acid. Such a current, in terms of the theory of Clausius, would simply exert a directing influence on the part-molecules already present, since it would be too weak to break down any of the whole molecules of water. The amount of this directing influence would be proportional to the strength of the current, as had been shown to be the case. In the opinion of Clausius the action of the current is primarily a directing one, but, at the same time, it facilitates a decomposition of the molecules into part-molecules. The theory of Clausius, which has just been considered at some length, will be recognized to be the father of the Theory of Electro- lytic Dissociation. This brief historical sketch brings us up to modern electrochemistry. ELECTRICAL ENERGY; UNITS; NOMENCLATURE Electrical Energy. — Electrical energy may be factored into two factors, as already stated, — an intensity factor or potential, and a capacity factor or amount of electricity. This is analogous to the factors of heat energy; an intensity factor or temperature, and a capacity factor or amount of heat. The unit for the intensity factor of heat energy is the degree, starting from the absolute zero. We have no corresponding unit for the intensity factor of electrical energy, and may, therefore, choose our unit arbitrarily. We can start from any constant potential as zero. In practice, we usually select the potential of the earth as the zero point. The capacity for electrical energy is the amount present in a given system, for a definite difference in potential. The relations between the different manifestations of energy, known as electricity and as heat, are, striking and interesting ; yet certain marked differences exist. One of these is so pronounced as to call for special comment. Conduction of Heat and of Electricity. — All known substance's^ conduct heat energy. Metals are the best conductors of heat, bothj as to quantity and rate. The best conductors of heat energy, ELECTROCHEMISTRY 359 however, as compared with the worst, hardly exceed the ratio of 100 to 1. Substances behave very differently with respect to their power to transmit electrical energy. Those like the metals conduct elec- tricity with the velocity of light, while glass, wax, etc., conduct with infinite slowness. The ratio between the best and poorest conduc- tors of electricity is about as 10 20 to 1. Of the chemically pure substances, solids conduct in general better than liquids ; yet, many non-conducting salts when fused become electrolytes. Gases, according to the recent work of J. J. Thomson, 1 undoubtedly conduct electrolytically. Substances like the metals, which carry the current without undergoing chemical decomposition, are termed conductors of the first class. Solutions of some substances in certain solvents are capable of conducting the current. Thus, acids, bases, and salts, in water, are conductors ; but at the same time they undergo chemical decomposi- tion. These are known as conductors of the second class. So little is known about the actual mode by which metals conduct the current, that it is difficult to say just how much importance should be attached to the distinction between metallic and electrolytic conduction. The most recent work, however, makes it very probable that there is a close relation between the two kinds of conductivity. It seems quite probable, though it has not been proved, that conductivity in metals, as well as in electrolytes, is ionic. Law of Electrostatic Force (Coulomb's Law). — If two bodies* are charged with electricity, the force acting between them depends upon the quantity of electricity upon the bodies, the distance be- tween the bodies, and the nature of the medium which surrounds them. If we represent the quantities of electricity by q x and q 2 , the distance between the bodies by d, and the specific inductive capacity or dielectric constant of the medium by 0, the law of electrostatic attraction is expressed thus : — in which F is the force acting between the charged bodies. This is known as the law of Coulomb, since it was he who first verified it experimentally. Law of Joule. — Whenever conductors at different potentials are brought in contact, a current of electricity passes from one to the 1 Becent Researches in Electricity and Magnetism (1893). 360 THE ELEMENTS OF PHYSICAL CHEMISTRY other. The current always flows from the conductor at higher to that at lower potential. During the passage of the current, certain effects are produced in the conductors which obey definite known laws. One of the most common of these is the heating of the con- ductor. Electrical energy disappears and heat energy appears. This fact must have been observed, qualitatively, by every one who has allowed a current to flow through a conductor. A quantitative relation between the resistance offered to the passage of the current, the strength of the current, and the amount of heat evolved was discovered experimentally by Joule. 1 Let r be the resistance to the passage of the current, c the strength of the current, and h the amount of heat evolved in a given time ; the following relation obtains : — h = re 2 . The heat evolved is proportional to the resistance and to the square of the strength of the current. This is the well-known law of Joule. law of Ohm. — A quantitative relation has also been established experimentally between the strength of the current, the electro- motive force, and the resistance. Let C be the strength of the cur- rent, E the electromotive force, and R the resistance : — C -R' which is Ohm's law. Electrical Units. — There are two systems of units known respec- tively as the electromagnetic and electrostatic. The units in the two systems are very different. In the electromagnetic system, that current is taken as the unit, which, when passed around a circular conductor of radius 2 ir, will produce a magnetic intensity of 1 at the centre. When unit current flows one second, we have unit quantity of electricity. In the electrostatic system, that quantity of electricity is taken as the unit, which, when placed at a distance of a centimetre from an equal quantity, the two being separated by air, will exert a force of a dyne, or will produce an acceleration in a gram-mass, of a centi- metre per second. The nature of the medium separating the two quantities is essential to the definition, since the force exerted depends upon the dielectric constant of the medium. The unit quantity in the electromagnetic system is very nearly 3 X 10 10 times the unit quantity in the electrostatic system. i Phil. Mag. [3] 19, 260 (1841). ELECTROCHEMISTRY 361 The Electromagnetic System of Units. — The electromagnetic system has by far the widest application. In practice the unit of quantity is not that stated above, but one-tenth this amount. The unit of potential is called a volt. The Clark element con- sisting of mercury, mercurous sulphate, zinc sulphate (saturated solution), amalgamated zinc, has an electromotive force of — 1.4328 - 0.0012 (t° - 15) volts. The unit of quantity most frequently used is called a coulomb. It is defined as the quantity which, when it falls one volt in poten- tial, sets free 10 7 absolute units of energy. This, as stated above, is one-tenth of the electromagnetic unit. The unit of energy is 10 7 in absolute units, and is called a joule. When a coulomb passes in a second at a uniform rate, it gives a unit current, which is called an ampere. The unit of resistance is that offered by a uniform column of mercury 106.3 cm. in length (containing 14.4521 grains) at 0°. It is called an ohm. Electrostatic System. — The unit of quantity in the electrostatic system is, as stated above, much smaller than in the electromagnetic. The real electromagnetic unit of quantity is about 3 x 10 10 as great as the electrostatic unit. But the electromagnetic unit actually in use — the coulomb — is only one-tenth of the true electromagnetic unit. Therefore, one coulomb = 3 x 10 9 electrostatic units. The electrostatic unit is employed in measuring charges at rest. The unit of energy is the erg instead of 10 7 ergs, and the unit of poten- tial is 300 volts. Electrochemical Nomenclature. — We owe to Faraday the nomen- clature in vogue even at the present day. The conduction of the current in a solution of an electrolyte is accompanied by a mechani- cal movement of the parts of the dissolved substance. These parts Faraday called ions or wanderers. Those moving in the direction of the positive current he called cations, and those in the opposite direction anions. The substances which conduct the current by undergoing decomposition he termed electrolytes, the decomposition effected by the current electrolysis. That portion of the conductors of the first class from which the current passes into the solution of the electrolyte he termed electrodes. That electrode toward which the cation moves he called the cathode, that toward which the anion moves the anode. 362 THE ELEMENTS OF PHYSICAL CHEMISTRY THE LAW OF FARADAY Relation between Quantity of Electricity and Amount of Decom- position. — The law of Faraday, to which reference has already been made, is so important in connection with all electrochemical work that it should be considered more in detail. Faraday undertook a careful quantitative study of electrolysis, and determined the rela- tion between the amount of electricity which passed through a solu- tion of an electrolyte, and the amount of decomposition which it effects. He took into account the effect of changing the size and chemical nature of the electrodes, also the amount of electrolyte used. Further, he varied the amount of current which passed in a given time. In all cases he found that the amount of decomposi- tion was the same for the same amount of current. He concluded that the amount of decomposition effected by the current in a conductor of the second class is proportional to the amount of electricity which is passed through it. He then electrolyzed solutions of salts of several different metals by passing the same current through them in series, and weighed the metal which was deposited from each solution. He found that the masses which separated were proportional to the combining weigMs of the elements. Where the ion is elementary, as in the case of a metal, the com- bining weight is equal to the atomic weight divided by the valency. Where the ion is complex, as is true especially of many anions, the combining weight is equal to the molecular weight of the ion divided by its valency. These two facts lead to the following wide-reaching generaliza- tion : The amounts of decomposition effected in all conductors of the ■second class by the passage of equal quantities of current are, for the same electrolyte, equal; for different electrolytes are proportional to the combining weights of the ions. From this, we see that chemically equivalent quantities of all ions have the same capacity for electrical energy. This is analogous to the law of Dulong and Petit, which says that all atoms have the same capacity for heat energy. Testing the Law of Faraday. — Faraday 1 concluded from his own experiments that very small currents can pass through solutions of electrolytes without effecting chemical decomposition. The work of Shaw 2 on copper solutions showed slight deviations from the 1 Exp. Researches (1834). 2 Brit. Ass. Report (1886), 318. ELECTROCHEMISTRY 363 law of Faraday as the intensity of the current varied. This is sup- posed to be due to the solvent action of the solution of the copper salt on the copper which had already been precipitated. A careful quantitative study of the law of Faraday was made by Buff, 1 using the silver voltameter. The strengths of current employed varied as much as from 1 to 200, yet the law was always found to hold within the error of the experiment. Ostwald and Nernst 2 tested the law of Faraday for very small amounts of electricity, and showed that when 0.000005 coulomb is passed through a dilute solution of sulphuric acid, hydrogen is liberated at the cathode. They measured the amount of gas set free and the current which passed, and found that the law of Fara- day held for such an infinitesimal quantity of electricity. Some doubt was thrown a few years ago on the universal appli- cability of the law of Faraday. Solutions of electrolytes were electrolyzed under high pressure, and it was found that the amount of the electrolyte decomposed was less than would correspond to the law of Faraday. This has since been satisfactorily explained. Under the high pressure some gas dissolved in the water containing the electrolyte. This was slightly ionized in the solution, and helped to conduct the current. More current therefore passed than corre- sponded to the amount of the electrolyte decomposed. Perhaps the most careful experimental test to which the law of Faraday has been subjected, and through which it has passed suc- cessfully, is in connection with the determination of the electro- chemical equivalents of the ions. Meaning of the Law of Faraday. — We have seen that the laws of definite and multiple proportions were interpreted by Dalton in terms of the atomic theory. Indeed, no other satisfactory interpre- tation has been proposed even up to the present. Elements consist of units of matter, called atoms, which enter into chemical reaction. Parts of atoms never enter into reaction, whence the laws of definite and multiple proportions. A question strictly analogous to the above arises in connection with the law of Faraday. Why do ions carry only whole units of electricity ? — a univalent ion one unit, a bivalent ion two units, and so on. Unless electricity is composed of units, somewhat analogous to the atomic units of matter, it would be very difficult indeed to ex- plain the facts generalized as the law of Faraday. 1 Lleb. Ann. 85, 1 (1853). 2 Ztschr.phys. Chem. 3, 120 (1889). 364 THE ELEMENTS OF PHYSICAL CHEMISTRY That electricity is composed of such units — the electrons — has been made highly probable by the work of J. J. Thomson (see page 40). Indeed, this conception was in vogue at an earlier date. Helmholtz was forced to the conclusion that electricity is of an atomic nature, and Lorenz and Larmor have dealt with the electron. It, however, remained for Thomson to prove the existence of the electron by direct experiment, to show its order of magnitude, and to study many of its properties. It is true that the electrons are the units of negative electricity, the corresponding units of positive electricity not yet having been discovered. In terms of the electron, which is the ultimate unit of electricity, the meaning of Faraday's law is perfectly clear. A univalent, negative element is one that carries one electron in excess; a bivalent, nega- tive element, two electrons in excess, and so on. A univalent, posi- tive element has lost one electron ; a bivalent, positive element two electrons, and so on. The electron theory of electricity, which shows that it is com- posed of ultimate units, explains the fact that we do not have ele- ments with fractions of valence, just as we do not have compounds with fractions of atoms. It explains for the first time the real meaning of the law of Faraday. The Electrochemical Equivalent. — If the quantities of all ions which stand to one another in the relations of their combining weights, carry equal amounts of electricity, then it is of great scientific and practical importance to know the exact amount of electricity which a unit quantity of ions will carry. This can be determined by passing a given quantity of electricity through a solution of an electrolyte and weighing the amount of metal deposited upon the cathode, or measuring the amount of gas liberated. This has been done very carefully by Lord Rayleigh and Mrs. Sedgewick, who found that one coulomb of electricity deposits 1.1179 mg. of silver. W. and F. Kohlrausch, working with equal care, found under the same conditions 1.1183 mg. The mean of these values is 1.1181 mg. The mass of the ions taken as the unit is purely arbitrary. Here, as in so many other cases, it is convenient to use the gram-molecular weight for univalent, and gram-equivalent weight for polyvalent ions. In case the ion is elementary and univalent, as with silver, the gram-molecular weight is identical with the gram-equivalent weight. The atomic weight of silver, in terms of oxygen = 16, is 107.93. ELECTROCHEMISTRY 365 In order to separate a gram-atomic weight of silver it will require 107 93 nnmiisi = 96>530 coulombs of electricity. This is the electrochemical equivalent that has been frequently- used. A more recent determination of the electrochemical equivalent of silver by Richards, Collins, and Heimrod 1 gives 1.1175 mg. of silver as equivalent to one coulomb. This is also the mean of the best values that have been obtained, when properly corrected, and will be the value accepted. Using this value, the electrochemical equivalent is 0^5 = 96,580 coulombs. The Voltameter. — The fact that a given amount of current always separates the same quantity of any metal from its salts, furnishes us with a simple and efficient method of measuring the amount of electricity which flows through any conductor in a given time. From the above figures it is clear that whenever a current deposits one milligram of silver from a solution of a silver salt, 0.8944 of a coulomb of electricity has passed through the solution. The principle of the voltameter is thus very simple. Suppose it is desired to know the amount of electricity which flows through a given conductor in a given time. The current is passed through a solution of some silver salt — say the nitrate — for the given length of time and the amount of silver deposited on the cathode deter- mined. Knowing the amount of silver deposited, the calculation of the amount of electricity which has passed follows at once from what is given above. This is not the place to discuss the details of the use of the silver voltameter. A general description of the apparatus should, however, be given. The form which, perhaps, is the most conven- ient consists of a platinum dish about three inches in diameter, which serves as the cathode. This is filled to a convenient depth with a 15 to 20 per cent solution of silver nitrate. A thick disk of silver serves as the anode. This is wrapped with a piece of fine linen, or filter paper, to prevent particles from dropping off from the anode into the dish. The source of the current is connected 1 Ztschr. phys. Chem. 32, 321 (1900). See Richards and Heimrod : Ztschr. phys. Chem. 41, 302 (1902). Patter- son and Guthe : Phys. Rev. 7, 268 (1898). Guthe : Phys. Bev. 19, 138 (1904). 366 THE ELEMENTS OF PHYSICAL CHEMISTRY directly with the anode. The platinum dish, serving as a cathode, should rest in a wire frame which touches it at many points. After the experiment is over, the solution of silver nitrate is poured out of the dish, and the silver, which should be deposited uniformly and coherently upon the platinum, carefully washed and dried. The dish, which was weighed before the experiment began, is now re- weighed. The gain in weight is the weight of the silver which has been deposited upon its surface. Theoretically the salt of any metal which is deposited as such by the current might be used to measure the amount of the current. But practical difficulties come into play in many cases, so that only a few metals are well adapted to this purpose. Some of these difficulties may be indicated by stating that many metals do not separate uniformly upon the surface of the cathode and do not adhere firmly to it. In these cases it is difficult and often impos- sible to wash and weigh the deposit. Other metals easily undergo oxidation during deposition, or when exposed to the air in a finely divided state in washing and drying them. The metal best adapted to the uses of the voltameter is silver, and next to silver comes copper. In addition to the metal voltameters, there is another form which depends for its utility upon the amount of gas set free when the current is passed through a dilute solution of sulphuric acid. In this form, which is called the gas voltameter, the gases are collected, reduced to standard conditions of temperature, pressure, and dry- ness, and then measured. A comparatively large volume of gas is liberated by a small amount of current. Thus, one gram of hydro- gen ions carries 96,530 coulombs. One gram of hydrogen gas has a volume of 11,188 c.c. Since it is possible to measure a small part of a cubic centimetre of gas, it is possible to measure a very small quan- ' tity of electricity by means of the gas voltameter. THE MIGRATION VELOCITIES OF IONS Electrolysis. — The phenomenon of electrolysis shows that when a current is passed through a solution of an electrolyte, there is a mechanical movement of the ions of the electrolyte toward the electrodes. It becomes, then, a matter of interest and importance to determine the relative velocities with which the ions move, and also their absolute velocities under given conditions. If we pass a current through a solution of copper sulphate, using copper electrodes, there will be a deposition of copper at the cathode, ELECTROCHEMISTRY 367 and exactly an equal amount of copper will pass into solution from the anode. The total amount of copper in solution will remain con- stant, but the color in the neighborhood of the anode will become deeper, while in the neighborhood of the cathode it gradually be- comes less intense. The solution becomes more concentrated in copper around the anode and less concentrated around the cathode. If in this experiment platinum electrodes are employed, copper would separate at the cathode ; present to pass into solution, the amount in solution would become constantly less. In this case the color would dis- appear more rapidly around the cathode. Hittorf 's Theory.— Hittorf 1 explained these facts as due to the ions moving with different velocities through the solution — either the cation or the anion might have the greater velocity. That such an ex- planation can account for the facts, can be clearly seen from Fig. 49, which we owe in prin- ciple to Ostwald. 2 A repre- sents the condition in the solution of the electrolyte before any current is passed. The white circles represent the anions, and the lined circles the cations. For each anion present in the solution there is a corresponding cation; and separated at the electrodes. but since there is no metallic copper A ? A O O OOjO oo o e e e eie e e e A oo eeejee k oo ee ooopoo eee o o o eee' A A c Fig. 49. neither anions nor cations have Let us take a case where the velocity o/the anion differs greatly from that of the cation, and for the sake of simplicity let us say that the velocity of the anion is twice that of the cation. Let the current pass through the solution until three molecules have been electrolyzed, when the condition represented i Pogg. Ann. 89, 177 ; 98, 1 ; 103, 1 ; 106, 337, 513 (1853-1859). Tiber dia Wanderungen der Ionen, Ostwald's Klassiker, 21, 22. 2 Lehrb. d. Allg. Chem. II, 595. 368 THE ELEMENTS OF PHYSICAL CHEMISTRY in B will exist. Three anions will have separated at the anode, and three cations at the cathode. But the solution of undecomposed electrolyte will have become relatively more concentrated on the anode side of the middle layer, marked m. Of the three molecules which have been decomposed and separated from the solution, two have come from the cathode side of the middle layer m, and one from the anode side, as is seen in 0, which represents the solution after the electrolysis. If we divide the loss around the cathode by the total number of molecules electrolyzed, we shall obtain the value -§. If, on the other hand, we divide the loss around the anode by the total number of molecules decomposed, the result is £. These two values bear the same relation to one another as the velocities of the anion and cation. From this we may draw two general conclusions : First, to find the relative velocity of the cation, divide the loss around the anode by the total amount of electrolyte decomposed. Second, to find the relative velocity of the anion, divide the loss around the cathode by the total amount of the electrolyte decomposed. There are, then, three quantities which can be determined experi- mentally: the change in concentration around the cathode, the change in concentration around the anode, and the total amount of the electrolyte decomposed. It is necessary to determine only two of these, since the third is given by the sum or difference. The two which are chosen depend upon the ease and accuracy involved in making the measurements. Since the total amount of electrolyte decomposed is proportional to the amount of current which is passed through the solution, it is only necessary to measure the latter in order to know the former. This can be done conveniently by inserting a silver voltameter into the circuit, and weighing the amount of silver deposited. This is one of the quantities usually determined in carrying out such measurements. Experimental Methods for Determining the Relative Velocities of Ions. — In determining the relative velocities of any given anion and cation, it is necessary to effect the electrolysis of a solution contain- ing these ions, using as the electrodes the same metal as the cation. After the electrolysis has proceeded far enough to produce a deter- minable difference in concentration around the electrodes, and at the same time to leave a middle layer of unaltered concentration, the solution must be separated into two parts through the unaltered layer, and the change in concentration around one or both electrodes ascertained by analysis. The apparatus in which such determina- ELECTROCHEMISTRY 369 tions are carried out must be so constructed that the effect of diffu- sion, which would tend to mix the solutions of different concentra- tions around the electrodes, is reduced to a minimum. Several forms of apparatus have been devised for determining the relative velocities of ions. Indeed, Hittorf, 1 in his own classical work upon this problem, devised a number of forms. In principle, however, they all closely resemble one another, and consist of a vertical tube divided into a number of compartments by means of horizontal diaphragms. Into the upper portion the cathode is in- serted, into the lower the anode, around which the solution becomes more and more concentrated. After the electrolysis has been carried as far as desired, the solutions around the electrodes were removed and analyzed, and the changes in concentration thus determined. The membranes used in the forms of apparatus devised by Hittorf are objectionable, since they are liable to be acted upon by the electrolyte and produce indeterminable errors in the results. The more improved forms of apparatus for determining relative velocities avoid this source of error by doing away entirely with all membranes. The form devised and used by Loeb and Nernst 2 is essentially a Gay-Lussac burette. The electrode around which the solution will become more concentrated (usually the anode) is placed below. The electrolysis is carried on until there is considerable change in con- centration around the electrodes, but it must be interrupted while there is still a middle layer of unaltered solution. In carrying out a determination with this apparatus the corks and electrodes were placed in position and the whole weighed. The solution was then introduced through C, by closing A and evacuating B with the mouth. The apparatus is so constructed as to hold from 40 to 60 c.c. of solution. The openings at C and B are then closed, the whole apparatus placed in a thermostat and the current passed. After the electrolysis is ended, G is opened, and portions of the solution blown out, weighed, and analyzed. That part of the solution remaining in the apparatus Fig. 50. 1 Ostwald's Klassiker, 21, 22. * Ztschr. phys. Ohem. 8, 948 (1888) ; 39, 612. 2b 370 THE ELEMENTS OF PHYSICAL CHEMISTRY can be determined at any time by the gain in weight of the appa- ratus. The portion first removed contains the heavier, more concen- trated solution around the anode ; the second, the unaltered middle layer ; and the third, the more dilute solution around the cathode. This method is scarcely capable of any very high degree of accu- racy. If it even overcomes satisfactorily the effect of diffusion, it is still open to a serious objection. After the electrolysis is ended there is no means by which the solutions of different concentrations can be completely separated from one another, removed, and ana- lyzed. The method of blowing out the solution around the anode, together with enough of the unaltered middle layer to wash out the heavier solution, is not in keeping with the most refined work. From some work which has been carried out on this problem in this university, it seems better to measure the amount of current directly by means of a voltameter, than by any indirect method such as that employed by Loeb and Nernst. The methods of Kisliakowsky l and of Bein 2 are the same in prin- ciple as that just described. The burettes are given different forms in the two cases, and also differ in form from the burette in the method just described. The same objection offered to the method of Loeb and Nernst applies here. There is no means of completely separating the two parts of the solution after the electrolysis is brought to an end. Quite recently Bein 3 has carried out an elabo- rate investigation on the velocities of ions, which, on the whole, probably contains some of the best results thus far secured. A large number of forms of apparatus are described, and much care and ingenuity are displayed in meeting special conditions. The means of separating the solutions, however, after the electrolysis is ended, could be improved. A form of apparatus has recently been devised by Jones and Bassett 4 and used by them, and by Jones and Rouiller. 5 This form is free from many of the objections that can be urged against other forms. The apparatus is represented in Pig. 51. The two outer limbs are 20 cm. long and 2 cm. in diameter and are connected 3 cm. below the stoppers, by a U-tube 1.5 cm. in diameter. Each arm of the U-tube is 10 cm. long, and at the centre of it is a stopcock of large bore (1 cm.). Into the electrodes, made of disks of pure silver, is riveted a short piece of stout platinum wire, which is then sealed into thick-walled glass tubes of 2 mm. 1 Ztschr. phys. Ghem. 6, 97 (1890). « Wied. Ann. 46, 29 (1892). » Ztschr, phys. Chem. 27, 1 (1898) ; 28, 439 (1899). 1 Amer. Chem. Journ. 32, 409 (1904). * iud. 31, 427 (1906). ELECTROCHEMISTRY 371 bore. The exposed end of the platinum wire on the under side of the electrode is covered with fusion glass. The tubes carrying the electrodes are forced through holes bored into the ground-glass stoppers, which close the upper ends of the limbs of the apparatus. To the limbs of the ap- paratus, just below the stoppers, are attached small, graduated tubes, 3 mm. in diameter, ex- tending outward and upward. It was found, especially with alcohol and acetone solutions, that when the apparatus was placed in the 25° bath, a small quantity of gas always collected under the stopper and forced out some of the liquid through the side tubes. The advantages of this form of apparatus are evident. It is easily made and handled. It is perfectly symmetrical, so that either side can be used as cathode chamber. All danger of diffusion is done away with and no membrane is necessary. The stoppers being at the top, there can be no leakage, its comparatively large capacity, about 130 ec, which may be very accurately determined, making it possible to work with large quantities of solution. By means of the small side tubes the liquid in both arms can be very accurately levelled, and, finally, the stop- cock at the center of the U-tube makes it possible to separate completely the cathode and anode solutions, and to rinse out the two sides as thoroughly as may be desired. Reference 1 only can be given to other recent investigations on the velocities of ions. 1 Kohlrausch : Wiect. Ann. 66, 785 (1898). K. Hopfgartner: Ztschr. phys. Chem. 25, 115 (1898). G. Kummel : Wied. Ann. 64, 655 (1898). V. Gordon: Fig. 51. 372 THE ELEMENTS OF PHYSICAL CHEMISTRY Causes which may affect the Relative Velocities of Ions. — It does not follow that the relative velocities of two ions obtained under one set of conditions is the same as the relative velocities under other conditions. This could be determined only by experi- ment. The effect of changing several of the conditions was studied by Hittorf. 1 He studied first the effect of changing the strength of the current. The currents in three determinations were of very dif- ferent strengths. The first precipitated 0.0042 g. silver in a minute. The second precipitated 0.00113 g. silver in a minute. The third precipitated 0.00958 g. silver in a minute. The substance used was copper sulphate, and the relative veloci- ties of copper and S0 4 were determined in the three cases, using the same concentration of the salt. The migration velocities of the copper in the three cases were 0.285, 0.291, and 0.289. From these results Hittorf concluded that the relative velocities are indepen- dent of the strength of current. This statement of Hittorf applies, of course, only to relative velocities. The absolute velocity with which the ions move is directly dependent upon the strength or driving power of the current. The second question, says Hittorf, 3 which we must settle, has to do with the effect of concentration on migration velocity. Six solutions of copper sulphate of very different concentrations were subjected to electrolysis. Hittorf expresses the concentrations in terms of one part of copper sulphate to so many parts of water. Ztschr. phys. Chem. 23, 469 (1897). W. Bein : Ibid. 27, 1 (1898); 28, 439 (1899). O. Masson: Ibid. 29, 501 (1899); Phil. Trans. 192, A, 331. F. Kohlrausch : Wied. Ann. 66, 785 (1899). A. A. Noyes : Ztschr. phys. Chem. 36, 63 (1901). B. D. Steele: Journ. Chem. Soc. 79, 414 (1901) ; Ztschr. phys. Chem. 37, 673 (1901). Steele and Denison : Journ. Chem. Soc. 81, 456 (1902). Steele : Ztschr. phys. Chem. 40, 689 (1902). Schlundt : Journ. Phys. Chem. 6, 159 (1902). Hittorf : Ztschr. phys. Chem. 39, 613 (1902). Abegg and Gans : Ibid. 40, 737 (1902). Noyes and Sammet : Ibid. 42, 49 (1902) ; Journ. Amer. Chem. Soc. 24, 944 (1903). Carrara: Qazz. chim. ital. 33, I, 241 (1903). Denison : Ztschr. phys. Chem. 44, 575 (1903). Tower : Journ. Amer. Chem. Soc. 26, 1039 (1904). Burgess and Chapman: Journ. Chem. Soc. 85, 1305 (1904). Lorenz and Pausti : Ztschr. Elektrochem. 10, 630 (1904). Dempwolf : Physikal. Ztschr. 5, 637 (1904). Franklin and Cady : Journ. Amer. Chem. Soc. 26, 499 (1904). McBain: Ztschr. Elektrochem. 11, 215,961(1904). Steele, Mcintosh, and Archibald : Phil. Trans. A, 99 (1905). Jahn : Ibid. 53, 641 (1905). Denison and Steele : Ztschr. phys. Chem. 57, 110 (1907). 1 Pogg. Ann. 89, 177 (1853). OstwaWs Klassiker, 21, 15. 2 Ostwald's Klassiker, 21, 17. ELECTROCHEMISTRY 373 Parts Water to One Migration Velocity of Part Copper Sulphate Copper 1st solution .... 6.35 0.276 2nd solution .... 9.56 0.288 3rd solution .... 18.08 0.325 4th solution .... 39.67 0.355 5th solution .... 76.88 0.349 6th solution .... 148.30 0.362 The migration velocity of the copper with respect to the S0 4 increases as the dilution increases, until a certain dilution is reached. Beyond this it remains practically constant. It, however, does not follow from this that the velocity of the cation with respect to the anion always increases with increase in dilution. This is shown by the work of Hittorf l on solutions of silver nitrate. Parts Water to One Part Silver Nitrate Migration Velocity of Silver 2.48 5.18 14.50 49.44 247.30 0.532 0.505 0.475 0.474 0.476 The velocity of the silver ion decreases as the dilution increases up to a certain limit, beyond which it remains constant. It is possible that the explanation of such facts is to be found in the more complex ions which may exist in the more concentrated solutions. These may break down into simpler ions as the dilution increases. In measuring the relative velocities it is, therefore, necessary to work at dilutions so great that when the dilution is further increased the relative velocities remain unchanged. There is a third condition according to Hittorf, 2 which may affect the migration, i.e. the effect of temperature. He concluded from his work on solutions of copper sulphate that between 4° and 21° the temperature coefficient was zero. The work of Loeb and Nernst 3 on a few silver salts between 1 Ostwalcf s Klassiker, 21, 22. 2 Pogg. Ann. 89, 177 (1853). OstwaWs Klassiker, 21, 21. 3 Ztschr. phys. Chem. 2,962 (1888). 374 THE ELEMENTS OF PHYSICAL CHEMISTRY 0° and 25° indicated that with rise in temperature all ions tend to move with the same velocity, which is 0.5. This point was in- vestigated much more fully by Bein. 1 A few of his results for the anions will show that this conclusion is probably true. 20° 75° 95° Sodium chloride Calcium chloride Cadmium iodide Silver nitrate 0.608 0.602 0.640 0.470 10° 0.600 0.551 0.549 0.490 90° Migration Velocities a Periodic Function of Atomic Weights. — Bredig 2 pointed out that it had already been recognized that the migration velocities of elementary cations are a function, and a periodic function, of the atomic weights. Ostwald had already shown that this was true for elementary ions which consist of only one atom or element. Take the following anions and cations : — Velocity Velocity Velocity Fl 50.8 Li . 39.8 £Mg . . 58 CI 70.2 Na . 49.2 |Ca . . 62 Br 73.0 K . 70.6 £Sr . . 63 I 72.0 Kb Cs . 73.5 . 73.6 £Ba . . 64 £Cu . 59 Ag . . 59.1 iAl . . 42 £Zn . 54 Tl . 69.5 iCr . . 61 *Cd . 55 These relative velocities are plotted in a curve (Fig. 52). The ordinates represent velocities, and the abscissas atomic weights. A glance at the curve brings out the periodic nature of the veloci- ties in terms of atomic weights. At, or very near, the maxima of the curve we find the halogens. Here also we find the alkali metals. At the extreme minima we find aluminium and chromium. At breaks on the descending arms of the curve we find the mem- bers of the calcium group. Zinc and cadmium also occur near the minima. The significance of this periodic recurrence of velocities with respect to atomic weights is at present not known. Yet it 1 Wied. Ann. 46, 29 (1892). 2 Ztschr. phys. Ohem. 13, 242 (1894). ELECTROCHEMISTRY 375 is certainly an interesting fact, and another example of that periodicity among the properties of the elements which appears in so many directions. ' 80 20 40 80 120 160 200 atomic weight Fig. 52. The Absolute Velocities of Ions. — The methods hitherto considered give only the relative velocities with which the ions move. To deter* mine the absolute velocities some other method must be employed. Two general methods have been employed for determining the abso- lute velocities with which ions move. The one is direct and measures at once the absolute velocities. This will be taken up here (Fig. 53). There is also an indirect method of determining absolute velocities, involving the conduc- tivity of solutions and the relative velocities. This will be taken up Fig. 53. later under conductivity. The Method of Lodge 1 for determining the absolute velocities of ions is the following : A glass tube t, 40 cm. long and 8 cm. wide, is graduated and bent at right angles near the ends. This is filled with an aqueous solution of gelatine, to which some sodium chloride had been added. The contents of the tube are colored red by phenolphthalein to which just a trace of alkali had been added to 1 Brit. Ass. Report, 1886, p. 393. Also 1887, 389. See Mcintosh : Journ. Phys. Chem. 2, 273, 496 (1888). 376 THE ELEMENTS OP PHYSICAL CHEMISTRY bring out the red color. One end of this tube passes into the larger vessel A (Fig. 53). A piece of platinum foil' is introduced into the vessel A and con- nected with a platinum wire so as to serve as an electrode. The other end of the tube t dips into a vessel B, into which an electrode is introduced as shown in the figure. For the sake of simplicity and clearness let us suppose that both vessels A and B are filled with dilute sulphuric acid. A current is then passed from one electrode to the other through the tube t. The hydrogen ions move with the current from the vessel A into the tube t. They displace the sodium from the sodium chloride and from hydrochloric acid, which decolorizes the phenolphthaleiin. After a given time the space in t over which the decolorization has extended is measured. In making such measurements it is necessary to know the differ- ence in potential at the two ends of the tube, or, as it is called, the drop in potential along the tube. A potential gradient of a volt a centimetre is taken as the unit. Knowing the drop in potential along the tube, the time during which the experiment has lasted, and the length of the tube in which the solution is decolorized, we have all the data necessary for calculating the absolute velocity of ions. For unit gradient, i.e. a drop in poten- tial of one volt a centimetre, Lodge found the following velocity for hydrogen, which is the swiftest of all ions. 0.0026 cm. per second is the mean of three values which were found. These are 0.0029, 0.0026, and 0.0024 cm. per second. It will thus be seen small indeed when NHiC\'fM CuClj ions is very Fig. 54. that the absolute velocities of subjected to a unit drop in potential. The results obtained by the indirect method already referred to will be compared a little later with those given by this direct ELECTROCHEMISTRY 377 method. The absolute velocities of a number of other ions, obtained by the indirect method, will also be given in the proper place. The Method of Whetham 1 for measuring the absolute velocities of ions differs somewhat from that of Lodge. The apparatus used is seen in Fig. 54. Into each arm an electrode is inserted as seen in the figure. Let us take two chlorides, the one colored and the other col- orless, say copper and ammonium chlorides. The denser solution is introduced into the longer arm, and then the lighter solution is carefully poured into the shorter arm. The current is now passed through the two solutions from the ammonium to the copper chloride. The cupric chloride is colored, due to the presence of copper ions. These, like the ammonium ions, move with the current; and consequently the bounding layer be- tween the colorless and colored compound will move with the cur- rent. By noting the time of the experiment, the distance travelled by the bounding layer, and the potential gradient, Whetham could calculate the velocity of the copper ion. The velocities of the copper ion and of the ion Cr 2 7 , obtained by Whetham, agree with those found by the indirect method to be considered hereafter. THE CONDUCTIVITY OP SOLUTIONS OF ELECTROLYTES Conductivity. — The conductivity of a substance is its power to carry the current. The conductivity of a conductor is the reciprocal of its resistance. The following relation between the resistance r, the current c, and the electromotive force w is expressed in Ohm's law: — r = -. c The electromotive force ir is the difference in the potential of the two ends of the conductor carrying the current. The reciprocal of the resistance, or the conductivity C, is, therefore, — 0=°. Two units of resistance have been employed. The one most com- monly used is that of a column of mercury 106.3 cm. in length and i Phil. Trans. 1893, A, 337 ; 1895, A, 607 ; 186, A, 507. Steele and Denison : Phil. Trans. (A) 198, 105 (1902). Ibid. (A) 1906, 449. Ztschr. phys. Chem. 40, 737 (1902). Ibid. 44, 575 (1903). 378 THE ELEMENTS OF PHYSICAL CHEMISTRY 1 sq. mm. in cross-section. The Siemens unit is that offered by a column of mercury 100 cm. long and 1 sq. mm. in cross-section. Specific Conductivity. — The resistance offered by conductors de- pends upon two things, their nature and their form. To compare the resistances of different substances we must use forms which are comparable. There are two forms which have been used : that of a cube whose edge is 1 cm. long, and that of a cylinder 1 m. in length and 1 sq. mm. in cross-section. It is obvious that the resistance of the latter form is ten thousand times the former. When the resist- ance of such forms of substances is measured in ohms, it is known as the specific resistance. The specific conductivity is the reciprocal of the specific resistance. These terms can be also applied to conductors of the second class. Such conductors are mainly solutions of some electrolyte in some dis- sociating solvent, and we must deal with comparable quantities of dissolved substances. In this case, as in so many others, we use gram-molecular weights of the different electrolytes. Molecular Conductivity. — Place a litre of a normal solution of an electrolyte between two electrodes which are 1 cm. apart. Since the section of this solution is 1000 sq. cm., the conductivity of this solution will be 1000 times that of a cube of the same solution whose edge is equal to the distance between the plates. Let n be the num- ber of cubic centimetres of a solution containing a gram-molecular weight of the electrolyte, and s the specific conductivity of the cube of the solution, then the molecular conductivity, which we will rep- resent by /«., is expressed thus : — /* = 71S. If, on the other hand, we represent the specific conductivity of a cyl- inder of the solution 1 sq. mm. in cross-section and 1 m. in length by s, this will have l0 % 00 of the conductivity of the cube above de- scribed. The molecular conductivity /*. would then be calculated thus : — p. = 10 ; 000 ns. Since in the case of a normal solution n = 1000 H = sx 10,000x1000 = s x 10 7 . The molecular conductivity, then, is equal to the specific conductivity referred to the cylinder unit, multiplied by 10 7 . Method of Measuring the Conductivity of Solutions. — A number of methods have been devised for measuring the conducting power of solutions. The earlier methods attempted to measure conductiv- ELECTROCHEMISTRY 379 ity by means of a continuous current. But when such a current is passed through a solution, the electrodes become quickly polarized. This would increase the resistance of the solution, and seriously affect the result obtained. A number of attempts have been made to do away with the effect of polarization. Thus, Guthrie and Boyes abandoned the electrodes entirely, making use of induction currents in the solution. Others have used as the electrodes the same metal as the cation of the electrolyte. The chemical nature of the elec- trode would, then, not be changed when the current is passed. All of these methods have, however, given place to one which was de- vised by F. Kohlrausch, 1 in which an alternating current is used. The use of the alternating current makes us practically independent of the effect of polarization. A galvanometer cannot be used with an alternating current. A dynamometer may be used, but is less con- venient and far more expensive than the ordinary telephone receiver, which answers every purpose. In the Kohlrausch method, then, an alternating current is passed between platinum electrodes, through the solution whose conductiv- ity it is desired to study. The resistance of the solution is balanced against a rheostat on a Wheatstone bridge, the point of equilibrium being determined by means of a telephone. The apparatus used in the method of "K"b"hlrausch is sketched in Fig. 55. Wis a, rheostat or set of resistance coils. The metre stick 1 Wied. Ann. 6, 145 (1879) ; 11, 653 (1880); 26, 161 (1885). Pogg. Ann. 138, 280 (1869) ; 151, 378 (1874); 184, 1 (1875); 159, 233 (1876). "Platinized Electrodes." See F. Kohlrausch: Wied. Ann. 60, 315 (1897). 380 THE ELEMENTS OF PHYSICAL CHEMISTRY AB is divided into millimetres, and over this is stretched a manga- nine wire (manganine being an alloy of German silver and manga- nese). J"isasmall induction coil which furnishes the alternating current. R is a glass cup which contains the solution whose resist- ance is to be measured. The electrodes are cut from thick sheet platinum, and a piece of platinum wire is welded into the centre of each plate. This wire is then sealed into a glass tube, which is filled with mercury to make electrical contact with a copper wire intro- duced into the mercury. The telephone is connected between the rheostat and resistance vessel, and also with the bridge wire by means of a slider. The point of equilibrium is ascertained by mov- ing the slider along the wire until the sound of the coil is no longer audible in the telephone. Let this be a point G Let us call the distance AG, a, BG, b, the resistance in the box r, and the resistance in the vessel r x . From the principle of the Wheatstone bridge we would have — rb = r-fl ; rb f\ = — a Since conductivity c is the reciprocal of the resistance r t — a rb This expression does not take into account the concentration of the solution. In practice it is best to express concentrations in terms of gram-molecular weights of the electrolytes in a litre (gram- molecular normal). As we have seen, the number of litres of the solution containing a gram-molecular weight of the electrolyte may be represented by n, when the above expression becomes — na rb By introducing n into the above expression, we pass from specific to molecular conductivities, and we express the molecular conduc- tivity by the letter /u.. In order to indicate the concentration n to which /* applies, we write for the molecular conductivity /*„, — na rb This expression takes into account all of the factors except the cell constant k, which depends upon the size of the electrodes which we are using, and their distance apart. Introducing, the constant, we have — 7 na *» = 7C rb' ELECTROCHEMISTRY 381 Making a Conductivity Measurement. — If we examine the above equation, we shall find that there are two unknown quantities, fi n and k. The first step in applying the Kohlrausch method is, then, to determine the value of one of these unknown quantities, and, in fact, the value of the cell constant k. In order to determine k, some solution must be used whose value of /*„ is known. The concentra- tion n must be known, and a, b, and r ascertained. The solution most commonly employed is a — =rr — solution of potassium chloride. At 25° the conductivity of this solution, or the value of fin, = 129.7. This solution is poured into the cell until both electrodes are covered. The cell is then placed in the thermostat, and the solution warmed to 25°. The readings are then made on the bridge, and the value of k calculated. The value of k having been determined, the cell is ready for conductivity measurements. Before the constant of the cell is determined, it is necessary to cover the electrodes with platinum black in order to secure a sharper minimum in the telephone. This is effected by electrolyzing in the cell a dilute solution of platinic chloride. The current is passed first in one and then in the other direction, until both plates are covered with the finely divided platinum. In order to measure the conductivity of any substance a solution of known concentration must be prepared. This is poured into the cell until the electrodes are covered. The cell is then placed in the thermostat and its contents brought to the desired temperature. The coil is started and the readings a and b determined, n having been noted. All of the quantities in the conductivity equation are thus known except jx n , which is calculated at once. 1 Conditions which must be fulfilled in Making Conductivity Meas- urements. — In order that accurate conductivity measurements may be made by the method of Kohlrausch, it is desirable that the wire on the bridge should have uniform resistance throughout. If this is not the case, as in fact it never is, the wire must be calibrated and corresponding corrections applied. The most convenient method of calibrating a wire is that devised by Strouhal and Barus. 2 The prin- ciple of the method is analogous to that which is employed in cali- brating a thermometer, when a thread of mercury is broken off from 1 For details in connection with the Conductivity Method, see Freezing- point, Boiling-point, and Conductivity Methods, by Jones (Chem. Pub. Co., Easton, Pa.). 3 Wied. Ann. 10, 326 (1880). 382 THE ELEMENTS OF PHYSICAL CHEMISTRY the column and moved along the capillary, the space occupied in each position being noted. For a detailed description of the method some laboratory guide 1 must be consulted. Another factor of prime importance in all conductivity measure- ments is the conductivity of the water which is used as the solvent. When we measure the conductivity of a solution of an electrolyte in water, we actually measure the sum of the conductivities of the water and of the electrolyte. In order to know the conductivity of the electrolyte, it is necessary to know that of the water used, in order that it may be subtracted from the conductivity as measured. For conductivity work it is very desirable to have water of a high degree of purity. A large number of methods have been suggested for purifying water for such purposes. The purest water which has ever been obtained was prepared by Kohlrausch and Heydweiller. 2 Water of a high degree of purity was distilled in a vacuum, and its conductivity determined without allowing it to come in contact with the air. The degree of purity attained by this method is best realized by the following comparison of the conductivity of the water with that of a metal. A cubic millimetre of this water at zero degrees had a resistance which was equal to that of a copper wire one millimetre in diameter extending around the earth one thousand times. It is not possible, nor is it at all necessary, to prepare water of this degree of purity for ordinary conductivity work. In such work com- paratively large quantities of water are needed, and methods are available for obtaining an abundance of water of a high degree of purity. A method has been devised by Jones and Mackay 3 in which the water is twice distilled, but the process is a continuous one. Ordi- nary distilled water is placed in a large balloon flask, and some potas- sium bichromate (or potassium permanganate) and sulphuric acid added. When this water is boiled, the organic matter is burned up, and the ammonia held back as the sulphate. The vapor from this flask is led into a large retort containing an alkaline solu- tion of potassium permanganate, which absorbs the carbon diox- ide. The water vapor is then condensed in a tube of block tin, and received in a glass bottle which has been cleaned with especial care. 1 Traiibe : Physikalisch-chemische Methoden. Jones : Freezing-point, Boil- ing-point, and, Conductivity Methods. Ostwald : Hand- und Hilfsbuch sur Aus- fuhrung PhysiJco-chemische Messungen. 2 Ztschr. phys. Chem. 14, 317 (1894). 8 Ibid. 22, 237 (1897). Amer. Chem. Journ. 19, 91 (1897). ELECTROCHEMISTRY 383 By this method from five to six litres of water can be obtained daily, having a conductivity of from 1.5 to 2 x 10" 6 . This is sufficiently pure for general conductivity work. The correction which must be applied to the values of /*,„ for the conductivity of water of this degree of purity, is so small that it can be entirely neglected in the more concentrated solutions. It attains an appreciable value only in the more dilute solutions. Other methods of purifying water have been described by Nernst 1 and Hulett. 2 Temperature Coefficient of Conductivity. — There are few proper- ties affected by temperature to the same extent as the conductivity of solutions. Great care must therefore be taken to keep the temperature con- stant during conductivity measurements. For this purpose any accu- rate thermostat may be used. It is necessary in all such work that a thermoregulator be employed, which shall keep the temperature constant to within a tenth of a degree. A thermostat well adapted for conductivity measurements is that devised and used by Ostwald, 3 and this is now generally employed wherever conductivity work is done. The thermostat bath contains a large volume of water to reduce the effect of changes in the tem- perature of the surrounding objects. A large glass tube containing a ten per cent solution of calcium chloride is placed in the bath, and connects above with an Ostwald regulator. The temperature of the bath is regulated by the expansion and contraction of the solution of calcium chloride, which has a large temperature coefficient of expansion. The Ostwald thermoregulator is shown in Fig. 56. The bottom of the U-shaped tube is filled with mercury, as shown in the figure. Gas enters at A. The tube A is inserted into one arm of the regulator, and shoved down until it nearly touches the mercury. This tube also contains a small hole in the Fig. 56. side. When the bath becomes warmer than the regulated temperature, the solution of calcium chloride expands, drives up the right arm of mercury, and cuts off the gas. The small hole in the side of A prevents the flame from becoming i Ztschr. phys. Chem. 8, 120 (1890). 2 Ibid. 21, 297 (1896). See F. Kohlrauseh : Ibid. 41, 193 (1902). 8 Ztschr. phys. Chem. 2, 565 (1888). 384 THE ELEMENTS OF PHYSICAL CHEMISTRY extinguished. When the bath cools the solution contracts, the mercury falls in the right arm, and opens the end of the tube A, when an abundance of gas escapes and the size of the flame beneath the thermostat bath increases. Thus the regulator works auto- matically. The solution whose conductivity it is desired to measure is placed in the resistance vessel, and the vessel suspended in the thermostat bath. The solution is stirred by raising and lowering the electrodes, and should be allowed to remain in the bath at least an hour at con- stant temperature, in order to insure that temperature equilibrium has been established. Magnitude of the Temperature Coefficients of Conductivity for a Number of Substances. — Table I. — Substances with Slight Hydrating Power Temperature Coefficients in Conductivity Units V=2 u = 1024 2.07 2.94 2.16 2.86 2.84 2.18 2.91 2.09 2.91 1 86 2.71 Table II. — Substances with Large Htdkating Power Calcium chloride . Calcium bromide . Strontium bromide Barium chloride . Magnesium chloride Manganese chloride Manganese nitrate . Cobalt chloride Cobalt nitrate Nickel chloride Nickel nitrate Copper chloride Copper nitrate ELECTROCHEMISTRY 385 It will be seen from the above data, taken from the work of Jones and West, 1 that the temperature coefficients of conductivity are large, and this must be carefully taken into account in making con- ductivity measurements. The Bearing of Hydrates on the Temperature Coefficients of Con- ductivity. A Fifth Argument for the Existence of Hydrates.— Jones and West 2 have shown that for temperatures ranging from 0° to 35°,. electrolytes are slightly less dissociated at the higher tempera- ture. This same fact is established at much higher temperatures by the work of Noyes and Coolidge. 3 The following discussion is taken from the work of Jones and West. Having eliminated the factor of increase in dissociation causing an increase in conductivity at the higher temperature, we are forced to conclude that this increase is due to an increase in the ionic veloc- ities at the higher temperature. The ion would move faster at the higher temperature, since the viscosity of the solvent becomes less at the more elevated temperature, and, further, the mass of the ion decreases with rise in temperature. This does not refer to the charged atom or group of atoms which we usually term the ion, but to this charged nucleus plus a larger or smaller number of molecules of water which are attached to it, and which it must drag along with it in its motion through the remainder of the solvent. That ions are hydrated has been shown beyond question by Jones and his coworkers. That these hydrates are relatively unstable compounds has also been demonstrated, the higher the temperature the less complex the hydrates existing in the solution. This can be seen from one example. In a solution of a certain definite concen- tration, every molecule of calcium chloride, or the ions resulting from it, holds about 30 molecules of water. From such a solution practically all of the water can be removed by simply boiling it, except 6 molecules of water to 1 of calcium chloride — this number being brought out of the solution by the salt as water of crystalliza- tion. The higher the temperature, then, the less complex the hydrate formed by the ion. The less the number of molecules of water combined with the ion, the smaller the mass of the ion, and the less its resistance when moving through the solvent. Conse- quently, the ion will move faster at the high temperature. This conclusion can be tested by the results of experiment. If this factor 1 Amer. Chem. Journ. 34, 357 (1905). 2 Ibid. 8 Ztschr.phys. Chem. 46, 323 (1903). 2c 386 THE ELEMENTS OF PHYSICAL CHEMISTRY of diminishing complexity of the hydrate formed by the ion with rise in temperature, plays any prominent role in determining the large temperature coefficient of conductivity, then we should expect to find those ions with the largest hydrating power, having the largest temperature coefficients of conductivity. This will readily be seen to be the case. The more complex the hydrate, i.e. the greater the number of molecules of water combined with an ion, the greater the change in the complexity of the hydrate with rise in temperature. We can readily test this conclusion by the results of the experi- mental work of Jones and West. 1 Let us compare the temperature coefficients of conductivity per degree rise in temperature, for some of those substances which have slight hydrating power, with the corresponding coefficients for a few of the substances which have a much greater power to combine with water. The volumes for which the comparisons are made range from 2 to 1024, and the temperatures from 25° to 35°. A comparison of Table I with Table II will show that the above conclusion is confirmed by the experimental results. The substances included in Table I have very slight hydrating power. Those in Table II have very much greater hydrating power. It will be remembered that hydrating power is a function of water of crystallization — the larger the number of molecules of water of crystallization the greater, in general, is the hydrating power of the substance. It will be seen that the substances in Table I have little or no water of crystallization, while those in Table II crystallize with large amounts of water. The water of crystal- lization may be taken as roughly proportional to the hydrating power of the substance. The substances in Table I have much smaller coefficients of con- ductivity than those in Table II, even taking into account the fact that those in Table II are ternary electrolytes, while those in Table I are binary electrolytes. Another fact, of equal importance, is brought out by comparing the results in Table I with one another, and, similarly, those in Table II with one another. If the temperature coefficient of conductivity is a function of the decrease in the complexity of the hydrate formed by the ion, with rise in temperature, then we should expect that those substances which have equal hydrating power would have approximately the same temperature coefficients of conductivity. 1 Ainer. Ohem. Journ. 34, 357 (1905). ELECTROCHEMISTRY 387 If we examine the above tables, we shall see that this is true. The substances in Table I all have only very slight hydrating power, as would be expected from the fact that they all crystallize without water. Their temperature coefficients of conductivity are all of the same order of magnitude and, indeed, are very nearly equal. The substances in Table II all have very great hydrating power, and all have a hydrating power of the same order of magnitude. This would be expected, since nearly all of these substances crystal- lize with 6 molecules of water. There are a few compounds in this table calling for special comment. Barium chloride crystallizes with only 2 molecules of water, yet it forms hydrates comparable with those substances with larger amounts of water of crystallization. It is, therefore, perfectly in keeping with the above relation that its temperature coefficients of conductivity should be of the order of magnitude that they are in the above table. Manganese chloride crystallizes with only 4 molecules of water, but the work of Jones and Bassett 1 shows that it forms hydrates about as complex as the other salts in Table II. Its temperature coefficients of conductivity are of the same order of magnitude as the other substances in this table. Of the compounds recorded in Table II, the one which, appar- ently, presents the most pronounced exception to the relation that we are now considering, is copper chloride. This salt crystallizes with only 2 molecules of water, and yet has a temperature coefficient of conductivity that is nearly as large as the salts with 6 molecules of water of crystallization. It might be inferred that this salt has much less hydrating power than the others in Table II. The work of Jones and Bassett 2 shows that this is not the case. Copper chlo- ride has a large hydrating power ; indeed, much larger than would be expected from the amount of water with which it crystallizes. Its temperature coefficient of conductivity is, therefore, not surprisingly great. A third point that is brought out by the results in the above tables is the following: At the higher dilution the temperature coef- ficient of conductivity for any given substance is greater than at the lower dilution. That this is a general relation will be seen by refer- ence to the work of Jones and West. 3 This is explained very satis- factorily on the basis of the suggestion made in this paper. The complexity of the hydrate at the higher dilution is greater than 1 Amer. ahem. Journ. 33, 562 (1905). 2 Ibid. 33, 577 (1905). 8 Ibid. 34, 357 (1905). 388 THE ELEMENTS OF PHYSICAL CHEMISTRY at the lower dilution, as is shown by the experiments of Jones and his coworkers on the composition of the hydrates formed by differ- ent substances at different dilutions. The hydrate being more complex at the higher dilution, the change in the composition of the hydrate with change in tempera- ture would be greater at the higher dilution, and consequently the temperature coefficient of conductivity is greater the more dilute the solution. All three of these conclusions are necessary consequences of the assumption that the large change in conductivity with change in tem- perature is due, in part, to the decreasing complexity of the hydrates formed around the ions, with rise in temperature. Since these con- clusions are all verified by the results of experiment, we must accept the assumption which led to them as containing a large element of truth. The Relative Conductivities of Different Substances. — The first generalization reached through the study of the conductivities of aqueous solutions of different substances is that chemical com- pounds can be divided into two large classes. First, those which in the presence of water conduct the current, undergoing simultane- ously decomposition or electrolysis. These are called electrolytes. Second, those substances which, in the presence of water, do not conduct the current, and do not undergo any decomposition when an attempt is made to pass a current through their solutions. These are called non-electrolytes. The electrolytes themselves differ greatly in their conducting power. They may be divided roughly into two classes : those with high conductivity, as the strong acids, strong bases, and salts ; and those with low conductivity, as the organic acids and bases. This division into two classes is more or less arbitrary, since among the electrolytes we find nearly every degree of conductivity represented. It is true, however, that most substances which conduct belong near the extremes. Again, we recognize marked differences between the good conductors. The strong monobasic acids, such as hydrochloric, hydrobromic, nitric, etc., are the best conductors. The strong bases, such as sodium and potassium hydroxides, come next in order, and then the salts. Demonstration of the Different Couductivities of Different Sub- stances. — It can be readily demonstrated that different electrolytes have very different conductivities. This has been shown by Noyes and Blanchard 1 in an experiment which they state was devised by 1 Joum. Amer. Chem. Soc. 22, 736 (1900). ELECTROCHEMISTRY 389 Fig. 57. Whitney. Prepare half-normal solutions of hydrochloric, sulphuric, chloracetic, and acetic acids. Introduce these into four glass tubes, A, B, G, D, about 20 cm. long and 3 cm. internal diameter, as shown in Fig. 57. These glass tubes are closed by rubber stoppers, through which pass glass tubes. These tubes carry copper wires, the wires terminating in platinum disks as shown in the TJJ Tg JZ figure. We must be able to move these glass tubes through the rubber stoppers. The wire com- ing from the bottom of each tube is connected with a 32 candle-power, 110-volt lamp. The other side of each lamp is connected with one wire from, a 110-volt, alternating-current dy- namo. The wires from the tops of the glass tubes are connected with the other wire from the dynamo. Add 100 cc. of pure water to each glass tube. Add 5 cc. of the solution of hydrochloric acid to the tube A ; add an equal quan- tity of the sulphuric acid to the tube B ; of chloracetic acid to the tube G; and of acetic acid to the tube D. After each solution has become homogeneous, close the circuit in a dark room, and so adjust the height of the upper electrode that all the lamps are equally brilliant. Then examine the heights of the electrodes in the four cylinders. If in the hydrochloric acid the upper electrode is at the top of the cylinder, in the sulphuric acid it will be about one-fourth from the top, in the chloracetic acid about three-fourths from the top, and in the acetic acid the electrodes will nearly touch. This shows the different amounts- of dissociation of the four acids at the same concentration — the hydrochloric acid being the most, the acetic acid the least, dissociated. This experiment can be used to illustrate another fact. If the acid in each cylinder is just neutralized with sodium hydroxide, and the experiment repeated as above, the electrodes being adjusted so that all the lights are equally brilliant, it will be seen that the distance between the electrodes in the four cylinders is very nearly 390 THE ELEMENTS OF PHYSICAL CHEMISTRY the same, showing that the sodium salts of all four acids are equally dissociated. Increase in Molecular Conductivity with Increase in Dilution. — The study of the relation between molecular conductivity and dilution of the solution soon led to the conclusion that the mo- lecular conductivity increases with the dilution. The resistance of a solution increases with the dilution, which is the same as to say that the actual conducting power decreases as the dilution increases. While this is true, the conductivity does not decrease as rapidly as the dilution increases, hence the molecular conductivity increases with the dilution. There are so few exceptions known to this generalization that it may be regarded as almost a general truth. This increase in molecular conductivity with increase in dilution is, however, not unlimited. The molecular conductivity of the best conductors becomes constant at a dilution of from 1000 1. to 10,000 1., and remains constant from this point, however far the dilution may be carried. The same general relations hold for the poorer conductors, but in these cases the constant value of the molecular conductivity is reached only at dilutions much greater than those named above. For many of the poorest conductors, the constant value of the mo- lecular conductivity cannot be obtained directly by the conductivity method. In such cases an indirect method must be applied, as we shall see later. The facts stated above in reference to the good conductors can be seen more clearly by examining a few data obtained with an acid, a base, and a salt, at different concentrations, v is the volume of the solution in litres which contains a gram-molecular weight of the electrolyte ; /^ is the molecular conductivity at the dilution v. Hydrochloric Acid Sodium Hydroxide Potassium Chloride V lj.v 18° V |Ml8° V »»»18° 0.333 201.0 0.333 100.7 0.333 82.7 1.0 278.0 1.0 149.0 1.0 91.9 10.0 324.4 10.0 170.0 10.0 104.7 100.0 341.6 100.0 187.0 100.0 114.7 500.0 345.5 500.0 186.0 500.0 118.5 1000.0 345.5 1000.0 10,000.0 119.3 120.9 The maximum constant value which ^ attains at high dilution is termed p.^, and its significance will be seen when we study the ELECTROCHEMISTRY 391 application of the conductivity method to the measurement of elec- trolytic dissociation. These results serve also to illustrate the three degrees of conductivity possessed by the good conductors, — acids, bases, and salts. The Law of Kohlrausch. — A relation of -wide-reaching significance was discovered by Kohlrausch by comparing the values of ^ for different substances. He found that the difference between the values of ^ for two electrolytes having a common anion and differ- ent cations, is the same as the difference between the values of ^ for any two electrolytes having a common anion, and the same cations as the above electrolytes. An example will make this clear : The value of ^ for potassium bromide at 18° is The value of ^ for sodium bromide at 18° is Difference The value of ^ for potassium nitrate at 18° is The value of ^ for sodium nitrate at 18° is Difference 141.0 120.0 21.0 121.0 97.5 23.5 The same relation obtains for a common cation as for a common anion. In this case the difference between the values of ^ for two electrolytes having a common cation and different anions is the same as the difference between the values of /a. ooi for any two elec- trolytes having a common cation and the same anion as the electro- lytes in question. This can be seen from the example given : — ^ KBr - ^ KN0 3 = 141 - 121 = 20.0; ^ NaBr - ^ NaNO s = 120 - 97.5 = 22.5. The difference between the two values is hardly larger than the ex- perimental error. The value of p^ for any electrolytes is, then, the sum of two constants, the one depending on the anion and the other on the cation. The conductivity of a solution depends on the number of ions present, and the velocity with which they move. The value of the molecular conductivity at complete dissociation, since it deals with comparable quantities of ions, depends on the velocities with which the ions move. The value of ^ for any substance depends on the velocities of the ions into which the substance dissociates. The constants above referred to are, then, proportional to the veloci- ties of the cation and anion respectively. If we represent by c the velocity of the cation, and by a the velocity of the anion, — A*„ = c + a. 392 THE ELEMENTS OP PHYSICAL CHEMISTRY Expressed in words, the velocity with which any ion travels is a constant for a given solvent and a given potential gradient, and is inde- pendent of the nature of the other ion or ions with which it is present in the solution. This generalization is usually referred to as the law of the inde- pendent migration velocities of ions. The law in this form holds, in general, only for very dilute solutions, since it is only in such solu- tions that the true values of ^ are obtainable directly by experi- ment. Ostwald's Modification of Kohlrausch's Law. — The law as enun- ciated by Kohlrausch applies only to very dilute solutions. Ostwald 1 has shown that the law of Kohlrausch is of general applicability, and can be used with more concentrated as well as with more dilute solu- tions. If, however, the solutions are more concentrated and not com- pletely dissociated, the amount of their dissociation must be taken into account. If we represent this, as is usually done, by a, the law of Kohlrausch as applied to incompletely dissociated solutions be- comes — /*„ = a (c + a). As the dilution increases a approaches more and more nearly to unity, and when the dissociation is complete it becomes unity. The Ostwald modification of the Kohlrausch law becomes, at this point, identical with the original law proposed by Kohl- rausch. The Law of Kohlrausch used to determine the Velocity of Ions. — It is obvious from what has already been said, that the law of Kohl- rausch can be used to determine the velocity of ions. The law states that for completely dissociated solutions the velocity of the cation c, plus the velocity of the anion a, is a constant. The value of this constant, or fx, a , is determined at once by applying the conductivity method to completely dissociated solutions, and measuring the mo- lecular conductivity. In a word, we can determine at once the value Q of c + a. We determine the value of — by the Hittorf method of a J determining relative migration numbers. Knowing c + a and -, we obtain at once absolute values for the velocities of both ions. If this method is correct, then the velocity of any given ion must be the same, whether determined from one substance, or from any other substance in which it may occur. This was tested by Kohl- i Lehrb. d. Allg. Ohem. II, 672. ELECTROCHEMISTRY 393 rausch 1 for the chlorine ion. The velocity of this ion was calculated from several salts and was found to be the same in each case. The velocities are expressed in 10" 6 centimetres per second. The poten- tial gradient is 1 volt per centimetre ; the temperature, 18°. Concentration Normal KC1 NaCl LiCI c + a a c + a 6 a c+a C a 0.1 1153 564 589 952 360 592 853 259 594 0.01 1263 619 644 1059 415 644 962 318 644 0.001 1313 643 670 1110 440 670 1013 343 670 0.0001 1335 654 681 1129 448 681 1037 356 681 The results for the velocity of the chlorine ion are the same for the different salts. Kohlrausch 2 determined the velocities of a number of ions in centimetres per second, under unit potential gradient, i.e. a drop in potential of one volt a centimetre. Cations Velocity in Centimetres per Second Hydrogen . 0.00320 em. Potassium . 0.00066 cm. Sodium . 0.00045 cm. Lithium . . 0.00036 cm. Ammonium 0.00066 cm. Silver 0.00057 cm. Anions Velocity in Centimetres per Second Hydroxyl . . 0.00182 cm. Chlorine 0.00069 cm. Iodine 0.00069 cm. Nitro group 0.00064 cm. It will be seen that hydrogen is the swiftest of all ions, and that hydroxyl comes next with respect to its velocity. It will, however, be observed that even the swiftest ions move very slowly through the solvent in which they are contained. APPLICATIONS OF THE CONDUCTIVITIES OF SOLUTIONS OF ELECTROLYTES The Dissociation of Electrolytes. — The most important application of the conductivity of electrolytes is to measure their dissociation. If the dissolved substance is not dissociated at all, the conductivity would be zero. If it were completely dissociated, the conductivity would be a maximum. If it were partly dissociated, the conduc- 1 Wied. Ann. 50, 385 (1893). 2 Ibid. 50, 403 (1893). 394 THE ELEMENTS OF PHYSICAL CHEMISTRY tivity would lie somewhere between zero and the maximum value. Since conductivity and dissociation are proportional, to determine the latter it is only necessary to divide the conductivity at the dilu- tion in question by the conductivity at complete dissociation. The conductivity at any dilution, v, is represented by /*„. The conduc- tivity at complete dissociation is represented by ^ ; the percentage of dissociation, by a. We have the following relation : — ■v « x, *■ It is very simple to determine the value of p v for any dilution of any electrolyte in water. It is only necessary to apply the Kohl- rausch method directly, and calculate the molecular conductivity. It is not always such a simple matter to determine the value of p, . Some of the more complicated cases will be considered. Determination of the Maximum Molecular Conductivity. — If the compound is strongly dissociated, such "as the strong acids and bases, and the salts, the value of fi a is determined by increasing the dilution of the solution until a value for the molecular conductivity is reached which remains constant. If, on the other hand, the compound is not strongly dissociated, it is not possible to determine p^ by the above procedure. The dilution at which the dissociation would be complete is so high that it is not possible to use the conductivity method with any degree of accuracy. An indirect method of determining p^ for the weakly dissociated substances has been worked out and applied. Let us take first the weak acids, say the organic acids. These acids dissociate like all other acids into a hydrogen cation and a complex organic anion. If the hydrogen of the acid is replaced by a metal, we have a salt formed, and all salts are strongly dissociated substances. The value of p a for the salt can be determined readily by means of the conductivity method. Ostwald used the sodium salt. The value of p m for this compound is from Kohlrausch's law the sum of two constants, the one depending upon the anion and the other on the cation. If from the value of p x for the sodium salt we subtract the constant for the sodium ion, which is known, the remainder is the constant for the anion. If to this constant we add the constant for hydrogen, we have the value of p x for the acid, since all acids are made up of an anion and the cation hydrogen. The value of the constant for the sodium ion at 25°, as given by Ostwald, is 49.2, and that of the hydro- gen ion 325. The value of p x for an acid at 25° is the value of p a ELECTROCHEMISTRY 395 for the sodium salt of that acid, minus 49.2, plus 325 ; i.e. /*,„ for the sodium salt plus 275.8. If we wish to determine ^ for a weak base, we proceed in a strictly analogous manner. The nitrate or chloride of the base is prepared. This, being a salt, is strongly dissociated, and the value of /^ for the chloride or nitrate can be determined directly by the conductivity method. The value of ^ for the chloride of a base is the sum of two constants, the one depending upon the cation of the base, and the other upon the chlorine anion. The value of p a for the free base is the value of (i x for the chloride, minus the constant for chlorine, plus the constant for hydroxyl. The value of the constant for chlorine at 25° is 70.2 ; that of hydroxyl, 170. The value of n x for the base is, then, the value of ^ for the chloride, minus 70.2, plus 170, or plus 99.8. If the nitrate is used the value of the constant for the N0 3 anion is 65.1. To obtain ^ for the base we must, therefore, add 104.9 to the value of fi m for the nitrate of the base. An empirical method has been worked out by Ostwald * for de- termining the value of ^ for the sodium salt of an acid, from the value of p v at any ordinary concentration. As the result of the study of a large number of acids he found that ^ v at a given volume differed by a constant quantity from p^. These differences for volumes ranging from 32 to 1024 1. are given below: — Volumes : 32 64 128 266 512 1024 Differences : 12 10 8 6 4 2 By adding these differences to /*.„ at any of the above volumes, we obtain ^ at once. Knowing the value of ^ for any compound, and also the value of ft„, we obtain at once the dissociation a — which is equal to /*„ divided by /x^. Is Conductivity an Accurate Measure of Dissociation? — It is gen- erally assumed that the conductivity method is an accurate measure of electrolytic dissociation. If there is no dissociation, there is no conductivity. If dissociation is at a maximum, conductivity is a maximum. The dissociation of any solution is taken as proportional to its conductivity. In order that this should be true, there must be no change in the velocity of the ion as the dilution of the solution changes. In very concentrated solutions we know that the viscosity is much greater than in dilute solutions, and consequently the ions i Lehrb. d. Allg. Ohem. II, 693. 396 THE ELEMENTS OF PHYSICAL CHEMISTRY move more slowly. Conductivity is, therefore, not an accurate measure of dissociation in concentrated solutions, as is well known. In dilute solutions there is considerable doubt as to the accuracy of dissociation as measured by conductivity. The work of Jones and his assistants has undoubtedly shown that the ions are hydrated, and, further, that the amount of hydration increases with the dilution of the solution (see page 247). The ion is thus becoming heavier as: the dilution of the solution increases and consequently moves more slowly. The ratio Hi. would, then, not give the true value for the dis- sociation. Indeed, it is very doubtful whether we have at present any thoroughly reliable method for measuring electrolytic dissociation. Comparison of Dissociation from Conductivity with Dissociation from Freezing-point Lowering. — A Sixth Argument for the Hydrate Theory. — We have thus far studied two methods of measuring electrolytic dissociation, — the conductivity and freezing-point meth- ods. The question is whether the results obtained by the two methods for the same substance at the same dilutions are the same, or different. A few results will answer this question. In the following table the conductivity measurements and freezing-point lowerings were made by Jones and Pearce: 1 — Concentration Dissociation from Dissociation from COMPOUNDS Gr. Moleo. Normal Conductivity Freezing-point Lowering Per Cent Per Cent Ba(N0 3 ) 2 • 0.01 86.37 99.06 Ba(N0 8 ) 2 0.025 77.32 84.19 Ba(NO„) 2 0.05 70.47 75.18 Ba(N0 3 ) 2 0.075 65.51 67.20 Ba(NO s ) 2 0.10 61.36 62.95 Ba(N0 3 ) 2 0.15 55.47 57.40 Ni(N0 3 ) 2 0.01 91.10 98.03 Ni(NO s ) 2 0.025 85.58 89.75 Ni(N0 3 ) 2 0.05 79.83 83.72 Ni(NO s ) 2 0.075 76.67 81.32 Co(N0 3 ) 2 0.01 92.40 98.65 Co(N0 3 ) 2 0.025 85.62 93.65 Co(N0 3 ) 2 0.05 81.73 88.26 Co(N0 3 ) 2 0.075 77.95 86.09 Co(N0 3 ) 2 0.10 76.48 85.48 1 Amer. Chem. Joum. 38 (1907). ELECTROCHEMISTRY 397 _ Compounds Concentration 6b. Molec. Normal Dissociation prom Conductivity Dissociation from Freezing-point Lowering Per Cent Per Cent CaCl 2 . 0.01 89.67 90.61 CaCl 2 . 0.025 84.37 84.21 CaCl 2 . 0.05 80.62 80.96 CaCl 2 . 0.075 76.60 78.04 CaCl 2 . 0.10 74.35 76.35 3aCl 2 . 0.01 90.87 96.85 BaCl 2 . 0.025 84.16 94.06 BaCl 2 . 0.05 80.09 83.19 BaCl 2 . 0.705 76.24 79.49 BaCl 2 . 0.10 75.65 78.83 MgCl 2 . 0.01 90.90 97.10 MgCl 2 . 0.031 83.16 94.03 MgCl 2 . 0.051 79.78 90.97 MgCl 2 . 0.071 76.73 88.25 MgCl 2 . 0.10 73.61 87.68 MgClj . 0.25 64.72 82.81 SrCl 2 . 0.01 89.37 91.87 SrCl 2 . 0.029 82.56 91.93 SrCl 2 . 0.039 80.32 86.91 SrCl 2 . 0.05 78.08 82.65 SrCl 2 . 0.071 76.27 81.88 SrCl 2 . 0.10 74.17 81.46 The dissociation calculated from freezing-point lowering is larger -than that calculated from conductivity. This is exactly what should be expected in terms of the present theory of hydrates. The hydrates in aqueous solution affect the freezing-point lowering, as we have seen. Indeed, it was the abnormally great freezing-point lowerings produced by concentrated solutions of electrolytes, that led to the work on hydrates that has been carried out in this labora- tory. The water of hydration is removed from the field of action as far as freezing-point lowering is concerned, and, consequently, we have too great lowering of the freezing-point. The water of hydration apparently does not affect conductivity directly. That it affects it indirectly will be seen a little later. It is quite certain that the freezing-point method is not a true measure of dissociation. It is doubtful, as we have seen, whether conduc- tivity is an accurate measure of the dissociation of electrolytes. It should be noted that in the above tables the conductivity measurements were made at zero, i.e. at nearly the same temperature as the freezing-points. 398 THE ELEMENTS OF PHYSICAL CHEMISTRY The Dilution Law of Ostwald. — Since the molecular conductivity of solutions of electrolytes increases with the dilution, and since dissociation is proportional to conductivity, it follows that dissocia- tion increases with the dilution of the solution. This holds up to a certain point, as we have seen. Beyond a certain dilution the con- ductivity remains constant, which means that the dissociation at this dilution is constant. For the good conducting substances the molec- ular conductivity increases slowly with the dilution. It increases much more rapidly for the poorer conductors, such as the organic acids and bases. The difference between the molecular conduc- tivities of the good and bad conductors thus becomes less as the dilution increases. Ostwald 1 found from his own work that the molecular conductivi- ties of all monobasic acids pass through the same series of values. Thus, if any two acids A and B have the same molecular conduc- tivities at volumes v Y and v 2 , they will have the same conductivities at any other volumes. Ostwald 2 went much farther, and discovered the mathematical expression connecting dissociation and dilution. He gave us our first rational dilution law. The law was deduced as follows: — If the laws of gas-pressure hold for dilute solutions, and if the Arrhenius theory of electrolytic dissociation to account for the excep- tions shown by electrolytes is true, then the formula connecting the degree of dissociation with the volume of gases must apply directly to the relation between the dilution and the dissociation of electro- lytes. 8 The law of the dissociation of gases must apply also to the dissociation of dilute solutions. For a homogeneous system of one volume of a gas dissociating into two volumes of gaseous products, Ostwald 4 deduced the formula: B log -£— = 2- + const, ftfti T p,p u and^>n are, respectively, the pressures of the undissociated gas and of the decomposition products, q is the heat of decom- position. If the temperature is constant and neither of the decomposition 1 Journ. prakt. Chem. 31, 433 (1885). * Ztschr. phys. Chem. 2, 36 (1888) ; 3, 170 (1889). * Planck: Wied. Ann. 34, 139 (1888). * Ztschr. phys. Chem. 2, 36 (1888). Lehrb. d. Allg. Chem. (1st edition), II, 723. ELECTROCHEMISTRY 399 products is present in excess, the above expression becomes — &-. = const. (1) Pi p is the pressure of the un dissociated gas, and p x that of the decom- position products. Turning now to solutions, we have to deal with osmotic pressure instead of gas-pressure. The osmotic pressure is proportional to the amount of dissolved substance, and inversely proportional to the volume. Let u be the mass of the undissociated electrolyte, and w, the mass of the dissociated products, and v the volume of the solution: u Wi P--\ Pi=~- V V Substituting these values in equation (1), we have — - = const. (2) We have seen, however, that the amount of dissociation v^ (or a) is measured by the relation between the conductivity at the given volume v, and at infinite dilution : — ft« The amount of undissociated substance u = 1 — — . Substituting these values for u and «i in equation (2), we have — /*, (ft, — /*■») v = const, ft.* ft* This expression can be simplified by writing « = — , when we ft M have — „2 = const. (l—a)v This expression is known as the Ostwald dilution law. Testing the Ostwald Dilution Law. — Ostwald 1 tested his law by applying it to a large number of substances. He determined the conductivity of a number of solutions of any given substance, and 1 Ztschr. phys. Chem. 3, 170, 241, 869 (1889). Jahn: Ibid. 33, 545 (1900). 400 THE ELEMENTS OF PHYSICAL CHEMISTRY from these results calculated the dissociation at the different dilu- tions. He then substituted the value of a for any given value of v, in the equation expressing his law, to see whether the result came out a constant over any wide range of dilution, v is the volume of the solution, or number of litres that contain a gram-molecular weight of the electrolyte. The results for two organic acids are given below: — Fokmic Acid V a COH8T. X 100 8 4.05 0.0214 16 6.63 0.0210 32 7.79 0.0206 64 10.78 0.0203 128 14.76 0.0200 256 20.12 0.0198 512 27.10 0.0197 1024 35.80 0.0195 Butyric Acid V a Const, x 100 8 1.068 0.00144 16 1.536 0.00150 32 2.165 0.00149 64 3.053 0.00150 128 4.292 0.00150 256 5.988 0.00149 512 8.300 0.00147 1024 11.410 0.00144 The results show that the value comes out very nearly a constant. In a word, the Ostwald law holds with fair approximation for this class of substances. The law was applied to between 200 and 300 organic acids, and was found to hold approximately for this class of substances. These organic acids all belong to the weakly disso- ciated substances. The law was tested for the weakly dissociated organic bases by Bredig. 1 The results for two substances are given. He applied the law to about thirty weak bases. 1 Ztschr. phys. Chem. 13, 289 (1894). ELECTROCHEMISTRY Ammonia 401 * a CONBT. X 100 8 1.35 0.0023 16 1.88 0.0023 32 2.65 0.0023 64 3.76 0.0023 128 5.33 0.0023 256 7.54 0.0024 Trimethylamote V a Const, x 100 8 2.31 0.0069 16 3.36 0.0073 32 4.77 0.0075 64 6.73 0.0076 128 9.35 0.0075 The values found by Bredig for the weak bases are rather nearer a constant than those found by Ostwald for the weak acids. The weak organic bases, like the weak organic acids, belong to the gen- eral class of weakly dissociated compounds. The law of Ostwald evidently applies to such substances. When we turn to the strongly dissociated substances, such as the strong acids and strong bases, and salts, the dilution law of Ostwald does not apply at all satisfactorily. The values found are not at all constant over any considerable range of dilution, but vary greatly with the dilution. No satisfactory reason has yet been furnished, which explains why the law of Ostwald holds for weakly dissociated substances, but does not hold for the strongly dissociated electro- lytes. Another, purely empirical expression has, however, been dis- covered, which applies as well to the strongly dissociated compounds as that of Ostwald to the weak acids and bases. The Dilution Law of Rudolphi. — The dilution law which was found to hold for the strongly dissociated electrolytes was discov- ered by Eudolphi. 1 In attempting to apply the Ostwald law to solu- tions of silver nitrate, he made the following observation: If we iZtschr. phys. Chem. 17, 385 (1895). croft: Ibid. 31, 188 (1899). 2d Euler: Ibid. 29, 603 (1899). Ban- 402 THE ELEMENTS OF PHYSICAL CHEMISTKY represent the volumes of the solution by v, and the constant by c, we obtain from the Ostwald formula : — v = lQ, c = 0.26; v = 64, c = 0.13; v = 256, c = 0.065. A glance at these figures will show that a constant would be ob- tained, if the values of c were multiplied by the square root of v in each case: — 0.26 x Vl6 = 0.13 x VM = 0.065 x V256. Eudolphi substituted for v in the Ostwald equation the square root of v, and obtained — : const. (1 — a)Vv He applied this equation to between fifty and sixty strongly dissoci- ated compounds, and the values found for c always approached closely to a constant. The results for a few substances will be given. Hydrochloric Acid Potassium Sulphite Potassium Acetate V C V c V C 2 4.36 2 0.453 2 1.24 4 4.45 8 0.454 100 1.19 8 5.13 32 0.455 1000 1.18 16 5.13 128 0.544 10000 1.03 Although considerable deviations from a constant exist in some cases, yet the law of Eudolphi holds about as well for the strongly dissociated electrolytes as that of Ostwald for the weakly dissociated substances. The physical significance of the y/v in the Eudolphi equation is at present entirely unexplained. We thus seem to have two expressions for the relation between the dissociation of electrolytes and the dilution of the solutions; the expression of Ostwald, which has a rational basis, and whose physical significance is known, holding for the weakly dissociated compounds ; and the purely empirical equation of Eudolphi, which holds for the more strongly dissociated electrolytes. The relation between gaseous and electrolytic dissociation is, then, established as far as the less strongly dissociated compounds are concerned. Several further modifications of the dilution laws have been pro- ELECTROCHEMISTRY 403 posed. 1 That suggested by Van't Hoff should be especially men- tioned. He showed that the equation — « s — = const. (1 — ayv holds much more satisfactory than that proposed by Eudolphi. Kohlrausch has given this same equation a simpler expression. Why does not the Ostwald Law apply to Strongly Dissociated Elec- trolytes ? — The answer to this is probably to be found in the fact that the conductivity method as already pointed out (see page 395) is not a true measure of electrolytic dissociation. If the electrolyte is weak, i.e. not much dissociated, the error in measuring its dis- sociation by the conductivity method does not have much signifi- cance when the results are inserted into the Ostwald equation. When, however, the electrolyte is strongly dissociated, an appreciable error in the measurement of its dissociation would produce a large effect when the results were inserted into the equation expressing the dilution law. It is highly probable that when we have some means of ascer- taining the true value of dissociation, it will be found that the Ost- wald law, or some rational modification of it, will hold for strongly dissociated electrolytes, as well as it now holds for weakly dis- sociated compounds. It would be very remarkable, indeed, if this deduction, based upon the law of mass action, as it is, should ulti- mately be found not to be in accord with the facts. The Conductivity of Organic Acids and the Determination of Dis- sociation Constants. — The conductivities of from two to three hun- dred of the more common organic acids have been measured by Ostwald, 2 at dilutions ranging from a few litres to two or three thousand litres. The general fact established by this work is that this whole class of substances is comparatively weakly dissociated even at dilutions of one thousand litres. It is true that they show marked differences in the degree of their dissociation, but few of them are sufficiently dissociated to determine the value of ^ directly by the conductivity method. The indirect method, 3 using the sodium salt, was employed. Knowing the value of ^ for the acid, the disso- ciation at any dilution could be calculated from the molecular con- 1 Van't Hoff: Ztschr. phys. Chem. 18, 300 (1895). Kohlrausch : Ibid. 18, 602 (1895). Bancroft : Ibid. 31, 188 (1899). 2 Ibid. 3, 170, 241, 369 (1889). s lm . 2) 8 40 (1888). See Lellmann : Ber. d. chem. Gesell. 22, 2101 (1889). Bethmann : Ztschr. phys. Chem. 5, 385 (1890). Bader : Ibid. 6, 289 (1890). D. Berthelot : Ann. Chim. Phys. (6) 23, 5 (1891). Walden : Ztschr. phys. Chem. 8, 433 (1891) ; 404 THE ELEMENTS OF PHYSICAL CHEMISTRY ductivity at that dilution. Knowing the dissociation, the dissociation constant for the acid was calculated from the dilution law, — (1 — a)v The value of c for different dilutions, which in most cases is fairly constant, gives us a deep insight into the nature of the com- pound. Knowing its value, we know the relative strength of the acid, with all that is implied by this term. The effect of replacing hydrogen by different groups was studied by Ostwald, and the influence of constitution as well as composition on the acidity was determined in a number of cases. Thus, the in- troduction of a halogen, sulphur, or oxygen atom, or the nitro group, increased the acidity. The presence of the amido group diminished it. The presence of oxygen or the nitro group in the ortho position has a greater influence than in the meta position, and in the meta position a greater influence than in the para. For further details reference must be had to the tabulated statement which has been pre- pared by Ostwald. 1 Basicity of an Acid determined Empirically from its Conductivity. — An empirical relation between the rate of increase in the conduc- tivity of the sodium salts of acids with increase in dilution, and the basicity of the acids, was discovered by Ostwald. 2 If we subtract the molecular conductivity of the sodium salt at a dilution containing a gram-molecular weight in 32 J.., from its molecular conductivity at a dilution of 1024 1., the difference will be about 10 for monobasic acids, 20 for dibasic, etc. Or if we represent the basicity of the acid by b, the molecular conductivity at 1024 1., minus the molecu- lar conductivity at 32 1., = 10 b : — /*1024— /* 32 = 10 6. These determinations of conductivity were made at 25°. A few examples from the work of Ostwald, 3 on acids whose basicity varies from one to five, will make this point clear. Ibid. 10, 563 (1892) ; Ibid. 10, 638 (1892). Ebersbach : Ibid. 11, 608 (1893). Schall : Ibid. 14, 701 (1894). Jahn : Ibid. 16, 72 (1895). Euler: Ibid. 21, 256 (1896). Szyszkowski: Ibid. 22, 173 (1897). Smith: Ibid. 25, 144 (1898). Arrhenius : Ibid. 81, 197 (1899). Walker and Carmaok ; Journ. Chem. Soc. 77, 5 (1900). Hofmann: Ztschr. phys. Chem. 45, 584 (1903). Drucker: Ibid. 52, 641 (1905). 1 Ztschr. phys. Chem. 3, 418 (1889). 2 Ibid. 1, 105 (1887) ; 2, 902 (1888). 3 Ibid. 2, 901 (1888). " Dissociation of Dibasic Acids." Wegschneider : Monatsch. 23, 599 (1902). ELECTROCHEMISTRY 405 Sodium Nicotinate (monobasic) 32 68.4 1024 mjs 10.4 difference = 10 x 1 Sodium Quinolinate (dibasic) 32 69.2 1024 90.0 20.8 difference = 10 x 2 Sodium Pybidinetbicaebonate (tkibasic) V fj.v 32 82.1 1024 113.1 31.0 difference = 10 x 3 Sodium Pyeidinetetbacabbonate (teteabasic) 32 80.8 1024 121.2 40.4 difference = 10 x 4 Sodium Pybidinepentacaebonate (pentabasic) 32 77.7 1024 127.8 50.1 difference = 10 x 5 The extension of this empirical relation to acids more complex than pentabasic cannot be made. Walden 1 has shown that many exceptions exist when the supposed relation is applied to acids of higher basicity. The Determination of the Conductivity of Organic Bases and their Dissociation Constants. — An elaborate piece of work on the conduc- tivity of organic bases was carried out in the laboratory of Ostwald by Bredig. 2 From his measurements the dissociation constants of these substances were calculated, as in the case of the organic acids, by means of the Ostwald dilution law. The substances studied by Bredig include a large number of substituted ammonias, — primary, secondary, tertiary, and quaternary, the aromatic amines, and a 1 Ztschr. phys. Chem. 1, 529 (1887); 2, 49 (1888). 2 Ibid. 13, 289 (1894). See Smith : Ibid. 25, 193 (1898). Walker and Aston : Journ. Chem. Soe. 576 (1895). 406 THE ELEMENTS OF PHYSICAL CHEMISTRY number of other organic and a few inorganic bases. The quaternary amines are by far the strongest, approaching in strength the strongest alkalies. The secondary amines have a larger dissociation constant than either the primary or tertiary, and the primary and tertiary amines are much more strongly dissociated than ammonia itself. The effect of constitution on the strength of bases is seen when isomeric substances are compared. As with organic acids so with organic bases, constitution has a marked influence on the strength. The conductivity of salts of a large number of organic bases was also measured by Bredig. Migration Velocities of the Complex Organic Anions. — We have seen from the law of Kohlrausch that the conductivity method can be used to determine the velocities of ions. The value of ^ for a compound is the sum of the migration velocities of the two ions. If the value of ^ for the sodium salt of an organic acid is determined, and the velocity constant for sodium subtracted, the remainder is the migration velocity of the anion of the acid. Extensive application has been made of the conductivity method for determining the migra- tion velocity of organic anions, and, as we shall also see; of organic cations. Ostwald 1 has arrived at general conclusions from his measure- ments as to the effect both of composition and constitution of the ion on its velocity. The effect of increasing complexity is illustrated by the following example : — Velocity Anion of formic acid, HCOO 55.9 Anion of acetic acid, CH 8 COO 43.1 Anion of propionic acid, CH 3 CH2COO 39.0 It is obvious that as the ion becomes more complex its velocity becomes smaller. When hydrogen is replaced by chlorine the velocity becomes less, as is shown by the following example : — Velocity Anion of acetic acid, CH 8 COO 43.1 Anion of monochloracetic acid, CH 2 ClCOO .... 42.0 Anion of dichloracetic acid, CHCI2COO 40.1 Anion of trichloracetic acid, CClsCOO 37.5 The effect of constitution on migration velocity was studied with isomeric ions. The following results show that isomeric ions move with very nearly the same velocity : — 1 Ztschr. phys. Chem. 2, 848 (1888). ELECTROCHEMISTRY 407 {Anion of butyric acid, CH s CH 2 CH 2 COO Anion of isobutyric acid, CH s\ CHCOO CH 3 / _ /N0 2 <°> J Anion of orthonitrobenzoic acid, CeH^v \coo lAnion of paranitrobenzoic acid, CeH^ (p) /NO. \coo [Anion of ortboamidobenzoic acid, CeH^ ! \COO (.Anion of metaamidobenzoic acid, CeH^. /NH 2 < ra > COO Velocity . 35.4 . 36.6 . 34.5 . 34.8 . 35.7 . 34.6 Other relations were pointed out by Ostwald for the organic anions, but for these his original paper must be consulted. Migration Velocities of the Complex Organic Cations. — The veloc- ities of many organic cations were calculated from the conductivities of salts of the organic bases, by a method strictly analogous to that already discussed for the anions of organic acids. The value of ^ for a salt of the base was determined directly by the conductivity method, the velocity of the anion of the salt subtracted, and the re- mainder, from the law of Kohlrausch, is the velocity of the cation. Some of the relations which obtain for the cations are similar to those already pointed out for the anions. A few of these will be referred to, but for a full discussion of this subject reference must be made to the elaborate investigation of Bredig. 1 The more complex the cation, the slower its velocity. Velocity Ammonium, NH4 70.4 Methylammonium, CH 8 NH 3 57.6 Ethylammonium, C2H 6 NH a 46.8 Isomeric ions which have analogous constitution have approxi- mately the same velocities. Velocity Propylammonium, CH 8 CH 2 CH 2 NH 3 40.1 Isopropylammonium, ^ s NcH - NH 3 40.0 If they differ greatly in constitution, isomeric ions usually have different velocities. 1 Loc. cit. 408 THE ELEMENTS OF PHYSICAL CHEMISTRY Velocity Trimethylpropylammonium, (CH 8 ) 8 C8H 7 N 36.2 Dimethyldiethylammonium, (CH 8 )2(C 2 H5)2N .... 38.2 The effect of constitution may in some cases overcome that of composition, and the more complex ion move the faster. Velocity Methyldiethylammonium, CH 8 (C 2 H5) 2 NH 35.8 Dimethyldiethylammonium, (CH 3 ) 2 (C 2 H5) 2 N .... 38.2 This last example serves also to illustrate another fact. The more symmetrical the substitution, or the more symmetrical the ion, the swifter its movement. The second ion, although more complex than the first, is more symmetrical and has a greater velocity. Effect of Pressure on the Conductivity of Solutions. — The effect of pressure on the conductivity of solutions was studied by Fanjung. 1 The pressure was produced by means of a Cailletet pump. We should expect that whatever the effect of pressure on the amount of disso- ciation of the compound, it would increase the friction on the ions as they move through the electrolyte, and consequently diminish the conductivity. The fact is, the conductivity is increased by pressure. This is shown by the following example : — Atmospheres Pressure Molecular Conductivity Acetic Acid. Normal Solution 1 42 91 138 182 224 560 1.38 1.39 1.42 1.44 1.46 1.48 1.50 Since conductivity is conditioned both by the number of ions present and the velocity with which they move through the solution, an increase in conductivity may be due to either of two causes ; an increase in the amount of dissociation, or an increase in the velocity with which the ions move. To determine which of these influences was at work, Fanjung took solutions which were so dilute that they were completely dissociated, and studied the effect of pressure on their conductivity. In these cases the conductivity was increased by pressure. 1 Ztschr.phys. Chem. 14, 673 (1894). See Tammann: Ibid. 17, 725 (1895). Bogojawlensky and Tammann: Ibid. 27, 457 (1898). Wied. Ann. 69, 767 (1899). ELECTROCHEMISTRY 409 w-H It is obvious that in all such cases the effect of pressure is not to increase the dissociation, since it is complete at ordinary pressure. The increase in the conductivity must, therefore, be due to an in- crease in the velocity with which the ions move. By comparing the amount of increase in conductivity with press- ure in the case of completely dissociated solutions, with the increase iu the conduc- tivity with pressure when the dissociation is not complete, we seem to be justified in concluding that the effect of pressure in all cases is to increase the velocity of the ions and not their number. Conductivity at High Tem- peratures. — Measurements of the conductivity of aque- ous solutions of a number of substances, up to 100°, have been made by Schaller. 1 Kraus 2 has also measured a number of conductivities of potassium iodide in methyl and ethyl alcohol at elevated temperatures; but the most important work by far, in this field, is that of Noyes, Coolidge, 3 and their co- workers. In carrying out this work a new form of apparatus had to be devised, which would withstand high pressure and not contaminate dilute aqueous solutions even at the highest temperatures employed. The Apparatus. — The cell, or " bomb," which was finally devised by Noyes and Coolidge as the result of several years' work, is shown in cross-section in Pig. 58. It consists of a cylindrical steel vessel A, of about 125 cc. capacity, provided with a steel cover B, which i Ztschr. phys. Chem. 25, 497 (1898). "Phys. Rev. 18, 40, 89 (1904). » Ztschr. phys. Chem. 46, 323 (1903). Fig. 58. 410 THE ELEMENTS OF PHYSICAL CHEMISTRY is held in place by a large steel nut C. The bomb is lined internally with sheet platinum about 0.41 mm. thick. The cover is made tight by a small packing ring of pure gold wire, which fits into a shallow V-shaped groove. The wall of the bomb serves as one electrode. The second elec- trode is introduced through the bottom of the bomb, being insulated outside by mica layers M, and inside by a piece of quartz Q. The body of the electrode is of steel, the top of platinum coated with plati- num black. The piece of quartz is in the form of a cylindrical cup about 2 cm. in external diameter, and about 2.7 cm. in height. A sharp V-shaped ridge is turned on the bottom of the quartz, and this rests on a flat gold washer, inserted between the crystal and the bottom of the bomb. The nut N draws the electrode down, thus forcing the ridges of the crystal into the soft gold, and making the joints tight. In the cover there is a narrow cylindrical chamber, provided with an auxiliary electrode, T 2 , which is insulated in the same manner as the lower electrode. The object of this is twofold. It serves to show from the conductivity that the bomb is not completely filled with the liquid, and it furnishes a means of measuring the volume of the solution in the bomb. The bomb must never be filled with the solution at ordinary temperatures, since it will not withstand the liquid pressure at the higher temperature — only the vapor press- ure. The specific volume of the solution at the temperature in question must be determined in order to calculate the equivalent from the observed conductivity. The small platinum tube T' serves to exhaust the air from the bomb. Like the lower electrode, the auxiliary electrode is well platinized. The solution, then, comes in contact with nothing but platinum, gold, and quartz crystal, except where it touches the steel ball at the top of the tube 7". 1 A bath of xylene or pseudocumene was used for the lower tem- peratures : — Boiling brombenzene for 156°, Boiling naphthalene for 218°, Boiling isoamylbenzoate for 260°, Boiling bromnaphthalene for 281°, Boiling benzophenone for 306°. 1 The above description of the apparatus is taken from the paper by Noyes and Coolidge, Proc. Amer. Acad. Arts and Sciences, 39, 163 (1903), and from a private communication from Noyes to the author. ELECTROCHEMISTRY 411 •In the later work the bomb was rotated, thus thoroughly stirring the solution. Substances Used and Results Obtained. — The substances used by Noyes and his coworkers * are : Sodium, potassium, and ammonium chlorides ; barium and silver nitrates ; potassium and magnesium sulphates, and potassium acid sulphate ; sodium and ammonium acetates ; sodium, ammonium, and barium hydroxides'; and hydro- chloric, nitric, sulphuric, phosphoric, and acetic acids. With most of these substances, four or more concentrations, ranging between 0.1 n and 0.002 n have been employed. Conductivity meas- urements have been made up to a temperature of 306°. In order to show the effect of temperature on conductivity by increasing the velocity of the ions, Noyes has calculated the conductivities for completely dissociated solutions of the different substances at the various temperatures employed. Some of his results are given in the following table. In the first column are given the temperatures at which the work was done ; in the second, the equivalent conductivity at unlimited dilution Aq, and in the third, the temperature coefficient of conduc- tivity. Tempera- Sodium Chloride Potassium Chloride Barium Nitrate Potassium Sulphate ture K Temp. Coef. \> Temp. Coef. *o Temp. Coef. A„ Temp. Coef. 18° 100 156 109.0 362.0 555.0 3.09 3.44 3 31 130.1 414.0 625.0 3.36 3.77 3 23 116.9 385.0 600.0 3.27 3.84 3.87 132.8 455.0 715.0 3.93 4.64 5.64 218 281 760.0 970.0 3.33 4 40 825.0 1005.0 2.86 4 60 840.0 1120.0 4.44 7.20 1065.0 1460.0 6.27 10.6 306 1080.0 1120.0 1300.0 1725.0 Tempera- Sodium Hydroxide Barium Hydroxide Nitric Acid Hydrochloric Aoid ture Ao Temp. Coef. *o Temp. Coef. *o Temp. Coef. *o Temp. Coef. 18° 100 156 216.5 594.0 835.0 4.60 4.30 3.63 222.0 645.0 847.0 5.16 3.58 377 826 1047 6.61 3.95 2.95 376 850 1085 5.76 4.20 2.90 218 1060.0 — 1230 1265 1.81 281 — — — — 306 — — — 1424 1 Meloher, Cooper, and Eastman. 412 THE ELEMENTS OF PHYSICAL CHEMISTRY Discussion of Results. — The results show that the values of A . for the binary electrolytes become more nearly equal with rise in tempera- ture. This indicates that the specific migration velocities of the ions are becoming more nearly equal with rise in temperature, which is in accord with what is known at lower temperatures. The conductivity of ternary electrolytes increases steadily with rise in temperature, and attains values that are much greater than those reached by any binary electrolyte. This is in keeping with the generalization, that with rise in temperature the velocities of all ioDS subjected to the same driving force tend to become equal. If an ion is bivalent as in a ternary electrolyte, the driving force is greater, and the ion would move faster and show greater conductivity. The rate of increase in conductivity with rise in temperature, for binary electrolytes, is greater between 100° and 156°, than below or above these values. With ternary electrolytes the rate of increase in conductivity steadily increases with rising temperature. In the case of acids and bases the rate of increase steadily decreases with rising temperature. It should also be noted that the fluidity of water shows nearly the same increase with rise in temperature, as the conductivity manifested by binary salts, at least up to 156°. Effect of Rise in Temperature on Ionization. — That the effect of rise in temperature on dissociation may be clearly seen, the percent- age of dissociation of most of the substances investigated at the different temperatures is given for the dilutions 0.01 and 0.08 normal. It will be seen that the dissociation decreases regularly with rise in temperature. This holds for all of the substances except water up to about 270°, and slightly dissociated acids and bases up to about 40°. The rate of decrease in dissociation is nearly the same for all of the strongly dissociated compounds of the same type. If the disso- ciations are equal at ordinary temperatures, they would be very nearly equal at the more elevated temperatures. It will be seen from the table, that the rate of decrease in ioniza- tion with rise in temperature is small between 18° and 100°, for all of the salts studied. The rate becomes much larger at the higher tem- peratures, especially for the ternary salts. At the highest tempera- tures employed, the dissociation decreases very rapidly with rise in temperature. The decrease in the dissociation of hydrochloric and nitric acids, and sodium hydroxide, is about of the same order of magnitude as that shown by binary salts. Nitric acid decreases in dissociation, ELECTROCHEMISTRY Percentage of Dissociation' 413 Substance CONO. 18° 100° 156° 218° 281° 306° HC1 0.01 97.1 95.0 93.6 92.2 82 0.08 93.2 89.7 87.2 82.5 60 HNO s 0.01 96.8 95.2 93.4 — 0.08 92.6 89.9 85.3 75 — 33 NaOH 0.01 96.2 95.7 94.3 92.0 — — KC1 0.01 94.2 91.1 89.7 89.8 87 81 0.08 87.3 82.6 79.7 77.3 72 64 NaCl 0.01 93.6 92.7 92.1 90.2 84 80 0.08 85.7 83.2 81.2 77.7 69 63 AgNO s 0.01 93.3 91.8 88.8 86.3 82 77 0.08 83.3 80.2 75.8 70.8 64 57 -CHsCOONa 0.01 91.2 88.8 88.0 82.2 — 76 0.08 81.1 77.6 75.6 68.5 — — Ba(OH) 2 0.01 93 85 85 — — — 0.08 83. 69 65 — — — K 2 S0 4 0.01 87.2 80.3 75 63 47 37 0.08 73.2 64.8 58 45 31 23 Ba(NO s ) 2 0.01 86.7 83.6 80 74 59 47 0.08 70.1 66.9 62 53 38 — MgS0 4 0.01 66.7 52.4 35 13 — — 0.08 45.5 31.9 19 7 — — H s P0 4 0.01 60 42 29.4 — — — 0.08 31 19.5 12.5 — — — CHsCOOH 0.01 4.17 3.24 2.26 1.26 — — 0.08 1.50 1.17 0.82 0.46 — 0.14 NH 4 OH 0.01 4.05 3.59 2.46 1.36 — — 0.08 1.45 — — 0.47 — 0.11 between 156° and 306°, much more rapidly than other substances of the same type. Isohydric Solutions. — If we mix two solutions of electrolytes, the ■conductivity of the mixture is not, in general, the mean of the con- ductivities of the constituents, but is usually less. There are, how- ever, concentrations at which solutions of electrolytes can be mixed without affecting each other's conductivities. This fact was known, but no satisfactory explanation was offered until the problem was taken up by Arrhenius. 1 He worked with acids, and showed that when a solution of an acid is mixed with a solution of another acid of a certain concentration, the conductivity of the mixture is the jnean of the conductivities of the two solutions. Such solutions i Wied. Ann. 30, 51 (1887). 414 THE ELEMENTS OF PHYSICAL CHEMISTRY Arrhenius termed isohydric. They are defined by him 1 as fol- lows : — " Two solutions of acids are isohydric whose conductivity, or, in other words, whose electrolytic dissociation is not changed if they are mixed." The conditions which must be fulfilled in order that two solutions containing a common ion may be isohydric, have been worked out by Arrhenius, 2 assuming that each electrolyte is partly dissociated into ions : — Given two weak monobasic acids dissolved in water, they are par- tially dissociated. In the solution of the first acid : — Let c be the number of the cations. Let o be the number of the anions. Let m be the number of the undecomposed molecules of the acid. Let M be the number of molecules of water. Let C be the dissociation constant of the acid. In the solution of the second acid : — Let c' be the number of the cations. Let a' be the number of the anions. Let m' be the number of the undecomposed molecules of the acid. Let M ' be the number of molecules of water. Let C" be the dissociation constant of the second acid. Tor the first acid we would have — M In the solution of the second acid : — M' " If the solutions are isohydric, the dissociated part, and conse- quently the undissociated part, will undergo no change or mixing." 2 If the solutions are sufficiently dilute, the volume, after mixing, will be the sum of the two volumes before mixing, and the number of hydrogen ions will be the sum of the numbers before mixing = c + c'. 0m = (c + cX M + M> „, i (c + c'W Cm = - — ■ — ' — • M + M< From the above equations, M M 1 ' i Ztsehr. phys. Vhem. 2, 28 (1888). * Ibid. ELECTROCHEMISTRY 415 Arrhenius points out that solutions of two acids are isohydric if they contain in unit volume the same number of hydrogen ions. And, further, that two solutions are isohydric if they have certain definite concentrations, and, therefore, this is independent of the amount of either solution mixed with the other. Isohydric solutions can be mixed in any proportion without destroying their isohydric nature. The discovery of the nature of isohydric solutions is of consider- able importance in physical chemistry. It comes into play especially in connection with problems in chemical equilibrium, and the condi- tions which must be fulfilled in order that equilibrium may exist. The Condition of Double Salts in Solution. — One other applica- tion of the conductivity method to aqueous solutions must be considered before this section is closed. The question as to the condition of double salts in solution has been repeatedly the object of investigation. Do double salts like the alums, double halides, etc., break down in water into their constituent salts, and then these constituents undergo dissociation as if they were alone, or do the double salts dissociate as if they were salts of complex acids ? This difference can be made clear by the following example. Does the compound K 2 CdI 4 break down into 2 KI and Cdl 2 , and then these undergo electrolytic dissociation into their ions, or does it dissociate + + = at once into K + K + Cdl 4 ? This can be decided by the conductivity method. If they break down as first suggested, the conductivity of the double salt would be the sum of the conductivities of the constituents at the same con- centration, less, of course, the effect of each salt on the dissociation of the other due to the fact that the solutions are not isohydric. If they dissociate as salts of complex acids, the conductivity of the double salt would be much less than the sum of the conductivities of the constituents, since the number of ions in the solution would be much less. Among those who have applied the conductivity method to this problem are Grotrian, 1 Arrhenius, 2 Klein, 3 and Kis- tiakowsky. 4 Four investigations on this problem have been carried out recently in this laboratory by Mackay, 5 Ota, 6 Knight, 7 and Cald- well. 8 The general result obtained is that double salts break down 1 Wied. Ann. 18, 177 (1883). 6 Amer. Chem. Journ. 19, 83 (1897). 2 Ibid. 30, 51 (1887). • Ibid. 22, 5 (1899). 8 Ibid. 27, 151 (1886). 7 Ibid. 22, 110 (1899). * Ztschr.phys. Chem. 6, 97 (1890). 8 Ibid. 25, 349 (1901). See MacGregor : Phil. Mag. 41, 276 (1897) ; 33, 529 (1900). Ztschr. phys. Chem. 23, 374 (1897). MacGregor and Archibald : Phil. Mag. (5) 45, 151 416 THE ELEMENTS OF PHYSICAL CHEMISTRY in concentrated aqueous solution to some extent as if they were salts of complex acids. As the dilution increases the complex ions break down more and more, until at very great dilution they are completely dissociated into the simplest possible ions, just like their constituents. The effect due to the solutions not being isohydric is determined by studying mixtures of salts which cannot combine and form double salts. The Conductivity of Fused Electrolytes. — We have seen that aqueous solutions of acids, bases, and salts conduct the current to a greater or less extent, and are, therefore, electrolytes. The question remains whether the substances would conduct under any conditions in the pure state, if there was no water present. If they do not conduct in the solid state, would they conduct when fused? This has been repeatedly investigated. The work of Poincare : and Bouty 2 on this problem is very important. They devised a special method and applied it to a large number of fused salts. They determined the specific conductivities and also calculated the molecular conductivities in a number of cases, knowing the specific and molecular volumes of the fused salts. A few results are given, the molecular conductivities being expressed in re- ciprocal ohms, to show the order of magnitude of the conductivity of fused salts. Temp. j-.- Barmwater :•' JMd. 45, 557 (1903); 56, 225 (1906). Bouty: Compt. rend. 103, 31 (1886); 104, 1699 (1887). 1 Ann. Chirn. Phys. [6], 17, 52 (1889). * Ibid. 6, 21, 289 (1890). 8 Wied. Ann. 40, 18 (1890). ELECTROCHEMISTRY 417 showed very marked conductivity. "With certain salts this increased regularly up to and through the melting-point. With others the in- crease is very rapid near and at the melting-point. General Relations in Connection with the Conductivity of Fused Electrolytes. — The most important relation thus far established in this field is that Faraday's law holds for fused electrolytes as it does for solutions of these substances. In this connection Faraday's own papers 1 should be consulted. Faraday regarded water as play- ing no essential part in electrolysis, and naturally drew the conclu- sion that his law also held for fused electrolytes. He, however, verified this conclusion experimentally. Among the most important of the recent investigations bearing upon this problem are those of Lorenz z and his coworkers. If we take into account all of the " disturbing influences " that come into play in the electrolysis of fused electrolytes, the law of Faraday so nearly obtains, that we seem justified in concluding that this gener- alization holds for fused electrolytes, probably as well as for solu- tions of electrolytes. In this same connection we should mention the important work of Eichards 3 and his students. This work confirms the validity of Faraday's law as applied to fused electro- lytes. - ' If Faraday's law holds for fused electrolytes, we should expect to find a movement of the ions in electrolysis somewhat analogous to that observed in the case of solutions of electrolytes. Considerable work has already been done on this problem by Lehmann 4 in connec- tion with fused silver iodides. He showed that there is a move- ment of the ions, and especially of the silver ion. Warburg 5 has shown that in heated glass and quartz, at least the cations move during electrolysis. Lorenz and Fausti 6 studied the migration velocities of ions in the electrolysis of certain pairs of fused salts (KC1 and PbCl 2 ) and ob- tained results similar to those found earlier by Hittorf, in connec- tion with the electrolysis of solutions of potassium silver cyanide. These results all demonstrate the existence of ionic movement in the electrolysis of fused electrolytes. 1 Phil. Trans. 1834. * Ztschr. anorg. Oiem. 23,255 (1900); 28, 1 (1901); 36, 36 (1903); 39, 389 (1904). s Ztschr. phys. Ohem. 32, 321 (1900); 41, 302 (1902); 42, 621 (1903). * Wied. Ann. 24, 1 (1885); 38, 396 (1889). 5 Ibid. 21, 622 (1884); 35, 455 (1888); 41, 18 (1890). 6 Ztschr. Elektrochem. 10, 630 (1904). 2e 418 THE ELEMENTS OF PHYSICAL CHEMISTRY In connection with the conductivity of fused salts the following investigations should especially be consulted : 1 — The more recent investigations in connection with the conduc- tivity of glass, quartz, and porcelain, are the following : 2 — In connection with the whole subject under discussion see the admirable monograph by Lorenz on "Die Elektrolyse geschmolzener Salze." The Dissociation of Fused Salts. — It is well known that fused electrolytes often show high conductivity. Is this due to their high dissociation, or to the great velocity with which the ions move at the high temperature ? This problem is not a simple one, on account of the difficulties involved in determining the velocities of the ions at the high tempera- tures. The first attempts in this direction were made by Lorenz, 3 while Gordon 4 resorted to the measurement of the electromotive force of certain types of concentration elements, in which the solvent was a mixture of fused potassium nitrate and sodium nitrate, and the dissolved substance silver nitrate — the latter being used at different concentrations. He concluded from his measurements that the dis- sociation of a 50 per cent solution of silver nitrate in the fused solvent is 69 per cent ; while pure fused silver nitrate is about 58 per cent dissociated. Similar measurements have been made by J Davy: Journ. Boy al Institution, 1801, p. 53. Faraday: Phil. Trans. 1833, 507. Quincke: Fogg. Ann. 138, 141 (1869). Braun : Ibid. 154, 161 (1875). Foussereau : Ann. Chim. Phys. [6], 5, 241, 317 (1885). Lorenz and Schultze : Ztschr. anorg. Chem. 20, 333 (1899). Lorenz: Ibid. 23, 97 (1900). Lorenz: Ztsehr. Elektrochem. 25, 436 (1900). Auerbach : Ztschr. anorg. Chem. 28, 1 (1901). 2 Warburg : Wied. Ann. 21, 622 (1884). Foussereau : Ann. Chim. Phys. [6], 5, 375 (1885). Barus : Amer. Journ. Sci. 37, 339 (1889). Warburg and Teget- meier: Wied. Ann. 32, 442 (1887); 35, 455 (1888). Tegetmeier : Ibid. 41, 18 (1890). LeChatelier: Compt. rend. 108, 1046 (1889); 109, 264 (1890); 110, 399 (1890). "Conductivity of Hot Vapors." See Arrhenius : Wied. Ann. 42, 18 (1891). Pringsheiin : Ibid. 55, 507 (1895). McClelland : Phil. Mag. (5) 46, 29 (1898). Wesendonc : Wied. Ann. 66, 121 (1898). " Conductivity of Pressed Powder." See Streintz : Ann. d. Phys. (4) 3, 1 (1900) ; 9, 854 (1902). " Heat Conductivity of Glasses." See Winckelmann : Wied. Ann. 67, 132, 160 (1899). s Ztschr. Elektrochem. 10, 630 (1904). Ber. 40, 3308 (1907) * Ztschr. phys. Chem. 28, 302 (1896). ELECTROCHEMISTRY 419 Lorenz, 1 Suchy, 2 and others. The results showed a high dissociation for the fused salts. Another method, based upon the voltage required to discharge an ion, was employed by Abegg, 3 and this would indicate much smaller dissociation of the fused salt. Goodwin and Wentworth 4 have taken up this same problem, using the principle of the concentration element. They worked with fused silver nitrate in fused sodium nitrate, and with fused silver chlorate in fused silver nitrate. In all such work the problem is complicated by the fact that the fused solvent is itself dissociated to a greater or less extent. They conclude that their results show that the same laws seem to hold for fused salts dissolved in fused solvents with a high melting-point, as obtain in water, which has a comparatively low melting-point. Just as fused solvents are themselves considerably dissociated, so, also, water at high temperatures is considerably dissociated, as we have just seen from the work of Noyes. Goodwin and Wentworth do not think that their results justify them in making any final statement as to the magnitude of the dis- sociation of fused solvents or fused dissolved substances. W. Kohlrausch 5 showed that the halogen salts of silver have a marked conductivity long before the melting-point is reached. The chloride and bromide show regular conductivity up to and through the melting-point, but the conductivity increases rapidly with rise in temperature after the salt has fused. Silver iodide behaves ab- normally ; its conductivity increases slowly with increasing tempera- ture above the melting-point, but for a long distance below the melting-point the conductivity decreases very slowly. The con- ductivity does not decrease rapidly until a temperature as low as 160° is reached. DISSOCIATING ACTION OF WATER AND OTHER SOLVENTS Modes of Ion Formation. — From what has been said thus far, the impression might be gained that ions can be formed from mole- cules in only one way — the molecules breaking down directly into an equivalent number of anions and cations. This is one way in i Lorenz: Ztschr. anorg. Chem. 19, 283 (1899); Ibid. 22, 241 (1900). 2 Ibid. 27, 152 (1901). Weber : Ibid. 21, 305 (1899). 8 Ztschr. fflektrochem. 5, 353 (1899). i Phys. Bev. 24, 77 (1907). 6 Wied. Ann. 17, 642 (1882). "Electrical Conductivity of Hot Salt Vapors." See Smithells, Dawson, and Wilson : Ztschr. phys. Chem. 32, 302 (1900). 420 THE ELEMENTS OF PHYSICAL CHEMISTRY which ions are formed, and the way with which we are most familiar, since it occurs most frequently. The following examples illustrate this mode of ion formation : — 1. HC1 = H +01, H 2 S0 4 = H +H + SO* NaOH = Na + 0~H, Ba(OH) 2 = Ba + 0~H + OH, KN0 3 = K +N0 3 , K 2 S0 4 = K +K + S0 4 . Another method by which an ion can be formed, is for an atom to take the charge from an ion, converting it into an atom — the original atom becoming an ion. Thus, when a bar of zinc is dipped into a solution of copper salt, the copper which was present in the solution as an ion gives up its two charges to an atom of zinc, becoming an atom; while the zinc, having received the charges, becomes an ion. This is the well-known precipitation of copper from a solution, by zinc. We will call this the second mode of ion formation. 2 Cu + S0 4 + Zn = Zn + S0 4 + Cu. All that occurs is a transference of electricity from the copper to the zinc. This is exactly analogous to what takes place whenever one metal replaces another, as it is said, from its salts. The replacement of the hydrogen ion from acids by a metal like zinc is an illustration of the same mode of ion formation. H, CI + H, CI + Zn = Zn + 01 + 01 + H 2 . What takes place here is simply the transference of the electrical charge from the hydrogen which does not hold its charge firmly, to the zinc which holds its charge much more firmly than the hydrogen, and, therefore, takes the charge from the hydrogen. This is typical of the reaction of acids on metals in general ; and is probably typical of substitution in general. The work of Thomson (page 351) makes it highly probable that when substitution takes place in organic compounds, the entering atom or group takes the charge away from the atom or group displaced. The substituting atom or group always has the same charge that the substituted atom or group had when in the compound. The entire act of substitution is essentially an electrical act, and not a chemical act, as that term is usually understood. This is true whether we are dealing with the substitution of the hydrogen ions of an acid by a metal, or with substitution in organic compounds. Another method of ion formation is where an atom of one sub- ELECTROCHEMISTRY 421 stance passes over into a cation, at the same time that an atom of another substance passes over into an anion. When gold is dipped into chlorine water, both the gold and chlorine are in the atomic or molecular condition. But under these conditions the gold can be- come a cation, and the chlorine can form anions. This we will term the third method of ion formation. Au + CI + CI + CI = Au + + CI + CI + CI. This is usually expressed by saying that gold dissolves in chlorine water. The fourth and last method by which ions are formed is where an atom passes over into an ion, at the same time converting an ion already present into one with a different quantity of electricity upon it. Thus, chlorine brought in contact with ferrous chloride in solu- tion forms an anion, at the same time converting the ferrous ion into a ferric ion. 4. Fe + Cl + Cl + Cl = Fe + Cl+Cl+Cl. This is an example of what has so frequently been called in chem- istry, oxidation. The reverse phenomenon is, of course, what has been termed reduction. In this sense oxidation is simply increasing the number of charges carried by an ion, and reduction is diminish- ing the number of such charges. These four methods of ion formation, which have been so clearly pointed out by Ostwald, 1 include all the cases which are known. If we study them carefully and apply them to chemical reactions, we shall see that they throw much light on many problems in chemistry, the meaning of which has hitherto been concealed in darkness. The Dissociating Power of Different Solvents. — Frequent refer- ence has been made to the power of water to dissociate molecules into ions. From this the conclusion might be drawn that water is the only solvent which has this power. Such is not at all the case. Practically all liquids have the power of dissociating strong acids and bases, and salts when dissolved in them. But they possess this property to a very different degree. We should be familiar with the relative dissociating power of some of the more common solvents. The same methods are available, at least theoretically, for measuring dissociation in non-aqueous solvents, as have been em- ployed with water. These are, as will be remembered, the freezing- 1 See Lehrb. d. Allg. Chem. II, 786. 422 THE ELEMENTS OF PHYSICAL CHEMISTRY point, boiling-point, and conductivity methods. The freezing-point method, however, can be applied to only a few solvents, since the freezing-points of most liquids are either too high or too low to come within the range of this method. The boiling-point method for a long time was not applied to the problem of electrolytic dissociation, because it was not regarded as sufficiently accurate to give results which would have much value. This method has recently been im- proved l and applied to the determination of dissociation in some df the alcohols, with a fair degree of success. The conductivity method has been used extensively to determine the dissociating power of a large number of solvents, but even with this method a serious difficulty is encountered. In order to measure dissociation by the conductivity method, it is not only necessary to know the molecular conductivity of the solution in question, but the molecular conductivity at complete dissociation. As will be remem- bered, a = — . To determine «, it is necessary to know both /*„ and ju,^. The great difficulty in applying the conductivity method to measure dissociation in a solvent with small dissociating power, lies in obtaining the value of ft,^. Unless the solvent has very great dissociating power, the dilution at which the dissolved substance is completely dissociated is so great that the conductivity method can- not be applied to it. To determine the value of ^ in such solvents it is necessary to make some assumption which often has not been proved, and, consequently, the results obtained may be inaccurate to the extent of several per cent. Yet, on the whole, the conductivity method is the best at our disposal for determining approximately the dissociating power of a large number of solvents ; and the results obtained by means of it are probably, in most cases, a fair approxi- mation to the truth. The dissociating power of a few of the more common inorganic and organic solvents will be considered. Inorganic Solvents. — Schlundt 2 has measured the dielectric con- stant of liquid hydrocyanic acid, and found the very large value of 95 at 21° — that of water being about 80 at the same temperature. Centnerszwer 8 showed that liquid hydrocyanic acid has greater dis- sociating power than any other known solvent. The dissociating power of water has been measured by a variety of methods, including the conductivity method of Kohlrausch, 4 the i Jones : Ztschr.phys. Chem. (Jutoelband zu Van't Hoff), 31, 114 (1899). 2 Journ. Phys. Chem. 5, 157 (1901). 8 Ztschr.phys. Chem. 39, 217 (1902). 4 Wied. Ann. 26, 160 (1885). ELECTROCHEMISTRY 423 freezing-point method of Raoult, 1 Jones, 2 Loomis, 3 Abegg and Nernst, 4 and others ; and the solubility method of Nernst 5 and Noyes. 6 The result is to show that water is the strongest dissociant of all of the common solvents — a' strong acid or base, and a binary salt of a strong acid and base, being nearly completely dissociated at a dilu- tion of a thousand litres. The corresponding ternary electrolytes are not completely dissociated until a dilution of about five thousand litres is reached. Nitric acid has been shown by the work of Bouty 7 to be a very strongly dissociating solvent. He studied the conductivity of cer- tain alkaline nitrates in nitric acid with the above result. Several years ago Cady 8 noticed that solutions of salts in liquid ammonia are good conductors. Goodwin and Thomson 9 made some measurements of the conductivity of solutions in liquid ammonia ; but by far the most elaborate work in this field is that of Franklin and Kraus. 10 They measured the conductivity of a large number of inorganic and organic compounds in liquid ammonia, and found greater conductivities than in water. They also call attention to the fact that " as found by Cady ammonia solutions of the alkali metals conduct electricity without polarization at the electrodes, and that the conductivity changes but slightly, if at all, with the concen- tration." The large conductivity of electrolytes in liquid ammonia was shown by Franklin and Cady xl to be due, not to the very great dis- sociating power of this solvent, but to the high velocity with which the ions travel through it — the velocity of a number of univalent ions in this solvent at — 33°, being from 2.4 to 2.8 times as great as they are in aqueous solution at 18°. This accounts for the very high conductivity in liquid ammonia, notwithstanding the fact that it has much less dissociating power than water. 1 Ztschr. phys. Chem. 27, 617 (1898) ; Ann. Chim. Phys. (7) 16, 162 (1899). 2 Ztschr. phys. Chem. 11, 110, 529 (1893) ; 12, 623 (1893). 8 Wied. Ann. 51, 500 (1894) ; 57, 495, 591 (1896) ; 60, 523 (1897). * Ztschr. phys. Chem. 15, 681 (1894). 6 Ibid. 4, 372 (1889). « Ibid. 6, 241 (1891) ; 9, 603 (1892) ; 12, 162 (1893) ; 16, 125 (1895). 7 Compt. rend. 106, 595 (1888). 8 Journ. Phys. Chem. 1, 707 (1897). 9 Phys. Mev. 8, 38 (1899). w Amer. Chem. Journ. 20, 820, 838 (1898) ; 21, 8 (1899) ; 23, 277 (1900) ; 24, 83 (1900). 11 Journ. Amer. Chem. Soc. 26, 499 (1904). " Specific Heat of Liquid Ammonia." See Ludeking and Kraus : Amer. Journ. Sci. 45, 200 (1893). 424 THE ELEMENTS OF PHYSICAL CHEMISTRY Lewis 1 has recently done some interesting work in liquid iodine as the solvent, obtaining results that are quite different from those found by Platnikow 2 in liquid bromine. The electrodes were made of platinum-iridium foil, containing fifteen per cent of iridium. The concentrations were expressed in terms of so many grams of potassium iodide in one hundred grams of iodine. The conductivity at first increases very rapidly with the concentration, until a concen- tration of about five grams of the salt in one hundred grams of iodine is reached; and then the conductivity decreases with fair regularity, with further increase in the concentration. The best of the recent work on the conductivity of electrolytes in non-aqueous solvents is that of Walden. 3 He has shown that sul- phur dioxide has very marked dissociating power. He worked with a number of halogen salts in this solvent, and compared the values of their conductivities with those of the same salts in water at 0°. In liquid sulphur dioxide the salts have from one-fourth to one-half the conductivities in water, under the same conditions of concen- tration. Walden determined the molecular weights of a number of salts in liquid sulphur dioxide, using the boiling-point method. In a number of cases he obtained abnormally large molecular weights, showing that the undissociated molecules were polymerized in this solvent, Walden 3 has also shown that the following solvents have consid- erable power to break molecules down into ions : Sulphur dichloride, sulphuryl chloride, thionyl chloride, phosphorus oxychloride, arsenic trichloride, and antimony trichloride. Walden found that the following solvents have little or no ion- izing power : Boron trichloride, phosphorus trichloride, phosphorus tribromide, antimony pentachloride, silicon tetrachloride, stannic chloride, sulphur trioxide, and bromine. We see that phosphorus trichloride cannot dissociate electrolytes, while phosphorus oxychloride has marked dissociating power. Anti- mony pentachloride has very little dissociating power, while the trichloride has considerable power to break molecules down into ions. Walden 4 extended his investigation also to the following inor- ganic solvents : Arsenic tribromide, dimethyl sulphate, chlorsulphuric 1 Ztschr. phys. Chem. 56, 179 (1906). 2 Ibid. 48, 220 (1904). 3 Ztschr. anorg. Chem. 25, 209 (1900). * Ztschr. anorg. Chem. 29, 371 (1902). ELECTROCHEMISTRY 425 acid, and sulphuric acid. The tribromide of arsenic has an appreci- able power to dissociate molecules, but less than arsenic trichloride. The other three solvents mentioned above also have considerable ionizing power. Indeed, all the derivatives of sulphuric acid, as we have seen, have considerable power to effect dissociation. Walden and Centnerszwer 1 continued their earlier work with liquid sulphur dioxide as solvent, but it would lead us too far to discuss in detail the results of this elaborate investigation. The same authors 2 showed that sulphur dioxide combines with potassium iodide forming a number of compounds. Centnerszwer 3 has carried out an elaborate investigation in liquid hydrocyanic acid, and in liquid cyanogen. While cyanogen has only slight dissociating power, liquid hydrocyanic acid has greater dis- sociating power than even water itself. This is in perfect accord with the Thomson-Nernst hypothesis, which states that the disso- ciating power of solvents is a function of their dielectric constants. Hydrocyanic acid has a higher dielectric constant than water. Walden 4 has recently published an interesting article under the heading " abnormal electrolytes.'' He found that in certain solvents, especially liquid sulphur dioxide, sulphuryl chloride, and arsenic trichloride, certain substances which are neither acids, bases, nor salts show considerable conductivity. Among these substances are the halogens, phosphorus, arsenic, antimony, tin, sulphur, a number of nitrogen bases such as quinoline, pyridine, and the like. These substances are obviously not electrolytes as that term is ordinarily employed. They have been termed by Walden " abnormal electro- lytes " ; and he has attempted to ascertain the exact nature of the cations and anions formed by them. Some of the results which he reaches are, to say the least, surprising. For details reference must be had to the original paper. • Oddo 5 has also shown that phosphorus oxychloride strongly ionizes electrolytes. Tolloczko, 6 as well as Garelli and Bassoni, 7 worked with the halides of arsenic and antimony, showing them to have ionizing power. Centnerszwer 8 is authority for placing cyan- ogen among the solvents that have little or no dissociating power. Franklin and Farmer 9 have also shown that nitrogen peroxide does 1 Ibid. 30, 145 (1902) ; Ztschr. phys. Chem. 39, 513 (1902). 2 Ztschr. phys. Chem. 42, 432 (1903). s Ztschr. phys. Chem. 39, 217 (1902). 4 Ibid. 43, 385 (1903). 6 Atti. B. Accad. dei Lincei, Roma (5) 10, 452. 6 Ztschr. phys. Chem. 30, 705 (1899). 7 Atti. E. Accad. dei Lincei, Roma (5) 10, 255. s Journ. Chem. Soc. 79, 1356 (1901). 9 Arner. Chem. Journ. 26, 383 (1901). 426 THE ELEMENTS OP PHYSICAL CHEMISTRY not dissociate, while Skilling 1 has found that solutions in hydrogen sulphide show no conductivity. An interesting investigation in nonaqueous solvents is that by Archibald and Mcintosh. They worked with solutions of certain organic compounds in such solvents as hydrochloric, hydrobromic, and hyriodic acids, hydrogen sulphide, etc. They found that the molecular conductivities of the dissolved substances increased with the concentrations of the solutions. The following table of inorganic solvents is given to show what relations exist between dissociating power, dielectric constants, and -the association factor : — Inorganic Solvents which effect Dissociation a „,„„ DlBLECTRIO ASSOCIATION SoLTENT Constant Faotoe Hydrocyanic acid 95 ? "Water 81.12 3.7 Ammonia 16.2 1.0 Sulphur dioxide 13.75 1.0 Nitric acid ? 1.7-1.9 Arsenic trichloride 12.35 1 Arsenic tribromide ? ? Phosphorus oxychloride 13.9 1.00 Antimony trichloride 33.2- 1 Thionyl chloride 9.05 1.08 Sulphuryl chloride 9.15 0.97 Dimethyl sulphate ? ? Chlorsulphuric acid ? ? Sulphur^ acid ? 32.0 Sulphur monochloride 4.8 0.95-1.05 Inorganic Solvents which do not dissociate Electrolytes Bromine 3.18 1.2-1.3 Cyanogen 2.52 ? Sulphur trioxide 3.56 Boron trichloride , ? ? Phosphorus trichloride 3.36 1.02 Phosphorus tribromide ? 1 Antimony pentachloride 3.78 ? Silicon tetrachloride ? 1.06 Tin tetrachloride 3.2 ? Hydrogen sulphide ? ? Nitrogen peroxide ? ? The values for the association factors are taken from the re- searches of Eamsay and Shields, 2 and Ramsay and Aston, 8 while i Proc. Boy. Soc. 78, 454 (1904). 2 Ztsckr. phys. Chem. 12, 433 (1893). 8 Journ. Chem. Soc. 65, 167 (1894). ELECTROCHEMISTRY 427 those for the dielectric constants are almost wholly taken from the work of Turner. 1 Organic Solvents. — A large amount of work has already been done on solutions in organic solvents. Kablukoff 2 showed that the conductivity of hydrochloric acid in the hydrocarbons, benzene, xylene, and hexane, is very small, and this is true of the hydro- carbons in general. Fitzpatrick 3 studied the conductivity of a number of salts in methyl alcohol, and found that, although it was less than in water, still it was very considerable. Paschow, 4 Vollmer, 6 and Holland 6 also did considerable work in methyl alcohol as the solvent. A very extensive investigation in methyl alcohol was made by Carrara. 7 He measured the conductivities of a fairly large number of salts in this solvent. Schall 8 determined the conductivity of a number of acids in methyl alcohol ; but the most satisfactory work in this solvent is that of Zelinsky and Krapiwin. 9 They worked with a large number of salts in the pure solvent, and in mixtures of this solvent with water. Jones 10 has attempted to measure the dissociation of salts in methyl alcohol by means of his boiling-point apparatus, and obtained values that are about two-thirds of those found in water under the same conditions. Considerable work has been done in ethyl alcohol as the solvent. We should mention in particular that of Fitzpatrick, 11 Hartwig, 12 Yollmer, 13 Kawalki, 14 and Schall. 15 Kablukoff 16 measured the con- ductivity of hydrochloric acid in ethyl alcohol. Jones 17 applied his boiling-point method to ethyl alcohol, as he had done to methyl alcohol. The dissociating power of ethyl alcohol is about half that of methyl. Comparatively little work has been done in the higher alcohols. Schlamp u has shown that the conductivity of a number of salts in propyl alcohol is less than one-half that in ethyl alcohol. Carrara 19 i Journ. Phys. Chem. 5, 603 (1897). 10 Ibid. 31, 114 (1899). 2 Ztschr.phys. Chem. 4, 429 (1889). u Phil. Mag. 24, 378 (1887). » Phil. Mag. 24, 378 (1887). " Wied. Ann. 33, 58 (1888) ; 43, 838 (1891). * Charcow (1892). ls Ibid. 52, 328 (1894). s Wied. Ann. 52, 328 (1894). « Ibid. 52, 324 (1894). 6 Ibid. 50, 263 (1893). 15 Ztschr. phys. Chem. 14, 701 (1894). i Gazz. chim. ital. 26, (I) 119 (1896). 16 Ibid. 4, 429 (1889). » Ztschr. phys. Chem. 21, 35 (1896). « Ibid. 31, 133 (1899). 9 Ztschr.phys. Chem. 21, 35 (1896). 18 Ztschr. phys. Chem. 14, 272 (1894). w Gazz. chim. ital. 27, 1, 221 (1897). 428 THE ELEMENTS OF PHYSICAL CHEMISTRY made a few measurements in propyl, isopropyl, and amyl alcohols. Schall 1 measured the conductivity of picric acid in isobutyl alcohol ; but special mention should be made of the work of Kablukoff 2 in isobutyl and isoamyl alcohols. He found that the molecular conduc- tivity of hydrochloric acid in isoamyl alcohol decreases with increase in the dilution of the solution. The more complex the alcohol, the less its dissociating power. Practically the only work in ether as the solvent is that of Cat- taneo 3 and Kablukoff. 4 It was found that solutions in ether have a negative temperature coefficient of conductivity, and that the molecular conductivity of hydrochloric acid in ether decreases with increase in the dilution. Ether has very small dissociating power. Considerable work has already been done in the ketones as sol- vents. St. v. Laszczynski s studied the conductivity of a number of salts in acetone, and similar measurements were made by Carrara. 6 Dutoit and Aston 7 and Dutoit and Friderich 8 have worked with a number of solutions in acetone and other ketones. Acetone has slightly less dissociating power than ethyl alcohol. The dissociating power of certain organic acids is very great. Formic acid as a solvent has been studied by Zanninovich-Tessarin, 9 using both the freezing-point and conductivity methods. He found that formic acid is a very strongly dissociating solvent, standing next to hydrocyanic acid and water in the order of dissociating power. The same experimenter worked with acetic acid as a solvent, and found that it had much less dissociating power than formic acid. Jones 10 measured the conductivity of sulphuric acid in acetic acid, and found that after a certain dilution was reached the molecular con- ductivity decreased with further increase in the dilution. Dutoit and Aston 11 determined the conductivity of a number of salts in propionitrile, and Dutoit and Friderich 12 extended the inves- tigation to acetonitrile and butyronitrile. The simpler nitriles have high dissociating power, but not nearly so great as water or hydrocyanic acid. The more complex nitriles have less dissociating power. This is a general rule with dissociating organic solvents; the 1 Ztschr. phys. Chem. 14, 707 (1894). * Compt. rend. 125, 240.(1897). 2 Ibid. 4, 432 (1889). 8 Bull. Soc. Chim. (3) 19, 321 (1898). 8 Bend. B. Accad. dei Lincei (5) 2, 295. * Ztschr. phys. Chem. 4, 431 (1889). 9 Ztschr. phys. Chem. 19, 251 (1896). 6 Ztschr. Mektrochem. 2, 55 (1895). 10 Amer. Chem. Journ. 16, 13 (1894). 6 Gazz. chim. ital. 27, I, 207 (1897). n Compt. rend. 125, 240 (1897). i 2 Bull. Soc. Chim. (3) 19, 321 (1898). ELECTROCHEMISTRY 429 lower members in an homologous series have greater dissociating power than the higher — dissociating power decreasing as the complexity of the molecule increases. Werner 1 studied the conductivity of certain inorganic salts in pyridine and found considerable conductivity. It is, however, to St. v. Laszczynski and St. v. Gorski 2 that we owe most of our knowl- edge of the dissociating power of pyridine. For the determination of molecular weights in pyridine we must consult the work of Wal- den and Centnerszwer. 3 Other Organic Solvents. — So few measurements have been made in other organic solvents that they can be passed over with brief reference. Thus, Werner 4 found that cuprous chloride in ethyl sulphide conducts very poorly. Cattaneo s studied a few solutions in glycerol, and found that they had a larger con- ductivity than the corresponding solutions in ether. They also had larger temperature coefficients of conductivity. Dutoit and Aston 6 measured the conductivities of electrolytes in benzene chloride, ethyl bromide, and amyl acetate, and found that these solutions conduct very poorly. They found, on the other hand, that solutions in nitroethane conduct very well. Dutoit and Friderich 7 worked with acetophenone as a solvent, and with cadmium iodide, mercuric chloride, and ammonium sulphocyan- ates as electrolytes. The conductivity in this solvent was very small. Having carried out an investigation with inorganic solvents, Walden 8 turned his attention to organic solvents. He studied typical compounds belonging to the following general classes: Alcohols, aldehydes, acids, acid anhydrides, acid chlorides and bromides, esters, acid amides, nitriles, sulphocyanates, mustard oils, nitro-compounds, nitrosodimethylene, ethylaldoxime, and ketones. He determined the dissociating powers of these substances and their dielectric constants, and established a number of relations of interest and importance. Walden 9 has recently continued this work, including in the list 1 Ztschr. anorg. Chem. 15, I, 39 (1897). 2 Ztschr. EleUrochem. 4, 290 (1897). 3 Ztschr. phys. Chem. 55, 321 (1906). * Ztschr. anorg. Chem. 15, 1, 139 (1897). 5 Beibl. Wied. Ann. 17, 365 (1893). 6 Compt. rend. 125, 240 (1897). ' Bull. Soc. Chin. (3) 19, 325 (1898). 8 Ztschr. phys. Chem. 46, 103 (1903). • Ztschr. phys. Chem. 54, 129 (1906) ; 55, 207, 281, 682 (1906) ; 58, 479 (1907) ; 59, 192, 385 (1907); 60, 87 (1907). 430 THE ELEMENTS OF PHYSICAL CHEMISTRY of substances with which he worked, epichlorhydrine. A large number of empirical relations were established. These investigations of Walden and his coworkers have probably thrown more light on the dissociating power of organic and inor- ganic solvents in general, than all the other investigations that have ever been carried out on this problem. Apparently Abnormal Results obtained in Non-aqueous Solvents. — While the conductivities in non-aqueous solvents follow the same rules, in general, which obtain for aqueous solutions, yet exceptions are not wanting. Thus, it is a general rule in aqueous solutions that the molecular conductivity increases with the dilution of the solution up to a certain point, where it becomes constant. There are several exceptions to this general relation, already discovered in non-aqueous solvents. Kablukoff 1 has shown that the molecular conductivity of hydrochloric acid in ether decreases with increase in the dilution of the solution, and hydrochloric acid dissolved in isoamyl alcohol showed the same phenomenon. On the other hand, hydrochloric acid dissolved in isobutyl alcohol gave perfectly normal results. Jones 2 found results similar to those obtained by Ka- blukoff with sulphuric acid in acetic acid. The molecular conduc- tivity of the sulphuric acid decreased with increase in the dilution of the solution. The meaning of these results is at present entirely unknown. Abnormal results of an entirely different character were obtained in certain mixed solvents. When Zelinsky and Krapiwin 3 were measuring the conductivities of salts in methyl alcohol, it occurred to them to measure their conductivities also in mixtures of methyl alcohol and water. The conductivities in water are considerably higher than in methyl alcohol under the same conditions of temper- ature and concentration, so that we should expect the conductivities in a mixture of the two solvents to be higher than in pure methyl alcohol. Exactly the opposite was found. The conductivity in a mixture of 50 per cent alcohol and 50 per cent water was less than in pure methyl alcohol, as will be seen from the following results for potassium bromide, v is the volume or number of litres containing a gram-molecular weight of the electrolyte. The molecular con- ductivities (/*„) in pure water, in pure methyl alcohol, and in 50 per cent water and 50 per cent alcohol are given in the three columns : — 1 Ztschr. phys. Ohem. 4, 429 (1889). 2 Ibid. 13, 419 (1894). Amer. Chem. Journ. 16, 1 (1894). 8 Ztschr. phys. Ohem. 21, 35 (1896). Ibid. 39, 515 (1902). ELECTROCHEMISTRY Potassium Bromide 431 « Wateb Methyl Aloohol One-Half "Water and One-Half Methyl Aloohol V 16 123.1 »*« 59.82 32 127.5 69.02 62.46 64 130.5 76.70 65.36 128 132.9 83.60 67.11 256 136.4 88.96 69.26 512 140.2 93.26 70.53 1024 143.4 97.25 The presence of the water in the methyl alcohol decreases very con- siderably the conductivity of the dissolved salt. 1 For a further dis- cussion of the work already done in mixed solvents, see Carnegie Institution Publication Memoir 80, by H. C. Jones and his coworkers. Conductivity in Mixed Solvents and the Viscosity of the Mix- tures. — Jones and his students — Lindsay, 2 Carroll, 3 Bassett, 4 Bing- ham, 5 McMaster, 6 Rouiller, 7 and Veazey 8 — have made a somewhat extended study of the conductivity of certain salts in mixtures of water, methyl alcohol, ethyl alcohol, and acetone, each with the other, and have also determined the viscosity of a number of such mixtures. Lindsay found that solutions of potassium iodide, strontium iodide, lithium nitrate, ferric chloride and the like, in mixtures of methyl or ethyl alcohol with water, showed a minimum in the con- ductivity for a certain mixture of the two solvents. The conductivity was less in the mixture than in either solvent separately, and passed through a well-defined minimum. (See Fig. 59.) He attempted to explain this minimum as due to the effect of one associated solvent on the association of another associated solvent. Jones and Murray 9 i Cohen : Ztschr. phys. Chem. 25, 1 (1898). 2 Amer. Chem. Journ. 28, 329 (1902); Ztschr. phys. Chem. 56, 129 (1906). 3 Amer. Chem. Journ. 32, 521 (1904); Ztschr. phys. Chem. 56, 150 (1906). 4 Amer. Chem. Journ. 32, 409 (1904). 6 Ibid. 34, 481 (1905); Ztschr. phys. Chem. 57, 193 (1906). 6 Amer. Chem. Journ. 36, 325 (1906) ; Ztschr. phys. Chem. 57, 257 (1906). 1 Amer. Chem. Journ. 36, 427 (1906). 8 Ztschr. phys. Chem. (1907). 8 Amer. Chem. Journ. 30, 193 (1903). For a discussion of the earlier work on the relation between conductivity and viscosity in mixed solvents, see Carnegie Institution Publication Memoir 80; by H. C. Jones and coworkers. 432 THE ELEMENTS OF PHYSICAL CHEMISTRY showed that one associated liquid diminishes the association of an- other associated liquid with which it is mixed. Since dissociating power is a function of the association of the solvent, it follows that 50 0* 25* 100* 50* 75* Concentration of Alcohol Fig. 59. These curves correspond to the volumes 32, 64, 128, 256, 512 and 1024. such a mixture would dissociate less than the pure solvents ; and the conductivity in such a mixture would be less than in the pure solvents. Carroll showed that the above explanation was not sufficient. We must take into account also the viscosity of such mixtures of solvents. When we mix alcohol and water, the viscosity of the mix- ture is greater than that of either solvent when pure. The mixture ELECTROCHEMISTRY 433 CONDUCTIVITY OF LITHIUM NITRATE IN MIXTURES OF ACETONE AND METHYL ALCOHOL AT 0° of maximum viscosity corresponds to the mixture in which minimum conductivity occurs. The minimum in conductivity is, then, due in part to the diminution in the velocity of the ions produced by the more viscous solvent. The investigation of Bassett led to the same general conclusions. The work of Bingham included not only water, methyl and ethyl alcohols, but also acetone. Lithium nitrate, potassium iodide, and calcium nitrate were studied in these solvents, and in binary mix- tures of them. The viscosities of the pure solvents alone and when mixed were measured; and also the viscosities of solutions of cal- cium nitrate in the pure solvents and in the mixtures. The con- ductivities in the mixtures of acetone and water show the minimum already referred to, and this is very closely connected with the maximum in viscosity in these mixtures. One of the most important facts es- tablished by this in- vestigation is that lithium nitrate and calcium nitrate, in mixtures of acetone with methyl alco- hol and with ethyl alcohol, show a very pronounced maxi- mum in conductivity. (See Pig. 60.) This was shown not to be due to any marked increase in dissocia- tion in such mix- tures, but to a diminution in the size of the ionic spheres, or the com- plexity of solvate which the ion must drag with it through the solution. The solvate about the ion, becoming less complex, would move faster, and the conductivity would show a maximum. Rouiller studied the conductivity of silver nitrate in mixtures of the above-named solvents, and found also a pronounced maximum in 2f 85* 50* 75* Percentage of Acetone 100 J5 Fig. 60. These curves correspond to the volumes 5, 10, 25, 50, 100, 200, 400, 800, 1200 and 1600. 434 THE ELEMENTS OF PHYSICAL CHEMISTRY conductivity in mixtures of methyl alcohol and acetone, and ethyl alcohol and acetone. (See Fig. 61.) His work on the migration velocities in these solvents indicated that the above explanation of CONDUCTIVITY OF SILVER NITRATE IN MIXTURES OF ETHYL ALCOHOL AND ACETONE ATO° 75 * 100 i 25* 50* Percentage of Acetone Fiq. 61. These curves correspond to the volumes 50, 100, 200, 400, 800 and 1200. the maximum is correct. There is a change in the atmosphere of the solvent about the ion. McMaster worked with the same solvents that had been used by Bingham, and with binary mixtures of these with one another. As electrolytes he used lithium bromide and cobalt chloride. He studied both conductivities and viscosities. In mixtures of water with the alcohols and acetone he found again the conductivity mini- mum, which was closely connected with the viscosity maximum. (See Fig. 59.) The conductivity maximum was found by McMaster in the mixtures of the alcohols with acetone. This was shown to be due to the change in the size of the spheres about the ions. Cobalt chloride in the 75 per cent mixture of acetone with methyl alcohol, and in the 50 and 75 per cent mixtures of acetone with ethyl alcohol, showed negative temperature coefficients of conductivity, at ordinary temperatures. Negative temperature coefficients of con- ductivity had previously been observed in a few cases, but only at low temperatures. What is the meaning of such coefficients ? With rise in temperature the solvent becomes less viscous, which would ELECTROCHEMISTRY 435 increase the velocity of the ions. With rise in temperature the association of the solvent becomes less and less, and, consequently, its dissociating power, which would diminish the number of ions present. These two influences, then, act counter to one another. A negative temperature coefficient of conductivity means that the latter influence more than overcomes the former. It is interesting to note that a zero temperature coefficient of con- ductivity was found for a solution of cobalt chloride in a 75 per cent mixture of acetone with methyl alcohol, the solution of cobalt being one two-hundredth normal. The work of Veazey had to do chiefly with the measurement of the conductivities and viscosities of solutions of potassium sulpho- cyanate and copper chloride in water, methyl alcohol, ethyl alcohol, and acetone, and in binary mixtures of these solvents. The mini- mum was found to be a more general phenomenon than had hitherto been supposed. The explanation was found for the increase in viscosity on mixing water and alcohol. These are both strongly associated liquids. The work of Jones and Murray had shown that each di- minishes the association of the other. The water breaks the mole- cules of the alcohol down into smaller molecules, and the alcohoL breaks down the molecules of the water into smaller molecules. In the mixture we have a much larger number of molecules present than in the separate solvents. These molecules are, however, much smaller in size. Now, it is obvious that smaller molecules would have greater friction than larger ones in moving over one another, hence the greater viscosity of the mixture. It should be pointed out that the strongly associated liquids show the great viscosity on mixing; and further, that the viscosity maximum corresponds to that particular mixture where the sum of the diminution in association is a maximum. This explains also why the conductivity curves for different di- lutions of the same substance generally approach one another as they approach the minimum. (See Fig. 59.) Those mixtures of the solvents in which the conductivity minima occur are the least associated, and therefore have the least dissociating power. It is . obvious that such mixtures would produce the least increase in dis- sociation, with increase in dilution, and, consequently, the conduc- tivity curves for the different dilutions would approach one another as they approach the minima. Fact and theory are here in perfect accord. The maxima in conductivity were found to correspond to the 436 THE ELEMENTS OF PHYSICAL CHEMISTRY minima in viscosity. These minima in viscosity are due, as has been shown, to an increase in the size of the molecules of the solvent. This is caused by a combination of one solvent with the other. The viscosity of the solvent being diminished, the ion would move through it with greater velocity, and this would increase the con- ductivity. The conductivity maximum is due to the smaller atmos- phere of solvent about the ion, and the diminished viscosity of the solvent ; both factors increasing the velocity of the ion. Why Certain Salts Lower the Viscosity of Water. — Potassium sulphocyanate dissolved in water lowers the viscosity of water, i.e. the solution has a smaller viscosity than water itself. On ex- amining the literature it was found that salts of potassium, rubidium, and caesium are practically the only known electrolytes which lower the viscosity of water when dissolved in it. Certain salts of potas- sium, however, do not lower the viscosity of water, just as might be expected, since viscosity is an additive property of both the ions present in the solution. The anions tend to increase the viscosity of the solvent, while certain cations, viz. potassium, rubidium, and caesium, tend to diminish the viscosity of the solvent. If the effect of the negative ion more than overcomes that of the cation, potassium, rubidium, and caesium, then the solution is more viscous than water. If it does not, then the solution is less viscous than pure water. The explanation ' of the diminution in viscosity produced by the above-named cations is comparatively simple in the light of the con- ception of viscosity proposed on page 435. If the atomic volume of the ions introduced were much larger than the molecular volume of the solvent molecules, the effect would be to diminish the frictional surfaces that would come in contact with one another in the solu- tion, and, consequently, the friction of the movement of the mole- cules over one another would be diminished. The question, then, is, Are the atomic volumes of potassium, rubidium, and caesium very large ? And are they much larger than the atomic volumes of other elementary cations ? If we turn to the well-known atomic volume curve (page 29) we see that potassium, rubidium, and caesium occupy the maxima of the curve, and have much larger atomic volumes than any other known elements. Even the atomic volume of potassium, which is smaller than that of rubidium and caesium, is much larger than that of any other known element except rubidium and caesium. i Jones and Veazey : Amer. Chem. Journ. 37 (1907). ELECTROCHEMISTRY 437 If we test this relation quantitatively, the result is very satisfac- tory. By comparing the viscosities of solutions of the same concen- tration of potassium chloride, rubidium chloride, and caesium chloride, we find that, while all of these viscosities are less than the viscosity of pure water, the viscosity of the solution of rubidium chloride is less than that of potassium chloride, and the viscosity of the solution of caesium chloride is less than that of rubidium chloride. Similar relations 1 are pointed out for a number of the elements with smaller atomic volume. Indeed, the above relation seems to be so general that we can accept it, at least tentatively, as showing that there is a large element of truth in the above explanation of the negative viscosity produced when certain salts are dissolved in water. For a fuller discussion of this subject, see " Conductivity and Vis- cosity in Mixed Solvents," by H. C. Jones and coworkers, Carnegie Institution of Washington Memoir No. 80. Relation between the Dissociating Power and Other Properties of Solvents. — Attempts have been made to discover relations be- tween the dissociating power and other properties of solvents. J. J. Thomson, 2 and a little later Nernst, 3 have pointed out that if the forces which hold the atoms in the molecule are of an electrical na- ture, those solvents which have the highest dielectric constant should have the greatest dissociating power. That this is true can be seen from Coulomb's law — the larger the dielectric constant of the medium, the smaller the electrical attraction between two op- positely charged particles. The smaller the attraction between the two oppositely charged parts of the molecule, the more likely the mole- cule is to fall apart into its ions. The work which has thus far been done shows that this is, in general, true. There is not, however, a proportionality between the dielectric constants and the ionizing power of solvents. The exact relation between the two has not yet been pointed out, nor can we hope to discover it until we can meas- ure dissociation in non-aqueous solvents far more accurately than is possible at present. An entirely different relation has been suggested by Dutoit and Aston. 4 It is well known, especially from the work of Ramsay and Shields, 5 that in many liquids the molecules are not the simplest possible, but are aggregates of these simplest molecules of various 1 Jones and Veazey : Ztschr. phys. Chem. (1907). 2 Phil. Mag. 36, 320 (1893). 3 Ztschr. phys. Chem., 13, 531 (1894). * Compt. rend. 125, 240 (1897). 6 Ztschr. phys. Chem. 12, 433 (1893). 438 THE ELEMENTS OF PHYSICAL CHEMISTRY degrees of complexity, — the liquid molecules are polymerizations of the simplest gas molecules. The relation suggested by Dutoit and Aston is that in only those solvents which are polymerized do dis- solved substances conduct the current. That there is a relation between the amount of polymerization and the dissociating power of a solvent was shown in a number of cases by Dutoit and Aston, and in a number of other cases by Dutoit and Friderich. 1 The latter concluded that the values of ^ for a given electrolyte in different solvents are a direct function of the degree of polymerization of the solvents, and an inverse function of their coefficients of viscosity. If a solvent is not polymerized at all, its solutions are all non-conductors. There is undoubtedly some truth in this relation. Water, the strongest dissociant known, represents the highest degree of poly- merization of any known liquid. Its molecule, according to Ramsay and Shields, is to be represented by (H 2 0) 4 . Formic acid and methyl alcohol come next in order of polymerization, and, as we have seen, they stand next to water in dissociating power. Those substances, on the other hand, which have slight ionizing power show very slight polymerization of their molecules. Briihl 2 attempts to go one step farther. He thinks that oxygen is generally quadrivalent, and that water and other liquids contain- ing oxygen are unsaturated compounds. This explains, according to Briihl, their polymerization, their large dielectric constant, and their high dissociating power. Electrolytic Dissociation and Chemical Activity. — We have seen that most solvents are capable of breaking down to some extent into their ions strong acids and bases, and salts. We have also seen that heat can effect electrolytic dissociation. When we remember that some acid, base, or salt is used in almost every chemical reaction, we shall see that ions are almost always present whenever chemical action takes place. It is true also that in most chemical reactions molecules are likewise present. These facts would naturally raise the question whether chemical reaction is due directly to the ions or to molecules. We cannot answer this off-hand, since under ordinary conditions we have both ions and molecules present. We must, on the one hand, exclude the molecules, having nothing but ions present; and then see whether we have any chemical activity between the ions. On the other hand, we must exclude the ions, having only molecules present, and then see whether we have any chemical activity. 1 Bull. Soc. Chim. [3], 19, 321 (1898). 2 Ztschr. phys. Chem. 18, 514 (1896). ELECTROCHEMISTRY 439 The first part of the problem is solved by working with strong acids and bases, and salts, in very dilute solutions. Under these conditions we know that all the molecules are broken down into ions. We know that it is under just these conditions that the acids, bases, and salts have the greatest chemical activity. We do not, of course, mean that a thousandth normal solution of an acid has greater chemical activity than a normal solution, but that it has more than one-thousandth the activity. In a word, the strength of electrolytes increases with the dilution up to a certain point, which represents complete dissociation. The experimental solution of the second part of the problem is not so simple, because it is difficult to obtain substances which exist entirely in the molecular condition free from ions. This is due chiefly to the difficulty of removing every trace of water from the presence of substances, and wherever water is present we are liable to have molecules dissociated into ions. This has, however, been accomplished in a number of cases, by taking very special pre- cautions to dry the substances themselves, and also the atmosphere around them. Having removed every trace of all dissociating agents, it only remained to bring the molecules of substances into the presence of one another and to see whether they reacted or not. A few of the most striking results which have been obtained will be given. Wanklyn 1 showed that dry chlorine does not act on fused metal- lic sodium. Baker 2 found that sulphur, boron, amorphous and ordinary phosphorus do not burn in dry oxygen. Hughes 3 demonstrated that dry hydrochloric acid does not de- compose carbonates to any appreciable extent. Marsh 4 has shown that pure sulphuric acid, free from every trace of moisture, has no action on blue litmus. Similar results have been obtained with dry hydrochloric acid. Hughes found that dry hydrogen sulphide does not act on dry metallic oxides, and does not precipitate a solution of mercuric chloride in absolute alcohol. It should be stated that mercuric chloride is one of the few salts which is only slightly dissociated by water. It is not dissociated at all by absolute alcohol. The most astonishing experiments are, however, the following : Hughes 6 stated that when ammonia is dried over lime, and hydro- 1 Chem. News, 20, 271 (1869). * Ghem. News, 61, 2 (1890). 2 Phil Trans. 571 (1888). 6 Phil. Mag. 35, 531 (1893). » Phil. Mag. 34, 117 (1892). 6 Loc. cit. 440 THE ELEMENTS OF PHYSICAL CHEMISTRY chloric acid is dried over phosphorus pentoxide, the two would remain in the presence of each other for twenty-four hours uncom- bined. Baker 1 dried both gases very carefully over phosphorus pentoxide, and brought them together in such a form of apparatus that any change in volume, however slight, could be readily ob- served. He found that perfectly dry ammonia is entirely without action on perfectly dry hydrochloric acid. Although the conclusion of Baker was called in question by Gutmann, 2 it has since been established beyond question by Baker 3 himself. One other experiment in this connection. An experiment was performed before the Chemical Society of London 4 in which a piece of dry metallic sodium was plunged into pure, dry sulphuric acid. A piece of wire, serving as a handle, was wrapped around the metallic sodium. At first there was a flash of light, then the sodium remained perfectly quiescent in the sulphuric acid. The reaction at first was due to a few ions formed on the surface of the metal by the moisture of the air, to which it was exposed for an instant before it was plunged into the sulphuric acid. It is needless to add that in all the experiments just described, very special precautions must be taken to dry all the substances in question. The ordinary methods of drying are, of course, entirely insufficient. These experiments show conclusively that molecules as such have little or no chemical activity, and taken along with the pre- ceding experiments, show that ions are the chief if not the only agents which bring about chemical activity. We have already reached a point where we can say that nearly all, if not all chemical reactions are due to ions, molecules as such not entering into chemi- cal action. The molecules which are present gradually dissociate as the reaction proceeds, and furnish ions which then react. We can now see why inorganic reactions in general proceed to the limit rapidly, wnile organic reactions take place much more slowly. Inorganic compounds, including the strong acids and bases, and salts, are in general strongly dissociated substances. The ions are already present and they react very rapidly. Organic compounds, on the other hand, are weakly dissociated. There are only a few ions present, and considerable time is required,- under ordinary conditions, for the dissociation to proceed very far. The Passive State of the Metals. — It has long been known that when certain of the metals are subjected to special kinds of treat- 1 Journ. Chem. Soc. 65, 611 (1894). 3 Journ. Ohem. Soc. 73, 422 (1898). 2 Lieb. Ann. 299, 1, 267 (1898). 4 Proceed. Chem. Soc. (1894), p. 86. ELECTROCHEMISTRY 441 ment, they no longer have the properties that they usually possess. As early as 1790 Kier ] observed that when iron is dipped in nitric acid having a specific gravity of 1.45, it becomes passive, i.e. it is no longer attacked by dilute nitric acid. Further, it no longer has the power to precipitate metallic copper from a solution of a copper salt. Other strong oxidizing agents, such as chromic acid, also render the iron passive. The same result is frequently obtained when iron is made the anode in electrolysis. A number of metals other than iron can be rendered passive. We should mention especially chromium, copper, cobalt, and nickel. A number of attempts have been made to explain the passivity of the metals. Faraday 2 and Schonbein explained the passivity in the case of iron, as due to the formation of a layer of oxide on the surface of the metal. This was natural when we consider that iron is rendered passive by strong oxidizing agents, and loses its passivity when heated in a reducing gas. The oxide layer theory of passivity is now regarded as untenable, since the passive state has been brought about under conditions where oxidation is impossible; and, further, has been destroyed under conditions where any layer of oxide if formed would not be disturbed. The same fate has befallen the theory that passivity is due to the formation of a protective layer of gas over the surface of the metal. The two views of passivity that have acquired the greatest promi- nence are those of Finkelstein 3 and Hittorf. 4 According to the former, active iron is bivalent and passive iron trivalent. This con- clusion was based upon the difference in potential between iron electrodes and the iron salt in which they were immersed. The potential difference depends upon whether the iron salt is in the ferrous or in the ferric condition. Hittorf also points out that in the case of chromium, the passive condition corresponds to the highest valence, ana the active to the lower valence. He thinks that we have to do with two allotropic modifications of the elements, one of which is active and the other not. See Nichols and Franklin : Amer. Journ. Science, 34, 419 (1887). Houlle- vigne: Journ. de Phys. (3) 7, 408 (1898). Miiller: Ztschr. phys. Chem. 48, 577 (1904). Sackur: Ibid. 54, 641 (1906). See Ostwald : Ztschr. phys. Chem. 35, 33 (1900); 35, 204 (1900). Brauer : Ibid. 38, 441 (1901). Ruer : Ztschr. Elektrochem. 14, 309, 633 (1908). 1 Phil. Trans. 80, 359 (1790). 2 Phil. Mag. [3] 9, 53 (1836); 10, 175 (1837). 3 Ztschr. phys. Chem. 39, 91 (1901). 4 Ibid. 30, 481 (1899); 34, 385 (1900). 442 THE ELEMENTS OF PHYSICAL CHEMISTRY ELECTROMOTIVE FORCE OF PRIMARY CELLS Measurement of Electromotive Force. — Certain forms of appara- tus and cells used in measuring electromotive force must be de- scribed. More than one form of the Lippmann electrometer has been devised. The form described by Le Blanc x is very convenient for ordinary purposes. It was devised by Ostwald. Fig. 62. The glass tube d (Fig. 62) is filled to a convenient height with mercury, which penetrates into the capillary c. The bottom of the tube b is covered with mercury, and then filled with a ten per cent solution of sulphuric acid, which also penetrates into the capillary c. The apparatus is supported on a wooden stand, and the position of the meniscus between the mercury and the sulphuric acid regulated by means of the thumb-screw/. A platinum wire, sealed into a glass tube and projecting beyond the sealed end, dips into the mer- cury in b. A platinum wire dips into the mercury in d. Beneath the capillary c is a scale divided into centimetres and millimetres. If the two platinum wires are brought in contact, the mercury will take a definite position in the capillary, which can be regarded as the zero for the instrument. If the instrument is now thrown into a circuit, there will be a difference in potential between the two wires, and the mercury will be displaced in the capillary in one direction or the other, depending upon the direction of the current. The amount of this displacement, depending upon the difference in the potential of the two wires, is used to measure differences in potential. By this means differences in potential can be measured to a few thousandths of a volt. Ostwald has given the Lippmann electrometer other forms. 1 Ztschr. phys. Chern. 5, 471 (1890). ELECTROCHEMISTRY 443 The vertical form is very convenient for use with a small microscope, which is employed in reading the scale divisions. A more sensitive form of the Lippmann electrometer is shown in Fig. 63. The capillary is drawn out very fine, and by means of a suitable microscope it is pos- sible to read the differences in potential to a few ten-thousandths of a volt. The movement of the mercury in the capillary when the current passes is due to the change in the surface-tension produced by the current. The form of resistance box, which is very convenient for measuring the electromotive force of elements, is shown in Fig. 64. On the left side of the box are ten metal plugs connected by wires, each having a resistance of ten ohms. On the right side are ten plugs connected by wires, having a resistance of one hundred ohms each. The two end plugs on this side are con- nected by a strip of metallic copper, which has practically no resistance. The total resistance of the box is, then, one thousand ohms. A number of normal ele- ments have been devised and used. The best known of these is the Clark 1 element. It consists of mercury over which is placed a thick paste of mercurous sul- phate. Above this is a thick paste of zinc sulphate into which a zinc bar is immersed, serving as the second pole. This element has an electromotive force of 1.4328 volts - 0.0012 (t — 15°), t being the temperature at which the element is used. The objection to this element is that its temperature coefficient is so large. The Weston 2 element has the advantage that its temperature coefficient is practically zero. It consists of mercury covered with a paste of 9 100* 9 •900 90 • •800 80 • •700 70 • •600 60 • •500 50* •400 40 • •300 30* •200 20 • •100 10» < I — «0 3 Fig. 64. » Jager : Wied. Ann. 63, 354 (1897). 2 See Jager and Wachsmuth : Wied. Ann. 59, 575 (1896). Kohnstamm and Cohen: Ibid. 65, 344 (1898). Mcintosh: Journ. Phys. Chem. 2, 185 (1898). Cohen : Ztschr. phys. Chem. 34, 621 (1900). Barnes : Journ. Phys. Chem A, 339 444 THE ELEMENTS OF PHYSICAL CHEMISTRY mercurous sulphate, and above this a paste of cadmium sulphate, into which a bar of cadmium dips. Its electromotive force is 1.0186 volts. Ostwald 1 recommends the use of a one volt element prepared as follows from the Helmholtz calomel element. Mercury is covered with mercurous chloride. Upon this is poured a solution of zinc chloride having the specific gravity 1.409, and into this solution is dipped a bar of amalgamated zinc. Its electromotive force at ordi- nary temperatures is just one volt, and its temperature coefficient is very small — 0.00007 volt per degree. Such an element must be compared, however, with a standard Clark or Weston element. The measurement of electromotive force, by means of the apparatus just described, is comparatively a simple matter. The method con- sists in balancing the electromotive force of the element in question against that of a standard element. It is known as the compensa- tion method of Poggendorff. This method will be readily understood from Fig. 65. An ele- ment of constant electromotive force is placed at C, and connected ELEMENT QHHHQHHQmC □□□□□□00 Fig. 65. with the two end plugs of the resistance box just described. There is a definite fall in potential as the resistance increases from plug to plug along the box. The element whose electromotive force is to be measured is placed at E, and connected with the plugs in the box by means of metallic caps, which fit tightly over the plugs. The caps are moved from plug to plug, until the electromotive force to be measured is equal to the drop in the potential of the original cur- (1900). Jager: Ann. d. Fhys. (4)4, 123 (1901); (4) 6, 1 (1901). Jager and St. Lindeck: Ztschr. phys. Ghem. 37, 641 (1901). Carhart : Phys. Bev. 12, 129 (1901). Hulett: Journ. Phys. Chem. 8, 190 (1904). Hulett: Ztschr. phys. Chem. 49, 483 (1904). Barnes and Lucas: Journ. Phys. Chem. 8, 196 (1904). 1 Ztschr. phys. Chem. 1, 406 (1887). ELECTROCHEMISTRY 445 rent caused by the resistance in the box. This equality is estab- lished by means of the Lippmann electrometer. These two equal values, being opposite in character, completely compensate each •other, and there is no movement of the mercury in the electrometer. When larger electromotive forces are to be balanced, one or more one-volt elements may be introduced into the circuit with the element E. It is necessary to determine, for any given element, the drop in potential from plug to plug along the box. This is accomplished by introducing a standard element — say a one-volt element — into the secondary circuit, and moving the caps from plug to plug until "the electrometer shows complete compensation. Knowing the elec- tromotive force of the standard element, we know the drop in poten- tial produced by a given resistance in the box, since the two are ■equal. We can then calculate at once the drop in potential which would be produced when any other resistance was introduced into the path of the current from G, by moving the caps along the plugs. It is obvious that the element C must have a larger electromotive Horce than the normal element which is used. This compensation method has been extensively used in recent years, in connection with the large number of measurements of the electromotive force of elements which have been carried out from an electrochemical standpoint. Transformation of Intrinsic Energy into Electrical. — It follows from the law of the conservation of energy, that whenever one form of energy appears, an equivalent amount of some other form dis- appears. Thus, when electrical energy appears in the cell, it is at the expense of the intrinsic energy of the substances present in the cell. It has already been pointed out that the best means of measuring intrinsic energy, or better, difference in intrinsic energy, is to transform this into heat and measure the amount of heat developed, — in a word, to determine the heat tone of the reaction. The assumption was made by Helmholtz and Kelvin that in the simplest form of cell, the intrinsic energy which becomes free during the reaction passes over quantitatively into electrical energy. This was shown first by J. Willard G-ibbs, 1 in 1878, and a little later by Helmholtz, 2 not to be true in general. Indeed, it is true only in very special cases. An element may either take up heat from the 1 Proceed. Conn. Acad. Translated into German by Ostwald : Thermody- namische Studien, p. 397. Leipzig, 1892. 2 Sitzungsber. Ber. Akad., February, 1882. 446 THE ELEMENTS OF PHYSICAL CHEMISTRY surrounding medium, or give out heat, and this must be taken into account. The electrical energy produced in the cell is, then, equal to the intrinsic energy which has disappeared, plus a term which is proportional to the electromotive force and to the absolute tempera- ture. This is formulated as follows : If we represent the electrical energy by E„ the intrinsic energy by E a the quantity of electricity generated in the cell by e , the electromotive force by ir, and the absolute temperature by T, we have — E e = E c + e T^. The last term may be either positive or negative, but is more fre- quently negative ; i.e. the element gives out heat while it is working. A purely physical chemical method of calculating the electromotive force of elements was worked out by Nernst, 1 and to this we shall now turn. Calculation of Electromotive Force from Osmotic Pressure. — The method of calculating electromotive force from osmotic pressure is based upon the deduction by Ostwald 2 from the work of Nernst. If we allow a substance to pass, isothermally, from one condition to another, the maximum amount of external work is always the same, regardless of how this takes place, whether osmotically, or electrically, or in any other way. If we know the maximum exter- nal work which is obtainable from a process, we know the amount of electrical energy; and, as we shall see, the electromotive force is calculated directly from the electrical energy. The first step is, then, to determine the maximum external work which is obtainable in a given process. This can be done by allowing the substance to pass at constant temperature, in a reversible manner, from one condition over to the other. Given a gas under a pressure p lt and volume v, and allow it to expand isothermally to a pressure p 2 . When a gas expands iso- thermally it takes up heat, and gives it up as volume energy. The energy set free under these conditions is — Pi — I vdp. Pi iZtschr.phys. Ghem. 4, 128 (1889). * See Lehrb. d. Allg. Chern. II, p. 825. See Lehfeldt : Ztschr. phys. Chem. 35, 257 (1900). ELECTROCHEMISTRY 447 But pv — BT, where B is the gas constant and T the absolute temperature, whence the above expression becomes for gram-molecu- lar weights : — Pt dp -BTf® J p Pi which expresses the volume energy obtained under the condition. This becomes on integration — BTln*^. Pi This amount of energy, which is converted into work by an ideal gas in passing from pressure p x to pressure p 2 , is exactly equal to the work obtained from an ideal solution under the same conditions ; that is, a solution of volume v passing isothermally from an osmotic pressure p 2 to an osmotic pressure p 2 . But with the movements of the ions, we have the movements of the electrical charges which they carry. And from what has been said, the amounts of work corresponding to the movements of the ions can be transformed into electrical energy. We have then shown, thus far, how to calculate the maximum external work obtainable, when a solution of osmotic pressure p x passes isothermally and reversibly over to osmotic pressure p 2 , and the relation between this work and the electrical energy obtainable. Knowing the electrical energy, how can we determine the electromotive force? Electrical energy, like every other manifes- tation of energy, can be factored into an intensity and a capacity factor. The intensity factor of electrical energy is the electromotive force or potential, and the capacity factor the amount of electricity. If we call the former ir, and the latter e , we have the electric energy E e = ire . If we know E e , we can calculate ir at once, since e is known from "Faraday's law. Knowing the quantity of ions which pass from one osmotic pressure over to the other, we know the amount of electricity e ; knowing E e , we calculate x. Let us deal with a gram-molecular weight of univalent ions. These will carry 96,530 coulombs of electricity, and this quantity we will now designate by e . If the ions are bivalent, they will carry twice as much ; if trivalent, three times ; and so on. Let us represent the valence of the ions by v; then a gram-molecular * In is natural logarithm. 448 THE ELEMENTS OF PHYSICAL CHEMISTRY weight will carry ve amount of electricity. Suppose a gram- molecular weight of these ions is charged ir potential. The amount of electrical energy required to effect this charge is — irve . But this electrical energy is equal to the osmotic, calculated above, where a gram-molecular weight was taken into account. We have — wve = BTln^, Pi BTln^l •° r > Pi IT = • ve a This is the fundamental equation for calculating the electro- motive' force of elements, from the osmotic pressures of the electro- lytes around the electrodes. -This equation has been very much simplified by Ostwald, 1 by introducing numerical values wherever it is possible. B = 2 calories, and 1 calorie = 4.18 x 10 7 ergs. T, the absolute temperature, can be taken as 290° C. for the average conditions. T>rp The constant = 0.0251 volt, since volt X coul = 10 7 ergs. The above equation then becomes — 0.0251, ft V Pi or in case the ions are univalent — » = 0.0251 In ?l Pi Thus far we have been using the natural logarithm obtained in the process of integration, which we have written In. It is far more convenient in practice to use the Briggsian. To pass from the former to the latter we must divide the above constant by 0.4343, when we obtain 0.058. The final expression of the general formula for calculating the electromotive force of an element, from the osmotic pressure of the electrolytes around the electrodes, is then — *■== 0.058 log^, Pi 1 See Lehrb. d. Allg. Chem. II, p. 827. ELECTROCHEMISTRY 449 where log. is the Briggsian logarithm. If the valence of the ion is greater than one, this must be divided by the valence. Before attempting to apply this expression to any concrete cases, we must examine another conception introducd by Nernst. Electrolytic Solution-tension. — We are perfectly familiar with the fact that when a solid or liquid is evaporated, the molecules pass into the space above the liquid ; and equilibrium is established, for a given temperature, when the vapor exerts a certain definite pressure. This pressure is designated as the vapor-tension, or vapor-pressure of the substance in question. Says Nernst : 1 " If, in accordance with Van't Hoff's theory, we assume that the molecules of a substance in solution exist also under a definite pressure, we must ascribe to a .dissolving substance in contact with a solvent, similarly, a power of expansion, for here, also, the molecules are driven into a space in which they exist under a certain pressure. It is evident that every substance will pass into solution until the osmotic partial pressure of the molecules in the solution is equal to the ' solution-tension ' of the substance." Nernst thus introduced the conception of solution-tension ; and, at the same time, called attention to the close analogy between evap- oration and solution, which can be seen only through a knowledge of the osmotic pressure of solutions. The metals, like many other substances, have the possibility of passing into solution as ions. Every metal in water has, then, a certain solution-tension peculiar to itself, and we will designate this by P. If we dip a metal into pure water, let us see what will take place. In consequence of the solution-tension of the metal, some ions will pass into solution. When metallic atoms pass over into ions, they must secure positive electricity from something. They take it from the metal itself, which thus becomes negative. The solution be- comes positive, because of the positive ions which it has received. At the plane of contact of the metal and solution, there is formed the so-called electrical double layer, whose existence was much earlier recognized by Helmholtz. 2 The positively charged ions in the solu- tion and the negatively charged metal attract one another, and a difference -in potential arises. The solution-tension of the metal tends to force more ions into solution, while the electrostatic attrac- tion of the double layer is in opposition to this. Equilibrium is es- tablished when these two forces are equal. Since the ions carry such i Ztschr. phys. Chem. 4, 150 (1889). 2 Wied. Ann. 7, 337 (1879). 2a 450 THE ELEMENTS OF PHYSICAL CHEMISTRY enormous charges, the number that will pass into solution before equilibrium is established is so small that they cannot be detected by any ordinary method. When we are dealing with a metal im- mersed in pure water, it is evident that the difference in potential which obtains in the double layer is conditioned only by the magni- tude of the solution-tension of the metal in question. If we dip a metal of solution-tension P into a solution of one of its salts, the case is not quite as simple. Let the osmotic pressure of the metallic ions in the solution of the salt be p, then any one of three conditions may exist. The solution-tension may be greater than the osmotic pressure, less than the osmotic pressure, or just equal to it. We may have — P>P, (1) P<», (2) P = p. (3) Let us first take case No. 1, where a metal of solution-tension P is immersed in a solution of one of its salts, in which the osmotic pressure p of the metallic ions is less than its own solution-tension. At the moment the metal touches the solution, a number of metallic ions, which always carry a positive charge, will pass into solution. These ions have carried positive electricity from the metal into the solution, and the metal has thus become negative, the solu- tion positive. At the places where the metal and solution come in contact, the double layer is formed, due to the attraction of the opposite charges. " This double layer has a component of force, which acts at right angles to the plane of contact of the metal and solution, and tends to drive back the metallic ions from the electrolytes to the metal. It acts in direct opposition to the electrolytic solution-tension." l The condition of equilibrium is reached when these two opposing forces just equalize one another ; and the final result is the existence of an electromotive force between the metal and the solution, the metal being negative, the solution positive. It is clear that a metal cannot throw as many ions into a solution of its salt as into pure water, because the osmotic pressure of the metallic ions already in the solution acts against the solution-tension of the metal. Let us now take the second case ; where the solution-tension of the metal is less than the osmotic pressure of the metallic ions in the so- 1 Ztschr. phys. Chem. 4, 151 (1889). ELECTROCHEMISTRY 451 lution. Metallic ions will separate from the solution upon the metal. When a metallic ion passes over into an atom it gives up its positive charge, and in this case it gives it up to the metal, which becomes positive. The solution, having lost some of its positively charged ions, becomes negative. At the points of contact of solution and metal, we have again the electrical double layer, but this time the metal is positive and the solution negative, which is exactly the reverse of the case first considered. Metal ions will separate from the solution until the electrostatic component of force of the double layer, at right angles to the plane of contact of metal and solution, is just equal to the excess of the osmotic pressure over the solution- tension. Equilibrium is established when the sum of the solution- tension of the metal and this component of force is just equal to the osmotic pressure of the metallic ions in the solution. An electro- motive force exists here, also, between the metal and the solution, but in the reverse direction from the case first considered. The third case is where the solution-tension of the metal is just equal to the osmotic pressure of the metallic ions in the solution. Just as soon as the metal touches the solution, equilibrium is es- tablished. Ions neither dissolve from the metal, nor separate from the solution. There is no double electrical layer formed, and there is no difference in potential between the metal and the solution. If now we inquire which metals have high, and which low solution- tensions, we shall find that magnesium, zinc, aluminium, cadmium, iron, cobalt, nickel, and the like are always negative when immersed in solutions of their own salts. This means that the solution-tension of the metal is always greater than the osmotic pressure of the metal ion, in any solution of their salts which can be prepared. If, on the other hand, we take gold, silver, mercury, copper, etc., we usually find the metal positive when immersed in a solution of its salt. This means that the solution-tension of the metal is so small, that it is less than the osmotic pressure of the metallic ions in the solution. When a very dilute solution of salts of these metals is prepared, the osmotic pressure of the metallic ions may become less than the very slight solution-tension of these metals ; and then the metal would be negative with respect to its solution. We have, thus far, spoken chiefly of the solution-tension of metals, which tends to drive the metal over into cations. Substances which can pass over into anions have also a solution-tension, as is pointed out by Le Blanc. 1 If the chlorine ions in a solution had an osmotic 1 Lehrb. Mektrochemie, p. 121. See also Lehfeldt : Phil. Mag. (5) 48, 430 (1899) ; Ztschr.phys. Chem. 32, 360 (1900) ; Kriiger : Ibid. 35, 18 (1901). 452 THE ELEMENTS OF PHYSICAL CHEMISTRY pressure which was greater than the solution-tension of chlorine, the chlorine ions would pass over into ordinary chlorine. But Le Blanc adds that, as far as we know, all substances which can yield negative ions have a high solution-tension. Demonstration of the Solution-tension of Metals. — A demonstra- tion of the solution-tension of metals has been furnished by Palmaer. 1 Mercury is a metal whose solution-tension is very small. Even when in contact with a very dilute solution of a mercury-salt, the solution-tension of the mercury is less than the osmotic pressure of the mercury ions in the solution ; and some of the mercury ions will separate from such a solution. Given a vessel whose bottom is covered with metallic mercury, and over this is placed a solution of mercurous nitrate having a volume of 2000. A few mercury ions will separate from the solution and give up their positive charges to the mercury. The positively charged mercury will attract electrostatically a few negative NO s ions to form the double layer. This will be continued until a cer- tain difference in potential has been reached, when equilibrium will be established. If a drop of mercury is now let fall into the solution, a few mercury ions will separate upon it, charge it positively, and it will then attract an equal number of negative N0 3 ions and drag them down with it through the solution. The next drop of mercury will behave iu exactly the same manner, and thus the top of the solution will become continually poorer and poorer in the salt. When the drop of mercury comes in contact with the mercury at the bottom of the vessel where equilibrium is already established, what will happen ? When the drop has united with the mercury, this will contain an excess of positive electricity, and therefore a small quantity of mercury ions will pass into solution. And, indeed, exactly the same number as there are N0 3 ions brought down from the top to the bottom of the solution. The solution will thus become more concentrated just above the layer of mercury on the bottom of the vessel. A fine glass tube from which mercury flows is known as a drop- electrode. . To produce changes in concentration sufficient for the purposes of a demonstration, a very powerful drop-electrode must be used. This is made by inserting a conical glass stopper into a conical glass tube, so that the junction is mercury-tight. A large number of fine grooves are then etched on the outside of the stopper, so that 1 Ztschr.phys. Chem. 25, 266 (1898); 28, 257 (1899). Ztschr. Elektrochem. 7, 287 (1900). See also Outlines of Electrochemistry, Jones (Elec. Kev. Pub. Co.). Ztschr. phys. Chem. 25, 265 (1898); 28, 257 (1899), ELECTROCHEMISTRY 453 the mercury will stream through as a fine mist. To assist this process the mercury is subjected to four or five atmospheres of pressure. Under these conditions, however, the mercury cannot be allowed to flow directly into a vessel filled with a dilute solution of a mer- cury salt, and containing mercury at the bottom, since there would be too much commotion in the solution. The arrangement which was used is shown in Fig. 66. The drop-electrode T dips into the funnel-shaped vessel 0, which is connected by a narrow tube and a rubber tube with the larger vessel M. This is in turn con- nected with the vessel U, -where the change in concentration can be observed. When the mer- cury has been allowed to flow for five minutes under a pressure of five atmospheres, distinct changes in concentration can be detected. Palmaer gives data which show that the con- centration above had been diminished as much as fifty per cent, and increased below as much as forty per cent. This will be recognized at once to be a very remarkable experiment, and before our modern physical chemical theories were proposed would have been entirely inexplicable. The results of this experiment were predicted before the experi- ment was tried. FlG - 66 " Calculation of the Difference in Potential between Metal and Solution. — The difference in potential between a metal of solution- tension P, and a solution of one of its salts in which the metal ion has an osmotic pressure p, can be calculated as follows: — When a substance of solution-tension P is converted into ions of osmotic pressure P, no work is done. Therefore, to convert a sub- stance of solution-tension P into ions of osmotic pressure p, the maximum work to be obtained is the same as that obtained by trans- ferring the ions from osmotic pressure P to osmotic pressure p. Now we have seen that the gas laws apply to the osmotic pressure of solutions, and the amount of work can be calculated from a gas in passing from gas-pressure P to gas-pressure p. If we deal with a gram-molecular weight, we have seen (p. 447) this to be — BT\n-- p SeeBraun: Wied. Ann. 41, 448 (1890). Meyer: Ibid. 67, 433 (1899). 454 THE ELEMENTS OF PHYSICAL CHEMISTRY We have also seen that this osmotic work is equal to the electrical work for an isothermal transformation. The electrical work is the potential times the amount of electricity. If we are dealing with gram-molecular quantities, it is 7rye . Equating these two values, we have — irve t = RThx-, P or, if the ions are univalent, v = l, when we have — RT, P it = ■ In — • e P D/TT Now we know, from page 448, that = 0.0251 volt. Passing from natural to Briggsian logarithms, this becomes 0.058 volt. The potential between metal and solution is then, when T = 290°, 7T = 0.058 log - • P We have learned thus far how to calculate the electromotive force of elements from the osmotic pressures of the solutions around the electrodes, and also how to calculate the potential between a metal and the solution of one of its salts in which the metal is immersed. With these two conceptions in mind, we shall now study a few elements to see how these principles are applied. Types of Cells. — We know a large number of cells, and they may be classified under the following heads : Constant and Inconstant, and constant elements may be reversible or non-reversible. If the chemical process in the cell remains the same during the time it is closed, the cell is constant; if the chemical process changes, it is inconstant. Constant elements differ among themselves. Through some of these we can send a current in the opposite direction, without changing their electromotive force. This class of constant elements is termed reversible. This applies to elements in which the elec- trodes are immersed in solutions of their salts. Take as an example the Daniell element. This consists of a bar of zinc immersed in a solution of zinc sulphate, and a bar of copper in a solution of copper sulphate. When the current is passed in the opposite direction through this cell, its nature is not changed. The normal action is that the zinc dissolves and copper separates. When a current is passed in the opposite direction, copper dissolves and zinc separates. But neither process changes the nature of the cell. ELECTROCHEMISTRY 455 If the electromotive force is changed when a current is passed in the opposite direction, the element is non-reversible. Concentration Elements of the First Type. — We will first con- sider a very simple type of a reversible element, the two electrodes being of the same metal, and immersed in solutions of the same salt of that metal, the solutions having different concentrations. To take a concrete example : Two bars of metallic zinc are immersed in solutions of zinc chloride, the one bar in a tenth-normal solution of the salt, the other in a hundredth-normal solution. The two solu- tions are connected by a tube filled with either solution. When the two zinc bars, which are the electrodes, are connected externally, the current flows and we have an element. Ostwald defines a cell or element as any device in which chemical energy is converted into electrical. The only difference between the two sides of this element is in the concentration of the electrolytic solutions. The element is there- fore termed a " concentration element. " Further, since the salt of the metal is soluble, this is termed a " concentration element of the first class " to distinguish it from other concentration elements which will be taken up later. Take the example given above, of two bars of zinc in two solu- tions of zinc chloride of different concentrations. The action of the cell is such as to make the two solutions become more and more nearly of the same concentration. The more dilute solution becomes more concentrated, and the more concentrated more dilute, until when the two become equal the element ceases to act. Zinc then passes into solution in the more dilute solution, and zinc ions separate as metal on the bar from the more concentrated solution. The electrode in the more concentrated solution is always positive, since metallic ions are giving up their positive charges to it and separating as metal upon it. The electrode in the more dilute solution is nega- tive, because ions are passing from it into the solution, and carrying with them positive charges which come from the electrode. In an element of this kind the current always flows on the outside from the electrode which is immersed in the more concentrated solution. The action of this cell is just what we should expect. The solu- tion-tension of the zinc is the same on both sides of the cell. The osmotic pressure of the zinc ions is, of course, greater in the more concentrated solution. The osmotic pressure, which works directly against the solution-tension, will cause the ions to separate from the solution in which this pressure is the greater. The electromotive 456 THE ELEMENTS OF PHYSICAL CHEMISTRY force of such an element would be the difference in the potential upon the two sides of the cell : — BT. P BT, P BT, »! w = In In — = In— • ve p 2 ve pi ve p 2 Here v is the valence of the cation, p L and p 2 the osmotic press- ures of the zinc ions in the two solutions. This, however, does not take into account the changes in the concentrations of the solutions, which are taking place while the current is passing. If e electricity passes from the electrode into the electrolyte, a gram-molecular weight of univalent cations separates from the elec- trode, dissolves, and increases by unity the concentration around this electrode. But, at the same time, cations are moving from this electrode with the current, over towards the other electrode. The amount depends upon the relative velocities of anion and cation. If we represent the relative velocity of cation by c, and of anion by a, the number of the cations which will move over with the current is The increase in the concentration, due to a gram-molecular c+ a jo weight of cations passing into the solution, is then, — c + a c + a This factor is to be multiplied into the former equation to obtain the osmotic work, which can then be equated to its equal, the elec- trical energy. Let n t represent the number of ions in the electro- lyte. We have — a n,BT . », — In- ■ c + a ve p 2 or, ,r = -^- -'0.0002 Tlog^. According to this formula, the only variables are p v and p 2 , the osmotic pressures of the cation in the two solutions around the electrodes. The electromotive force of such elements should de- pend only upon the relative osmotic pressures of the solutions, and not upon the absolute osmotic pressures. This has been found to be true. The electromotive force should also be independent of the kind of zinc salt used, provided the salt is soluble, and yields the same number of zinc ions in each solution as the salt in question. Thus, the chloride could be replaced by the bromide iodide, nitrate, etc., of such concentration that the osmotic pressure of the zinc ions remained the same, and the electromotive force of the element should ELECTROCHEMISTRY 457 remain unchanged, and again such is the fact. The reason for this will be seen at once by examining the last equation, since it is only the osmotic pressure of the cations which comes into play — the anion having nothing whatever to do with the electromotive force of the element. The electromotive force of a number of elements of the type we are considering has been measured, and to within the limits which could reasonably be expected, has been found to agree with that calculated from the above equation. To calculate the electromotive force, a number of quantities must be measured, c and a, the rela- tive velocities of cation and anion, must be determined ; similarly, p l and p 2 , the osmotic pressures of the cations in the solutions, must be ascertained by indirect methods, which involve the measurement of the dissociation of these solutions. Since each of these processes introduces an error of greater or less magnitude, we could not expect a very close agreement between the electromotive force as measured and as calculated. When we take all of these facts into account the agreement is often surprisingly close. The following results, obtained by Moser for solutions of copper sulphate with copper electrodes, are cited by Ostwald. 1 The con- centrations of solutions I and II are the number of parts of water to one part of copper sulphate, w is the electromotive force ex- pressed in thousandths of a Daniell cell. The unit is 0.0011 volt. I II w Observed it Calculated 128.5 4.208 27 27.4 6.352 25 23.8 8.496 21 21.4 17.07 16 15.8 34.22 10 10.3 The concentration of one solution was maintained constant throughout, and that of the other varied at will. The agreement in these eases is very satisfactory. Concentration Elements of the Second Type. — The characteristic of the element which we have just been considering is that the metal is surrounded by one of its soluble salts. We may also have con- centration elements in which the metal is surrounded by one of its i Lehrb.. d. Allg. Chem. II, p. 833. 458 THE ELEMENTS OF PHYSICAL CHEMISTRY insoluble salts; thus, silver surrounded by silver chloride. In the latter ease we must have present, in addition, a soluble chloride; and the soluble chloride must be of different concentrations on the two sides of the cell. The element would consist then of a bar of silver, surrounded by solid silver chloride ; and over this a solution of some chloride, say potassium chloride ; and on the other side, a bar of silver surrounded by solid silver chloride, and over this a solution of potassium chloride, of different concentration from that used on the side first described. This element is termed a concentration element of the second class. The action of this cell will be such as to dilute the more concen- trated solution of potassium chloride, and to concentrate the more dilute solution. Silver dissolves from the electrode surrounded by the more concentrated potassium chloride, and the ions of silver unite with the chlorine ions, and solid silver chloride is formed. The potassium ions move with the current over to the other side of the element, and form potassium chloride with some of the chlorine which was there in combination with silver as silver chloride. This silver then separates as metal upon the electrode. In this way the more concentrated potassium chloride becomes more dilute, and the more dilute becomes more concentrated. The electrode immersed in the more concentrated potassium chloride is the one from which silver ions separate ; therefore, this is the negative pole. The pole in the more dilute solution of potas- sium chloride, receiving silver ions, is positive. The current then flows on the outside, from the pole in the more dilute potassium chloride to the pole in the more concentrated. This is exactly the reverse of what takes place in a concentration element of the first type. There, as we have seen, the current flows on the outside from the pole surrounded by the more concentrated electrolyte. The electromotive force of a concentration element of the second type is calculated in a manner perfectly analogous to that employed with concentration elements of the first type. The electromotive force ir is equal to the difference in the potential at the two poles : — BT, P RT, P ET, Pl tt= In In — = In—. ve p 2 ve jh v «o Pi As in the case of the concentration element of the first class, this does not take into account the changes in the concentrations of the electrolytes which are taking place. At the anode the metallic ELECTROCHEMISTRY 459 silver is passing into solution, and when e electricity is allowed to flow, a gram-molecular weight of the silver will pass over into ions — will dissolve. This will change the concentration of the potassium chloride around this pole by — 1. But at the same time potassium is moving with the current, and chlorine in the opposite direction, and this further changes the concentration. If we represent the relative migration velocities of K and CI, respectively, by c and a, the total change in concentration around the anode will be — -1 + c + a c + a The change in concentration around the cathode would be, of course, — n. + c + a This factor, , c + a must be multiplied into the above expression for electromotive force, when we have — c riiBT. pi ir= ; in—; c + a ve p 2 -'0.0002 Tlog^-S c + a v where n t is, as before, the number of ions yielded by the electrolyte, and v the valence of the cation. The electromotive force of a num- ber of such elements has been measured by Nernst. 1 Mercury was used as the metal, since it could easily be obtained in pure condi- tion. It was covered with an insoluble salt of mercury, and the soluble electrolyte then added. The chloride, bromide, acetate, and hydroxide of mercury were used, and the soluble electrolyte on both sides, of the cell must contain the same anion as the salt of mercury which was employed. If the chloride was used, the soluble electro- lyte must be a chloride. If the hydroxide of mercury was employed, a soluble hydroxide must be used, and so on. Some of the combinations which were made and measured by Nernst are given in the following table. The first column contains the soluble electrolyte which was employed. Columns II and III give the concentrations of the solutions of this electrolyte on the two sides of the cell. a w calculated" is the electromotive force cal- l Ztschr. phys. Ohem. 4, 159 (1889). 460 THE ELEMENTS OF PHYSICAL CHEMISTRY culated from the preceding formula, and " w found " is the electro- motive force of the combination, as measured by Nernst. I II III IT IT Soluble Electrolyte Concentration 1 Concentration 2 Calculated Found HC1 .... 0.105 O.018 0.0717 0.0710 HC1 . 0.1 0.01 0.0939 0.0926 HBr . 0.126 0.0132 0.0917 0.0932 KC1 . 0.125 0.0125 0.0542 0.0532 NaCl . 0.125 0.0125 0.0408 0.0402 LiCl . 0.1 0.01 0.0336 0.0354 NH4CI . 0.1 0.01 0.0531 0.0546 NaBr . 0.125 0.0125 0.0404 0.0417 CH 3 COONa 0.125 0.0125 0.0604 0.0660 NaOH . 0.235 0.030 0.0183 0.0178 KOH . 0.1 0.01 0.0298 0.0348 NH4OH 0.305 0.032 0.0188 0.024 Liquid Elements. — It has long been known that there may be differences in potential at the contact of two solutions of electro- lytes. This can be shown by constructing an element in which the two electrodes are of the same metal, and immersed in the same solution of the same electrolyte. There can, therefore, be no differ- ence in potential between the two metals, nor between the metals and electrolytes, for the tensions between the metals and electro- lytes are the same on the two sides, and act in direct opposition to one another. If two solutions of electrolytes of different concentra- tions are introduced into the circuit between the solutions in which the electrodes are immersed, we shall have an element with a certain definite electromotive force. A typical liquid element would be the following : — Mercury — mercurous chloride. — potassium chloride. -^- potassium chloride. 100 V -^— hydrochloric acid. — hydrochloric acid. — potassium chloride. 10^ Mercurous chloride — mercury. ELECTROCHEMISTRY 461 Theory of the Liquid Element. — The first satisfactory theory of the liquid element we owe to Nernst. 1 What is the source of the differences in potential in liquid elements? That differences in potential should exist in electrolytes there must be a lack of uni- form distribution of ions. The region which is positive must con- tain an excess of cations, and that which is negative an excess of anions. The cause of this lack of uniform distribution of ions is to be found in the different velocities with which the different ions diffuse. Take the case of a solution of hydrochloric acid in contact with pure water. The hydrogen and chlorine ions in the solutions of the acid are present in the same number. They are, therefore, under the same osmotic pressure, and are driven with the same force into the water. But they move with very different velocities, from regions of higher to those of lower osmotic pressure. Hydrogen is, as we have seen, the swiftest of all ions, and moves very much faster than chlorine. It will thus diffuse into the water more rapidly than chlorine, and will tend to separate from the chlorine. But the positive ions cannot separate from the negative ions with- out producing a separation of the two kinds of electricity. There will result, therefore, electrostatic attractions between the layers, which will retard the hydrogen ions and accelerate the chlorine ions, until the two have the same velocity. Differences in potential will result; and always in the sense that the water or the more dilute solution will have the sign of the swifter ion. Hydrogen being the swiftest of all ions, water or the more dilute solution of acid is always positive with respect to the more concentrated. Next to hydrogen, in order of velocity, comes hydroxyl. Water, or the more dilute solution of a base, must, therefore, always be negative with respect to the more con- centrated. Nernst has shown not only how it is possible to account, quali- tatively, for the differences in potential between electrolytes, but has furnished us also with a method of calculating these differences quantitatively. Given two solutions of different concentrations of an electrolyte like hydrochloric acid, which is composed of a univalent cation and a univalent anion. Let the velocity of the cation be c, and that of the anion a. Let p t be the osmotic pressure of both ions in the more concentrated solution, and p 2 the osmotic pressure in the more dilute. If e electricity is passed from the more concentrated to the 1 Ztschr. phys. Chem. 4, 140 (1889). 462 THE ELEMENTS OF PHYSICAL CHEMISTRY more dilute solution, c of a gram-equivalent of cations will c + a move with the current, and of a gram-equivalent of anions C ~J~ Oi will move against the current. — — of cations have moved from a region of greater to one of less osmotic pressure. The work is : — ^RT ln*L c + a j9 2 But — — — of anions have moved from a region of lower into one of higher osmotic pressure. The work done upon them is : — -^RT ln*L c+a p 2 The total gain is the difference between these two : — C -^BT lnl\ c + a p 2 Equating this against the electrical energy we , we have — c—aRT. p, jr = — - In — ; c + a e„ p 2 or, it = £Z1^ 0.0002 T log^ 1 . c + a °p 2 If c is greater than a, the more dilute solution is positive, as already stated, and the current flows on the outside from the more dilute solution to the more concentrated. If a is greater than c, the more dilute solution is negative, and the current flows in the oppo- site direction. If the velocities of the two ions are equal (c = a), the right member of the above equation becomes zero, and there is no elec- tromotive force. It is, therefore, impossible to construct a liquid element from solutions of an electrolyte whose cation and anion have the same velocities. If the valence of either ion is greater than unity, this must be taken into account. If we represent the valence of the cation by v, and that of the anion by v 1 , the above expression becomes — c a ,r = ^—^ 0.0002 Tlog^. c + a °p 2 ELECTROCHEMISTRY 463 Nernst prepared liquid elements and determined their electro- motive force. He then calculated the electromotive force from the above equation, and compared the values found experimentally with those from calculation. The following element already referred to was constructed : — 12 3 4 Hg - HgCl - KC1 - KC1 - HC1 - HC1 - KC1 - HgCl - Hg. n n n n n io 100 loo 10 io' The potential differences at the ends are equal and opposite, and therefore equalize one another. The four differences in potential which must be taken into account are indicated above. But the potential differences are dependent upon the relative, not upon the absolute osmotic pressures. The potentials at 2 and 4 are, there- fore, equal and opposite, and can also be left out of account. This leaves the potentials at 1 and 3, and these can be calculated by the method already given. Let C[ and a^ be the relative velocities of potassium and chlorine ions, and c 2 and 02 the relative velocities of hydrogen and chlorine ions ; the electromotive force of this element would be calculated as follows, from the equation just deduced. The electromotive force would be the difference between these two potentials : — Ci — axRT. p Ci — OiRT ' p' it = Ci + «i e Pi c 2 + a 2 e jV p and p^ are the osmotic pressures of the potassium and chlorine ions in the more concentrated and more dilute solutions, respectively ; p'andjVthe osmotic pressures of the hydrogen and chlorine ions in the solutions of hydrochloric acid : — P_ = P_, Pi Pi Introducing this into the last equation, we have — \[ v' vj Ol + o,! c 2 + a 2 0.0002 T log£. Pi The electromotive force of the liquid elements which have been studied, as calculated from the above equation, agrees with that measured, to within the limits of experimental error. It should be observed that the expression deduced above holds only for the potential at the contact of solutions of the same electro- lyte, the solutions being of different concentrations. If different electrolytes are used, we have no general means of calculating the potential at their surface of contact. It should be stated before leaving the subject of liquid elements, that the potential at the contact of two solutions is usually not great, and that the electromotive force of liquid elements is in general not large. Sources of Potential in a Concentration Element. — We may now analyze more closely the electromotive force in a concentration ele- ment in the light of what we have learned about the liquid element. Thus far we have dealt with the concentration element as if the only sources of the potential were at the points of contact of the elec- trodes and the solutions. And indeed this is practically true in the cases of the concentration element which we have studied. We have learned from the study of the liquid element that the plane of contact of two solutions of an electrolyte is also a seat of potential. In the concentration element there is always such a contact between two solutions of the electrolyte, and this must be a source of potential. In the concentration element which we have studied, this potential is so small that it can practically be neglected. While the potential between solutions is usually small, it may, how- ever, easily assume proportions which must be taken into account. We must now see how it is possible to calculate the potential at the contact of the two solutions in the concentration element. We can then analyze the electromotive force of a concentration element into its three constituents, and calculate the magnitude of the potential at each electrode, and also at the surface of contact of the elec- trolytes. Let the potential at one electrode be tt', at the other electrode ir", and at the contact of the two electrolytes ir'". The values ELECTROCHEMISTRY 465 of these potentials are calculated by means of the following formulas : — *' = 0.0002 T log-; ft it" =- 0.0002 T log-; ft *■"' = 0.0002 T ^^ log & • c + a Pi These equations obtain for univalent ions. If the valence of the ion is greater than one, this must be taken into account in the way already described. The sum of the three potentials must then be the potential of the concentration element. 7r' + 7r"= -0.0002 T log &; ft ( T r + „m + „■»/ = 0.0002 r- 2 -^- log Sii c + a j3i This must be the same as the equation already deduced (p. 456) for the concentration element. It will be seen to be the case, if we consider that m f = 2, and v for univalent ions equals 1. We can thus calculate the magnitude of the three sources of potential in a concentration element of the first class. An element of this class has been chosen, since the relations are somewhat simpler. The main sources of potential are at the contact of elec- trode and electrolyte, while a very small potential exists at the con- tact of the two electrolytes. In elements of this kind it is perfectly clear that there is no potential where the two electrodes come in contact, because these are of the same metal. Chemical Elements. — In the elements which we have thus far considered, the electrical energy is not produced at the expense of intrinsic energy, as Le Blanc 1 clearly points out. Since the intrin- sic or chemical energy of the substances in the cell remains unaltered, the electrical energy produced in the cell must come mainly from the heat of surrounding objects, which is converted into electrical energy in the cell. There are, however, forms of elements in which intrinsic energy is converted into electrical, and these are termed chemical elements. Such elements may transform the intrinsic energy quantitatively into electrical; or only a portion of the intrinsic energy may be transformed into electrical, the remainder appearing as heat ; or, 1 Lehrbuch der Elektrochemie, p. 160. 2h 466 THE ELEMENTS OF PHYSICAL CHEMISTRY finally, a part of the electrical energy may come from the intrinsic energy, and the remainder from the heat taken up by the cell and transformed into electrical energy. There is thus no very sharp distinction between chemical elements and non-chemical elements. There are, however, elements in which most of the electrical energy comes from intrinsic energy, and these ■we will include under the head of chemical elements, to distinguish them from those elements where practically no intrinsic energy is converted into electrical. It is obvious that there might be a large number of elements in which a small portion of the electrical energy was produced from intrinsic energy, and the remainder from heat energy. Such would obviously not fall into either of the above classes. We will take as a type of the chemical element the Daniell ele- ment, which consists of zinc immersed in a solution of zinc sulphate, and copper immersed in a solution of copper sulphate. Zinc dis- solves, passing into solution as ions, while ions of copper separate from the solution in the metallic form. The zinc electrode is there- fore negative, and the copper positive; the current passing on the outside from the copper to the zinc. In calculating the electromotive force of the Daniell element, the solution-tension of both the copper and the zinc must be taken into account. In the elements which we have thus far considered, both electrodes were of the same metal. The solution-tension of the metal was, therefore, the same upon both sides of the cell, and being of equal value and opposite sign, it disappeared from the equation for the electromotive force of the element. Whenever the electrodes are of different substances, their solution-tensions, being of unequal values, must be taken into account. The application of our fundamental equation to the electromotive force of the Daniell element will serve as an example of the way in which it may be applied to other well-known elements. The electro- motive force is equal to the difference in potential at the two elec- trodes, since the potential at the contact of the zinc sulphate and copper su.lph.ate is so slight that we can practically disregard it. Eepresenting the potential at the two electrodes by ir x and t 2 , we haVe - RT, P *i=-^— ln -; 2e p *2 = -S— ln — 2e jp! in which P and P x are the solution-tensions of the two metals : — ELECTROCHEMISTRY 467 RT/, P , PA T,-7r 2 = 7r=-— In ln^). 2e \ p PiJ In the light of this example, the application of the conceptions here developed to other special cases should be a simple matter. Oxidation and Reduction Elements. — A type of elements which illustrates very well the transformation of intrinsic energy into electrical, is known as the oxidation and reduction elements. These must be considered very briefly. In a paper on " Chemical Action at a Distance," 1 Ostwald described such phenomena as the follow- ing. If we have a solution of ferrous chloride in contact with a solution of potassium chloride which contains free chlorine, and plunge carbon or platinum electrodes into the two liquids, we have an element. It is not even necessary that the two solutions should come in contact ; they may be separated by an electrolyte, say a solution of potassium chloride. Ostwald recommended the following experiment: Two beakers are filled — the one with a solution of ferrous chloride, the other with a solution of potassium chloride saturated with chlorine. Platinum electrodes are introduced into each vessel, and are connected with each other through a galva- nometer. The two beakers are connected by means of a siphon filled with a solution of potassium chloride, and the ends loosely stoppered with rolls of filter-paper. When the circuit is closed the galvanometer shows that a current is passing; and it flows in the liquid from the ferrous chloride to the chlorine. Within the cell the ferrous ion passes over into the ferric ion, and at the same time an equivalent number of chlorine ions are formed on the other side of the cell. There is evidently an oxidation of the iron and a re- duction of the chlorine taking place. We must now define oxidation and reduction in an electrical sense. An electrical oxidizing agent is one in which there is a tendency to form new negative charges, or to cause positive charges to disappear. An electrical reducing agent is one in which there is a tendency to form new positive ion charges, or to cause negative charges already present to disappear. In the above element the ferrous ion takes up a positive charge from the electrode with which it is in contact, becoming a ferric ion, and the corresponding negative charge is taken from the other electrode by the chlorine, which becomes an anion. The electrode ■ i Ztschr. phys. Ohem. 9, 549 (1894). See Peters : Ibid. 26, 193 (1898). Fredenhagen : Ztschr. anorg. Chem. 29, 396 (1902). 468 THE ELEMENTS OF PHYSICAL CHEMISTRY immersed in the reducing agent (FeCl 2 ) is, therefore, the anode, while the electrode immersed in the oxidizing agent is the cathode. As Ostwald observes, this element seems to represent chemical action as taking place at a distance, — the chlorine in one vessel con- verting the ferrous iron in another vessel into ferric iron. But as we have just seen, it is readily explained in the light of the theory of electrolytic dissociation. The measurement of the electromotive force of a number of such elements was carried out in Ostwald's laboratory by W. D. Bancroft. 1 The more important conclusions at which he arrived are : — The electromotive force is an additive property, i.e. the sum of two constants, one depending on the oxidizing agent, the other on the reducing agent. It is independent of the concentration, and of the nature of the electrodes, if these are not attacked by the electrolytes. It is also independent of the nature of the electrolyte used in the siphon. The Gas-battery. — The typical gas-battery consists of an electro- lyte, two gases which can act chemically upon one another, and two platinum electrodes which are partly surrounded by the electrolyte, and partly by the gases. Take as a simple example, hydrogen over one electrode and chlorine over the other, the electrolyte hydrochloric acid, and the electrodes platinum. Hydrogen and chlorine will pass into solution at the two poles until there is an equilibrium between the force driving these substances into solution (solution-tension), and the osmotic pressure of the hydrochloric acid solution, which acts against the above-named force. The hydrogen pole is negative, since the solution-tension of the hydrogen is greater than the osmotic pressure of the solution; the hydrogen atoms becoming ions by taking positive electricity from the platinum electrode, which thus becomes negative. Exactly the opposite result is obtained at the other electrode, chlorine atoms becoming ions by taking negative electricity from the electrode, which therefore becomes positive. Ostwald 2 has shown that the theory of Nernst can be applied also to the electromotive force of the gas-battery. He has worked 1 Ztschr. phys. Chem. 10, 387 (1892) ; 29, 305 (1899). 2 Lehrb. d. Allg. Chem. II, p. 895. See Heathcote : Ztschr. phys. Chem. 37, 368 (1901). Markousky •- Wied. Ann. 44, 457 (1891). Bauer : Ztschr. anorg. Chem. 29, 305 (1902). Czepinski : Ibid. 30, 1 (1902). Bose : Ibid. 38, 1 (1901). Wulf : Ibid. 48, 87 (1904). Levi : Oazz. chim. ital. 35, 1, 391 (1905). Sauer: Dissertation, Gottingen (1906). ELECTROCHEMISTRY 469 out even a simpler case than the one given above. We will take up first the simplest possible case, where we have the same gas, say hydrogen, over both electrodes, the hydrogen upon the two sides being at different pressures. The action of such an arrangement would be, as Ostwald shows, to equalize the pressure of the gas on the two sides of the cell. Hydrogen must pass into solution as ions upon the side where it is under the greater pressure, and ions of hydrogen must separate as gas upon the other side of the cell. Upon the side where hydro- gen atoms are becoming ions, they take positive electricity from the electrode, which becomes negative, and the other electrode positive, because positive hydrogen ions are giving their charges up to it. We have here an analogue of the concentration element, and the electromotive force can be calculated in a similar manner. The electromotive force of this element also is the difference in the potential upon the two sides : — BT , P BT, P ir = In In — , ve pn ve p 1 where P is the solution-tension of hydrogen, and p^ and p 2 the press- ures of the hydrogen gas upon the two sides. The solution-tension, being the same upon both sides of the cell, disappears as in the concentration element, and then we have — , = Q-0002 r log &. i> Pi Since for the hydrogen molecule, v = 2, we have — * = 0.0290 log Si- Pi Ostwald 1 has also calculated the electromotive force for a gas- battery consisting of two gases. But as this has been worked out much more fully by Smale, 2 we will turn to his work. Take the case of oxygen at one pole and hydrogen at the other. Let P 1 be the solution-tension of hydrogen. Let P 2 be the solution-tension of oxygen. Let T be the absolute temperature. The potential at the hydrogen pole is — *-! = 0.0002 T log 5t- Pi Since the solution-tension of oxygen is negative, — ir 2 = 0.0002 Tlogi^; 1 Loc. cit. o Ztschr. phys. Chem. 14, 577, and 16, 562. 470 THE ELEMENTS OF PHYSICAL CHEMISTRY TTj - tt 2 = ir = 0.0002 T log^ - 0.0002 T log^: Pi Pi ir = 0.002 T log £ + 0.0002 T log ^ . ' The theoretical consequences of this equation are very interest- ing. P x and P 2 , the solution-tensions of the gases, are independent of the nature and concentration of the electrolyte used on the two sides of the element; andjpj andp 2 are practically constant for solutions of nearly the same dissociation. Smale 1 has tested this point, using seven acids, three bases, and seven salts. The concentrations for the same electrolyte vary in most cases from 0.1 to 0.001 normal. He found that the electro- motive force of the hydrogen-oxygen battery was practically con- stant, independent of both the nature and concentration of the electrolytes used beneath the gases. A few results taken from the work of Smale will bring out this fact. Electrolyte Used Concentration Normal E. M. F. HC1 0.1 0.998 HC1 0.01 1.036 HC1 0.001 1.055 KOH 0.1 1.098 KOH 0.01 1.095 KOH 0.001 1.093 K 2 SO* 0.1 1.074 K 2 S0 4 0.01 1.069 K 2 S0 4 0.001 1.069 The results thus agree satisfactorily with the deduction from theory. If instead of oxygen other gases, as chlorine, are used, the electromotive force depends upon the concentration of the electro- lyte, which also agrees with theory, as is shown by Smale. This work of Smale furnishes then another beautiful experi- mental confirmation of the consequences of that theory, which has enabled us to calculate the electromotive force of concentration elements, liquid elements, etc. A number of other types of elements might be taken up, and their electromotive force calculated from the method of Nernst, which, as we have already seen, is based upon Van't Hoff's laws of x Loc. tit. ELECTROCHEMISTRY 471 osmotic pressure and Arrhenius' theory of electrolytic dissociation. This is, however, not necessary, since the application to special cases is simple if the fundamental principles are once grasped. MEASUREMENT OF DIFFERENCES OF POTENTIAL BETWEEN METALS AND ELECTROLYTES — CALCULATION OF THE SOLUTION-TENSION OF METALS Differences of Potential between Metals and Electrolytes. — It is obvious from our studies of the action of the primary cell, that when a metal is immersed in a solution of one of its salts, there is established a difference in potential between the metal and the solution. In- deed, we have seen that this is the chief source of the electromotive force in such elements. The cause of this difference in potential we have learned is, on the one hand, the solution-tension of the metal tending to drive ions from the metal into the solution, and the osmotic pressure of the solution acting counter to this, tending to cause the cations already present to separate on the electrode in the metallic condition. The result is the formation of the Helmholtz double layer, and a difference in potential between the metal and the solution. It is very desirable to know the magnitude of these potential differences, and to the measurement of such differences we shall now turn. Measurement of Individual Differences of Potential. — A number of methods have been devised and used for measuring differences of potential between metals and solutions. Reference only can be made to that involving the use of drop-electrodes. 1 We shall now study in some detail the method involving the use of the " normal electrode." This method is based upon the use of an electrode whose potential is known. This is connected with the electrode whose difference in potential it is desired to measure, and the electromotive force of the whole determined. Since the potential of the normal electrode is known, that of the electrode in question is determined at once, the electromotive force of the two when com- bined being the difference between the potentials on the two sides. The form of "normal electrode" used by Ostwald is shown in Pig. 67. The bottom of a glass tube A, about 8 cm. high, and 2 to 2\ cm. in diameter, is covered with mercury. Over the mercury is placed a layer of mercurous chloride, and the glass vessel is then filled with a normal solution of potassium chloride. 1 Ostwald : Ztschr. phys. Chem. 1, 583 (1887) ; see also Outlines of Electro- chemistry, Jones (Elec. Eev. Pub. Co.). See Wilsmore: Ztschr. phys. Chem. 35, 291 (1900). Ostwald : Ibid. 35, 333 (1900). Sauer: Ibid. 47, 146 (1904). 472 THE ELEMENTS OF PHYSICAL CHEMISTRY -SOLUTION -.= Fig. 67. A platinum wire, Pt, passed into a glass tube and protruding beyond its end, dips into the mercury. This serves as one electrode. The other glass tube, t, passing through the cork, is filled also with the normal solution of potassium chloride. The glass tube, t u at the end of the rubber tube, is inserted into the liquid whose potential against a given metal it is desired to measure. The metal serves as the second electrode. The electromotive force of the whole system is now meas- ured. Knowing the potential on the one side, that on the other is obtained at once. If the liquid in the electrode whose potential it is desired to measure, acts chem- ically upon potassium chloride, a solution of some indifferent sub- stance is interposed between the two. Thus, if we were measuring the difference in potential between lead and lead nitrate, a solution of some neutral nitrate (as potassium or sodium) would be interposed in the circuit. The use of potassium chloride is very desirable, since the potassium and chlorine ions move with very nearly the same velocity, and, therefore, any potential difference at the contact of the two electrolytes would be very small. The potential of the normal electrode just described is 0.56 volt. The metal is positive, the electrolyte negative, which means that there is a tendency for the mercury ions present to separate from the solution as metallic mercury ; and this tendency is expressed in potential by 0.56 volt. In such measurements the potential of the metal is taken as zero, and the electrolyte expressed as either positive or negative. The normal electrode just described has then a potential of — 0.56 volt. By means of this normal electrode, potential differences between metals and electrolytes can be easily measured. Let us take as an example, the potential difference of magnesium against a normal solution of magnesium chloride. The "normal electrode" is connected with a vessel containing a normal solution of magnesium chloride, into which a bar of magnesium dips. The electromotive force of this combination was measured and found to ELECTROCHEMISTRY 473 be 1.791 volts. We know that the electromotive force, w, of this element is expressed thus: — -ln = p Pi (1) in which P is the solution-tension of magnesium, p the osmotic pressure of the magnesium ions in the solution, 2 the valence of magnesium ; Pj the solution-tension of mercury, and pi the osmotic pressure of the mercury ions in the solution. We have just seen, however, that, —In ^=-0.56 volt. e Pi Substituting in equation (1) we have — 1.791=— In ^+0.56, 2e„ p or, ^ln- = 1.231 volts. 2e p But, #^ln^= 0.029 log-; ^e„ p p therefore, 0.029 log-= 1.231 volts. p The difference in potential between magnesium and a normal solu- tion of magnesium chloride is, then, 1.231 volts. The differences of potential between a number of metals and normal or saturated solutions of their salts have been measured by Neumann, working in Ostwald's laboratory. The following data are taken from the results which he obtained : — Metal Sulphate Chloride Volts Volts + 1.239 + 1.231 + 1.040 + 1.015 + 0.524 + 0.503 + 0.162 + 0.174 + 0.093 + 0.087 Cobalt - 0.019 - 0.015 - 0.022 - 0.020 - 0.085 - 0.095 - 0.515 - — - - 0.980 - 0.974 Gold - 1.356 - 1.066 474 THE ELEMENTS OF PHYSICAL CHEMISTRY Effect of the Nature of the Anion. — The question as to the effect of the anion on the potential between the metal and the solution was raised by Neumann. In addition to sulphates and chlorides, which gave very nearly the same results, he used also nitrates and acetates. The results in the latter cases were very different from those obtained with the chlorides and sulphates. The discrepancies in the case of the acetates may be accounted for in part as due to differences in the degree of dissociation of the different salts. In the case of the nitrates the NO s ion undoubtedly has some action on the metal electrodes. If, however, we take all of these possibilities into account, there are still discrepancies which are not satisfactorily explained. To test the effect of the anion on the potential difference, Neumann 1 prepared twenty-three salts of thallium, and studied the potential between the metal and their solutions at different concen- trations. These include the thallium salts of seventeen organic acids, five inorganic acids, and the hydroxide. A few of his results are given below. Salts of Thallium n 10 n 50 71 100 Potential Potential Potential Hydroxide 0.670 0.704 0.715 Nitrate .... 0.671 0.7055 0.716 Formate .... 0.675 0.7045 0.715 Acetate .... 0.677 0.7055 0.715 Malonate .... 0.678 0.705 0.715 Tartrate .... 0.677 0.705 0.715 Benzoate .... 0.680 0.705 0.7155 These results show that for equally dissociated substances, the anion is without influence as far as the salts of thallium are con- cerned. Calculation of the Solution-tension of Metals. — The difference in potential between a metal and the solution of the electrolyte in which it is immersed is due, as we have seen, to the solution-tension of the metal, and to the osmotic pressure of the cations in the solution. If we know the value of this potential difference and of the osmotic pressure of the cations in the solution, it is obvious that we can cal- 1 Ztschr. phys. Chem. 14, 225 (1894). ELECTROCHEMISTRY 475 culate the solution-tension of the metal. We have seen that the potential difference, which we will call ■*, is expressed thus : — 0.058 , P n. P where n e is the valence of the cation, p the osmotic pressure of the cations in the solution, and P the solution-tension of the metal. If ■n- and p are known, P can be calculated at once. Thus : — The solution-tensions of some of the more common metals calcu- lated from this equation, using the values of ir as found by Neumann, are given in the following table. The values of ir for the chlorides are used whenever they were determined ; when this is not avail- able, the value for the sulphate was used. The value of the osmotic pressure of the cations in the normal solutions is taken as 22 atmos- pheres. 1 Atmosphkbes Magnesium 10 44 Zinc 10 18 Aluminium 10 1S Cadmium 3 x 10 s Iron 10* Cobalt 2 x 10° Nickel 1 x 10° Lead lO* Mercury • 10- K Silver 10-" Copper lO- 30 The Tension Series. — When the metals are arranged as above in the order of their solution-tensions, we have what is known as the tension series. The position of a metal in the tension series, like its position in the Periodic System, conditions many of its properties. Thus, a metal anywhere in the series will tend to precipitate from its salts any metal lower in the series. It is well known that zinc will precipitate copper from its salts, and so on. A metal at any point in the series, when made one pole of a battery against a metal lower in the series as the other pole, will throw off ions into solution, and thus become the negative pole. Thus, zinc is the negative pole in almost all elements in which it occurs. The position of an element in the tension series is thus a matter of fundamental importance, being very closely connected with the inherent nature of the metal itself. 1 See Rothmund: Ztschr.phys. Chem. 15, 1 (1894). 476 THE ELEMENTS OF PHYSICAL CHEMISTRY Constancy of Solution-tension. — It was supposed for a time that the solution-tension of a metal is a characteristic constant for the substance. This view was held by Ostwald and developed in his Lehrbuch. On page 852 it is stated that " the value P, of the elec- trolytic solution-pressure, is a constant peculiar to the metal, which depends upon the temperature only, and generally increases with increasing temperature. " So far as we know this holds for a given solvent, but does not apply to different solvents. Jones 1 has found that the solution-ten- sion of metallic silver, when immersed in an alcoholic solution of silver nitrate, is only about one-twentieth of that in an aqueous solution. We can, therefore, regard solution-tension as a constant only for any given solvent in which the salts of the metal are dis- solved. Indeed, this is what we would expect, when we consider that nearly every substance dissolves differently in, or has a specific solution-tension toward, every solvent. If the substances which dissolve readily in solvents vary so greatly from solvent to solvent, as we know they do, why should not substances which are only slightly soluble, such as the metals, show this same difference ? Quite recently, Jones and Smith 2 have shown that the solution- tension of zinc in water is 10 8 times its solution-tension in ethyl alcohol. Difference in Solution-tensions of Metals. Chemical Action at a Distance. — Eef erence 8 has already been made to the paper by Ost- wald on " Chemical Action at a Distance." Under that same head he describes an experiment which must be referred to here. Ost- wald begins his paper by calling attention to the fact that amalga- mated zinc is not dissolved by dilute acids, but if the zinc is surrounded by a platinum wire, it is dissolved by the acid. It is not even necessary for the platinum wire to surround the zinc, for if the wire touches the zinc at any one point, solution will take place. Ostwald suggests that the zinc and platinum wire be joined at one place, and then the free ends of both immersed in a vessel con- taining, say, potassium sulphate. Let a screen of some porous ma- terial be placed between these free ends of the platinum and zinc, so that the salt solution around the one is separated from that around the other. He then asks the question, to which metal must 1 Ztschr. phys. Chem. 14, 346 (1894). Phys. Mev. 2, 81 (1894). 2 Amer. Chem. Joitm. 23, 397 (1900). 3 Ztschr. phys. Chem. 9, 540 (1892). ELECTROCHEMISTRY 477 sulphuric acid be added in order that the zinc may be dissolved by the acid ? " The question seems at first sight to be absurd ; since in order that the zinc should dissolve, it appears to be self-evident that the acid should be added to the zinc. If we carry out the experiment, we find exactly the reverse to be true. The zinc does not dissolve rapidly, if acid is added to the solution of potassium sulphate around the zinc. If, on the contrary, the acid is added to the solution around the platinum, the zinc dissolves with a copious evolution of hydrogen gas. The hydrogen appears on the platinum, as is always the case when zinc is in combination with platinum. To dissolve the zinc under the conditions described, the solvents must not be allowed to act on the metal to be dissolved, but on the platinum which is in contact with the zinc." A number of other cases are cited. Zinc in sodium chloride behaves in the same manner when hydro- chloric acid is added to the platinum. Cadmium also behaves like zinc. Tin, surrounded by sodium chloride, dissolves when hydro- chloric acid is added to the platinum. Aluminium behaves like tin. Silver connected with platinum dissolves in sulphuric acid when a few drops of chromic acid are added to the platinum. Gold dis- solves in sodium chloride, if chlorine is brought in contact with the platinum. Experiment to demonstrate Chemical Action at a Distance. — Fill a beaker with a solution of potassium sulphate. Take a piece of glass tubing about 10 cm. long and 2 cm. wide, and close the lower end with vegetable parchment. Fit a bar of pure zinc, about 10 cm. long, tightly into a cork which just closes the top of this glass tube. Fill the glass tube with some of the same solution of potassium sulphate, and insert the bar of zinc — the cork closing the top of the glass tube. Around the top of the zinc bar above the cork wrap a piece of platinum wire of sufficient length to reach nearly to the. bottom of the beaker, when the glass tube is introduced into the beaker in the manner to be described hereafter. The free end of the platinum wire should be coiled upon itself a number of times, or it is better if it is connected with a piece of platinum foil a few centimetres square, so as to expose a larger surface. The glass tube is now immersed in the beaker until the surface of the solution in the tube is only a centimetre or two above the surface of solution in the beaker, the free end of the platinum wire, or the platinum foil, being allowed to rest on the bottom of -the beaker. 478 THE ELEMENTS OF PHYSICAL CHEMISTRY If a few drops of sulphuric acid are introduced into the potassium sulphate just around the bar of zinc, the zinc will be very slightly affected. But if a few drops of sulphuric acid are poured upon the coiled end of the platinum wire, or upon the platinum foil, the zinc will dissolve rapidly in the neutral potassium sulphate which sur- rounds it, and a copious evolution of hydrogen will take place from the platinum, where it is in contact with the sulphuric acid. After a few moments the presence of zinc can be demonstrated in the inner tube, by any of the well-known reactions for zinc. As Ostwald states, similar phenomena have long been known. More than forty years ago Thomsen 1 described a galvanic element, which consists of copper in dilute sulphuric acid, and carbon in a chromate mixture. When the carbon and copper were connected, the metal dissolved as the sulphate in sulphuric acid, in which copper alone is not soluble. Becquerel 2 observed a similar phe- nomenon in the case of the element Cu-ZnS0 4 -ZnS0 4 -Zn. While many similar facts were known, there was no rational explanation offered to account for them until Arrhenius proposed the Tlieory of Free Ions. It is almost self-evident that the phenomenon is closely connected with electrical changes. Ostwald demonstrated this by introducing between the metal and the platinum a fairly sensitive galvanoscope. When the acid was added to the platinum, the presence of a current was shown by the throw of the instrument. The explanation of this phenomenon is perfectly simple, now that we have the theory of electrolytic dissociation and are familiar with its application to the primary cell. When metallic zinc is immersed in a solution of a neutral salt, like potassium sulphate, it sends, in consequence of its own solution- tension, a certain number of zinc ions into the solution. The zinc is thus made negative, and the solution, which has received the posi- tive ions, positive. This continues until a definite difference in potential between metal and solution is established. The amount of metal required to effect this condition is, as we have seen, so small that it cannot be detected by any chemical means. The zinc cannot dissolve further, because of the excess of positive ions in the solution. In order that more zinc may pass into solution, some of these positive ions must be removed. If the zinc is in contact with another metal, such as platinum, the latter takes the same negative charge as the zinc. When the platinum is immersed 1 Pogg. Ann. Ill, 192 (1860). 'Ann. Chim. Phys. [2], 41, 5 (1829). ELECTROCHEMISTRY 479 in the solution, it attracts the excess of positive ions in the solution, and these collect upon the platinum. We would expect the excess of positive ions in the solution to give up their charge to the negative platinum, and separate from the solution, or, in case of potassium, decompose the water which is present. This depends both upon the nature of the ion and of the electrode. If the positive ion is the potassium of potassium sul- phate, the difference in potential produced by introducing the zinc is not sufficient to cause this ion to lose its charge to the platinum. If sulphuric acid is added to the platinum, the difference in poten- tial produced by introducing the bar of zinc is sufficient to compel the hydrogen to give up its positive charge to the platinum, and separate as ordinary hydrogen. The platinum, having received positive electricity from the hydrogen ions, conducts this over to the zinc. The zinc becomes less negative than before the hydrogen separated at the platinum, and the difference in potential between the zinc and the surrounding solution is less than before. More zinc dissolves or passes over into ions, more hydrogen ions give up their charge to the platinum and separate as gas; and this continues until all of the zinc has dissolved, or all of the hydrogen ions have separated as gas. As Ostwald observes, this explanation shows not only why the acid must be added to the platinum and not to the zinc, but throws light also on the problem of the solution of metals in general. A word or two on this subject. It has long been known that pure zinc does not dissolve in acids, while impure zinc readily dissolves. It is quite evident that the zinc in the two cases has the same tendency to dissolve. Pure zinc dissolves readily when in contact with a metal, such as platinum, which has a small solution-tension. As we have seen from the foregoing explanation, the difference is not in the solution of the zinc, but in the ease with which the hydrogen can escape from the solution. The presence of a metal with small solution-tension allows this to take place more readily, and this is the reason that impure zinc dissolves in acids. The reason why pure zinc does not dissolve in acids is because this metal has a strong positive solution-tension; it sends positively charged ions into solution under a high solution-tension, and, there- fore, opposes the separation of any other positive ion, like hydrogen, upon it. Pure zinc, therefore, does not dissolve in acids, because the hydrogen ions cannot give up their positive charges and escape. When a metal like platinum, which has a small solution-tension, is present, the hydrogen can easily give up its charge to this metal 480 THE ELEMENTS OF PHYSICAL CHEMISTRY and escape as gas. The zinc, because of its high solution-tension, and because the hydrogen cations can so easily escape, then dissolves. To repeat the essential steps in the explanation of the experi- ment described above: Pure zinc immersed in potassium (or any soluble) sulphate, to 'which sulphuric acid is added, or in a solution of pure sulphuric acid itself, does not dissolve because the zinc has such a high solution-tension that the hydrogen ions cannot give up their charge to it and escape. The zinc, however, throws a few ions into solution and becomes negatively charged. If now the zinc is connected with platinum, which has a small solution-tension, and the acid added to the platinum, the hydrogen ions can easily give up their charge to the platinum and escape as gas. The platinum, which was at the potential of the zinc with which it is in contact, now becomes positive with respect to the zinc, and a positive charge therefore flows from the platinum to the zinc. The zinc, having received 'positive electricity, can begin dissolving anew, and continue to pass into solution as long as it receives positive electricity from the platinum — as long, therefore, as there are any hydrogen ions in the solution to furnish positive electricity to the platinum. Or, as we are accustomed to express it, as long as there is any acid in con- tact with the platinum. The following paragraph is taken from this fascinating paper by Ostwald : " We see that the usual explanation, that solution takes place because of galvanic currents between the zinc and the other metals, is not in strict accord with the facts. The galvanic currents are inseparably connected with the process of solution, but they are not the primary causes of the solution. They are set up, rather, by the process of solution, which they must necessarily accompany, since solution is a question of ion formation and disappearance. If it is possible for the positive ions present to separate in any way from the solvent, solution takes place." Another Experiment illustrating Chemical Action at a Distance. 1 — Pour into one beaker a solution of ferrous chloride, and into an- other beaker a solution of potassium chloride saturated with chlorine. Introduce a platinum electrode into each beaker, and connect these externally through a galvanometer. The solutions in the two beakers are connected by means of a siphon filled with a solution of pure potassium chloride, the ends of the siphon being loosely filled with rolls of filter paper. An electric current is set up at once, as is shown by the galvanometer, flowing on the outside 1 Ztschr. phys. Chem. 9, 560 (1892). Considered in another connection, p. 467. ELECTROCHEMISTRY 481 from the solution of potassium chloride containing the free chlorine to the solution of ferrous chloride. The ferrous chloride is oxidized around the electrode to ferric chloride, by chlorine which does not come in contact with it. This is obviously another example of chemical action at a distance. The explanation of what goes on in this experiment is com- paratively simple. The free chlorine passes into the ionic state, taking negative electricity from the electrode immersed in the potassium chloride containing chlorine. This electrode is thus left positively charged. The current flows from this electrode through the galvanometer, over to the other electrode. The ferrous iron, carrying two positive electrical charges, takes up another positive charge, passing over into the ferric condition. The extra chlorine moves against the current in the solution, i.e. from the potassium chloride, containing chlorine, over towards the solution of ferrous chloride. Instead of chlorine, in the above experiment, bromine can be used ; and instead of ferrous chloride other reducing solutions can be employed. The Bearing of this Experiment on Chemical Valence. — The preceding experiment is not only an illustration of chemical action at a distance, but also bears directly on a more important and wider- reaching principle in chemistry, i.e. chemical valence. There are few subjects in chemistry, the discussion of which has, in the past, been so unsatisfactory and confusing, as the discussion of chemical valence. This is due primarily to the lack of any exact definition of the subject under consideration. Chemical valence admits of an exact definition and rests upon a perfectly rigid physical basis — Faraday's second law. The valence of an ion is a function of the number of electrical charges that it carries. A univalent ion carries one electrical charge, a bivalent ion car- ries two such charges, an n valent ion n such charges. The second law of Faraday underlies the whole subject of valence, and is as fundamental a law of chemistry in general as it is of electrochemistry in particular. The combining power of an ion is a function of the number of electrical charges that it carries. With this definite physical basis as a starting-point, the discussion and application of the principle of valence to the whole subject of general chemistry is greatly simplified. 1 That the above experiment bears directly upon valence can be 1 See Principles of Inorganic Chemistry, and Elements of Inorganic Chem- istry, by the author of this work. 2i 482 THE ELEMENTS OF PHYSICAL CHEMISTRY seen at a glance. We raise the valence of iron from two in the fer- rous condition to three in the ferric condition. How is this done ? By adding electricity to it — by giving it one more charge. This we know takes place, and this, in the above experiment, is all that can take place. We have thus raised the valence of an element by in- creasing directly the charge which it carries, and we have done it under such conditions that we know that nothing else could have occurred. This is, then, an ideal demonstration of the relation between valence and the charge carried by the ion. ELECTROLYSIS AND POLARIZATION Passage of Electricity through Electrolytes. — When the two elec- trodes of a battery, or of any other source of electricity, are placed in a solution of an electrolyte, the current flows through the solution from one electrode to the other. Much confusion has existed in the naming of these electrodes. If we refer to them as positive and nega- tive, this is ambiguous. If we name them in terms of the direction of the flow of current, we must specify whether we mean the flow on the outside or on the inside of the cell. The best method is to call that electrode the cathode toward which the current flows in the cell, and the other electrode the anode. The current can pass through solutions of electrolytes, as we have seen, in only one manner ; i.e. by a simultaneous movement of the ions in the solution — the cations carrying the positive charge towards the cathode, the anions the negative charge towards the anode. These ions give up their charges to the respective electrodes or poles, and thus become atoms or groups of atoms. These may then separate from the solution, or secondary reactions may take place. This pro- cess is known as electrolysis. The actual process at the poles may be quite different, in many cases, from what was for a long time supposed ; but this will be con- sidered a little later. Products of Electrolysis. — When the ions give up their charges to the electrodes, they may be capable of an independent existence, or they may not, depending upon their nature. Many cations, such as some of the metals, are capable of such an existence, while very few anions can exist as such, after they give up their negative charge. In the latter case they may decompose into entirely new products, or may react with some other substance present and give rise to second- ary products. We must distinguish, then, between primary and sec- ondary products of electrolysis. The primary products of electrolysis are the metals, which sepa- ELECTROCHEMISTRY 483 rate as such from the solutions of their salts ; also other elements which separate as such, e.g. hydrogen, chlorine, etc. The attempt which has been made to place these substances among the secondary products, because the atoms polymerize to form molecules, and thus separating them from the metals which are primary products, does not seem to be well founded. It is, of course, true that two hydro- gen atoms, two chlorine atoms, etc., unite to form a molecule, but does any one suppose that the molecule of a metal in the solid state is identical with the atom? The fact that the molecule of many metals is identical with the atom when the metal is dissolved in mercury, which we have seen to be true, is no argument that such is the case in the pure metal. The metallic atoms probably polym- erize as much or more than the chlorine atoms. The secondary products of electrolysis may be formed in at least four ways : — (1) The ions may react with the water present as solvent. (2) They may react with more of the electrolyte. (3) They may react with the electrodes. (4) They may decompose into entirely new products. Polarization. — If a current is passed through an element contain- ing metal electrodes surrounded by salts of the same metal, the elec- trodes are not changed, and the solutions around the electrodes are not changed essentially, although they do undergo slight changes in concentration. The difference in potential between the electrode and the surrounding solution remains, therefore, practically constant, and such electrodes are termed non-polarizable. If, on the other hand, either the electrode or the electrolyte is changed appreciably by the passage of the current, the difference in potential between the two does not remain constant, but changes with the passage of the current. Such electrodes are termed polarizable. When such a change is effected, it always takes place in the sense to oppose the passage of the current. If two polarizable electrodes, through which a current has been passing for a time, are closed in circuit, a current will set up in the direction opposite to that which effected the polarization. This is known as the polarization current, and its electromotive force the electromotive force of polarization. A quantitative study of polarization currents will show that they gradually grow weaker and weaker. Method of Measuring Polarization. — When a current passes through an electrolyte there is electrolysis, and consequently polari- zation at both poles. The electromotive force of polarization is, See Tafeland Emmert : Ztsckr. phys. Ohem. 52, 349 (1905). 484 THE ELEMENTS OF PHYSICAL CHEMISTRY therefore, made up of two differences in potential between metals and electrolytes. In measuring polarization we must measure the potential at each, electrode. A method has been devised for this pur- pose by Fuchs. 1 The following modification of this method was used by Le Blanc. 2 The electrolyte whose polarization it is desired to study is intro- duced into the tube T (Fig. 68). Two electrodes connected with the element E, which furnishes the polarizing current, are introduced as shown in the figure. To measure the potential at either electrode, we connect this electrode with a normal electrode. To measure the potential at b, the arm of the normal electrode n is connected with the electrolyte in c, and the wire from the normal electrode con- nected with b through the arrangement for measuring electromotive force. The electromotive force of this element is then measured. Knowing the potential of the normal electrode and the potential at the contact of the two electrolytes in c, we know the potential at the I ^ FlQ. 68. electrode b. The potential at the electrode a can be measured in a similar manner. Results of the measurements of Polarization. — If the polarizing current is at first very weak and gradually increases in strength, the current of polarization will also increase rapidly in strength. After the electromotive force of the polarizing current has become quite large, the electromotive force of the current of polarization will in- crease as the former increases, but more and more slowly. There is, therefore, no maximum of polarization attainable. It is difficult to say how high an electromotive force of polarization can be realized. Streintz 3 has described an anode polarization of seventeen volts. i Pogg. Ann. 156, 156 (1875). 2 Ztschr. phys. Chem. 8, 299 (1891) ; 12, 333 (1893) ; 13, 163 (1894). See Jahn: Ibid. 26, 385 (1898). Gookel : Ibid. 34, 529 (1900). Coehn : Ibid. 38, 609 (1901). Tafel: Ibid. 50, 641 (1905). » Wied. Ann. 32, 116 (1887). ELECTROCHEMISTRY 485 Le Blanc * has measured the electromotive force which is required in order that a continuous steady current may be passed through an electrolyte so as to effect a continuous decomposition. He found that for a given substance under given conditions this had a definite value. This he termed the Decomposition Value of the substance. If the electromotive force of the current used is smaller than the " decomposition value " of the substance in question, a throw of the galvanometer will manifest itself; but the instrument will soon return to its original position, showing that there is only an instan- taneous passage of the current through the electrolyte. The "de- composition values " of electrolytes have been shown to be very interesting as throwing light on the nature of electrolysis itself. The " values " for normal solutions of a few acids, bases, and salts, taken from the paper by Le Blanc, 2 will, therefore, be given. Acids Sulphuric acid = 1.67 volts Malonic acid = 1.69 volts Nitric acid = 1.69 volts Hydrochloric acid = 1.31 volts Phosphoric acid = 1.70 volts Triazoic acid = 1.29 volts Monochloracetic acid = 1.72 volts Oxalic acid = 0.95 volt Dichloracetic acid = 1.66 volts Bases Sodium hydroxide = 1.69 volts Potassium hydroxide = 1.67 volts . Ammonium hydroxide = 1.74 volts Salts Barium nitrate =2.25 volts Barium chloride =1.99 volts Strontium nitrate = 2.28 volts Strontium chloride = 2.01 volts Calcium nitrate = 2.11 volts Calcium chloride = 1.89 volts Potassium nitrate = 2.17 volts Potassium chloride = 1.96 volts Sodium nitrate = 2.15 volts Sodium chloride = 1.98 volts If we examine the results for the acids and bases, we see that the " decomposition values " do not exceed 1.75 volts, and that these values for many substances are about 1.7 volts. In the case of salts of metals which decompose water, the " decomposition values " are practically constant for the salts of a given acid, as the nitrates, chlorides, etc. The explanation of these results has been furnished by Le Blanc. 1 Ztschr. phys. Chem. 8, 299 (1891). 2 Ibid. p. 315 (1891). See Pellat : Ann. Ohim. Phys. (6) 19, 556 (1890). 486 THE ELEMENTS OF PHYSICAL CHEMISTRY Primary Decomposition of Water in Electrolysis. — When solu- tions of salts, acids,. and bases are electrolyzed, we obtain hydrogen or a metal at the cathode, and oxygen at the anode. If the metal of the salt is capable of decomposing water, we obtain hydrogen at the cathode ; if it is not, the metal itself will separate at the cathode. How are these facts to be explained ? The explanation which has been accepted for a long time is as follows : Take the case of potas- sium sulphate; it dissociates into the cation potassium and the anion SO 4 . The potassium moves over to the cathode and gives up its charge to this electrode. The metallic potassium acts upon water, forming potassium hydroxide, and liberates hydrogen. The SO\ anion moves over to the anode and gives up its charge, but it cannot escape from the solution. It acts upon water, forming sulphuric acid, and liberates oxygen at this electrode. The decomposition of the water is then not a primary result of electrolysis, but a sec- ondary act. This view, of electrolysis has now been fundamentally changed, especially by the work of Le Blanc on the " decomposition values " of electrolytes. The view which is supported by these facts is that the decomposition of water is a primary act of electrolysis. Water is dissociated very slightly into hydrogen ions and hydroxyl ions, as is shown by many experiments, but especially by the small conductivity of the purest water. When a solution of potassium sulphate is electrolyzed, the potassium cations carrying the positive charge move over to the cathode. They do not give up their positive charge to the electrode ; but the hydrogen ions of the' water already present give up their charge to the electrode and separate as gaseous hydrogen. This leaves in the solution an equal number of hydroxyl anions, which with the potassium cations form potassium hydroxide. Similarly, the S0 4 anions move over to the anode, but they do not give up their charge to this electrode. The hydroxyl anions of the water give up their negative charges, form water and oxygen, and leave behind an equal number of hydrogen cations, which, with the S0 4 anions, form sulphuric acid. This explanation of the phenomena fits the facts as well as the older theory. Why should we reject the older and accept the newer view ? Evidence for the Primary Decomposition of Water in Electrolysis. — We shall not attempt to take up all the evidence 1 bearing upon this theory, but a few fundamental facts will be considered. 1 See Arrhenius: Ztschr. phys. Chem. 11, 805 (1893). Le Blanc : Ibid. 12, 333 (1893). Also Outlines of Electrocliemistry, Jones (Elec. Rev. Pub. Co.). ELECTROCHEMISTRY 487 If in terms of the old theory the cation — say potassium — moves over to the cathode and gives up its charge, and the metal then acts upon water forming potassium hydroxide and hydrogen gas, the atomic potassium must take the positive charge from the hydrogen ion. If the potassium is able to take the charge from the hydrogen ion, it must have a greater power of holding the charge than hydro- gen has. As this is the case, why should potassium ions give up their charge to the cathode when there are hydrogen ions present which hold their charge less firmly than potassium ? The objection might be raised in this connection that water is only slightly dissociated and there are, therefore, only a few hydro- gen ions present. These would soon be used up and then the potas- sium ions would have to give up their charges in terms of the old theory. This objection has of course no foundation in fact, since the water present will continue to dissociate as fast as the hydrogen ions are used up. We know from the law of mass action that the condition which will always obtain is, that the product of the number of hydrogen ions and the number of hydroxyl ions present will be a constant. The evidence for the new theory furnished by the " decomposi- tion values " of electrolytes must be considered. In terms of this theory, the electrolysis of the salt of any metal which decomposes water is the same as the electrolysis of the salt of any other metal which decomposes water, since in all such cases the hydrogen and oxygen which separate are the primary products of electrolysis. If this is true, then the decomposition values or electromotive force re- quired to affect continuous electrolysis must be the same for the salt of any acid, with different metals which decompose water. That such is the case is seen from the table on page 485. Again, take the acids and bases. Acids dissociate into hydrogen cations and anions which depend upon the nature of the acid ; and bases dissociate into hydroxyl anions and cations which depend upon the nature of the base. Take as an example sulphuric acid. In terms of the new theory of electrolysis the hydrogen cations move to the cathode, give up their charge and separate. The anion S0 4 moves to the anode, the hydroxyl ions from the water give up their charge, form water and oxygen which escapes ; an equal number of hydrogen ions from the water remaining in the solution and forming sulphuric acid with the S0 4 anion. There must, therefore, be a maximum decomposition value for acids, which corresponds to the potential required to discharge hydrogen ions on the one hand, and hydroxyl 488 THE ELEMENTS OF PHYSICAL CHEMISTRY ions on the other under these conditions. This is seen to be about 1.75 volts. If the acid yields an anion whose discharging value is lower than that of hydroxyl, its decomposition value will be less than the maximum 1.75 volts, and such is the case with the halogen acids and the organic acids. Bases dissociate into hydroxyl which moves to the anode and gives up its charge, and a cation which moves to the cathode. The latter does not discharge its posi- tive charge, since it loses its charge with greater difficulty than the hydrogen cations from the dissociated water already present around this electrode. The hydrogen ions lose their charge at this pole. The electrolysis of a base is therefore the same as that of an acid like sulphuric ; hydrogen ions discharged at the cathode, hydroxyl at the anode. The decomposition value of a base must therefore be the same as that of an acid like sulphuric or nitric. It must be the same as the maximum decomposition value of the acid, and such is seen at once from page 485 to be the case. One further point to make the reasoning from decomposition values complete. Acids and bases of the same ionic concentration must have the same decomposition values, as we have just seen, since the product of the number of hydrogen and hydroxyl ions in the solutions must, from the law of mass action, be a constant. It is, however, quite different with a salt. At the cathode hydrogen is liberated and a base is formed, which means an increase in the num- ber of hydroxyl ions around the cathode ; and, similarly, the forma- tion of an acid around the anode increases the number of hydrogen ions around this pole. Since the product of the number of hydroxyl and hydrogen ions is a constant, an increase in the number of hydroxyl ions around the cathode means a decrease in the number of hydrogen ions around this pole. And for the same reason an in- crease in the number of hydrogen ions around the anode would diminish the number of hydroxyl ions around this pole. Both of these influences would tend to increase the decomposition value of the compound. Here again fact and theory are in perfect accord. A comparison of the decomposition values of acids and bases with those of salts will show that the latter are considerably larger than the maximum values for the former. The evidence for the- primary decomposition of water in electroly- sis is then complete as far as the decomposition values for acids, bases, and salts are concerned. The Discharging Potential of Ions. Electrolytic Separation of the Metals. — When a current is passed through a solution of several ELECTROCHEMISTRY 489 electrolytes, all of the ions present take part in conducting the cur- rent. The amount of current which will be carried by any kind of ions will depend upon their relative numbers and the relative velocities. When the different kinds of cations reach the cathode, or anions the anode, it is not necessary that all kinds should separate. It requires a certain difference in potential between the electrode and the electrolyte to cause any given ion to give up its charge to the electrode. If the difference in potential is below the discharging value for any ion, this ion will not lose its charge and separate at the electrode in any quantity. Every ion has its own decomposition value, and these values differ very considerably for different ions. The fact that these values are quite different makes it possible to effect an electrolytic separation of many metals by at first' using a current of small electromotive force, which will cause the element with lowest decomposition value to separate, then increasing the electromotive force until the element with next higher value sepa- rates, and so on. Take two metals A and B, and mix solutions of their salts. Let the decomposition value of A be considerably less than that of B. Pass a current through the solution containing the mixed salts. When the electromotive force of the current has reached the decomposition value of A, this metal will separate on the cathode. The current will then cease to flow continuously unless its electromotive force is increased to the decomposition value of B. When it has reached this value, B will separate from the solution. The possibility of separating metals in general by means of cur- rents of different electromotive force was pointed out by Freuden- berg. 1 In an investigation 2 in Ostwald's laboratory, carried out with Le Blanc, Freudenberg effected a number of quantitative sepa- rations of metals by using different electromotive forces. Thus, he showed that mercury could be separated from copper, bismuth, arsenic, cadmium, etc. ; that copper could be separated from cad- mium, and so on. The importance of the electromotive force of the current used is, therefore, very great in effecting electrolytic separa- tion of the metals. It has, however, been clearly recognized that current strength or current density 3 is of fundamental importance in electrolytic sepa- rations. This conditions the number of ions which will separate in a given time ; and if the density is great it does not give time for i Ber. d. chem. Gesell. 25, 2492 (1892). 2 Ztschr. pkys. Chem. 12, 97 (1893). 3 Classen : Quantitative Chemical Analysis by Electrolysis. 490 THE ELEMENTS OF PHYSICAL CHEMISTRY all the more easily discharged ions to come over to the pole by diffusion, etc., in order to separate. Under such conditions, instead of effecting complete separations, only partial separations are secured. It is obvious from the above that in all such work we must take into account not only current density, but the electromotive force of the current used. Electrosynthesis of Organic Compounds. — The ions of inorganic compounds are relatively simple substances. The ions of organic compounds are often very complex, and after losing their charge are incapable of existence. They frequently break down and yield entirely new substances. Take the anion of acetic acid, GH 3 COO, when this reaches the anode it loses its charge, since it holds it less firmly than hydroxyl, and then breaks down in the sense of the following equation : — 2CH~C0 2 ==C 2 H 6 + 2C0 2 , yielding a hydrocarbon and carbon dioxide. The anion of propionic acid breaks down as follows : ■ — 2 C 2 H7C0 2 = C 3 H { COOH + C 2 H 4 + C0 2 . Facts of this kind have already been utilized quite extensively for effecting the synthesis of organic compounds. An examination of the literature L will show that a very large number of organic com- pounds in the aromatic series, as well as in the aliphatic, have been made in this way. That acetic acid when electrolyzed breaks down as shown in the above equation, yielding ethane and carbon dioxide, had been shown by Kolbe 2 as early as 1847. Some nine years later Guthries 3 showed the inactivity of the ester group. These investigations were the basis of the systematic work of Crum-Brown and Walker * in this field in 1891. They showed that from the monoester of a dibasic acid, the ester of a dibasic acid richer in carbon could be obtained. Thus : — rrirur ^^ — COOC 2 H 3 2CH 1 " It was found that alkyliodides react more rapidly than bromides, and the latter more rapidly than chlorides. The normal alkylhalides react more rapidly than the secondary or iso-compounds, and these, in turn, react more rapidly than the tertiary. The ethyliodide, as is shown in the above equations, reacts in the molecular condition. Action of Acids on Acetamide. — Another typical second order reaction is the action of acids on acetamide. This has been studied by Ostwald. 3 The reaction is expressed by the following equation: — CH 2 CONH 2 + CI + H +H 2 = NH 4 + CI + CH 3 C0 2 H. There are only two substances which undergo change in concen- tration, — the amide and the hydrogen ions. The water which is used 1 Ztschr. phys. Chem. 2, 284 (1888). 2 Amer. Chem. Journ. 37, 71 (1907). 8 Journ. prakt. Chem. 27, 1, (1883). 2n 546 THE ELEMENTS OF PHYSICAL CHEMISTRY up is so small in comparison with the total amount of water present that it can be neglected. A few results obtained by Ostwald with trichloracetic acid show a good constant for a second order reaction. t is Time in Minutes 1 . — - — t A — x 15 0.0088 60 0.0088 120 0.0089 180 0.0090 240 0.0090 Second Order Reactions where the Masses are not Equivalent. — It is not always desirable or even possible to use the masses of the two substances in equivalent quantities. In such cases the equation deduced from the law of mass action is more complex, but can be readily integrated. Thus, if the two substances A and B are not in equivalent quantities, — 4 f t = C(A-x)(B-x). Integrating and making t = and x = 0, we have — ln B{A-x) = {A _ B)a G= 1 ln (A-x)B. A(B-x) K ' (A-B)t (B-x)A We would not be justified in concluding that this equation holds because the equation for the two substances in equivalent quantities agrees with the facts. Eeicher 1 tested the above equation by study- ing the reaction between ethyl acetate and sodium hydroxide, using different quantities of the two substances. A few of his results will . show how satisfactorily the equation is verified. In the first table a large excess of sodium hydroxide was used ; in the second table a smaller excess of the hydroxide, and in the third an excess of ester was employed. t = Time in Minutes Constant 374 0.0347 I. \ 628 0.0348 1359 0.0344 393 0.0335 II. ■( 669 0.0342 1265 0.0346 III. 342 0.0346 670 0.0347 1103 0.0344 A good constant is not only obtained in every series, but we have 1 Lieb. Ann. 288, 257 (1885). CHEMICAL DYNAMICS AND EQUILIBRIUM 547 practically the same constant in all three series, which verifies the above formula in an entirely satisfactory manner. Trimolecular, or Third Order Reactions. — Just as we may have two substances entering into a reaction, and their active masses con- sequently changing as the reaction proceeds, so we may have three substances taking part in the reaction. Applying the law of mass action to a third order reaction, we would have — f t = C(A-x)(B-x)(D-x), where A, B, and D represent the masses of the three substances in question. In such cases it is much simpler to take all three substances in equivalent quantities : A = B = D. Then, — — = G(A-xf. dt v ' Integrating, making t = 0, x = 0, we have — /■)__! x(2A—x) ~ t 2A\A-x) 2 ' If A, B, and D are not taken in equivalent quantities, the equa- tions become very much more complex. 1 The number of third order reactions known is small, and very few have been studied quantitatively from the standpoint of the law of mass action. A third order reaction in which three substances un- dergo change in concentration was studied by Noyes and Wason. 2 The reaction is between potassium chlorate, ferrous sulphate and sul- phuric acid, and is expressed by the following equation : — 6 FeS0 4 + KC10 3 + 3 H 2 S0 4 = 3 1 , e 2 (S0 4 ) 3 + KC1 + 3 H 2 0. This reaction was supposed by Hood, 3 who first studied it, to be a second order reaction, but was shown by Noyes and Wason to be a reaction of the third order. They varied the concentrations of the different substances and determined the value of the constant under very widely different conditions. Although the values found differ as much as 20 per cent, yet they unmistakably verify the above equation for a third order reaction. Another third order reaction was studied by Noyes, 4 in which i Fuhrmann : Ztschr. phys. Chem. i, 89 (1889). 2 Ibid. 22, 210 (1897). * Phil. Mag. [5], 6, 371 (1878) ; 8, 121 (1879); 20, 323 (1885). * Ztschr. phys. Chem. 16, 546 (1895). Other third order reactions : ''Action of stannous chloride upon ferric chloride." 548 THE ELEMENTS OF PHYSICAL CHEMISTRY only two substances took part. The reaction is between ferric chlo- ride and stannous chloride — 2 FeCl 3 + SnCl 2 = 2 FeCl 2 + SnCl 4 . Although there are only two substances, there are three molecules involved in the reaction, and we should expect it to be a reaction of the third order. Noyes studied the reaction, using the varying quantities of the two substances, and found fairly satisfactory constants when equiva- lents were employed, but the values differed very considerably when non-equivalents were used. This might leave some doubt as to whether this is a true reaction of the third order ; but in addition to the fact that a fairly satisfactory third order constant was generally obtained, Noyes points out another argument in favor of this being a true third order reaction. If it is a second order reaction, a definite excess of either constituent must produce the same effect; thus, two equivalents of iron on one of tin must have the same influence as two equivalents of tin on one of iron. Noyes found that such is not the case, an excess of ferric chloride accelerating the reaction to a much greater extent than an equivalent of stannous chloride. There can, therefore, be little doubt that this is a true third order reaction. Reactions which are apparently Trimolecular. — In the last reac- tion studied only two substances took part, and yet we had to deal with a third order reaction. The difference between this and an ordinary second order reaction between two substances is that two molecules of one substance react with one molecule of the other. We might suspect from this that wherever two molecules of one substance react with one molecule of another substance, we have a third order reaction. Such, however, is not the case. Take the action of a univalent base on the ester of a bivalent acid, — say sodium hydroxide on ethyl succinate, — CH 2 COOC 2 H 6 NaOH _ CH 2 OOONa CH 2 COOC 2 H 6 + NaOH ~ CH 2 COONa + * ^"* u±1 > two molecules of the base and one of the ester being involved. Noyes: Ztschr. phys. Chem. 16, 546 (1895) ; 81, 16 (1896). "Action of silver nitrate on sodium formate." Noyes and Cottle: Ztschr. phys. Chem. 27, 579 (1898). " The reaction between oxygen and hydrogen." Bodenstein: Ztschr. phys. Chem. 29, 665 (1899). "Formation of sulphur trioxide in the presence of platinum." Bodlander and Koppen: Ztschr. Electrochem. 9, 559 (1903). CHEMICAL DYNAMICS AND EQUILIBRIUM 549 Knoblauch ' has shown that this is not a trimolecular reaction, but is probably made up of the following two bimolecular reactions : — (1) CH 2 COOC 2 H 5 _ CH.COOC.H, w CH 2 COOC 2 H 6 + ^ aU±i -CH 2 COONa +°^ u±1 ' ( CH 2 COOC 2 H 5 CH 2 COONa , CH0H W CH 2 COONa + ^ aU±± -CH 2 COONa +°^H 5 OH. Ail analogous case, where we might suppose that we were dealing with a trimolecular reaction, is in the saponification of an ester of a univalent acid by means of a bivalent base, — say ethyl acetate by calcium hydroxide, — 2 CH 3 COOC 2 H 5 + Ca(OH) 2 = (CH 3 C0 2 ) 2 Ca + 2 C 2 H 5 OH. This has been shown by Eeicher 2 to be a bimolecular reaction, just as when sodium or potassium hydroxide is used. The saponi- fication is effected by the free hydroxyl ions, and it does not affect the order of the reaction whether they come from a univalent or a bivalent base. Reactions of Higher Order. — It is possible to deal with reactions of much higher order in terms of the law of mass action. Thus, a reaction of the nth order would be formulated as follows : — Y = C(A - x)(B - x)(D - as)( E -»)••• (n - as). It is, however, not necessary to consider in any detail such cases, since there are very few reactions known of higher order than the third. A very few reactions have been shown to belong apparently to the fourth order, and one or two have been described that may belong to the fifth. Some of these cases, however, are not entirely free from doubt. The number of reactions belonging to the lower orders is, as we should expect, much larger than those belonging to higher orders. The chance of two molecules coming together in such a way that they can react chemically is greater than that of three molecules coming into a similar relation, and still greater than that a larger number than three should all be able to enter into a chemical reaction with one another. We frequently express chemical reactions as taking place between more than three molecules, but the study of the velocity of reactions in terms of the law of mass action has taught us that most of these reactions are not as complex as they seem, being in reality made up of a series of simpler reactions. As an example take the decompo- 1 Ztschr. phys. Chem. 26, 96 (1898). 2 Lieb. Ann. 228, 257 (1885). 550 THE ELEMENTS OF PHYSICAL CHEMISTRY sition of arsine by heat. Since the smallest molecule of arsenic known at these temperatures is As 4 , we would have to represent the reaction thus : — 4 AsH 3 =As 4 + 6H 2 , which would make it a fourth order reaction. 1 A The fact is, -In— is a constant, which shows that it is a first * A — x order reaction. The reaction whose velocity is measured must then be, AsH 3 = As + 3 H, and subsequently the arsenic atoms must combine and form As 4 , and the hydrogen atoms form H 2 . Many reactions of a similar character are known, the order being much lower than would be indicated by the usual chemical method of expressing the reaction. We thus see how the study of the velocity of reactions has thrown light on the inner mechanism of the reactions themselves, and has given us a deeper insight into what actually takes place than could have possibly been obtained by any purely chemical method. Other Methods of Determining the Order of a Reaction. — The method of determining the order of a reaction thus far considered, consists in measuring the velocity of the reaction and inserting the results into the equations for the constant as obtained from the first, second, third, or higher order of reactions. If the values obtained when the experimental results are introduced into the equation for a first order reaction are constant, the reaction belongs to the first order. If a better constant is obtained when the results are intro- duced into the equation for a second order reaction, the reaction in question belongs to this order, and similarly for a third order reaction. It, however, frequently happens that none of these equations give a satisfactory constant, and by the above method it would be impossible to determine to which order the reaction belongs. This is due to the fact that in such reactions disturbing influences, such Fourth order reactions. " Decomposition of potassium chlorate." Scobai : Ztschr. phys. Chem. 44, 319 (1903). "Reduction of bromic acid by hydrobromic acid." Judson, and J. W. "Walker : Journ. Chem. Soc. 73, 410 (1898). " Chemical dynamics of the action of bromine on benzene." Briiner: Ztschr. phys. Chem. 41, 513 (1902). Fifth order reactions. " Action of potassium iodide on potassium ferricyanide." Donnan and Rossignol : Journ. Chem. Soc. 83, 703 (1903). CHEMICAL DYNAMICS AND EQUILIBRIUM 551 as the setting up of side reactions, or of new reactions between the products of the original reactions, etc., come into play, which affect the velocity coefficients as the reaction proceeds. Methods for determining the order of a reaction, which largely exclude these influences, have been devised. The first method we owe to Van't Hoff. 1 The method is based on the effect of change in concentration on the velocity of the reac- tion, the velocity of a reaction of the nth order being proportional to the nth power of the concentration. The following deduction is given by Van't Hoff, changing the symbols to those used in this volume : — -^l = cC 1 ". dt If we use a different concentration, dt Consequently, ^ : ^= C 2 » : G, dt dt ui = \dt dt J 71 log (d : G n ) ' Van't Hoff applied this method of variable volume to the action of bromine on fumaric acid, and also to the polymerization of cyanic acid. The results for the first reaction are as follows : — The addition of bromine to an aqueous solution of fumaric acid giv- ing rise to dibromsuccinic acid, is accompanied by other reactions, which make it impossible to apply directly the equations for the first, second, and third order reaction, and determine the order of the reac- tion. Van't Hoff applied this method of variable volume or variable concentration in a satisfactory manner. The experiments were car- ried out by Eeicher 2 in Van't Hoff's laboratory. Time in Minutes Conoenteation t Ci dCi 8.88 dt 95 7.87 0.0106 The value ^ has been replaced in the calculation by the ratio dt of the differences — — ^— : — . 95 1 Etudes de dynamique Chimique, p. 87. 2 Ibid., p. 89. 552 THE ELEMENTS OF PHYSICAL CHEMISTRY Water was then added, increasing the dilution : — _Gi_ 132 3.81 0.00227 3.51 w was then calculated and shown to have the value 1.87. The value found should be 1 for a first order, 2 for a second order, and 3 for a third order reaction. Since disturbing influences must have some effect, we would expect the value found to differ somewhat from these whole numbers. The value 1.87 is sufficiently near to 2 to justify the conclusion that the reaction belongs to the second order. The second method of obtaining the order of a reaction, where dis- turbing influences come into play, is based upon the principle discov- ered by Ostwald that for analogous reactions " the amounts of time required to produce a definite degree of decomposition bear constant relations to one another, and are equal to the reciprocals of the cor- responding relative affinity coefficients " ; in a word, the amounts of time required are inversely as the velocity factors. This was shown by Ostwald 1 as follows : " The general form of the equation for reaction velocity is, — f=C/(*), whose integral is, Ct = («). " If we let x have the same value in a series of comparable experi- ments, (x) has a constant value, therefore, — Cth = CtU = G s ts ■ ■ ■ , or d : Q : Ci . . . =- : - : - ■ • • • ti t$ tg " The only assumption made is that the course of the reaction is affected, in all cases, in a like manner by the disturbing influences and side reactions." Carrying out experiments with different concentrations and allowing the reactions to proceed until equal fractions of the sub- stance are transformed, as Ostwald 2 points out, if the reaction be- longs to the first order, the velocity factors and also the amounts of time required are equal ; if it is a second order reaction the velocity factors are proportional to the concentrations, and the amounts of time are inversely proportional to the concentrations ; if we are deal- ing with a third order reaction, the velocity factors are proportional to the square of the concentrations, and the amounts of time in- versely as the square of the concentrations. 1 Ztschr. phys. Chem. 2, 127 (1888). 2 Lehrb. d. Allg. Chem. II [2], 236. CHEMICAL DYNAMICS AND EQUILIBRIUM 553 This deduction was applied to experimental results by Noyes, 1 who studied the reaction between hydriodic acid and hydrogen di- oxide, also that between hydriodic acid and bromic acid, and sev- eral other cases. He found in general that the reactions were of simpler order than would be indicated by the chemical equations expressing them. Influences which affect the Velocities of Reactions. — The veloci- ties of reactions are considerably affected by a number of influences and conditions, some of which will be considered. The influence of temperature on the velocity of reactions is usu- ally very great. A rise in temperature is generally accompanied by a great increase in the velocity of the reaction, a rise of 10° fre- quently doubling, and sometimes tripling, the velocity of a reaction. The effect of rise in temperature over a considerable range of temperature is shown very clearly by an example given by Van't Hoff. 2 The following reaction with dibromacetic acid was studied : — C 4 H 4 4 Br 2 = C 4 H s 4 Br + HBr. The range of temperature was from 15° to 101°, or 86°, and at the higher temperature the velocity was more than three thousand times that at the lower. Further, cane sugar 3 is inverted about five times as fast at 55° as at 25°. Hydrogen and oxygen do not combine at a measurable rate at 350°, while at 600° 4 the rate of combination is so rapid that an explosion results. Dewar 5 has observed that the photographic plate is affected only about one-tenth as rapidly at the temperature of liquid hydrogen as at ordinary temperatures ; and only about one-fifth as rapidly at the temperature of liquid air ; and Berthelot 6 has shown that the velocity with which an ester is formed is about twenty-two thousand times as great at 200° as at 7°. A number of attempts have been made to formulate the relation between the velocity of the reaction and the temperature. While all of these are empirical, it seems that the velocity is nearly pro- portional to the square root of the absolute temperature. The study of the effect of pressure on the velocity of reactions has led to interesting results. The pressure of a gas, or the osmotic pressure of a solution, can be readily dealt with from the standpoint i Ztschr. phys. Chem. 18, 118 (1895); 19, 599 (1896). 2 Vorlesungen iiber Theoretische und PhysiJealische Ohemie, I, 223. 3 Spohr : Ztschr. phys. Chem. 2, 195 (1888). * Meyer and Raum : Ber. d. chem. Gesell. 28, 2804 (1898). 6 Liquid hydrogen : Chem. News, 84, 281, 293 (1901). 6 Essai de Mecanique Chimique, 2, 93 (1879). 554 THE ELEMENTS OF PHYSICAL CHEMISTRY of thermodynamics, and the conclusions reached mathematically 1 are, that first order reactions are independent of pressure, second order are proportional to the pressure, while third order are propor- tional to the square of the pressure. The effect of pressure on only a few reactions has been studied experimentally. Rothmund 2 found that the velocity with which cane sugar was inverted by hydrochloric acid was diminished only slightly by changes in pressure. He worked at pressures from one to five hundred atmospheres, and found that at the latter pressure the velocity was about five per cent less than at the former. Ront- gen 3 also found that pressure diminishes the velocity with which cane sugar is inverted. Other 4 first order reactions have been studied at different press- ures, with the result that increase in pressure slightly increased the velocity of the reaction, but, on the whole, experiment shows that first order reactions are practically independent of pressure. As we should expect, the effect of pressure on the velocity of reactions is greatest for those reactions in which a gas is involved. Thus, Nernst and Tammann s showed that there is a definite press- ure at which the metals will cease to liberate hydrogen from acids. When the pressure of the hydrogen reached 18 atmospheres, zinc ceased liberating hydrogen from a 0.13 normal solution of sulphuric acid ; while 40.2 atmospheres were required when the concentration of the acid was 0.34. The equilibrium pressure for the hydrogen was 44 atmospheres when cadmium acted upon 0.62 normal hydrochloric acid. The equilibrium pressure for normal hydrochloric acid and man- ganese is 52 atmospheres. The corresponding pressure for nickel and 0.88 hydrochloric acid is 29 atmospheres, and so on. The effect of thus concentrating the hydrogen is to set up a reaction counter to the first, so that the equilibrium is produced, not simply by the pressure of the gas, but by the counter reaction acquiring under these conditions the same velocity as the initial reaction. 1 Van't Hoff : Vorlesungen uber Theoretische und Physikalische Chemie, I, 235. 2 Ztschr. phys. Ohem. 20, 168 (1896). 8 Wied. Ann. 45, 98 (1892). 4 Ztschr. phys. Ohem. 9, 1 (1892). 6 Ztschr. phys. Chem. 9, 1 (1892). Bodenstein : Ibid. 46, 725 (1903). Pelabon : Compt. rend. 119, 73 (1894). See Buohbock: Ztschr. phys. Ohem. 34, 229 (1900). CHEMICAL DYNAMICS AND EQUILIBRIUM 555 The effect of pressure on the velocity of reactions between liquids is, in general, small. This is what should be expected, since pressure changes the volume of liquids only to a slight extent. While the velocity of first order reactions is, in general, nearly independent of pressure, the velocity of second order reactions is greatly affected by pressure, and, indeed, nearly a linear function of -the pressure. This is shown by the work of Bodenstein 1 on the velocity of decomposition of hydriodic acid with varying pressure. The velocity of decomposition is practically proportional to the pressure to which the gas is subjected. The nature of the medium has a marked influence on the velocity ■of reactions. This applies especially to the nature of the solvent used. The experimental work of Menschutkin 2 shows the magni- tude of this influence. He studied a few reactions in a large num- ber of solvents, and in each case measured their velocities. A few of his results for the action of triethylamine on ethyl iodide, in dif- ferent solvents, are given. The reaction proceeds as follows : — (C 2 Hi) 3 K + C 2 H 5 I = (C 2 H 5 ) 4 NI. I II I II Heptane 0.000235 Methyl alcohol 0.0516 Xylene 0.00287 Acetone 0.0608 Benzene 0.00584 o-bromnaphthol 0.1129 Chlorbenzene' 0.0231 Acetophenone 0.1294 Ethyl alcohol 0.0366 Benzyl alcohol 0.1330 Allyl alcohol 0.0433 Column I gives the solvent used ; II, the velocity coefficient. The velocity of the reaction in benzyl alcohol is about seven hundred and forty times that in hexane. We would naturally try to refer the different velocities in the different solvents to the different dissociation powers of the solvents ; it is, however, impossible to account for the above facts in this way. The differences between the velocities in the different solvents are very much greater than the differences in the dissociating powers of the same solvents ; and, further, the solvents do not always stand in the same order with respect to their dissociating power and the velocity with which a reaction takes place in their presence. Thus, the formation of urea from ammonium cyanate takes place about 1 Ztschr. phys. Chem. 13, 116 (1894). 2 Ibid. 1, 611 (1887); 6, 41 (1890) ; 34, 157 (1900). 556 THE ELEMENTS OF PHYSICAL CHEMISTRY thirty times as rapidly in ethyl alcohol as in water, and the disso- ciating power of water is from three to four times ' as great as that of ethyl alcohol, and other examples are known. A satisfactory explanation of the great differences in the veloci- ties in different solvents has not yet been furnished. The presence of certain fore ign substances may considerably affect the velocity of the reaction. Ostwald 2 determined the effect of the presence of neutral salts on the action of hydrochloric and nitric acids on calcium and zinc oxalates. He found that the velocity of the reaction was increased by the presence of the salt, potassium having the greatest influence, ammonium and sodium less, and mag- nesium still less. On the other hand, Arrhenius s found that neutral salts diminished the velocity with which ethyl acetate was saponi- fied by bases, sodium salts having a greater influence than potassium, and barium still greater than sodium. However, results similar to those first considered were obtained by Arrhenius * and Spohr s from a study of the action of neutral salts on the velocity with which cane sugar is inverted by acids. The neutral salt increased the velocity of the reaction. Under the head with which we are now dealing attention should be called again to the effect of mere traces of moisture 6 on the velocity of many reactions. Dry chlorine is without action on many of the metals, including sodium, as Wanklyn 7 has shown, and Baker 8 and Dixon 9 demonstrated by a number of experiments the comparative inactivity of dry oxygen. That dry hydrochloric acid does not de- compose carbonates was shown by Hughes, 10 who also demonstrated that it does not precipitate silver nitrate dissolved in dry ether or benzene. That dry hydrochloric acid gas does not act on dry am- monia gas has been conclusively demonstrated by Baker," and it has even been shown on the lecture table that dry sulphuric acid is without action on dry metallic sodium. 12 The presence of moisture is necessary in order that the above- 1 Jones : Ztschr. phys. Chem. 31, 114 (1900). 2 Journ. prakt. Chem. (N. F.), 23, 209 (1881). 8 Ztschr. phys. Chem. 1, 110 (1887). 4 Ibid. 4, 226 (1889). 6 Ibid. 2, 194 (1888). 6 For a fuller discussion of this subject see Jones : Theory of Electrolytic Dissociation, pp. 163-170. 7 Chem. News, 20, 271 (1869). 8 Phil. Trans. 571 (1888). » Ibid. 617(1884). 10 Phil. Mag. 34, 117 (1892). a Journ. Chem. Soc. 65, 611 (1894) ; 73, 422 (1898). 12 Proceed. Chem. Soc. 86 (1894). CHEMICAL DYNAMICS AND EQUILIBRIUM 557 mentioned reactions should take place with any appreciable velocity — moisture is necessary to combination. On the other hand, a case has been found where moisture effects decomposition. If ammonium chloride is volatilized under ordinary conditions, it is dissociated by heat into ammonia and hydrochloric acid. If, however, the ammonium chloride is carefully dried, it volatilizes without undergoing decomposition, as is shown by the fact that under these conditions its vapor-density is normal. In this case water-vapor seems to be necessary in order that the gases may combine, and is also necessary in order that the compound should be decomposed by heat. That the presence of water is necessary to effect chemical combination is doubtless closely con- nected with its ionizing power; but it is not a simple matter to explain its action on the vapor of ammonium chloride, causing it to be dissociated by heat. Two other conditions must be considered in this section, viz. ignition temperature and ignition pressure. There are many reactions known which take place with an appreciable velocity only above a certain temperature. Below this temperature the reaction appar- ently does not take place at all. This temperature, at which the reaction apparently begins, is known as the ignition temperature. The study of this temperature for a large number of reactions has been made possible by the recent methods which have been devised for producing low temperatures, especially for producing liquid air on a large scale. It has been found that a large number of reactions, which take place with considerable velocity, do not proceed with any appreciable velocity at these very low temperatures. A careful study of reactions below the ignition temperature has shown that this is not a point at which the reaction begins, but that there is a very slow reaction below this point ; so slow, indeed, that in many cases it cannot be observed at all. In other cases, however, it can be observed, as in the action of phosphorus on oxygen. Below 40°, which is usually taken as the ignition temperature of oxygen and phosphorus, a slow oxidation 1 of the phosphorus takes place, giving rise to the compound P 2 0. At the ignition temperature the reaction becomes strongly exothermic, giving the pentoxide of phos- phorus. We should, therefore, regard the ignition temperature as that at which any given reaction acquires an appreciable velocity. Just as there is a temperature at which many reactions appar- ently begin, so there is a pressure at which some reactions between 1 Besson : Compt. rend. 124, 763 (1897). 558 THE ELEMENTS OF PHYSICAL CHEMISTRY gases and other substances apparently commence to take place. Temperature and pressure, however, act in opposite senses, increase in temperature increasing the velocity of the reaction, while 'de- crease in pressure increases the velocity of the reaction. That pressure at which a reaction begins with an appreciable velocity is known as the ignition pressure, and at lower pressure the reac- tion proceeds with still greater velocity. Thus, a mixture of oxygen with phosphine or with silicon hydride explodes on expansion. 1 Aldehyde 2 is not oxidized by oxygen under high pressure, and the ignition temperature of a mixture of hydrogen and oxygen is lowered from 620° to 540° by reducing the pressure from 760 mm. to 360 mm. Many phenomena similar to the above are known. Principle of the Coexistence of Reactions. — We have dealt with reactions thus far as if they occur singly, two or more substances reacting giving products which take no part in the reaction. This has been done for the sake of simplicity and clearness, that we might learn how to apply the law of mass action to ideal cases. In fact, most reactions are much more complex, several reactions occurring simultaneously. The question arises how would we apply the law of mass action to these more complex cases? This' becomes a simple matter after we are familiar with the fundamental principle that every reaction proceeds as if it alone were present. This applies to a number of coexisting reactions, and is known as the principle of the coexistence of reactions. This has been verified so often by experiment that it is now accepted beyond question. An application of this principle to a simple catalytic reaction of the first order will serve to make it clear. Take the decomposition of ethyl acetate by water in the presence of acids, and for the sake of simplicity use acetic acid. Let the amount of acetic acid be represented by A, and the amount of ethyl acetate by B. The velocity of the reaction would be — - = GA(B-x). dt v ' During the reaction, however, a certain amount x of acetic acid is set free, and this also acts catalytically on the ester, increasing the velocity of the reaction. The velocity due to the acetic acid set free is — ^=Cx(B-x). dt K ' iFriedel and Ladenburg: Ann. Chim. Phys. [4], 23, 430 (1871). 2 Ewan : Ztschr. phys. Chem. 16, 340 (1895). CHEMICAL DYNAMICS AND EQUILIBRIUM 558 Prom the principle of the coexistence of reactions the true veloc- ity of the reaction is the sum of these separate velocities, — f t = 0(A + x)(B-x). Integrating, If the acid used as the catalyzer is different from the acid of the ester, the constants are of course different, and we would have as the sum of the two velocities, — f t (0'A+Cx)(B-x), whose integral is, 0'A+Cx\ -& C'A (C'A+CB)t. Cases similar to the above were tested by Ostwald 1 and satisfac- tory constants obtained. If we understand the principle of the coexistence of reactions, we can proceed to study cases where a number of reactions are taking place simultaneously. Side Reactions. — It frequently happens that the substances which were brought together react in more than one way, giving more than one set of products. In addition to the principal reaction, we have then one or more side reactions with velocities of their own. The velocity coefficient which we measure is the sum of the coeffi- cients of the several reactions. The simplest case is where a principal reaction of the first order is accompanied by one side reaction of the same order. From the law of mass action and the principle of the coexistence of reactions this case would be formulated thus : — Integrating, ^CM-Q + GM-fy Ci + C 2 = hn. J t A — x The velocity constant of the reaction is the sum of G t and 2 - It is possible to determine the separate values of d and C 2 by determin- ing the amounts of the products of each reaction. If we represent the 1 Journ. prakt. Chem. [2], 28, 449 (1883). "Test of side reactions" — Wegschneider : Ztschr. phys. Chem. 30, 593 (1899). 560 THE ELEMENTS OF PHYSICAL CHEMISTRY ratio between the amounts of these products by r, -j4 = v. From this and Cj+ C 2 = K, we can calculate G± and C 2 . The application of the principle of coexistence of reactions to a second order reaction is as follows. Given a second order reaction with one side reaction also of the second order, — ^=C 1 (A-x) (B-x) + G 2 (A-x)(B-x) = (G 1 + G 2 )(A-x)(B-x). Integrating, Cl+t °-(A-B)t ln A(B-x) From this the application of the principle to reactions of higher order, and also to reactions where one is of one order and the other of a different order, is obvious. Counter Reactions. — It very frequently happens that substances react and give rise to products which in turn react with one another and reform the original substances. In such cases the velocity measured is the difference between the velocities of the two opposite reactions. From the principle of coexistence and the law of mass action, we would have for a first order reaction, — f t =G x {A, -x)-C 2 (A + x). (1) For a second order reaction we would have — ^=C 1 {A-x) (B-x)-C 2 (C+x) {D + x). (2) If C and D at the outset were zero, this equation would become — ^=C 1 (A-x)(B-x)-C 2 x*. The equation (1) for the first order reactions was tested by Henry, 1 who studied the dehydration of y-oxybutyric acid, giving the lac- tone, — CH 2 OH . CH 2 . CH 2 . COOH = CH 2 . C.H 2 CH 2 . CO + H 2 0. i o ' It was also tested by Kiister, 2 who studied the transformation of hexachlor-o-keto-j8-E-pentane into the a-y-isomer. i Ztschr. phys. Chem. 10, 115 (1892). 2 76^. 18, 161 (1895). "Side reactions." See Blanchard : Ztschr. phys. Chem. 41, 681 (1902). Kiister: Ibid. 18, 161 (1895). Bugarky : Ibid. 11, 668 (1893) ; 12, 223 (1893). CHEMICAL DYNAMICS AND EQUILIBRIUM 561 Satisfactory constants "were obtained as the result of both, inves- tigations. The equation for a second order reaction was tested by Knob- lauch. 1 He studied the reaction between alcohol and acetic acid, and obtained very satisfactory constants. Since all reactions are to be regarded as reciprocal, every reaction is accompanied by a counter reaction of greater or less magnitude. It, however, frequently happens that the velocity in the one direc- tion is so great and in the other so small that the latter can be dis- regarded. Where the counter reaction has an appreciable velocity it must be taken into account. More Complex Reactions. — The conditions which we have just con- sidered are more complex than those which were taken up at first. But there are still more complex eases. We may not only have two or more reactions proceeding in the same or in opposite directions, but we may have the products of a reaction reacting with the products of another reaction, or we may have the products of a reaction react- ing with some of the original substances. In such complex cases it is obvious that all the various quantities must be taken into account. The detailed study of such cases would scarcely be profitable in this connection, since no new principle is brought out or illustrated. If we understand the application of the law of mass action and the principle of the coexistence of reactions to simpler cases, no serious difficulty should be encountered in applying them to more complex reactions. Heterogeneous Reactions. — The reactions with which we have thus far had to deal are all homogeneous, i.e. every substance present is in the same state of aggregation before the reaction, and all the products of the reaction are in the same state of aggregation as the original substances. For example, the substances before the reac- tion are all liquid, and the products all liquid, or the substances are all in solution and the products are all in solution. We know, however, a large number of chemical reactions where a gas is formed or a solid is formed, and other reactions where a liquid or a solution acts on a solid. In such cases the substances are in different states of aggregation, and such reactions are termed heterogeneous. It is obvious that in such cases where there is a sur- face separating the substances which are in different states of aggre- gation, the velocity of the reaction will depend upon the magnitude of this surface. This must be taken into account in dealing with i Ibid. 22, 268 (1897). 2o 562 THE ELEMENTS OF PHYSICAL CHEMISTRY the velocity of such reactions. We shall now study a few types of heterogeneous reactions from the standpoint of the law of mass action. Heterogeneous Reaction of the First Order. — A heterogeneous reaction of the first order is one in which two substances in different states of aggregation react, the active mass of one of them changing as the reaction proceeds, while the active mass of the other, or the surface, remains constant. Applying the law of mass action to such a case, we would have — f t =CS(A-x), where S is the surface exposed to the liquid or solution, A the origi- nal concentration of the acid, and x the amount used up. Integrating, we have — ln-r^- = GSfc A — x It will be observed that this equation does not take into account the effect produced by the presence of the compound formed, and in some cases this might be quite considerable. This equation was tested by Boguski, 1 who studied the action of acids on Carrara marble. Plates of marble of known surface were dipped into acids of different concentrations, and kept rapidly in motion in order that the surface might not become covered with a layer of the carbon dioxide set free. They were removed, washed, and dried, and the loss in weight determined. Better constants were, however, obtained by Spring, 2 who studied the action of acids on Iceland spar. He had previously 3 studied the action of acids on marble, but finding this not sufficiently homogene- ous, he chose the better crystalline form. The spar was tested not only in its crystal planes, but in two other directions, the one paral- lel and the other at right angles to the principal axis. Although the velocity of the reaction between the spar and the acid was differ- ent in different directions, it was the same in any given direction. The result as a whole was that fairly good constants were obtained; indeed, as good as could be expected under the conditions. An analogous case, as Ostwald 4 points out, is the solution of solid in liquids, and the separation of solids from supersaturated solutions. Take the first case : The velocity with which the solid 1 Ber. d. chem. Gesell. 9, 1646 (1876) ; 10, 34 (1877). 2 Ztschr. phys. Chem. 2, 13 (1888). 8 Ibid. 1, 209 (1887). * LehrB. d. Allg. Chem. II, 127, p. 288. CHEMICAL DYNAMICS AND EQUILIBRIUM 563 dissolves depends upon the magnitude of the surface of contact be- tween the solvent and the solid, and, of course, decreases as the satu- ration point is reached. We thus see, in terms of chemical dynamics, why it is desirable to have as large a surface as possible of the solid exposed to the liquid. We know in fact that to saturate completely a solution, a large amount of the very finely powdered solid should be added after the saturation point is nearly reached. If the solution is supersaturated, it can best be brought to the saturation point by adding a large amount of the finely powdered solid, as this reaction also is one where surface comes into play. Since the velocity with which these processes take place dimin- ishes rapidly as the saturation point is approached, we see why such a long time is required to saturate completely a solution, whether we proceed from the side of the pure solvent or from that of the supersaturated solution. If, during reactions like the above, or like the solution of metals Other heterogeneous reactions. "Action of colloidal platinum on hydrogen peroxide." Bredig and Miiller von Berneck : Ztschr. phys. Ghem. 31, 258 (1899). " Surface of solid constant, amount of liquid varied." Kajander : Ber. d. chem. G-esell. 13, 2387 (1880) ; 14, 2050, 2676 (1881). Ericson-Auren and Palmaer : Ztschr. phys. Ghem. 39, 1 (1902) ; 45, 182 (1903). See also Noyes and Whitney : Ztschr. phys. Chem. 23, 689 (1897) ; Journ. Amer. Ghem. Soc. 19, 930 (1897). Bruner and Talloczko : Ztschr. phys. Chem. 35, 283 (1900) ; Ztschr. anorg. Chem. 88, 314 (1901) ; 35, 23 (1903) ; 37, 455 (1903). " Kate of precipitation." Gladstone and Tribe: Proc. Boy. Soc. 19, 498 (1871) ; Journ. Chem. Soc. 24, 1123 (1871) ; Journ. prakt. Chem. (1) 67, 1 (1856) ; 69, 257 (1856). See also Haber : Ztschr. phys. Chem. 32, 193 (1900) ; Ztschr. Elektrochem. 10, 156 (1904). " Reactions between immiscible liquids." Carrara and Zoppellari : Gazz. chim. ital. 25, 1, 1 (1894) ; 26, I, 483 (1896). Goldschmidt and Messerschmidt : Ztschr. phys. Chem. 31, 235 (1899). " Reactions between gases and liquids." Hood : Phil. Mag. (5) 17, 352 (1884). Bohr : Wied. Ann. 68, 644 (1897) ; 68, 500 (1899) ; Drude's Ann. 1, 244 (1900). Wanklyn : Phil. Mag. (6) 3, 347, 498 (1902). Perman : Journ. Chem. Soc. 73, 515 (1898) ; 83, 1168 (1903). "Reactions between gases and solids." Ikeda: Journ. Coll. Sci., Imp. Univ. Japan, 6, 43 (1893). Ewan : Ztschr. phys. Chem. 16, 315 (1895) ; Phil. Mag. (5) 38, 512 (1894), Russell : Journ. Chem. Soc. 83, 1263 (1903). 564 THE ELEMENTS OF PHYSICAL CHEMISTRY in acids, etc., the surface undergoes appreciable change, this must be taken into account. The way in which this would be done would, of course, depend upon the form of the surface. Since the active mass of a solid depends upon its surface, it is only necessary to know the surface before the reaction began, and the surface after the reaction had taken place, and, consequently, the change in surface, in order to calculate the velocity of the reaction. Heterogeneous Reaction of the Second Order. — There are many reactions between two homogeneous substances, which give rise to products of a different state of aggregation. The precipitation of one substance by another in inorganic chemistry furnishes examples. Indeed, qualitative and quantitative analyses are based upon this fact. It is, however, difficult, not to say impossible, to measure the velocity with which such reactions take place, because it is so great. That such reactions take place with a finite velocity is quite certain, and it seems probable that methods may be devised for measuring these very great velocities in the future. A reaction between two solutions giving a solid, with a velocity which can be measured, is the following: — Na 2 S 2 3 + 2 HC1 = 2 NaCl + H 2 + S0 2 + S. Such a reaction has been studied by Foussereau. 1 Summary. — After a discussion of the law of mass action as for- mulated by Guldberg and Waage, it was applied to first order, second order, and third order homogeneous reactions. By means of this law it was shown to be possible to determine the number of mole- cules which take part in a given reaction, and many of the results obtained pointed to the fact that many of our chemical equations are in error, the apparently complex reactions being made up of several simpler reactions. Two other methods of determining the order of a reaction were taken up, and then some of the influences which affect the velocity of reactions, such as tempera- ture, nature of the medium, foreign substances, traces of moisture, etc. The principle of the coexistence of reactions was then dis- cussed and applied to side reactions and counter reactions. Attention was next turned to heterogeneous reactions of the first and second orders. With this survey of the field of chemical dynamics we pass to a special phase of reaction velocities, where the two counter reactions have the same velocity, i.e. to chemical equilibrium. i Ann. Chim. Phys. 15, 533 (1888). CHEMICAL DYNAMICS AND EQUILIBRIUM 565 CHEMICAL EQUILIBRIUM Equilibrium in Chemical Reactions. — When substances are brought together which react chemically, the reaction starts with a certain velocity. This becomes less and less as the reaction proceeds, as the active masses of the original substances become less, and the active masses of the products of the reaction become greater. After a time a condition is reached where the products of the reaction attain a maximum value, and do not further increase no matter how long the reaction is allowed to proceed under the given conditions. Since the products of the reaction do not increase beyond this point, the active masses of the original substances do not diminish beyond this point. This condition of a reaction where the quantities of the substances taking part in the reaction do not change, and where the products of the reaction do not change in amount, is known as the equilibrium of the reaction. Let us take an example to illustrate this condition. When ethyl alcohol and acetic acid are brought together, they react, as is well known, in the sense of the following equation : — C 2 H 5 OH + HOOC . CH 3 = H 2 + CH 3 COOC 2 H 5 . Suppose we use one equivalent of the acid and one equivalent of the alcohol. The reaction starts with a certain definite velocity. This becomes less and less as the reaction proceeds — as the active masses of the alcohol and the acid become less and less and the active masses of the products — ethyl acetate and water — become greater and greater. Finally, the masses of the acid and alcohol do not further diminish, but remain constant; and the masses of the ester and water do not further increase. When this relation of things obtains, the reaction has reached the con- dition of equilibrium. The Condition of a Reaction when Equilibrium is Established. — What is the condition of things in a reaction when equilibrium is reached ? Take the above reaction : When equilibrium is reached we have present some free alcohol, some free acid, some of the ester and water. When equilibrium is reached are we to consider the reaction between the alcohol and the acid as having ceased to take place? This was the older way of regarding equilibrium, but it does not accord with the experimental facts. Ethyl alcohol and acetic acid will always react when in the presence of each other, whether or not water or ethyl acetate is present. It is, however, also a fact that when equilibrium is reached in the above reaction, the amount of the ester formed does not increase. 566 THE ELEMENTS OF PHYSICAL CHEMISTRY How are these apparently contradictory facts to be explained, and how can we account for the condition of equilibrium ? We have already seen that we must regard chemical reactions in general as reversible ; the reaction between the original substances giving rise to certain products, which then react with one another and reform the original substances. In the above reaction the alco- hol and acid react forming the ester and water, and then the ester and water react forming the original acid and alcohol. Instead of writing reactions, as we ordinarily do, from left to right, we must write them from left to right and also from right to left. Thus, the above reaction should be written : — C 2 H 5 OH + HOOC . CH s ^±:CH 8 COOC 2 H 5 + H 2 0, which means that we have two reactions taking place simultaneously in the opposite sense. This method of regarding reactions not only agrees with the experimental facts, but throws light on the whole problem of the equilibrium of reactions. "When, as in the above case, two sub- stances react, they do so with a definite velocity, which becomes less as the reaction proceeds, and the active masses of the original sub- stances become less. As quickly as the products of the reaction (ester and water) begin to be formed, they react with one another with a velocity which at first is very small, since the masses of those substances present are at first very small, but becomes greater and greater as the masses of these substances become greater. We have, thus, two reactions proceeding in the opposite sense : the one with a velocity which is continually becoming smaller, the other with a velocity which is ever becoming greater. There will be a condition where these two velocities will become equal, and this is the condition of equilibrium. Equilibrium in a chemical reaction is, then, that condition at which the velocities of the two opposite reactions are the same, and this conception greatly simplifies the whole problem. We can apply the law of mass action to the^equilibrium of chemical reactions, just as well as to the velocities of such reactions. It is only necessary to make the velocities of the two opposite reactions equal, and we have at once the condition of equilibrium. We shall now study reactions of different orders in the light of these conceptions. Equilibrium in First Order Homogeneous Reactions. — We have seen that the velocity of a homogeneous reaction of the first order is expressed by the equation, — CHEMICAL DYNAMICS AND EQUILIBRIUM 567 f=G(A-x), where A is the active mass of the original substance, and x the amount transformed during the reaction. Suppose that the active mass of the substance formed from A is Ai, and that x t of this is retransformed into A, the velocity of the second reaction is, — Since the two reactions are exactly the reverse of one another, the one representing the transformation of A into A h and the other the transformation of A t into A, we have x = — x x and dx = — dx x . Sub- stituting this value in the last equation, — § = - CtiA + x). The velocity of the reaction as a whole being the sum of the velocities of the two individual reactions, — ^=0(A-x)-0 1 (A 1 + x). As we have just seen, when equilibrium is established the total velocity of the reaction is zero, consequently, — C(A-x)-C 1 (A 1 + x) = 0, or, O (A — x) = d {A t + x), from which, Q- = 4l±^. ' d A-x When the equilibrium is established, the amounts of the two sub- stances A and A lt which are present, are proportional to the velocity constants C and Ci, of the two reactions. This is true independent of the amounts of the substances with which we start ; so that know- ing the velocity constants of the two reactions we can calculate at once how much of each substance will be present when equilibrium is established. An example of equilibrium in a homogeneous reaction of the first order would be the transformation of ammonium sulphocyanate, on fusion, into sulphourea. According to Volhard 1 equilibrium is established in this reaction while there is an appreciable quantity of both substances present, and the reaction may readily proceed in either direction, depending upon the amounts of the two substances 1 Journ. prakt. Chem. 9, 11 (1874). Lowry: Journ. Chem. Soc. 75, 211 (1899). 568 THE ELEMENTS OF PHYSICAL CHEMISTRY present. Other examples of equilibrium in first order homogeneous reactions are known, but the number is not large. Equilibrium in First Order Heterogeneous Reactions. — In such reactions, it will be remembered, the substances are in different states of aggregation : the one a solid and the other a liquid, the one a liquid and the other a gas, or the one a solid and the other a gas, and so on. Since, as we have seen, the active mass of a solid with re- spect to the other states of aggregation, or of a liquid with respect to a gas is a constant, the active mass of the other substance must also be a constant in order that equilibrium may be established. The transformation of matter from one state of aggregation into another belongs under this head. The passage from the solid to the liquid state is an example. The solid and liquid are in equilibrium at a definite temperature, regardless of the amount of matter present in either state of aggregation. Similarly, matter in the form of vapor is in equilibrium with the same kind of matter in the form of a liquid, when the amount of vapor in a given volume has reached a certain definite quantity. Such simple transformations as these will be dealt with later by another method, so that no further stress will be laid upon them here. The reciprocal transformation of cyanogen and paracyanogen is an excellent example of equilibrium in a first order heterogeneous reaction, cyanogen being at ordinary temperatures a gas and para- cyanogen a solid. At about 500° cyanogen undergoes transformation into paracyanogen, and above this temperature paracyanogen is transformed into cyanogen, as Troost and Hautefeuille ' have shown. Equilibrium exists at any given temperature between the two poly- meric forms, when the vapor-pressure has reached a certain definite value. Another example is the well-known reciprocal transformation of yellow and red phosphorus. When yellow phosphorus is heated to 260°, and still better at higher temperatures, it passes over into the red modification, as Hittorf 2 pointed out. When the red modifica- 1 Compt. rend. 66, 795 (1868). 2 Pogg. Ann. 126, 193 (1865). Ponsot : Compt. rend. 130, 829 (1900). Horstmann : Lieb. Ann. 170, 192 (1873). Foote : Ztschr.phys. Chem. 33, 740 (1900). Colson : Compt. rend. 132, 467 (1901). Troost and Hautefeuille : Compt. rend. 67, 1345 (1868). Hittorf : Pogg. Ann. 126, 193 (1865). Lemoine : Ann. Chim. Phys. [4], 24, 129 (1871) ; [5], 2, 153 (1874). Hollmann: Ztschr.phys. Chem. 43, 129 (1903). CHEMICAL DYNAMICS AND EQUILIBRIUM 569 tion is volatilized and the vapor suddenly condensed, the yellow modification is obtained again. These reciprocal transformations have been extensively studied by a number of investigators, 1 and especially by Lemoine, who pub- lished his results and the discussion of the whole subject in his book, JEtudes sur les Equilibres Chimiques, which is far less known than it deserves to be. For details in this connection reference must be had to his work. Equilibrium in Second Order Homogeneous Reactions. — The velocity of a reaction in which two substances take part, and where all the substances are in the same state of aggregation, is expressed thus : — f=C{A-x)(B-x), where A and B are the active masses of the two substances which react. The velocity of the opposite reaction which takes place between the products of the first reaction is expressed thus : — ^ = C 1 (A 1 -x 1 )(B 1 -x 1 ). Since we are dealing with equivalent quantities of the different substances, for equilibrium x = — xi and dx-= — dx±. From the velocities of the two reactions, we have the velocity of the reaction as a whole : — ||= (A - x) (B-x)- d (At + x) (B t + x). For equilibrium — must be equal to zero, whence, — C(A-x)(B-x)- C 1 (A 1 +x)(B 1 + x)=0, or, G(A -x){B-x) = d (A t + x) (B x + x). C _^ (A 1 + x)(B 1 + x) ' Ci (A-x)(B-x) ' iTroostand Hautefeuille : Ann. Ghim. Phys. [5], 2, 145 (1874). Moutier: Ibid. [5], 1, 343 (1874). Menschutkin : Ann. Chim. Phys. [5], 20, 289 (1880) ; 23, 14 (1881) ; 30, 81 (1885). Lieb. Ann. 195, 334 (1879) ; 197, 193 (1879). Berthelot and St. GUles : Ann. Chim. Phys. [3], 65, 385 (1862) ; [3], 66, 5 (1862) ; [3], 68, 225 (1863). Lemoine : Ann. Chim. Phys. [5], 12, 145 (1877). Bodenstein: Ztschr.phys. Chem. 22, 1 (1897). Brunner : Ztschr. anorg. Chem. 38, 350 (1904). 570 THE ELEMENTS OF PHYSICAL CHEMISTRY If we start with gram-equivalents of A and B, we should repre- sent their active masses by unity. Since at the beginning of the reaction neither A 1 nor Bi is present, their active masses would be zero. Substituting these values in the above equation, we have — C a? Gt (1-z) 2 The condition of equilibrium in a second order homogeneous reaction is, then, that the velocity coefficients are proportional to the square of the amounts of the substances which have been transformed. The above equation has been tested by a number of methods. Julius Thorn sen employed a method which has already been referred to, but which will be considered more fully in the next chapter, based upon the heat evolved when a salt of one acid is treated with another acid. Knowing the heat evolved when each acid acts sepa- rately upon the base, and the heat set free when a salt of one of the acids is treated with the other acid, we have the data necessary for calculating the amount of the base which goes to each acid ; in brief, the condition of equilibrium in such a reaction. Without giving details in this connection it may be said that the experimental results are in excellent agreement with the deduction from the law of mass action. The simplest and most direct method of testing the above equa- tion experimentally was that employed by Ostwald. When sub- stances react chemically there is almost always a change in volume produced, and the change in volume is different for reactions between different substances. Thus, when one acid is neutralized by a given base there results a certain change in volume, which is different from the change in volume produced when another acid is neutralized by the same base. The simplest method of measuring the change in volume is to measure the change in specific gravity, which is propor- tional to it. Ostwald carried out the following experiment by the above method. He wished to determine how sulphuric acid and nitric acid will divide a base between them. He determined the specific gravi- ties of normal nitric acid, normal sulphuric acid, and normal sodium hydroxide ; also of the solution containing equal volumes of the base and nitric acid, and of the solution containing equal volumes of the base and sulphuric acid. Nitric acid was then added to sodium sul- phate, and the specific gravity of the resulting solution determined. Prom the above data we could determine at once how the base divided itself between the two acids ; how much of the base went CHEMICAL DYNAMICS AND EQUILIBRIUM 571 to each acid when equilibrium was established. It was found that about one-third went to the sulphuric acid, and about two-thirds to the nitric acid. Ostwald used his results to test the above deduction, by calculat- ing the change in specific gravity which should be produced if this equation is true, and then comparing the values calculated with those found experimentally. The two sets of values agree as satis- factorily as could be expected when we consider that the change in volume which is to be measured is so very small. Equilibrium in Second Order Heterogeneous Reactions, where One Substance is Solid. — If the reaction is heterogeneous, i.e. the sub- stances in different states of aggregation, we may have several pos- sibilities. One substance may be solid and the others liquid, or two or three substances may be solid. We will take up the simplest case, where one of the products of the reaction is a solid and the other substances are liquid. We have seen that the active mass of a solid is constant, and we will call this constant 8. The velocity of this reaction is — f t = G(A-x){B-x). The velocity of the opposite reaction is — When equilibrium between the two reactions is established we would have — 0(A -x)(B-x) = d (At + x)S, QS (A-x)(B-x) or, — j— = i 7^ L - ' C A t +x If we start with unit quantities of A and B, at the outset A x = 0, we would have — Q 1 S = (l-x) 2 C x There are many examples of equilibrium known which belong to this class. Thus, when two soluble substances are brought together and a precipitate is formed and only one soluble substance remains in solution, we have an example of this kind of equilibrium. The action of sulphuric acid on barium chloride, giving barium sulphate and hydrochloric acid, will serve to illustrate this principle. It is not necessary that the insoluble substance should be formed 572 THE ELEMENTS OF PHYSICAL CHEMISTRY as the result of the reaction in order that it may belong to this class. One of the substances between which the original reaction takes place may be insoluble. The action of an acid on an insoluble oxa- late would be an example. When an equivalent of hydrochloric acid is allowed to act on an equivalent of calcium oxalate, a part of the oxalate dissolves, and we have two reactions taking place in the sense of the following equation : — (\ COOH >Ca+2HCl:Z±:CaCl 2 + I V COOH When the velocities of the two opposite reactions become equal, equilibrium will be established. The equation of equilibrium for such a case would be — C(A -x)S = C 1 (A t + x) (B t + x), or Cl = A ~ x CS (A 1 + x)(B 1 + x)' If we use unit quantity of acid, at the beginning A = l, Ax and Hi = 0, the above equation becomes — C t = l-x CS x* This reaction has been studied 1 in the way indicated above ; also by starting with calcium chloride and oxalic acid, when the equation first deduced applies to it. The conclusions from theory have been verified by experiment. Equilibrium in Second Order Heterogeneous Reactions, where Two Substances are Solid. — If two of the substances which take part in the reciprocal reactions are solids, their active masses will be constants. The equation for the equilibrium in such cases would be developed as follows. The velocity in the one direction would be — dx In the other direction, - ■=G(A-x)S. dt K ' ^ = C x (A 1 -xi)S 1 . 1 Journ. prakt. Chem. [2], 22, 251 (1880). Lang: Ztschr.phys. Chem. 2, 173 (1888). Ostwald : Journ. prakt. Chem. (2) 16, 385 (1877) ; 19, 468 (1879) ; 22, 259 (1880) ; 24, 486 (1881). Bugarsky : Ztschr.phys. Chem. 11, 668 (1893) ; 12, 223 (1893). CHEMICAL DYNAMICS AND EQUILD3RIUM 573 For equilibrium, — C(A -x)S= C^At + x) S t , from which — M? _ A^L. CS A t + x This equation was tested experimentally by Guldberg and Waage, and the results published in their Etudes sur les Affinitis Ghimiques. The following is one of the first examples which they brought for- ward in support of the law which they had just deduced. They studied the action of potassium carbonate on barium sulphate, which gives rise to potassium sulphate and barium carbonate. The follow- ing results are taken from their paper : 1 — A A x Observed as Caloitlatbd 200 39.5 40.0 250 50.0 50.0 350 71.9 70.0 250 25 30.0 30.0 300 25 40.8 40.0 200 50 0.5 (trace) 0.0 The agreement between the values of x, as found and as cal- culated, is excellent. Similar experiments were carried out by Ostwald, using sodium carbonate instead of potassium carbonate. The agreement between the values of x as calculated and as found experimentally is quite satisfactory, but not as close as the results obtained by Guldberg and Waage. Equilibrium in Second Order Heterogeneous Reactions, where Three Substances are Solid. — If three of the four substances which enter into the two reciprocal reactions are solids, their active masses are all constants. Three of the active masses are constants, and, consequently, the equilibrium depends upon the active mass of the fourth substance, which is not a solid. This case has also been tested experimentally 2 by the action of lead oxide on ammonium 1 Elass. d. exakt. Wissenschaft. 104, 22. Journ. prakt. Chem. [2], 19, 92 (1879). 2 Isambert: Compt. rend. 102, 1313 (1886). Guldberg and Waage : Ibid. [2], 19, 89 (1879). Smith : Journ. Chem. Soc. 81, 245 (1877). Jaeger: Ztschr. anorg. Chem. 27, 22 (1901). Bodlander and Storbeck : Ztschr. phys. Chem. 9, 730 (1892) ; 39, 597 (1902). Ztschr. anorg. Chem. 31, 458 (1902). 574 THE ELEMENTS OF PHYSICAL CHEMISTRY chloride, and it was found that the pressure of the ammonia gas set free at any given temperature was independent of the amounts of the solid substances which were present. The application of the law of mass action to the conditions of equilibrium in chemical reactions has been as successful as to the velocities of these reactions. We can deal with the equilibrium of the more common reactions more simply by means of this law than by any other method which has been thus far proposed. The problem is not only treated by the simplest method available, but by the most exact. The conditions which exist when equilibrium is estab- lished are determined with mathematical accuracy, probably far more accurately than by direct experiment. Because of the sim- plicity and accuracy of the method, it has been employed in con- nection with the problems of equilibrium in chemical reactions both homogeneous and heterogeneous, and of the first and second orders. THE PHASE RULE AND ITS APPLICATION TO CHEMICAL EQUILIBRIUM The Phase Rule of Willard Gibbs. — The meaning of the Phase Rule can be understood best by studying it in connection with simple substances which exist in different states of aggregation. We know most substances in three different states of aggregation, — solid, liquid, and gas. The different modifications of a substance are known as phases of that substance, and we therefore know most substances in three phases. It may oc- cur that the same substance exists in more than three phases, there being two or more phases ~ in the same state of TEMPERATURE Fig. 70. aggregation. These phases may exist separately, the phase depending chiefly upon the temperature and also to a considerable extent upon the pressure, or they may coexist in a condition of equilibrium with one another. Take a CHEMICAL DYNAMICS AND EQUILIBRIUM 575 simple substance like benzene ; at all ordinary temperatures it exists both in the liquid and vapor phase. At each given temperature the vapor is formed until it acquires a definite pressure, and when this is reached we have an equilibrium between the liquid and vapor phases. If we determine the tension of the vapor of benzene at different temperatures, and then plot the curve expressing the relation between temperature and vapor-pressure, it would have the following form (Fig. 70) : — The abscissas represent temperatures, and the ordinates pressures. The curve represents conditions of equilibrium between the liquid phase and the vapor phase. Below the curve we have only the vapor, and above only the liquid, in a condition of stable equilibrium. This is a very simple example, and but serves to show the mean- ing of the term " phase, " and of equilibrium between different phases. Let us now take a substance which exists in three phases, and a very good example is water. Water exists as a solid, liquid, or gas, depending chiefly upon the temperature, and also upon the pressure. If we draw the temperature-pressure curves representing the con- ditions of equilibrium between the different phases of water, the curves would take the following forms : — The curve PA (Fig. 71) represents the condition of equilibrium between liquid water and water-vapor. Below this curve the vapor is the stable phase, above it the liquid. B The curve PB is the line of equilibrium \ between the liquid \ and the solid phases \ LIQUID of water, the liquid \ being the stable CO to SOLID \ phase to the right UJ CC Q. \ of this curve and \ y* h above the curve PA, \^^^ while the solid is the stable phase to ^^^""^ VAPOR c ' the left of PB and above PC. The TEMPERATURE curve PC is the line Fig. 71. of equilibrium be- tween the solid phase of water and water-vapor ; above this curve and to the left of PB ice is the stable condition, while below this curve and PA water-vapor is the stable phase. 576 THE ELEMENTS OF PHYSICAL CHEMISTRY It will be observed that the three curves intersect in a point which we have called P. This point has properties which make it of special interest. Since it is common to all three curves, it means that at this temperature all three phases of water have exactly the same vapor-pressure. That such is the case can be shown by the following considerations. Take the liquid and solid phases. The point P represents the temperature at which ice and water are in equilibrium under their own vapor-tension. Since this is much less than an atmosphere, being in fact about 4 mm., the temperature of the point P is slightly above zero, since pressure lowers the freezing- point of water. If the vapor-tension of the ice is not the same as that of the water, it must be either greater or less. If it is greater, the ice will vaporize and the vapor condense as liquid ; if it is less, the water will vaporize and the vapor freeze to ice. Since, however, by hypothesis this point represents a condition of equilibrium be- tween these phases, where neither can increase at the expense of the other, we could not have either of the above conditions realized. Therefore, since the vapor-pressure of the ice cannot be greater than that of the water at this temperature, and cannot be less, it must be equal to it. A special name has been given to the point P. Since it repre- sents a condition of equilibrium between three phases, it is known as a Triple Point. The curves PA, PB, and PC represent conditions of equilibrium between two phases, and the areas PAB, PBC, and PGA represent conditions under which only one phase is stable. We can now state and apply the generalization known as the Phase Rule, — If the number of phases exceeds the number of components by two, the system is non-variant, or has no degree of freedom. This means that none of the conditions can be varied without destroy- ing the equilibrium. The triple point P is an example of a non- variant system. The number of phases is three and the number of components one, and we cannot vary either the temperature or the pressure without disturbing the equilibrium between the three phases. If the number of phases exceeds the number of components by one, the system^ is monovaridnt, having one degree of freedom. This is the case in the systems PA, PB, and PC. The number of phases is two, and the number of components one, and there exists one variable along these curves. We can vary either the temperature or the pressure, provided we keep on the curve, without destroying the equilibrium between the two phases. If the number of phases is equal to the number of components, the CHEMICAL DYNAMICS AND EQUILIBRIUM 577 system is divariant, having two degrees of freedom. This is exem- plified by the areas PAB, PBC, and PCA. The number of phases is one, and the number of components one, and two variables exist. We can vary both the temperature and the pressure provided that we keep within the given area, without in any wise destroying the equilibrium. We have now seen what the phase rule is and what is meant by a triple point, a non-variant, monovariant, and divariant system. It is possible to have more than three phases in equilibrium at a point. If there are four, the point is a quadruple point ; if five, a quintuple point, and so on. And just as we have had non-variant, monovari- ant, and divariant systems, so if the number of components is greater than one we may have systems where there are a still larger number of degrees of freedom. With these fundamental concep- tions clearly in mind, we shall now apply the phase rule to a number of problems in chemical equilibrium. Equilibrium between Different Phases of the Same Substance. — The cases which we have just examined represent conditions of equilibrium between different phases of the same substance. They have, however, been considered only from one standpoint as illustra- tions of the phase rule. We must now study more carefully a few cases where only one substance is involved. As an example of one substance existing in two phases we may take any two of the phases of water, or the two phases of benzene already considered. The curve represents an equilibrium between the two phases, and since there is one component and two phases, we have a monovariant system. We can vary either the tempera- ture or the pressure, provided we keep within the bounds of this curve, without destroying the equilibrium. The areas above and below the curve represent divariant systems, within which both temperature and pressure can be varied without destroying the phase. Being only one curve there is no point of intersection, and consequently no triple point. For an example of one substance existing in thr-ee phases let us return to the temperature-pressure diagram of water. The -follow- ing contains in addition to the above-mentioned curves the curve PG t , and this calls for special comment. The three curves PA, PB, PC, in the diagram for water, represent conditions of stable equilibrium ; but we know that we may cool water far below its freezing-point without the separation of ice if there is no dust or other solid matter present ; and we may heat water more than 100° above its boiling- point without ebullition taking place if all impurities have been re- 2p 578 THE ELEMENTS OF PHYSICAL CHEMISTRY moved. ' These conditions which were not taken into account at all in the original discussion are usually referred to as conditions of unstable equilibrium. Since such conditions simply represent de- grees of stability, this term has been abandoned in favor of meta- stable equilibrium. The curve PC 1 represents a condition of metastable equilibrium for water. The instant a mere fragment of the solid phase, ice, is introduced, freezing begins and ice separates until the metastable passes over into the stable condition. This shows that the stability of the different phases is purely relative. An idea of the quantity of the phase stable under the conditions, which is required to transform a metastable into a stable phase, can be obtained from an investigation by Ostwald. 1 He has shown that if an almost infinitesimal amount of the stable phase is present, the metastable phase can no longer exist as such, but passes over into the phase which is stable under the conditions. Attention must be called to one further point in connection with the temperature-pressure diagram of water. The curves do not run out indefinitely from the point P, but stop abruptly in the middle of the diagram. What does this mean ? Take the curve PA, which represents the condition of equilibrium between water aud water-vapor. We know that there is a tempera- ture above which the vapor of water cannot be liquefied, the two phases in this region existing as one phase. This is the well-known critical temperature of the substance. At the critical temperature we have also the critical pressure. These two critical constants for water-vapor are represented by the point A at the extremity of the curve PA. This comparatively simple diagram is, then, a shorthand expres- sion of a large number of experimentally established facts. We have in sulphur a good example of one substance existing in four phases. We know two solid phases of sulphur, — the one stable at ordinary temperatures, crystallizing in the orthorhombic system, the other stable at higher temperatures, crystallizing in the mono- clinic system. The orthorhombic melts at 115°, passing over into the liquid phase. If kept at a temperature just below its melting- point, it passes into the monoclinic form. The monoclinic sulphur is also formed when the liquid phase is cooled slowly. Monoclinic sulphur melts higher than orthorhombic, at 120°. When the mono- clinic phase is kept at ordinary temperatures, it passes over gradu- ' Ztschr.phys. Ckem. 22, 289 (1897). CHEMICAL DYNAMICS AND, EQUILIBRIUM 579 ally into the orthorhombic phase, which is the stable form at these temperatures. At higher temperatures, as we have seen, the orthorhombic passes into the monoclinic. Therefore, at low temperatures the orthorhom- bic is the stable, the monoclinic the metastable phase. At higher temperatures, up to 131°, the monoclinic is the stable phase, while the orthorhombic is the metastable phase. The temperature at which the two solid phases are in equilibrium — at which both solid phases can coexist without either passing into the other — is known as the transition temperature, and for sulphur this is 95°.6. In addition to the two solid phases of sulphur we have the liquid and the vapor phases. If we plot the temperature-pressure diagram of sulphur as we did that of water, it would have the following form : — 115" 120° temperature Fig. 72. The diagram is considerably more complex than the diagram for water, where only three phases were present; yet the principles involved are exactly the same ; and if we understood the diagram for water, this should offer no serious difficulty. 580 THE ELEMENTS OF PHYSICAL CHEMISTRY Beginning with the conditions of equilibrium between orthorhom- bic sulphur and sulphur vapor, these are represented by the curve PB. The curve PPi is the vapor-pressure curve of monoclinic sul- phur, while P t C is the vapor-pressure curve of liquid sulphur. The point P is the transition point of orthorhombic and monoclinic sul- phur. The curve PPu represents the conditions of equilibrium between orthorhombic and monoclinic sulphur, and any point on this curve is therefore a transition point. The curve PjPu repre- sents equilibrium between monoclinic and liquid sulphur, and is therefore the curve of the melting-point of monoclinic sulphur. Just as the curve (PPu) of the transition point of orthorhombic and monoclinic sulphur slopes to the right as it rises, showing an in- crease in temperature with increase in pressure, so the curve of the melting-point of monoclinic sulphur (P2P11) slopes to the right as it rises. This is but one of many analogies between transition points and melting-points. These two curves, however, meet at the point P u , which corresponds to a temperature of 131°. The curve P^E is the curve of equilibrium between orthorhombic and liquid sulphur, i.e. the curve of the melting-point of orthorhombic sulphur with increase in pressure, monoclinic sulphur being incapable of exist- ence beyond 131°, no matter how high the pressure. Let us turn now to the dotted curves. PA represents the vapor- pressure of metastable monoclinic sulphur. This is greater below the transition point, as we would expect, than the vapor-pressure of the stable orthorhombic phase. Above the transition point ortho- rhombic sulphur is the metastable phase, and it has in this region a higher vapor-pressure than the stable monoclinic phase. This is represented by the curve PPuu the prolongation of PB. If now we prolong the curve, P t C representing equilibrium between liquid sul- phur and its vapor until it meets the prolongation of PB, it will do so at P m . If now we join P m and P m the curve will represent the equilibrium between orthorhombic sulphur and liquid sulphur, i.e. the melting-point of orthorhombic sulphur, and the effect of pressure as increasing the temperature at which this phase will melt. We have now examined all the curves in the diagram. Let us see what kinds of systems they represent. The point P repre- sents equilibrium between the three phases orthorhombic, mono- clinic, and vapor, and is, therefore, a triple point. Similarly, P t represents equilibrium between monoclinic, vapor, and liquid ; P u , between orthorhombic, monoclinic, and liquid, and P m (in the meta- stable region) between orthorhombic, liquid, and vapor, and these are all triple points. We have, then, four triple points, CHEMICAL DYNAMICS AND EQUILIBRIUM 581 and since there is one component and three phases the systems are non-variant. Take the curves. PB represents equilibrium between orthorhom- bic and vapor, PP t between monoclinic and vapor, P X G between liquid and vapor, YiP n between monoclinic and liquid, P U P between ortho- rhombic and monoclinic. Take the dotted line curves representing equilibria in metastable regions. PA is the curve of equilibrium between monoclinic and vapor, PPm between orthorhombic and vapor, PiPm between liquid and vapor, and PuPm between orthorombic and liquid. These systems represent conditions of equilibria between two phases, and since the number of components is one they are mono- variant systems. Take finally the areas. Within BPPfi sulphur is stable only in the form of vapor, within CPxPuE the liquid is the stable form, within EPuPB the orthorhombic is the stable phase, and within PP t P n the monoclinic is the stable form. These areas each repre- sent one stable phase of the substance, and since there is only one component these systems are divariant. So much for the conditions of equilibria where there is one com- ponent and four phases. We have thus far considered the cases where there is one compo- nent and two, three, and four phases, there being two variables, — temperature and pressure. We must now consider a few cases where there is one com- ponent and three variables. Equilibrium between Two Phases of the Same Sub- stance when Three Conditions are Variable. — The phases which we will study are the liquid and vapor phases of a pure substance, like water. The relations between these two phases can be seen by reference to the pressure- volume curves or isother- mals, since for each curve the temperature is constant. If we start with a vapor under a small pressure, and increase the pressure, the volume will diminish. The isothermal ab (Fig. 73) VOLUME Fig. 73. 582 THE ELEMENTS OF PHYSICAL CHEMISTRY represents the relations between these two variables. At & a portion of the vapor may become liquid ; if so, further diminution in volume can take place without increasing the pressure. At c all the vapor has become liquid, and beyond this point enormous pressure is required to produce small changes in volume. This is shown by the dc portion of the isothermal rising nearly parallel to the ordinate. The isothermals for higher and higher temperatures resemble the one just considered, a greater pressure being required at the higher temperature to liquefy the vapor. Finally, the isothermal is reached which passes through the critical point C, and this takes the form of the highest curve shown in the figure. In any one of the above curves we have allowed only pressure and volume to vary. Suppose now we allow also temperature to vary, and use the three variables as coordinates on which to plot the relations of the liquid and vapor phases of a substance. The figure would have the form shown in the sketch (Fig. 74). The position of the isothermals is seen at once, also the regions of pure vapor and of pure liquid, and the inter- mediate heterogeneous region in which both phases are present. We may in the same manner have equilibrium between three phases of the same substance with three conditions variable, but a detailed study of such cases would scarcely add to what has already been learned. Equilibrium between Phases of Two Substances. — We shall not take up the large number of conditions of physical equilibrium between the substances, such as the solubility of a solid in a liquid, etc., since these have been referred to in other connections ; but pass at once to the conditions of chemical equilibrium, between two components and three phases. A case which is generally discussed because of its comparative simplicity, is the equilibrium between a salt containing water of crystallization and water-vapor. It has been shown that this depends upon the tension of the water-vapor, and we must first con- sider a method by which this is measured. CHEMICAL DYNAMICS AND EQUILIBRIUM 583 The apparatus first used by Frowein 1 was subsequently im- proved and used by the same investigator. 2 The tensimeter is represented in the following sketch (Fig. 75) : The finely powdered dry salt is placed in the bulb a, and sulphuric acid in b. The bottom of the bent tube is partly filled with oil, and the apparatus evacuated and sealed. The whole apparatus is placed in a thermostat bath and kept at a constant temperature until there is no further change in the levels of the oil in the two arms. The salt has then exerted its maximum vapor-tension, which is measured by the difference in the heights of the columns of oil in the two arms. If the salt is in the presence of water-vapor at a tension less than the maximum tension of its own water- vapor, it will continue to lose water until this tension is established. Take the case of copper sulphate with five molecules of water of crystallization. If this is placed in a desiccator where the tension of the water-vapor is practically zero, it will lose water and pass over into the hydrate with three molecules of water of crystallization. This will continue to lose water and form lower hydrates, and finally the monohydrate. The above transitions can be readily followed, since there is a sudden change in the maximum tension as we pass from one hydrate to another. The tension of aqueous vapor in pass- ing from the pentahydrate to the trihydrate, at the temperature at which the measurements were made (50°), was found to be 47 mm. As soon as the trihydrate was reached the tension of the aqueous vapor fell to 30 mm., and the monohydrate had a vapor-tension of only 4.4 mm. While there is any pentahydrate present the vapor-tension is 47 mm., while any of the trihydrate exists the tension is 30 mm., and so on, the tension being that of the highest hydrate present. This method has been used to good purpose in discovering the existence of new hydrates, which cannot be prepared by the ordi- nary methods. The higher hydrates are dehydrated at a constant temperature, and the vapor-pressure measured at short intervals during the process. Sudden drops in the vapor-pressure would Fig. 75. i Ztschr. phys. Chem. 1, 10 (1887). 2 Ibid. 17, 52 (1886). 584 THE ELEMENTS OF PHYSICAL CHEMISTRY show the existence of hydrates containing a definite number of molecules of water. We are dealing in the above example with equilibrium between three phases and two components; the phases being the higher hydrate, the lower hydrate, and aqueous vapor; the components being the anhydrous salt and water. The number of phases ex- ceeds the number of components by one, and the system is, there- fore, monovariant, or has one degree of freedom. We can vary either the temperature or the pressure, but for each temperature there is a definite pressure of the water-vapor. If we plot these curves in a pressure-temperature diagram, they would have the following form (Fig. 76), the curves OG, OB, OA, corresponding to the penta-, tri-, and mono-hydrates respectively. The vapor-tension curve for ice OP, for water PE, and for solu- tions saturated with the pentahydrate PJ) are added. Since a solution has a smaller vapor-pressure than the pure solvent, PJ) falls below PE, and it cuts the curve OP for the vapor-tension of ice at the point P lt which is the cryohydric point for the solution. This point represents equilibrium between the four phases, — solution, pentahydrate, ice, and vapor, — and is, therefore, a quadruple point. If we examine the regions we see that the anhydrous salt can exist in AOT, the monohydrate in AOB, the trihydrate in BOG, the pentahydrate in GOPJ), dilute temperature, t T solutions of the pentahydrate in Fig. 76. DP t PE, water in EPF, and ice in OP t PF. Let us turn next to conditions of equilibrium between two compo- nents and four phases. We shall deal with hydrated salts, i.e. those containing a certain number of molecules of water. We may have a number of such hydrates formed by the union of one molecule of the salt with a varying number of molecules of water. The hydrate containing a larger amount of water may pass over, while in solu- tion, into the hydrate with a smaller amount of water if the tem- perature is raised. Each of these hydrates represents a definite phase, the saturated solution represents another phase, and the water-vapor still another phase. We shall study in some detail the hydrates formed with ferric CHEMICAL DYNAMICS AND EQUILIBRIUM 585 chloride, these having been carefully investigated by Eoozeboom. 1 He found that there were four hydrates of this substance containing twelve, seven, five, and four molecules of water, and their melting- points were, respectively, 37°, 32°.5, 56°, and 73°.5 ; at the melting- point the liquid and the solid having the same composition. If to a fused hydrate anhydrous salt is added step by step, a new hydrate will make its appearance containing a smaller number of molecules of water. This is known as the transition temperature. Taking into account the formation of the highest hydrate by adding the anhydrous salt to water, and also the transition temperature from the lowest hydrate to the anhydrous salt, the transition temperatures are : - 55°, 27°.4, 30°, 55°, 66°. Eoozeboom also determined the composition of the saturated solutions of these hydrates, and from these data, together with the o X -30 K FejC^ L in -J O ■25 Fe 2 CI.4 Hj,0 J\ s H--""""^ o o ■20 P r--^7g O K -15 N ^-^CI 8 5H a O — M -10 cr~D > \Fe 2 CI 6 7H ]1 o U- "5 Fe B. HH «o_ Jc i/i B _j O "icF .A s -60° i -40° 20° 0° 20° i 40° 60° 8p° 100 i_ temperatures Fig. 77. melting-points and transition points, plotted the following curves (Fig. 77), 2 which are given in their original form. The abscissas are temperatures, the ordinates concentration of the solution expressed in number of molecules of Fe 2 Cl 6 3 to one hundred molecules of water. Starting from the point A, which represents equilibrium between water and ice, and adding the salt, the freezing-point of water is low- ered, and this is represented by the curve AB. When the tempera- ture — 55° is reached, the solution is saturated with the hydrate = Fe 2 Cl 6 12 H 2 0, 4 and this separates together with the ice. We have here a cryohydrate, and this is the cryohydric point. If more 1 Ztschr. phys. Chem. 10, 477 (1892). 2 Ibid. 10, 502 (1892). 3 Since Eoozeboom uses Fe 2 Cle it will be retained. 4 In connection with these more complex cases, symbols are frequently used instead of the names of compounds to simplify comparison with the diagrams. 586 THE ELEMENTS OF PHYSICAL CHEMISTRY salt is added, we have then the solubility of the dodecahydrate, and this is represented by the curve BO, the point O being that at which this hydrate separates in solid form, the saturated solution and the solid having here the same composition. Since the point of solidifi- cation is the same as the melting-point, this temperature, 37°, is the melting-point of the dodecahydrate. If more salt is added to the fused hydrate, the curve takes the form CDN, but at the point D a new hydrate makes its appearance, containing seven molecules of water. This is, therefore, a transition point. The curve DN represents a condition of metastable equilib- rium. Starting from D and continuing to add the salt, we have the pentahydrate separating at E (32°.5). We then pass through the transition point F (30°) into the metastable region FP. Starting at F and adding more salt, we pass through the melting-point G (56°) to the transition point H (55°), and so on until K is reached, and this is the transition point between the lowest hydrate and the anhydrous salt. The curve KL represents the solubility of anhy- drous ferric chloride. This curve presents a number of points of interest. It has a number of quadruple points. The transition points represent equi- libria between the two hydrates, the saturated solution, and water- vapor ; i.e. between four phases, and are therefore quadruple points. The curves AB, BOD, DEF, FGH, HIK, and KL represent solu- tions in stable equilibrium with, respectively, ice Fe 2 Cl e 12 H 2 0, Fe 2 Cl 6 7 H 2 0, Fe 2 Cl 6 5 H 2 0, Fe 2 Cl 6 4 H 2 0, and anhydrous Fe 2 Cl 6 . The ■curves DO, DN, FP, FM, and HB represent equilibria in metastable regions. As Eoozeboom points out, the two branches to each curve {BOD, DEF, FOR, etc.) show that there are two saturated solutions of each hydrate in equilibrium with the hydrate, within certain limits of temperature, the one containing more and the other less water than the solid hydrate. In his own words : * " The solubility curves of all the hydrates of ferric chloride present the phenomena that they consist of two branches which coalesce in the melting-point, so that at temperatures below the melting-point two kinds of saturated solu- tions are possible, the one containing more and the other less water than the solid hydrate. " I encountered such cases for the first time with hydrated salts in the hexahydrate of calcium chloride. 2 . . . For me the existence of such solutions was only a special case of a general phenomenon." i Ztschr. phys. Chem. 10, 486 (1892). * Ibid. 4, 34 (1889). CHEMICAL DYNAMICS AND EQUILIBRIUM 587 Eoozeboom points out that such solutions were to be expected from the thermodynamic deductions of Van der Waals. One further point must be mentioned. Of the four hydrates of ferric chloride only two were known before Eoozeboom carried out his investigation, the one with twelve and the one with five molecules of water, and the composition of the latter was not established with certainty. He found certain peculiarities in his curve, which could not be explained as due to the dodecahydrate nor to the pentahydrate, and was thus led to the discovery of the hepta- hydrate. In a similar manner the tetrahydrate was discovered. We see in these facts the real significance of the conception of phases as applied to problems in chemical equilibrium. In this case it has led to the discovery of two new substances, and in other cases to the discovery of a great number of compounds, whose existence could not have been demonstrated by any of the purely chemical methods applicable to such compounds. Equilibrium between Phases of Three Substances. — Systems con- taining three components are necessarily much more complex than those containing a smaller number. A number of such systems have been studied. Schreinemakers * investigated the system con- sisting of potassium iodide, lead iodide, and water. Meyerhoffer 2 studied cupric chloride, potassium chloride, and water. The system potassium sulphate, magnesium sulphate, and water was investigated by Van der Heide. 3 The most important applications of the phase rule to systems containing a number of components have been made in the last few years by Van't Hoff and his pupils. They have studied the con- ditions of equilibrium between complex systems, in order to obtain some light on the problem of the formation of the great salt beds, and interesting and valuable results have already been obtained. In such connections the phase rule has proved to be of value. It has led to the discovery of many new substances, and the conditions of equilibrium which exist between them. Before leaving this part of our subject, which has to deal with- ■chemical equilibrium, we must consider one or two matters of more than ordinary importance. Equilibrium in Condensed Systems. — Van't Hoff 4 has applied the term " condensed system " to those heterogeneous systems where all the components are liquid or solid, there being no gas present. 1 Ztschr. phys. Chem. 9, 57 (1892). 2 Ibid. 5, 97 (1890) ; 9, 641 (1892). 3 Ibid. 12, 416 (1893). * fitudes de Dynamique Chimique, pp. 139-148. 588 THE ELEMENTS OF PHYSICAL CHEMISTRY These obviously include solids in equilibrium with themselves in the fused condition. This is complete equilibrium, since for any given temperature there is only one pressure under which both phases are stable. The transition point in such a system is, of course, the melt- ing-point of the solid. Since we are dealing in such systems only with liquids and solids, the effect of pressure on the transformation temperature is very slight, and this is the characteristic of such systems. Van't Hoff * cites as a good example of condensed systems the transformation of cyamelide and cyanuric acid : — Cyamelide ^^ cyanuric acid. The transformation point is about 150°, and cyamelide passes into cyanuric acid by a simple rise in temperature. Determination of the Transformation Temperature. — First Method. Since transformations in condensed systems are always accompanied by volume changes, the specific volumes of the substances before and after the transformation being different, change in volume has been used to determine just when the transformation takes place. As an example, take sulphur; the rhombic' modification has a specific volume of , the monoclinic a specific volume of . 2.07 1.96 The apparatus used is known as a dilatometer, consisting of a glass bulb attached to a fine graduated glass tube. The substance whose transformation temperature it is desired to determine is intro- duced into the bulb, and the remainder of the bulb filled with some indifferent liquid (say an oil), which extends into the graduated tube. The apparatus is then placed in a bath whose temperature can be gradually raised. As the liquid in the dilatometer becomes warmer it expands gradually, the meniscus rising at a regular rate in the graduated tube. When the transformation temperature is reached the transformation takes place, and there is a sudden change in volume which manifests itself by a sudden change in the level of the liquid in the graduated tube. It has been recommended that a small amount of the products of the transformation be added, in order to insure transformation at the true transformation temperature. Otherwise this temperature might be passed somewhat before the transformation would take place, just as water can be readily supercooled some degrees without the separa- tion of ice. If a small fragment of ice is present, supercooling will be prevented; so, also, if a small particle of the product of the 1 Etudes de Dynamique Chimique, p. 141. CHEMICAL DYNAMICS AND EQUILIBRIUM 589 transformation is present, it will prevent the system from passing over into the metastable condition, and will cause the transformation to take place at the true transformation temperature. Second Method. Transformations are accompanied not only by volume changes, but also by heat changes. At the transformation temperature heat is either evolved or absorbed, and, by determining when this thermal change occurs, we can determine the transition temperature. The substance in question is placed in a tube, into which a thermometer is introduced. The substance is then warmed or cooled at a fairly uniform rate, and the thermometer noted. When the transformation takes place there is a thermal change, and this is readily seen on the thermometer. The general rule holds that the system formed at the higher temperature absorbs heat. Tliird Method. Another method of determining transformation temperatures is based upon the fact pointed out by Meyerhoffer, 1 that at this temperature the solution of the original substance is identical with that into which it is transformed. The two solutions have the same vapor-tension, solubility, etc. It is only necessary to determine the vapor-tension curves, or the solubility curves of the two substances, and then observe where these become identical, i.e. where they cross. This is the transformation temperature. Fourth Method. Another important method has been devised by Cohen, 2 based upon the concentration element which was studied under electrochemistry. The element used to study transformation temperatures was termed by Cohen the "transformation element." It is simply a concentration element in which the temperatures can be accurately regulated. The following transformation was studied : — ZnS0 4 .7H 2 0^±IZnS0 4 .6H 2 + H 2 0. The arrangement of the whole apparatus is shown in the. sketch (Fig. 78), which includes also the thermostat, T. B is a rheostat, S a key, and g the galvanometer. The vessels A and B are filled with saturated solutions of ZnS0 4 .7H 2 0. The solution in A is kept for some time above the transformation temperature, when ZnS0 4 .7H 2 passes over into ZnS0 4 .6H 2 0. The element is then placed in a thermostat at a few degrees below the transformation temperature, and the temperature 1 Ztschr. phys. Chem. 5, 105 (1890). Cohen : Ibid. 25, 300 (1898) ; 30, 623 (1899) ; 81, 164 (1889) ; 34, 179 (1900). 2 Ibid. 14, 53 (1894). 590 THE ELEMENTS OE PHYSICAL CHEMISTRY gradually raised to the transformation point, the galvanometer be- ing read every few minutes. As the temperature approaches that of transformation the readings of the galvanometer become less and less, since the difference between the concentration on the two sides of the element becomes less and less. At the transformation tempera- ture the concentrations on the two sides become the same, and, conse- quently, no current flows through the galvanometer. Since we have a stable phase on one side and a metastable phase on the other, this is known as the "transformation element with metastable phase." • A little later a " transformation element tvithout metastable phase " was devised by Cohen and Bredig. 1 This element consists of one .^^S£5^ Fig. 78. electrode surrounded by a normal solution of a salt without the solid phase of the salt ; and on the other side a similar electrode surrounded by a saturated solution of the same salt in the presence of the stable solid phase of the salt. The electromotive force of such an element 2 is a function of the 1 Ztschr.phys. Chem. 14, 535 (1894). 2 Ibid. 14, 536 (1894). "Physical chemical studies of tin." Ibid. 30, 623 (1899). Cohen : Ibid. 35, 588 (1900) ; 36, 513 (1901). Cohen and Goldschmidt : Ibid. 50, 225 (1905). "Physical chemical study of the so-called explosive antimony." See Cohen and Ringer : Ztsckr. phys. Chem. 47, 1 (1904). Cohen, Collins, and Strengers: Ibid. 50, 291 (1905). Cohen and Strengers : Ibid. 52, 129 (1905). CHEMICAL DYNAMICS AND EQUILIBRIUM 591 solubility of the stable solid phase of the salt. The temperature coefficient of the electromotive force is, therefore, a function of the temperature coefficient of solubility. It is well known that the latter changes suddenly at the transformation temperature, and, therefore, the temperature coefficient of the electromotive force changes sud- denly at this temperature. If we plot the electromotive force of this element as a function of the temperature both above and below the transformation tem- perature, the point where the two curves cross is the transformation temperature in question. For details in reference to the apparatus used reference must be had to the original paper. Effect of Temperature on Chemical Equilibrium. — When a sys- tem is in equilibrium at one temperature, it does not follow, and it is not generally true, that it is in equilibrium at other temperatures. Sometimes the equilibrium is displaced in the one, and sometimes in the other direction, the amount of displacement being in some cases very great, in others very small. A generalization has been reached connecting change in tem- perature with change in equilibrium, which is very important and accords with what we should think would take place. The effect of rise in temperature is to favor the formation of that system which absorbs heat when it is formed. An increase in temperature, there- fore, displaces the equilibrium toward the side of that system which is formed with absorption of heat. Examples are very abundant, ordinary vaporization being a striking illustration of the principle, — the higher the temperature the greater the amount of vapor formed. Some interesting relations between temperature and heat evolu- tion in chemical reactions have been discovered. Bodenstein and v. Meyer ' have shown that a much greater quantity of heat is absorbed in the formation of hydriodic acid at a lower than at a higher temper- ature. Thus 6100 calories are absorbed at 18°, while only 440 are absorbed at 186°, the reaction thus becoming less and less endothermic with rise in temperature. We should, therefore, think that the effect of rise in temperature would be to increase the amount of hydriodic acid formed, and such is the fact up to about 320°. With still further rise in temperature the amount of hydriodic acid formed undergoes diminution. This reaction which is endothermic at the lower temperatures passes over into an exothermic reaction at higher tem- 1 Ber. d. chem. Gesell. 26, 1146 (1893) ; Ztschr. pkys. Chem. 13, 56 (1894). 592 THE ELEMENTS OF PHYSICAL CHEMISTRY peratures. Exactly the opposite condition has also been realized experimentally. Troost and Hautefeuille * showed that when silicon tetrachloride is passed over very highly heated silicon, the compound Si 2 Cl 9 is formed. When the vapor-density of this substance was determined at different temperatures, it was found that the substance was stable at all temperatures up to 350°. Between 350° and 1000° it was un- stable, but became stable again at temperatures above 1000°. The maximum instability was shown at about 800°. Ozone 2 seems to be stable below 200° and above 1000°, and v. Meyer and Langer 3 have shown that chlorine acts vigorously upon platinum below 300 and above 1300 degrees. These examples show that a reaction which is exothermic at lower temperatures may become endothermic at higher temperatures. The question as to whether, a given reaction is exothermic or endothermic is, then, often a question of the temperature at which the reaction takes place. Effect of Pressure on Chemical Equilibrium. — The action of pressure on chemical equilibrium is through the resulting change in volume. Here also the equilibrium may be displaced in the one or the other direction, or may be only very slightly displaced. A generalization has been reached with respect to the effect of pressure, which is strikingly analogous to that just stated for the effect of temperature. Increase in pressure diminishes the volume, and therefore favors the formation of that system which occupies the smaller volume. Equi- librium is, then, displaced by increase in pressure towards the system which occupies the less volume. If there is no change in volume when the transformation of one system into the other takes place, increase of pressure has no influ- ence on the equilibrium. So, also, if the transformation is not ac- companied by change in temperature, which is the same as to say that the heat tone of each of the two systems in equilibrium is the same, rise in temperature would have no influence on the equilibrium. The above two generalizations have been unified by Le Chatelier 4 as follows : — 1 Ann.Chim. Phys. [5], 9, 70 (1876). 2 Troost and Hautefeuille : Compt. rend. 84, 1946. 8 Ber. d. chem. Gesell. 15, 2769 (1882). Brunck: Ber. d. chem. Gesell. 26, 1790 (1893). Zengelis: Ztschr. phys. Chem. 46, 287 (1903). 4 Les iSquilibres Chimiques, p. 210. CHEMICAL DYNAMICS AND EQUILIBRIUM 593 " The displacement of a system produced by varying one of the factors of equilibrium is defined by the following law, which I have proposed to call the law of opposition of action to reaction. " Every change in one of the factors of equilibrium, produces a trans- formation in the system, through which the factor in question is changed in the opposite direction." A few examples will serve to illustrate the above principles. When hydrogen acts upon oxygen, forming water, the resulting vapor occupies only two-thirds the volume of the original gases. In- crease in pressure would, therefore, favor the reaction. On the other hand, when chlorine acts on water, the resulting products — hydrochloric acid and oxygen — occupy a larger volume than the initial substances. Increase in pressure would, therefore, oppose this reaction. When hydrogen and iodine react and form hydriodic acid, there is no change in volume — the resulting gas occupying exactly the same volume as the original gases. Increase in pressure should, therefore, have no effect on this reaction. The work of Lemoine 1 shows that this is the case. In fact, all of the above conclusions have been verified experimentally. EQUILIBRIUM IN SOLUTIONS OF ELECTROLYTES Solubility and Dissociation of Electrolytes. — When different elec- trolytes are brought in contact with a solvent like water, very dif- ferent amounts dissolve, depending upon the nature of the substance. The electrolyte passes into solution, until, in a given time, the same amount dissolves as separates from the solution. The solution is then said to be saturated. In saturated solutions of electrolytes, as in all other concentrated solutions of electrolytes, we have both molecules and ions present. The amount of dissociation depends, as we have seen, upon the nature of the compound. Some electrolytes, such as the weak or- ganic acids and bases, are only slightly dissociated at moderate dilutions, i.e. there are only a few ions present and many molecules. Other electrolytes, such as the strong acids and bases, and the salts, are strongly dissociated even in the most concentrated solutions which can be prepared. The degree of dissociation represents a condition of equilibrium between the molecules and ions present in the solution. When we say that an electrolyte in normal solution is dissociated fifty per i Ann. Chim. Phys. [5], 12, 145 (1877). 2q 594 THE ELEMENTS OF PHYSICAL CHEMISTRY cent, we mean that when half the molecules are broken down into ions there is equilibrium between the ions and the molecules present. The condition of equilibrium between molecules and ions, like other conditions of chemical equilibrium, represents not a static but a dynamic condition. This is not a condition where a certain num- ber of molecules have dissociated, and the resulting ions and remain- ing molecules are in equilibrium ; but we must consider the mole- cules as continually dissociating into ions, and the ions as continually uniting. When equilibrium is reached, the same number of mole- cules dissociate in a given time as are reformed by combinations of the ions. In a sense, we have here two opposite reactions, the one involving the breaking down of molecules into ions, the other the recombination of the ions to form molecules ; and each reaction proceeds with its own definite velocity. When the velocities of the two opposite reactions become equal, equilibrium is established. We know already of one condition which can greatly influence this state of equilibrium. The amount of dissociation, i.e. the ratio between the number of dissociated and undissociated molecules, is changed with every change in the dilution of the solution. The number of molecules dissociated into ions increases, as we have seen, with increase in the dilution of the solution. We would naturally ask whether there are any other conditions which can affect the amount of the dissociation of electrolytes ? There is one which has proved to be of very great importance in connection with the whole subject of electrolytic dissociation, and this we must study with care before leaving the subject of chemical equilibrium. Solubility as affected by an Electrolyte with a Common Ion. — We must first ask what effect does the addition of an electrolyte with a common ion have on the solubility of the electrolyte in ques- tion ? To make this question clear by an example, What effect on the solubility of potassium chlorate would the addition of any solu- ble potassium salt or any soluble chlorate have ? Potassium chlo- rate dissociates thus : — KC10 3 =K + C10 3 ; any potassium salt represented by KA would dissociate thus : — KA = K + A; any chlorate represented by MC10 S , thus : — MC10 3 = M + ClOg. The second electrolyte would yield an ion in common with the first. CHEMICAL DYNAMICS AND EQUILIBRIUM 595 This question has been satisfactorily answered by experiment. If to a saturated solutibn of potassium chlorate dry potassium chlo- ride is added, some of the potassium chlorate is precipitated from the solution, showing that its solubility has been diminished by the presence of an electrolyte with a common cation. Similar results were obtained when dry sodium chlorate was added to a saturated solution of potassium chlorate. Some of the latter salt was precipi- tated, showing that its solubility was diminished by the presence of an electrolyte with a common anion. Again, prepare a saturated solution of potassium or sodium chlo- ride, and pass in dry hydrochloric acid gas. This dissolves and yields the common ion, chlorine. The result is that some of the potassium or sodium chloride is precipitated from the solution. This fact has long been known, and has been utilized as a means of purifying chlorides, but its relation to other things was entirely con- cealed. So much by way of qualitative demonstration of the prin- ciple, that the presence of a compound which yields a common ion diminishes the solubility of the compound in question. We must now study this phenomenon quantitatively, and see what relations exist between the amount of the substance with a common ion which is added, and the amount by which the solubility of the original electrolyte is diminished. The Deduction of Mernst. — Nernst l was the first to solve this question quantitatively from the theoretical standpoint. He applied the law of mass action as follows : 2 If we start with binary electro- lytes which are completely dissociated, the product of the active masses must be constant, and equal to the square of the solubility of the salt without the addition of a foreign substance. This he termed m 0) and the solubility of the salt after the addition of the second substance with a common ion m, the amount of the sec- ond salt added, in gram molecules per litre, being x : — m(m + x) = m„ 2 . (1) The dissociation, however, is not complete in solutions with which we ordinarily have to deal, and this must be taken into account. Let a be the dissociation of the first substance in saturated solu- tion before the second is added ; let a t be the dissociation of the added substance and a the dissociation of the first substance in the presence of the second; we must then multiply these factors into the above equation, when it becomes — mu(ma + xaj) = m 2 a 2 . (2) 1 Ztschr. phys. Ghem. i, 372 (1889). « Ibid. p. 379. 596 THE ELEMENTS OF PHYSICAL CHEMISTRY This formula simply expresses the fact that the product of the masses of the ions is constant. If we turn our attention to the undissociated portion, we find the following relations : Since m a represents the dissociated portion of the original electrolyte, m (l — «o) is the undissociated portion ; and since ma is the dissociated portion after the second electrolyte is added, the undissociated portion is m(l — «). The solubility of the undissociated portion is constant, and therefore we have — m (l — Kg) = m(l — a). (3) Solving for m, we have — 2 a a? 1 A '> «/. (4) If a = «j, equation (4) becomes — m =-2 + V m » 2 5 + 4- This equation enables us to calculate the solubility in the presence of a second salt with a common ion, from the solubility in pure water the amount of the second salt addea, d,nd the amounts of dissociation of the original substance and the added substance. Nernst tested his equation in a few cases, and found that it held approximately for the solubility of one substance in the presence of another. Solubility Experiments of Noyes. — The above equation was tested experimentally by Noyes, 1 who applied it to a number of substances. One of the first systems investigated by Noyes was silver bromate with silver nitrate, and with potassium bromate. 2 The following results were obtained : — Amount AgNOs or KBr08 Added to a Saturated Solution of AoBnOg Solubility op AoBltOg IN THE PRES- ENCE OF AGNOg Solubility of AgBrOs in the Pres- ence OF KBRO3 Solubility Calculated 0. 0.0085 0.0346 0.00810 0.00610 0.00216 0.00810 0.00519 0.00227 0.00504 0.00206 The solubility of silver bromate in the presence of an electrolyte with a common ion, agrees very well with that calculated by means of the above equation. It should be observed also that both electro- lytes diminish the solubility of the silver bromate to just about the 1 Ztschr. phys. Chem. 6, 241 (1890). 2 Ibid. 6,246 (1890). CHEMICAL DYNAMICS AND EQUILIBRIUM 597 same extent, and that a very small quantity of either produces a great lowering of the solubility. Other experiments were carried out with thallium salts, which are especially well adapted to this purpose, because they are not very soluble. Thallium nitrate in the presence of potassium nitrate, thallium bromide in the presence of thallium nitrate, and thallium sulphocyanate in the presence of thallium nitrate and of potassium sulphocyanate were studied. The agreement between the solubility of the electrolyte in the presence of the second electrolyte with a common ion, as found and as calculated, is only fairly satisfactory ; the solubility as calculated being several per cent less than the value found, and the difference increases as the quantity of the second electrolyte present increases. This discrepancy must be due to one of the following causes: Either the deduction of Nernst is incorrect, or dissociation as calcu- lated from conductivity measurements is not the true value of the dissociation of electrolytes. The first assumption is scarcely possible since Nernst's deduction is based directly upon the law of mass action, and Noyes concluded that conductivity is not a true measure of dissociation. This con- clusion Noyes thought was strengthened by the fact that the Ostwald dilution law does not apply to strongly dissociated electrolytes as measured by the conductivity method. Noyes investigated the influence of a number of ternary electrolytes and obtained results similar to those found with binary electrolytes. Having convinced himself that the conductivity method is not a true measure of dissociation, he reversed the above procedure and used the influence of one salt on the solubility of another with a common ion as a measure of the dissociation of the latter. Dissociation of Electrolytes as measured by Change in Solubility. — From the above discussion it is obvious that solubility determi- nations can be used to measure dissociation. 1 Take the two funda- mental solubility equations, (« = «/), m(m + x)a 2 = m 2 a :! , and m(l — a) = m fl (l— « ), and solve them for a, eliminating a , a = mo^™, 1 + a is the dissociation of the salt in the presence of the added salt, and is equal to the dissociation of the salt alone in water at the concen- i Noyes: Ztschr. phys. Chem. 6, 259 (1890). 598 THE ELEMENTS OF PHYSICAL CHEMISTRY tration (m+ x). From experimental data it is, then, perfectly simple to calculate the dissociation of the salt in question by means of the above equation. This was done by Noyes at first for hydrochloric acid in the presence of thallous chloride, since the latter is only fairly soluble in water, and the above and similar relations hold only for fairly dilute solutions. The results for the dissociation of hydro- chloric acid and thallous nitrate, as determined by the solubility method, did not agree with the dissociation of the same substances at the same dilution as determined by the conductivity method. Noyes introduced the dissociation values as found by solubility into the Ostwald equation (dilution law), and obtained a fairly satisfactory constant for a strongly dissociated electrolyte like thallous nitrate. It looked, therefore, as if the Ostwald dilution law would hold also for strongly dissociated electrolytes, when the true values for the dissociation of such substances were ascertained. A little later 1 Noyes carried out an elaborate investigation along the same line, using thallous chloride as the salt with which to saturate the solution, and then adding one and another of the soluble chlorides, and determining their dissociation. In this calculation it was necessary to know the dissociation of the thallous chloride in order to calculate that of the chloride which was added to its satu- rated solution, and which precipitated a certain amount of the thal- lous chloride. Noyes assumed that the dissociation of thallous chloride is the same as that of the alkali chlorides, and, as we shall see, made a slight error which, however, affected all of his calcula- tions. He determined the dissociation of potassium, sodium, and ammonium chlorides by means of the solubility method, and when the values for potassium chloride were introduced into the Ostwald equation, a very good constant was obtained ; while the law does not hold at all if the dissociation as measured by conductivity is used. Noyes also measured the dissociation of a number of ternary chlorides by the solubility method. These included magnesium, calcium, barium, manganous, zinc, cadmium, mercuric, and cupric chlorides. With most of these thallous chloride was used as the less soluble substance with which to saturate the solution, but in some cases lead chloride was employed. The most important result of this investigation was that the dissociation of electrolytes, as measured by the solubility method, differed from the dissociation of the same solutions of the same sub- stances as measured by the conductivity method. The results of the measurements of dissociation by solubility showed that the Ostwald i Ztschr.phys. Chem. 9, 603 (1892). CHEMICAL DYNAMICS AND EQUILIBRIUM 599 dilution law applied at least to a large number of strongly dissociated electrolytes, while from the measurements of dissociation by the con- ductivity method the law did not apply at all to this large and most important class of electrolytes. Taking all of the facts into account, Noyes was led to the conclusion that the conductivity method is not an accurate measure of the dissociation of strongly dissociated elec- trolytes. It seemed probable, however, that the conductivity method was capable of measuring the dissociation of weakly dissociated com- pounds with a fair degree of accuracy. Thus the problem stood at this time (1892). There were two methods available for measuring electrolytic dissociation, — the con- ductivity and the solubility method, — and these gave different results. The problem of determining accurately the amount of dissociation was of fundamental importance for the advancement of physical chemistry, and the only two methods available for measuring disso- ciation gave widely different results. What was to be done in the light of this serious discrepancy ? At the suggestion and under the guidance of Ostwald, Jones 1 im- proved the freezing-point method of Beckmann until it could be used to measure electrolytic dissociation. He applied it to a number of acids, bases, and salts at dilutions ranging from 0.1 normal to 0.001 normal, and obtained results for the dissociation of these substances which agreed very well with those obtained by the conductivity method. This still did not clear up the problem of measuring dis- sociation, since we then had two methods of measuring dissociation which gave concordant results, viz. the conductivity method and the freezing-point method, and the solubility method which gave very different results. Noyes 2 then extended his work with the solubility method in company with Abbot, and found that his original assumption that thallous chloride is dissociated to the same extent as the alkali chlo- rides, was not correct. He then determined the dissociation of thal- lous chloride, and when he inserted this value into the equation, and calculated the dissociation of the chloride which had been added to the saturated solution of thallous chloride, the results for the dissociation of the latter agreed satisfactorily with those obtained by the conduc- tivity and freezing-point methods. Thus was the whole problem of measuring electrolytic dissociation cleared up, and to-day we have the three methods, — conductivity, freezing-point, and solubility, — all giving concordant results. i Ztsehr. phys. Ohem. 11, 110, 529 ; 12, 623 (1893). 2 Ibid. 16, 125 (1895); 26, 152 (1898). 600 THE ELEMENTS OF PHYSICAL CHEMISTRY It is a remarkable coincidence that the results originally obtained by Noyes from the solubility method, when inserted into the Ost- wald equation gave fairly good constants, and thus indicated that Ostwald's dilution law held also for strongly dissociated electrolytes. Indeed, it was this fact more than any other which confirmed Noyes in the belief that the conductivity method was not a true measure of the dissociation of strongly dissociated substances, and that his solu- bility method gave the more accurate results. The applicability of the Ostwald dilution law to strongly dissociated electrolytes, we know to-day, was only apparent ; subsequent work by all the methods of measuring dissociation showing that it does not hold at all. When it was found that the three methods mentioned above gave concordant results for the dissociation of electrolytes, it was a matter of great relief to all who were working on this problem, not simply because these fundamental values were placed beyond question, but a great number of relations were thus cleared up. Each method was based upon a different principle ; and while there was discordance in the results, there was more or less confusion and doubt in many directions. Summary of the Discussion of Equilibrium. — The fundamental idea underlying the study of chemical equilibrium is that it is dy- namic. Equilibrium in chemical reactions was studied first as a spe- cial case of the velocities of reactions, where the velocities of the two opposite reactions are equal. The phase rule was then briefly dis- cussed, and a few of its simpler applications to systems containing one component, two components, three components, and four compo- nents. Equilibrium was studied where two conditions are variable, say temperature and pressure, and also when three conditions are variable, say temperature, pressure, and volume, and the corresponding diagrams plotted. Some of the applications of the phase rule, not simply as a system of classification, but as a direct guide in experimental work, were considered. This was seen to be the case especially where the number of components is large, or where the older methods of inves- tigation are insufficient on account of the comparative complexity of the phenomena dealt with. The methods of determining the tem- perature of transformation were considered, also the effect of temper- ature and pressure on chemical equilibrium, and then attention was directed to a special case of equilibrium which has proved to yield extremely important results. This refers to the effect of one salt on the solubility of another with a common ion, which has led to an important method of measuring electrolytic dissociation. CHAPTER X MEASUREMENTS OF CHEMICAL ACTIVITY METHODS EMPLOYED AND SOME OF THE RESULTS OBTAINED Great Differences in the Activities of Substances. — The student of chemistry recognizes at the very outset the great differences between the chemical activities of different substances. Some sub- stances react with the greatest ease, and often with violence, while others do not react at all; and all intermediate stages of activity exist. Take the action of acids on metals. Some acids act on a given metal very readily, others act more slowly, while others scarcely act at all. A problem which has attracted the attention of chemists from early times is the measurement of the relative activities of sub- stances. When we review the history of chemistry we find " affinity tables," as we have seen, obtained by a number of methods. These are mainly of historical interest to-day, since many of the methods which were used were either not accurate or did not measure the quantities alone with which they were supposed to deal. The importance of this problem is obvious, since if we knew the relative affinities of all chemical substances, we should be in a posi- tion to say just what would take place when such substances were brought into the presence of one another. We believe that at pres- ent we have methods of solving this problem in a large number of cases, and such will be considered in this chapter together with some of the more important results which have been obtained. Principles upon which the Measurement of Chemical Activity is Based. — In the study of chemical dynamics we saw that reactions proceed with very different velocities under conditions which, at first sight, seem comparable. Take the inversion of cane sugar by acids, the velocity of inversion depends greatly upon the nature of the acid used. If we use the same quantities of different acids, the velocities will vary from acid to acid, and may be a hundred times as great for one acid as for another. Take, on the other 601 602 THE ELEMENTS OF PHYSICAL CHEMISTRY hand, the saponification, of esters by bases ; the velocity depends upon the nature of the base used, and varies greatly from one base to another. The velocity with which a reaction proceeds has been used as a measure of the chemical activities of the substances which take part in the reaction. If we are dealing with reactions like the above, and measure the velocities with which a number of acids invert cane sugar, or a number of bases saponify an ester, we have at once the relative activities of the acids, or bases, in question. This is known as the dynamical method of measuring chemical affinity. When we were studying the conditions of chemical equilibrium, we saw that some reactions proceed very far before equilibrium is reached, while in others eqxiilibrium is established when only a small part of the substance has undergone transformation. We recall that equilibrium iu a chemical reaction represents that con- dition where the two opposite reactions have equal velocities. Knowing the conditions which exist when equilibrium has been established, we can calculate the relative activities of the substances which take part in the reactions. This method of measuring chemi- cal activity is known as the equilibrium or statical method. The Dynamical Methods of measuring Chemical Affinity. (A) Inversion of Cane Sugar. — We have already seen that acids in the presence of water have the power of causing cane sugar to take up a molecule of water and then breaking down into glucose and fructose. This catalytic reaction was found to take place with very different velocities when different acids were used, and Lbwenthal and Lenssen, 1 as early as 1862, used this reaction to measure the relative activities of acids. They determined the velocities with which a number of acids invert sugar, and also the effect of the presence of a number of substances on the velocity of inversion. Their work was, however, shown to be open to certain objections, and Ostwald 2 carried out an extensive investigation on the velocity with which cane sugar is inverted by different acids, using the polarimeter to measure the amount of inversion. He calculated the inversion coefficients by the method with which we are now familiar, — CB = -In— ^— , t and showed that they are identical with the activity coefficients of the acids used. That such is the case will be seen after we study 1 Journ. prakt. Chem. 85, 321, 401 (1862). 2 Ibid. [2], 29, 385 (1884). MEASUREMENTS OF CHEMICAL ACTIVITY 608 methods for measuring the activity coefficients directly. A few of the results obtained for the inversion coefficients of some of the more common acids are given below, hydrochloric acid being taken as unity : — Inversion Coefficients Hydrochloric acid 1.000 Nitric acid 1.000 Ethylsulphuric acid 1.000 Hydrobromic acid 1.114 Chloric acid 1.035 Benzenesulphonic acid 1.044 Sulphuric acid 0.536 Formic acid 0.0153 Acetic acid 0.0040 Monochloracetic acid 0.0484 Dichloracetic acid 0.271 Trichloracetic acid 0.754 Oxalic acid 0.1857 Succinic acid 0.00545 Citric acid 0.0172 Phosphoric acid 0.0621 Arsenic acid 0.0481 (B) Saponification of Methylacetate. — Methylacetate and simi- lar esters in the presence of water at ordinary temperatures, undergo a slow decomposition into the acid and alcohol. If a strong acid is present, the decomposition takes place much more rapidly ; indeed, its velocity may be increased a hundred times, or even more than this. The acid which is added to the ester does not undergo any change. It acts catalytically. The active mass of the ester is the only sub- stance which changes as the reaction proceeds, and, therefore, the reaction is of the first order. The constant is — CB = hn— ^—. This equation was tested experimentally by Ostwald, 1 who used this reaction to measure the relative activities of acids, and BG was found to be a constant for this reaction through a long interval of time. Ostwald worked out the velocity coefficients of a large number of acids by means of the above reaction. A few of his results are given below : — i Journ.prakt. Chem. [2], 28, 449 (1883). 604 THE ELEMENTS OF PHYSICAL CHEMISTRY Velocity Coefficients Hydrochloric acid 1.000 Nitric acid 0.915 Ethylsulphuric acid 0.987 Hydrobromic acid 0.983 Chloric acid 0.944 Benzenesulphonic acid 0.991 Sulphuric acid 0.541 Formic acid 0.0131 Acetic acid 0.00345 Monochloracetic acid 0.0430 Dichloracetic acid 0.2304 Trichloracetic acid 0.6820 Oxalic acid 0.1746 Succinic acid 0.00496 Citric acid 0.01635 A comparison of the velocity coefficients obtained by the methyl- acetate method, with the inversion coefficients obtained by the method involving the inversion of cane sugar, shows a general agree- ment between the two sets of values. Both of these methods can be used to measure the relative activities of substances. (C) The Decomposition of Amides. — Another dynamic method has been used to measure the relative activities of acids. This in- volves the action of acids on amides. Water alone decomposes an amide like acetamide, in the sense of the following equation : — CH 3 CONH 2 + H 2 = CH 3 COONH<. This reaction, however, takes place very slowly. If an acid is added the velocity of the reaction is increased, and very greatly increased if the acid is strong. In the presence of an acid the reaction takes place as follows : — CHjCONH, + H 2 + HC1 = CH 3 COOH + NH 4 C1, both the acid and amide being used up. Since the active masses of two substances undergo change, we have a reaction of the second order; and we have seen that in a reaction of the second order the activity coefficients are related as the square roots of the velocity coefficients. Since equivalent quantities of acid and amide are used up in the reaction, the constant is — t A — x Although side reactions come into play somewhat as the above reaction proceeds, their influence at the outset is small, and very MEASUREMENTS OF CHEMICAL ACTIVITY 605 nearly the true velocity coefficients for the different acids can be obtained by studying the decomposition of amides at the very out- set of the reaction. The following are the velocity coefficients for a number of acids, obtained by means of the method involving the decomposition of acetamide : — Velocity Coefficients Hydrochloric acid .... 1.000 Nitric acid . Hydrobromic acid Sulphuric acid Formic acid . Acetic acid . Monochloracetic acid Dichloracetic acid Trichloracetic acid Oxalic acid . Tartaric acid Succinic acid Citric acid . Phosphoric acid . 0.955 0.972 0.547 0.00532 0.000747 0.0296 0.245 0.670 0.169 0.0121 0.00195 0.00797 0.0449 If we compare the results obtained by the amide method with those obtained by saponifying an ester, we see that the two sets of values agree for the strong acids, although quite different temperatures were used in the two sets of experiments. Tor the weak acids the results obtained by the amide method are the smaller, and this is just what we would expect, since the presence of the neutral salt formed in the reaction diminishes the velocity with which the amide is decomposed. The three dynamic methods give, then, essentially the same Tesults for the activity coefficients of acids ; we shall now study the application of one dynamic method to the relative activities of bases. (D) Saponification of Esters by Bases. — An ester like ethyl- acetate is saponified by a base in terms of the following equation: — CH 3 COOC 2 H 5 + KOH = CH 3 COOK + C 2 H 5 OH. The reaction was first used by Warder 1 to measure the relative activities of bases, and afterward more extensively applied by Eeicher. 2 A few of the velocity coefficients of the more common bases are given below : — 1 Amer. Chem. Journ. 3, 340 (1882). 2 Lieb. Ann. 228, 257 (1885). 606 THE ELEMENTS OF PHYSICAL CHEMISTRY Velocity Coefficients Potassium hydroxide 2.298 Sodium hydroxide 2.307 Ammonium hydroxide 0.011 Barium hydroxide 2.144 Strontium hydroxide 2.204 The most striking feature in the above results is that ammonia is such a weak base in comparison with potassium or sodium hydroxide. We shall see that this result is confirmed by other methods. We shall now leave the dynamic methods of measuring relative activities, and pass to the static or equilibrium methods. The Equilibrium Methods of measuring Relative Activities. (1) Thermochemical Method. — These methods, as already stated, allow the substances whose relative activities are to be measured to come to equilibrium, and then determine the conditions of the equilibrium. If the reaction is heterogeneous, a solid entering into the reaction or being formed as the result of the reaction, it is a simple matter to determine the conditions which exist when equi- librium is established. It is only necessary to determine the amount of the solid present, or to separate the heterogeneous constituents, and determine their amounts by any of the ordinary chemical methods. If, on the other hand, the reaction is homogeneous, the problem of determining the amounts of the constituents when equi- librium is established is far more difficult. It frequently happens that the constituents cannot be readily separated by chemical means, and resort must be had to some indirect method of determining the quantities present. The change in some physical property which can be readily measured has been frequently utilized to determine the conditions of equilibrium in a homogeneous reaction. Julius Thomsen used the thermal change, or heat tone of a reac- tion, to measure the relative activities of the substances which take part in the reaction. If the heat of neutralization of a base, say sodium hydroxide, by an acid, say hydrochloric acid, is different from the heat of neutralization of the same amount of the same base under the same conditions, by a different acid, say sulphuric acid, it is quite simple to determine the division of the base between the two acids by means of the heats of neutralization. We must know the heat of neutralization of the first acid by the base, also the heat of neutralization of the second acid by the base, and in addition the heat set free when both acids are brought simul- taneously into contact with the base. Let us call these quantities, MEASUREMENTS OF CHEMICAL ACTIVITY 607 respectively, JVj, N 2 , and N 3 . If all of the base went to the first acid, N a would be equal to N t . If all of the base went to the second acid, N 2 would be equal to N t . But if part of the base goes to one acid and part to the other, as is always the case, N 3 will lie some- where between N t and N 2 . By simple proportion we can tell at once how much of the base has gone to each acid, and thus we have the relative activities of the two acids. In practice one acid is allowed to act on the salt of the other acid, but the principle is as indicated above. We can, of course, reverse the above procedure, and neutralize one acid by two bases separately, and then by both bases simultane- ously, and from the data thus obtained calculate the relative strengths of the bases. In this way tables of the relative strengths or activ- ities of acids and bases can be worked out by thermochemical meas- urements. In such investigations, however, side reactions may come into play, and such must of course be taken into account wherever they appear. It should be mentioned again in connection with this method, that thermochemical measurements are difficult to make with even a fair degree of accuracy, and this method is never used to-day, since, as we shall see, far simpler and more accurate methods are now available for measuring chemical activity. (2) Volume-chemical Method. — Just as chemical reactions are accompanied by thermal change, so, also, are they accompanied by change in volume. When a solution of an acid is brought in con- tact with a solution of a base, the resulting volume is different from the sum of the volumes of the two solutions. There is usually a contraction in volume under such conditions. Ostwald 1 has utilized the change in volume produced in chemical *eactions to determine the relative activities of acids and bases, in a manner strictly analogous to that of Thomsen just described. When a given base is neutralized by different acids, different changes in volume result. Ostwald has utilized these differences to deter- mine just how much of a base goes to each acid, or of an acid to each base ; and thus the relative activities of acids and bases. It is only necessary to know the change in volume when the base is neu- tralized by one acid, the change in volume when the base is neutral- ized by the second acid, and the change in volume when the base is neutralized by both acids simultaneously. In practice we do not proceed as described above, but allow one i Journ. prakt. Chem. [2], 18, 328 (1878). 608 THE ELEMENTS OF PHYSICAL CHEMISTRY acid to act on the salt of the other acid. The above procedure was described because it is exactly the same in principle as that which was actually employed in the experiment, and is far simpler to- com- prehend. The volume-chemical method is greatly to be preferred to the thermochemical, because of the ease with which it can be carried out. It is not necessary to measure the change in volume ; it is suf- ficient to measure the change in density or specific gravity, and this can be done very readily by any of the ordinary specific gravity methods. The method employed by Ostwald consists in weighing the solution in a modification of the Sprehgel pycnometer devised by himself. The method when carried out in this manner becomes one of the simplest laboratory methods of which we can conceive. It has been stated that in both of the above methods one acid is allowed to act on the salt of another acid, and from the division of the base between the two acids the relative strengths of the acids determined. At first thought this statement is liable to lead to con- fusion. It will be recalled at once that when sulphuric acid acts on a dry chloride, like sodium chloride, practically all of the hydro- chloric acid is displaced by the sulphuric acid ; and when sulphuric acid acts on dry nitrates, practically all of the nitric acid is driven out. This might be thought to indicate that sulphuric acid is in- finitely strong with respect to hydrochloric or nitric acid. Again, when hydrogen sulphide is allowed to act on a soluble chloride or nitrate of a heavy metal, the insoluble sulphide is pre- cipitated, and in many cases quantitatively. From this it might be concluded that hydrogen sulphide is a much stronger acid than hydrochloric or nitric. A moment's thought will show that these conclusions are neces- sarily erroneous. The error lies in not taking into account the fact that, under these conditions, a volatile compound is formed in the first case and escapes from the field of action, its active mass being, therefore, reduced to zero ; while in the second case an insoluble compound is formed and separates from the solution. In order to test the relative activities of two acids or bases, by allowing one to act on the salt of the other, the two acids or bases in question must be under comparable conditions, i.e. the active masses of both must be equal. This can be secured by working with solu- tions where everything is in solution before the reaction takes place, and remains in solution after the reaction is over and equilibrium is established. If we work with equivalent quantities of substances, under these conditions their active masses are equal, and the division MEASUREMENTS OF CHEMICAL ACTIVITY 609 of the base between two acids, or of the acid between two bases, gives at once the relative activities of the acids or bases in question. (3) Other Equilibrium Methods of measuring Relative Activities.— The two methods discussed above utilize, respectively, the thermal change and the volume change produced in chemical reactions. In a similar manner, the change in any other physical property produced by chemical action may be used to determine the conditions which exist when equilibrium has been established. A number of other properties have been utilized for this purpose, such as the change in the refractive power of the solution, in its color, in its power to rotate the plane of polarized light, etc. ; but no new principle is in- volved in these methods, and many of them are of limited applica- bility. These will not be discussed in detail, since the equilibrium methods, as well as the dynamic methods of measuring relative chemical activities, have, in general, given place in the last few years to a method which is more accurate and far easier to carry out in practice than any method thus far considered. This is the method with which we are already familiar, based upon the electri- cal conductivity of substances. The Conductivity Method of measuring Chemical Activity. — Since it has been shown that chemical activity is due only to ions, it is but necessary to determine the relative number of ions present in order to determine chemical activity. The problem of measuring chemical activity reduces itself, then, to the measurement of electrolytic dissociation. The conductivity method of Kohlrausch and its application to the measurement of electrolytic dissociation have been considered at sufficient length; it only remains to discuss some of the results which have been obtained. The strong mineral acids are dissociated to just about the same extent. These include hydrochloric, nitric, hydrobromic, chloric, and a few others. The strong bases, such as sodium, potassium, calcium, lithium, and rubidium hydroxides, are dissociated to just about the same extent, and to about the same extent as the strong acids under the same conditions. The salts are, in general, strongly dissociated compounds. They are dissociated to very nearly the same extent as the strong acids and bases. There are, however, some exceptions among the salts ; those of cadmium and mercury, and zinc to a less degree, are dissociated much less than the other salts. Indeed, some of the salts of mercury, such as the chloride and cyanide, are scarcely dissociated at all. The above statement, nevertheless, applies to most of the salts,- including those of very weak acids, such as car- 2r 610 THE ELEMENTS OF PHYSICAL CHEMISTRY bonic and hydrocyanic, potassium carbonate and cyanide being quite strongly dissociated compounds. Since dissociation and chemical activity are proportional, when we speak of a compound as being strongly dissociated we mean one whose chemical activity is great. Since conductivity has been used to measure chemical activity, we use the terms " dissociation " and " chemical activity " as synonymous. When we turn to the organic acids and bases, we find nearly all degrees of activity represented. Some of the organic acids as formic, oxalic, trichloracetic, and the like are quite strong ; while acids like acetic, succinic, citric, hydrocyanic, are very weakly dissociated com- pounds. 1 Similarly, when we deal with the organic bases, we find that many of the substituted ammonias are strongly dissociated substances, while ammonia itself is a very weak base. When we were studying the conductivity method itself, and its application ' to electrolytes, we saw that the molecular conductivity and, consequently, the dissociation increased with the dilution of the solution. In order that the results obtained by this method for different substances should be comparable, we must, therefore, work at the same dilutions, and this is always taken into account in applying the conductivity method to the measurement of chemical activity. The magnitude of the influence of dilution will be seen when we recall that a normal solution of a strong acid, base, or salt is about eighty per cent dissociated; while a thousandth's normal is completely dissociated. The importance of the dilution laws is especially great, in connec- tion with the application of the conductivity method to the measure- a 2 ment of chemical activity. Take the law of Rudolphi, ^ r — — »= constant, which applies to strongly dissociated electrolytes. The value of the constant is a measure of the chemical activity of the substance. Take the weakly dissociated compounds — the organic acids and bases — to which the dilution law of Ostwald applies. The value of „2 the constant in the equation. — = constant, has been used as a (1 — a)v direct measure of the strength of the acid and base, as we have seen. 1 For details in connection with the strengths of organic acids and bases see Ostwald : Ztschr. phys. Ohem. 3, 170, 241, 369 (1889); and Bredig: Ibid. 13, 289 (1894). MEASUREMENTS OF CHEMICAL ACTIVITY 611 In comparing the strengths of organic acids and bases by means of the conductivity method, we can measure the dissociations at the same dilutions and compare the results, or we can measure the dis- sociations at any dilutions, substitute the values in the Ostwald dilution law, and compare the values of the constants obtained. The latter mode of procedure is usually adopted because it is simpler and more convenient. The same remarks apply to the strongly dissociated compounds. "We thus see how the conductivity method can be used to measure chemical activity; we shall now learn what influence composition and constitution exert on the chemical activities of substances. EFFECT OF COMPOSITION AND CONSTITUTION ON CHEMICAL ACTIVITY Composition as conditioning Acidity. — We have already seen from the periodic system what elements are in general acid-forming, and what are base-forming. In this connection we should look a little more closely into this question, and inquire not only into the qualitative influence of the different elements, but the magnitude of the influence which they exert. This is now quite a simple matter, since we have such convenient methods for measuring chemical activity. If we look at the history of acids, we shall find that for a long time it was thought that acid properties are due entirely to the presence of oxygen. Indeed, the name of this element means acid- former. According to the earlier views it was impossible to have an acid without the presence of oxygen. So firmly rooted did this idea become, that when hydrochloric acid was discovered it was thought that; it must contain oxygen, notwithstanding the fact that no oxy- gen could be detected in its molecule. The only possibility of the presence of oxygen was that it was combined with the chlorine, so it was said that chlorine must contain oxygen and be an oxide, and not an element. It was regarded as the oxide of an unknown element " murium," whence the name muriatic acid. We know to-day that oxygen as such has nothing to do directly with acidity. The cause of acid properties is the hydrogen ion. Wherever we have hydrogen ions we have acid properties, and wherever we have acid properties we have hydrogen ions. The strength or activity of acids depends entirely upon the number of hydrogen ions present in their solutions — upon the dissociation. If acid properties depend entirely upon the hydrogen ions, how 612 THE ELEMENTS OP PHYSICAL CHEMISTRY do other elements affect acidity at all ? What do we mean by an acid-forming element ? Elements other than hydrogen do not affect acidity directly, but they may affect it very greatly indirectly, in that they may facilitate or retard the dissociation which yields the hydrogen ions. When we say that an element is acid-forming, we simply mean that it facilitates the dissociation of hydrogen from the molecule in which it is present. If we examine the strength of acids in the light of these newer conceptions, we shall find some surprising results even among the well-known compounds. Take first the four halogen acids, we have been accustomed to regard them all as very strong; perhaps, with the exception of hydriodic acid, which is somewhat weaker, we have regarded them as about of equal strength. If we compare their conductivities at the same dilutions, we find the following values : — Volumes HCl HBr HI HF M» y-v M« Co 4 343 354 353 27.8 16 362 367 367 42.5 256 378 380 381 129.0 1024 380 380 379 210.0 4096 376 372 373 295.0 We see that hydrochloric, hydrobromic, and hydriodic acids are of about the same strengths for all dilutions from four litres to four thousand ; but hydrofluoric acid is very much weaker, especially in the more concentrated solutions. As the dilutions become greater the hydrofluoric acid continues to dissociate, and approaches more nearly to the values of the other acids. Effect of Oxygen and Sulphur on Acidity. — Let us take next two very weak acids, — hydrogen sulphide and hydrocyanic acid, — and see how the introduction of oxygen into the one and of sulphur into the other affect the acidity. Hydrogen sulphide is a very weak acid indeed, as has been shown by the few conductivity measurements which have been made by Ostwald. 1 When oxygen is introduced into hydrogen sulphide, we have first sulphurous acid and then sulphuric acid. In order that the influence of oxygen in the molecule may be seen, the conductivi- 1 Journ. prakt. Chem. 32, 300 (1885) ; 83, 352 (1886). MEASUREMENTS OP CHEMICAL ACTIVITY 613 ties of hydrogen sulphide, sulphurous acid, and sulphuric acid, as far as they have been determined at comparable dilutions, are given below : — Volumes H S S H a SO, H,SO, n» *v »*» 16 0.70 — 407.0 32 0.91 177.5 448.0 256 — 279.0 582.0 1024 — 324.7 649.0 Sulphurous acid is obviously much stronger than hydrogen sul- phide, and sulphuric acid 1 much stronger than sulphurous. The introduction of oxygen into the molecule of hydrogen sulphide has thus very greatly increased the acidity, which is the same as to say has greatly facilitated the dissociation of hydrogen from the molecule. Let us see what influence the introduction of sulphur into the molecule of hydrocyanic acid has on its acidity. Comparing the conductivities of hydrocyanic acid and sulphocyanic acid, as deter- mined by Ostwald, 2 we have : — Volumes HON HSCN M» *v 4 0.33 337 8 0.38 345 16 0.43 352 32 0.46 358 The introduction of sulphur into the molecule of hydrocyanic acid has increased its acidity several hundred times. Indeed, hydro- cyanic acid is scarcely an acid at all, while sulphocyanic acid is to be ranked among the very strong acids, as will be seen from the results of the conductivity measurements. It might be concluded from the above results that the introduc- tion of oxygen or sulphur into a molecule always increased the acidity. Such might be the case, but the data thus far examined are too few to justify any such conclusion. Let us examine a number of 1 If the molecular conductivities of sulphuric acid are compared with those of hydrochloric acid at the same dilutions, it will be seen that the former are much the greater. This is because sulphuric acid splits off two hydrogen ions, both of which take part in the conductivity. It is only a little more than half as strong as hydrochloric acid. 2 Loc. cit. 614 THE ELEMENTS OF PHYSICAL CHEMISTRY other cases. Take the acids of phosphorus, where we have a number of members differing by an oxygen atom. Volumes H 3 PO, H.PO, H.PO, **» He e» 2 131 121 60 8 194 175 90 32 264 241 146 128 314 298 225 512 339 329 297 2048 346 339 335 Here the acidity continually decreases as the amount of oxygen increases, which is exactly the opposite of what we found with the acids derived from hydrogen sulphide by the introduction of oxygen. The evidence bearing upon the effect of oxygen on acidity seems con- flicting. What conclusion are we to draw ? If we examine a great number of cases, we find that the introduc- tion of oxygen usually increases the acidity; sometimes it has little or no influence on the acidity of the compound, and in a few cases like the above it actually diminishes the acidity of the compound into which it enters. An examination of the acids into which sulphur enters shows that the effect of the presence of sulphur is to increase acidity. Some other influence, as change in the constitution of the compound pro- duced by the introduction of sulphur, may offset the influence of the sulphur atom ; but this is of course a different matter, and does not detract from the truth of the above statement. Organic Acids and their Substitution Products. — Thus far we have considered mainly inorganic acids. The effect of composition on the strength of organic acids can be seen best by studying homologous series of the fatty acids, and then some of the substitution products of these acids. Take first the formic acid series, and compare the molec- ular conductivities of the first five members at the same dilutions : — Formic AOETIO Peopionio Butyric Valeric VOLUMBB Aoid Aoid Aoid Acid Acid f« Co P» t*« *S, 8 15.22 4.34 3.65 3.80 — 32 29.31 8.65 7.36 7.70 7.94 128 55.54 16.99 14.50 15.27 15.70 1024 134.70 46.00 38.73 40.62 41.90 MEASUREMENTS OF CHEMICAL ACTIVITY 615 These results show that formic acid is much stronger than any succeeding member of the series. The acidity of the following members does not change very appreciably with increase in the com- plexity of the molecule ; there is, perhaps, a slight decrease in the acidity as the molecule becomes more complex. Take the first three members of the oxalic acid series, — oxalic, malonic, and succinic acids, — and compare their conductivities in a similar manner : — Volumes Oxalic Acm Malonic Acid Succinic Acid l-v c. ^ 16 — 53.07 11.40 128 324 128.5 31.28 512 364 208.8 59.51 2048 409 294.5 109.5 In this series the decrease in acidity with increase in complexity is very marked indeed. Oxalic acid is much stronger than malonic, and malonic is a much stronger acid than succinic. Turning to the substituted acids of the formic acid series Ostwald 1 has measured the conductivities of the chloracetic acids and of mono- bromacetic acid. His results are given in the following table, to- gether with those of acetic acid itself for the sake of comparison : — Volumes Acetic Acid monochloracetic Acid DlCHLORACETIC Acid Trichloracetic Acid monobromaoetio Acid 32 8.65 72.4 253.1 323.0 68.7 128 16.99 127.7 317.5 341.0 122.3 512 32.2 205.8 352.2 353.7 199.2 1024 46.0 249.2 360.1 356.0 241.2 From acetic acid and its chlorsubstitution products we see the effect of substituting hydrogen, in the methyl group by chlorine. The acidity is greatly increased by the presence of the first chlo- rine atom; it is still further increased by the presence of the second chlorine atom, and trichloracetic acid is a very strong acid indeed. Bromine, like chlorine, also greatly increases the acidity of acetic acid, and to nearly the same extent. i Ztschr. phys. Chem. 3, 176-178 (1889). 616 THE ELEMENTS OF PHYSICAL CHEMISTRY Ostwald 1 next studied the effect of introducing an oxygen atom into the radical on the acidity of the compound. Take acetic acid, and its monoxygen derivative, glycolic acid : — Volumes Acetic Acid Glycolic Acid 32 128 1024 8.65 16.99 46.0 24.79 47.50 116.70 The introduction of an oxygen atom into acetic acid increases the acidity many times. Take propionic acid and compare its acidity with its oxygen derivatives : — Volumes Propionic Acid Lactic Acid p-OxYPROPioNic Acid 16 128 1024 5.21 14.50 38.73 16.46 44.47 109.70 7.88 21.90 57.80 Here we have two monoxy-derivatives to deal with, depending upon which group (CH 3 or CH 2 ) the oxygen enters. If it enters the CH 2 group, the acidity is greatly increased ; if the CH 3 group, the acidity is increased, but not to the same extent. Here we encounter the effect of constitution on acidity ; but more of this later. Turning next to the oxysuccinic acids, we have the monoxygen derivative or the malic acids, and the dioxy-derivative or tartaric acids. Ostwald 2 has also measured the conductivities of these sub- stances, and the following data are taken from his results : — Volumes Succinic Acid Malic Acid tf-TARTARic Acid ** "» *» 32 16.03 37.90 57.60 128 31.28 71.52 106.20 612 59.51 128.10 184.50 2048 109.50 313.0 291.1 1 Ztschr. phys. Chem. 3, 183 (1889). 3 Ibid. 3, 370-372 (1889). MEASUREMENTS OF CHEMICAL ACTIVITY 617 The introduction of oxygen into succinic acid also increases the acidity to a marked extent. The introduction of one oxygen atom more- than doubles the acidity, while the introduction of a second oxygen atom still further increases the acidity, especially in the more concentrated solutions. The influence of the presence of the nitro group is seen by com- paring the conductivity of an acid like benzoic acid with the con- ductivity of mononitro benzoic acid : — Volumes • Benzoic Acid 0-NlTROBENZOIC ACID ", *V 128 29.70 205.3 256 42.20 246.1 512 57.61 283.3 1024 78.94 312.3 The presence of the nitro group greatly increases the acidity of the compound into which it enters. The presence of the amido group has the opposite effect, as we would expect. Comparing the conductivities of benzoic acid and p-amidobenzoic acid, we see that this conclusion is justified by the facts : — Volumes Benzoic Acid P-Amidobenzoic Acid 64 256 1024 1„ 21.39 42.20 78.94 7.53 16.34 35.01 Constitution as conditioning Acidity. — We have seen one ex- ample of the effect of constitution on acid properties. Lactic acid and &-oxypropionic acid are isomeric, having the same composition ; but the acidity of the former is more than double that of the latter. We shall now study other isomeric substances to see whether the influence of constitution on acidity is general. Take the two acids having the composition C 3 H 7 COOH, — butyric and isobutyric acids, — and comparing their conductivities at the same dilutions, we have : — €18 THE ELEMENTS OF PHYSICAL CHEMISTRY Volumes Butyric Acid Ibobutyrio Acid Mo Mo 16 5.46 5.31 64 10.86 10.68 256 21.33 20.85 1024 40.62 39.97 The acidity of these two isomeres is very nearly the same, con- stitution having but little influence in these cases. Take next the two isomeric monoxy-derivatives of succinic acid, — malic and inactive malic acids : — Volumes Malic Aoid Inactive Malic Aoid 64 512 2048 Mo 53.08 128.1 213.0 Mo 53.5 128.6 212.2 Constitution seems to have little or no influence in the above eases. Comparing the acidities of the dihydroxysuecinic acids, Ostwald 1 has determined the conductivities of the three isomeric substances, — dextrotartaric acid, Lsevotartaric acid, and racemic acid : — Volumes Volumes JM li.ii 12.82 44.44 25.18 177.8 48.00 711.1 87.31 1422.0 115.9 We shall now turn to another kind of isomerism represented by the aromatic compounds, and see what effect this kind of difference in constitution has on the properties of the substance. The most probable formula for the constitution of benzene repre- sents its molecule as a hexagon, with the six CH groups at the corners of the hexagon. In terms of this conception we should have three kinds of disubstitution products, and three and only three are known : ortho, where the two substituents occupy ad- joining corners of the hexagon ; para, where they occupy opposite corners; and meta, where there is one corner between them. The question which arises in this connection is what influence would the position occupied by an atom or group have on the acidity of the compound ? Take as an example benzoic acid. It has the structure represented thus : — MEASUREMENTS OF CHEMICAL ACTIVITY 621 C -COOH HC. /\ vCH HCP CH XH If we replace one of the five hydrogen atoms by a hydroxyl group, or what is the same thing introduce an oxygen atom into the molecule, what influence on the acidity would the position of the oxygen atom have? This is answered by comparing the acidity of benzoic acid with that of ortho, meta, and para oxy benzoic acids, respectively. The following data are taken from the work of Ostwald: 1 — Volumes Benzoic Acid O-OxYBENZOIC AOID Salicylic Aoid TO-OxYBENZOIC Acid ;p-OXYBENZOIO Acid 64 256 1024 21.39 42.20 78.94 80.1 141.9 224.1 25.67 49.36 91.63 14.83 29.35 56.25 The position of the oxygen atom has thus a very marked influ- ence on its effect on the acidity of benzoic acid. In the ortho position it increases the acidity more than three times ; in the meta position the acidity is increased but only slightly, while the pres- ence of the oxygen in the para position actually decreases the acidity of benzoic acid. Let us examine next the effect of chlorine in the three posi- tions : — Volumes Benzoic Acid o-Chlobbenzoio Acid m-GHLORBENZOIO Acid ^-Chloebenzoio Acid 64 256 1024 21.39 42.20 78.94 89.2 156.1 238.7 64.3 116.2 125 Chlorine in the ortho position has the greatest influence, in the para position an intermediate influence, while in the meta position 1 Ztschr. phys. Chem. 3, 241 (1889). 622 THE ELEMENTS OF PHYSICAL CHEMISTRY it lias the least influence. This is not the order with respect to the influence exerted, which was observed with oxygen. Take the nitrobenzoic acids : — Volumes Benzoic Acip O-NlTEOBENZOIC Acid m-NlTEOBBNZOIC Acn> JJ-NlTBOBENZOIO Acid 128 256 1024 (Ml 29.70 42.20 78.94 205.3 246.1 312.3 67.5 90.9 157.6 97.0 164.7 The nitro group increases the acidity of benzoic acid when in any of the three positions. It has the greatest influence in the ortho position, less in the para, and the least influence in the meta posi- tion. Take, finally, the effect of position on the influence of the amido group : — Volumes Benzoic Acid 0-a.midobenzoio Acid m-AMIDOBENZOIC Acid ^-Amidobenzoio Acid 64 256 1024 21.39 42.20 78.94 7.21 16.11 33.51 22.16 44.39 88.30 7.53 16.34 35.01 The amido group in the ortho position and in the para position greatly diminishes the acidity of benzoic acid, while the amido group in the meta position has little or no influence on the acidity of ben- zoic acid. It is obvious from the above results that position has a marked effect on the influence of atoms and groups on the acidity of com- pounds. No wide-reaching generalization, which is free from excep- tions, has been arrived at, connecting these phenomena. It may be said in general that the greatest influence is exerted in the ortho position, while the smallest influence is shown by the substituent in the meta or para position. We have studied in this chapter the influence of composition on acidity, and also the influence of constitution on acidity. Let us now see what influence composition and constitution have on the strength of bases. Hantzsch : Ztschr. phys. Chem. 10, 1 (1892). MEASUREMENTS OF CHEMICAL ACTIVITY 623 Composition as conditioning Basicity. — We have seen that the cause of acidity is the presence of hydrogen ions, and an acid is strong or weak in proportion to the number of hydrogen ions pres- ent — in proportion to its dissociation. In an analogous manner, the cause of basicity is the presence of hydroxyl ions. Wherever we have hydroxyl ions we have basic property, and wherever we have basic property we have hydroxyl ions. A base is strong or weak just in proportion to the number of hydroxyl ions present, i.e. in proportion to its dissociation. The strongest of all bases, as we have learned, are the hydroxides of the alkali metals, — potassium, sodium, calcium, lithium, and ru- bidium hydroxides. These are dissociated to just about the same extent as the strongest mineral acids, under the same condition of concentration. When we come to ammonium hydroxide, we find a base which is incomparably weaker than those to which we have just referred. That this may be fully appreciated, the molecular conductivities of a few solutions of ammonium hydroxide are compared with the molecular conductivities of the corresponding solutions of potassium hydroxide, the measurements being made at the same tempera- tures : — Volumes Potassium Hydroxide Ammonium Hydroxide /*» /<•» 1 171.8 0.84 10 198.6 3.1 100 212.4 9.2 1000 211.0 26.0 In normal solution, potassium hydroxide is nearly two hundred times as strong as ammonium hydroxide ; as the dilution increases, the strength of ammonium hydroxide, relative to potassium hydrox- ide, increases, until at a dilution of 1000 litres, where potassium hydroxide is completely dissociated, ammonium hydroxide is about one-eighth as strong as potassium hydroxide. Ammonium hydroxide is an example of the way in which physi- cal chemistry has corrected errors in chemistry, which have persisted for a long time. Ammonium hydroxide was regarded as a very strong base, and there was no purely chemical means of correcting the error. It precipitated most of the substances with which potas- sium hydroxide formed a precipitate ; it acted vigorously upon the 024 THE ELEMENTS OF PHYSICAL CHEMISTRY raucous membrane of the throat and nose, and altogether behaved like a very strong base. It remained for a physical chemical method — the conductivity method — to show that it is relatively a weak base, by measuring the relative number of hydroxyl ions present. The hydroxides of the alkaline earths, — calcium, strontium, and barium, are very strong bases, but not as strong as the hydroxides of the alkalies. Halving the molecular conductivities of the former, and comparing these values with the molecular conductivities of potassium hydroxide under the same conditions, we have : — Volumes KOH J Ca(OH) 2 i 8r(OH), 4 B»(OH), fi> M« Mo »»« 32 207 — 190 193 64 210 190 197 201 256 214 220 209 216 1024 212 — 212 220 The relative strengths of the two sets of hydroxides are obvious from the above values. If we go farther and examine the hydroxides of the heavy metals, we would find that most of them are so slightly soluble that their conductivities cannot be measured satisfactorily. We would also find that some hydroxides, like aluminium and zinc, are acid under one set of conditions and basic under other conditions. In the presence of a strong acid they are basic, and in the presence of a strong base they are acidic. It may seem difficult at first to account for these facts in the light of the present simple conceptions of acid and base ; but they really present no difficulty. A substance like aluminium hydroxide in the presence of a strong acid dissociates like the alkaline hydroxides, yielding hydroxyl ions which give it its basic properties. In the presence of a strong base it dissociates yielding hydrogen ions, and a complex anion containing aluminium, oxygen, and probably some hydrogen. The way in which the molecule breaks down into ions may be conditioned by the nature of the substance with which it is in contact. Organic Bases. — The most accurate work on the conductivity of the organic bases we owe to Bredig, 1 who carried out this elaborate series of measurements in connection with his dissertation in Ost- wald's laboratory and under his guidance. Let us examine first the 1 Ztschr. phys. Chem. 13, 289 (1894). MEASUREMENTS OF CHEMICAL ACTIVITY 625 effect of composition on basicity among the primary amines, by comparing some of the members of the homologous series, — methyl- amine, ethylamine, etc. : — Volumes Ammonia Methylamine Ethylamine Propylamine P-v Hv C» f» 8 3.20 14.1 13.8 12.3 32 6.28 27.0 27.0 23.9 128 12.63 49.5 49.4 44.7 256 17.88 65.4 65.6 59.6 Methylamine is a much stronger base than ammonia itself, show- ing that the replacement of one hydrogen atom by a methyl group has greatly increased the basicity. Ethyl has just about the same influence as methyl, while propyl has a slightly smaller influence. The question which would next arise is what influence would the replacement of a second hydrogen atom by a radical have on the basicity ? This can be answered by studying the series of second- ary amines : — Volumes DlMETHYLAMINE Dietiiylamine DlPROPYLAMINE ft> H-v P« 8 16.1 19.1 16.6 32 31.0 37.1 33.1 128 57.2 67.1 60.0 256 75.4 86.6 77.6 Dimethylamine is slightly stronger than monomethylamine, and, similarly, for diethyl- and dipropyl-amines. We can go farther and introduce a third group into ammonia, giving the tertiary ammonium bases. It is of interest to see what influence the third group has on the basicity : — Volumes Trimethylamine Triethylamlne Tkipkopylamine f« Mv f*. 8 4.95 13.3 32 10.2 27.1 — 128 20.0 50.0 — 258 27.5 66.4 60 626 THE ELEMENTS OF PHYSICAL CHEMISTRY The introduction of the third radical diminishes the basicity very considerably. We can, however, go one step farther and introduce a fourth radi- cal into ammonia, giving the quaternary ammonium bases. What effect could the fourth group have on the basicity ? Since the third group lessens the basicity, we should expect the fourth group to still further diminish it. Let us see what are the facts : — Volumes Tetramethylammonium Hydroxide Tetraethylammonium Hydroxide 16 64 256 205 211 (213) 176 183 187 The fourth group increases the basicity to such an extent that the quaternary ammonium bases are not only stronger than the primary and secondary, but are to be ranked with the very strong bases, being nearly as strong as the alkali hydroxides themselves. The presence of four substituting groups in bases in general makes them very strongly basic. Take the weak bases, — phosphine, arsine, and stib- ine (PH S , AsH 3 , SbH 3 ). These compounds form derivatives which seem to be tetrasubstitution products of H 4 POH, H 4 AsOH, and H 4 SbOH, in which the four hydrogen atoms are replaced by methyl groups. These compounds are tetramethylphosphonium hydroxide, tetramethylarsonium hydroxide, and tetramethylstibonium hydrox- ide, having the respective formulas : (CH 3 ) 4 POH, (CH 3 ) 4 AsOH, and (CH 3 ) 4 SbOH. These are strongly basic substances, as will be seen from the following conductivity results taken from the work of Bredig: 1 — Volumes Teteamethylphos- phonifh Hydroxide Tetramethylaebo- nium Hydroxide Tetramethylstibo- nium Hydroxide 16 64 266 V-v 200 207 208 197 202 204 166 169 171 1 Ztschr. phys. chem. 13, 301 (1894). MEASUREMENTS OF CHEMICAL ACTIVITY 627 Constitution as conditioning Basicity. — The effect of constitution on basicity can be seen by comparing isomeric substances. Take propylamine and isopropylamine : — Volumes Propylamine Isopropylamine F« Md 8 12.3 13.0 32 23.9 25.7 128 44.7 47.1 256 59.6 62.3 Isopropylamine is a slightly stronger base than propylamine, but the difference is very slight. There are, however, many cases known, as Bredig points out, of isomeric and metameric compounds which have very different strengths as bases. This shows that constitution often has a marked influence on the strength of bases, as we have seen that it has on the strength of acids. Hantzsch's View as to the Strength of Ammonia. — In this connection the work of Hantzsch and Sebaldt L must be carefully considered. They raise the question as to whether the small conductivity of an aqueous solution of ammonia is due to the slight dissociation of the compound NH 4 OH ; or whether ammonia dis- solved in water is mainly in the form of NH 3 molecules — prac- tically all of the NH 4 OH formed being dissociated. From a study of the division of ammonia between various solvents, and the temperature coefficients of this partition, the above-named authors conclude that it is highly improbable that ammonium hydroxide exists in water to any very great extent in the undis- sociated condition. If ammonium hydroxide is a very weak base, then it should be expected that salts of this base, even with strong acids, would be considerably hydrolyzed, like the salts of other weak bases. - The fact is that ammonium salts with strong acids are hydrolyzed at ordinary temperatures to a comparatively slight extent. It is difficult to reconcile this fact with the view that ammonia is a very weak base. Taking all of the facts into account, Hantzsch thinks it probable that ammonia dissolved in water exists for the most part as ammonia 1 Ztschr. phys. Ohem. 30, 258 (1899). 628 THE ELEMENTS OF PHYSICAL CHEMISTRY (NH 3 ) — the small amount of ammonium hydroxide formed being strongly dissociated by the water. The results contained in this chapter, like those of the earlier physical chemistry, are purely empirical. We know how certain elements and groups affect the strength of the acid or base into which they enter, and that the effect may depend upon the way in which these are combined with other substances in the molecule. We do not know, nor do we have any idea, why this is the case. Why does an oxygen atom increase the acidity of certain compounds, and diminish the acidity of others ? and why does the presence of a nitro- group affect the acidity quite differently in different positions ? are questions to which we have absolutely no satisfactory answer. The physical chemist of to-day, like the physical chemist of the earlier part of the nineteenth century, must be content for the time being with empirical results in certain directions. He, however, recognizes that this is but a necessary stage in the development of the subject, and in no wise regards it as final. We have seen how great masses of empirically established facts have already been placed upon an exact physical and mathematical basis. The aim of the physical chemist in the future will be to extend and supplement these generalizations, which have already accomplished so much for the science of chemistry. INDEX Abbe-nollet demonstrated osmotic pressure, 188. Abegg and Nernst, freezing-point method, 234, 235, 423. Abnormal results in non-aqueous solvents, 430. Abnormal vapor-densities, 64. Abnormal vapor-densities, explana- tion of, 65. Absolute boiling-point of a gas, 92. Absorption spectra of gases, 80. Accumulators, 492. Acetamide, action of acids on, 545. Acetylene hydrocarbons, thermo- chemical measurements with, 342. Acid and basic properties, 27. Acid, basicity determined empirically from its conductivity, 404. Acidity as affected by oxygen and sulphur, 612. Acidity conditioned by composition, 611. Acids, action of on acetamide, 545. Acids, electrolysis of, 487. Acree, on reactions of the second order, 545. Actinium, 510. Actinometers, 494. Actinometry, 493. Active substances, optically, 125. Activities, equilibrium methods of measuring relative, 606. Activities of substances, great dif- ferences in, 601. Activity, optical and chemical con- stitution, 127. Adie, on osmotic pressure, 222. Affinity, chemical, 514. Alcohols, thermochemical results with, 343. Alexeew, 180. Alpha rays, 503. Amagat on gas-pressure, 47. Amalgams, freezing-point of, 250. Amalgams, vapor-pressure of, 269. Amides, decomposition of, 604. Amido-group, effect on acidity, 617. Ammonia, Hantzsch's view as to the strength of, 627. Ammonia, liquid, dissociating power of, 423. Amphoteric electrolytes, 297. Analogues, atomic, 32. Animal cells used in measuring rela- tive osmotic pressure, 200. Anion, 211. Anion, effect of the nature of on potential difference, 474. Archibald and Mcintosh, work in liquid halogen acids, 426. Arrhenius determines the value of the coefficient i, 227 '. Arrhenius, effect of neutral salts on the velocity of saponification, 556. Arrhenius, on additive properties and the theory of electrolytic dissocia- tion, 302. Arrhenius, on double salts in solution, 415. Arrhenius, on isohydric solutions, 413. Arrhenius, on saponification con- stants, 543, 545. Arrhenius, on the theory of electro- lytic dissociation, 209. Asymmetric tetrahedral carbon atom, 131. Atom, arrangement of the electrons within the, 41. Atomic nature of electricity, 363. Atomic refraction of some of the more common elements, 124. Atomic theory, 1. Atomic theory, origin of, 3. Atomic volumes, 28. Atomic weights and chemical proper- ties, combining power, 24. Atomic weights and combining num- bers, 4. Atomic weights and physical proper- ties, 27. Atomic weights corrected by the periodic system, 31. Atomic weights, determination of relative, 4. 629 630 INDEX Atomic weights from molecular weights, 8. Atomic weights from specific heats, 10. Atomic weights, isomorphism an aid in determining, 12. Atomic weights, most accurate method of determining, 14. Atomic weights, table of, 16. Atoms and molecules, 1. Autocatalysis, 540. Avogadro, apparent exceptions to the law of, 54. Avogadro's hypothesis, 6. Avogadro's hypothesis and molecular weights, 7. Avogadro's law for osmotic pressure, 205. Avogadro, law of, 53. Bacteria used in measuring relative osmotic pressures, 200. Baeyer, melting-points and composi- tion, 168. Baker, dry ammonia does not act on dry hydrochloric acid gas, 440. Baker showed that certain substances do not burn in dry oxygen, 439. Bancroft, study of oxidizing and re- ducing elements, 468. Barmwater, on osmotic pressure, 222. Barus and Strouhal, method of cali- brating a wire, 381. Base, effect of the dissociation of the, 544. Bases, conductivity of organic and their dissociation constants, 405. Bases, electrolysis of, 488. Bases, organic, strengths of, 624. Basic and acid properties, 27. Basicity conditioned by composition, 623. Basicity conditioned by constitution, 627. Basicity of an acid determined em- pirically from its conductivity, 404. Bassett, work in mixed solvents, 433. Batteries in general use, 491. Bayley, relation between melting- points and boiling-points, 169. Beccaria,electrochemicalworkof, 347. Beckmann boiling-point apparatus, 263. Beckmann boiling-point method, 264. Beckmann freezing-point apparatus, 228. Beckmann freezing-point method, 229. Becquerel discovers the Becquerel rays, 500. Becquerel, on electrical actinometers 495. Becquerel, on magnetic rotation, 302. Becquerel, on photochemical induc- tion, 496. Becquerel rays, 500. Becquerel, work on magnetic rota- tion, .136. Bein, method for determining the relative velocities of ions, 370. Benzene, constitution of from re- fractivity, 122. Benzene, thermochemistry of, 344. Bergmann's and Geoffroy's tables, 515. Berkeley and Hartley, method of measuring osmotic pressure, 217. Berthelot and Saint Gilles, bearing of their work on mass action, 520. Berthelot, principle of maximum work, 524. Berthelot, thermochemical work, 320. Berthollet, discussion with Proust, 2- 517. Berthollet, on the effect of mass, 566. Berzelius' electrochemical theory, 349. Berzelius' electrochemical theory, objections to, 350. Berzelius' electrochemical theory, Thomson overthrows the objec- tion to, 351. Berzelius' method of determining combining numbers, 5. Berzelius on the catalytic action of ferments, 536. Beta rays, 503. Biaxial crystal systems, 162. Bichromate cell, 491. Biltz, H., Practical Methods of Deter- mining Molecular Weights, 231. Bimolecular, or second order re- actions, 541. Bingham, work in mixed solvents, 433. Black and Morse, solubility of per- manganates, 186. INDEX 631 Blagden, on freezing-point lowering, 222. Bleier, molecular weights, 62. Bodenstein and v. Meyer, on heat absorbed in the formation of hy- driodic acid, 591. Boguski, heterogeneous reactions of the first order, 562. Boiling-point and lowering of freez- ing-point, relation between, 272. Boiling-point and vapor-pressure of liquids, 99. Boiling-point apparatus of Beck- mann, 263. Boiling-point method of measuring dissociation, 268. Boiling-point of a gas, absolute, 92. Boiling-points and composition and constitution, 102. Boiling-points, effect of certain atoms or groups on, 107. Boiling-points of liquid mixtures, 181. Boiling-points, work since the time of Kopp, 104. Boltwood, on the origin of radium, 510, 513. Boltzmann, on the free energy of surface, 540. Bomb, explosion, of Berthelot, 327. Bomb, for determining conductivity at high temperatures, 409. Boyle, exception to the law of, 47. Boyle, law of, 47. Boyle's law for osmotic pressure, 203. Brauner's modification of Mendel6eff 's table, 35. Bredig and Ikeda, catalytic action of finely divided metals, 538. Bredig and Reinders, catalytic action of finely divided metals, 539. Bredig and Von Berneck, catalytic action of finely divided metals, 538. Bredig and Von Berneck, method of preparing colloidal suspensions, 283. Bredig applies the Ostwald dilution law to weak organic bases, 400. Bredig determines the conductivity of organic bases and their disso- ciation constants, 405. Bredig, on colloidal solutions of the metals, 536. Bredig shows that migration veloci ties are a periodic function of atomic weights, 374. Bredig's work on the strength of organic bases, 624. Briihl, effect of constitution on re- fractivity, 120. Briihl, on the constitution of benzene from refractivity, 122. Briihl, unsaturation and dissociating power, 438. Bunsen and Roscoe, law of photo- chemical action, 499. Bunsen and Roscoe on photochemical extinction, 496, Bunsen and Roscoe, on photo- chemical induction, 497. Bunsen and Roscoe, on the hy- drogen-chlorine actinometer, 494. Bunsen and Roscoe, on the silver actinometer, 495. Bunsen ice-calorimeter, 112. Bunsen, method of, 62. Burton, on the coagulation of colloids by ions, 286. Bussy, liquefaction of gases, 85. Cady and Franklin, velocity of ions in liquid ammonia, 423. Cailletet liquefied oxygen, 87. Caldwell, on double salts in solu- tion, 415. Calorimeter, water, 325. Cane sugar, inversion of, 531. Cannizzaro and De Chancourtois, work of, 20. Carbon, from the thermochemical standpoint, 333. Carrara, conductivity in methyl alcohol, 427. Carroll, work in mixed solvents, 432. Catalysis, 533. Catalysis, theories to account for, 534. Catalytic action of ferments, 536. Catalytic action of finely divided' metals, 538. Catalytic action of hydrogen ions, 537. Catalyzers, negative, 536. Cathode particle, charge carried by, 39. Cathode particle, mass of, 38. Cathode particle, relation of — for, 37. m Cation, 211. 632 INDEX Cations, velocities of the complex organic, 407. Cattaneo, dissociation in ether, 428. Cavendish, nitric acid formed on sparking air, 515. Cells, types of, 454. Centnerszwer, on hydrocyanic acid and cyanogen as solvents, 425. Centrifugal force partly overcomes osmotic pressure, 213. Charge carried by the cathode par- ticle, 37. Chemical action at a distance, 476. Chemical activity and dissociation, 438. Chemical activity, measurements of, 601. Chemical activity, methods employed and some of the results obtained, 601. Chemical affinity, 514. Chemical affinity, dynamical method of measuring, 602. Chemical dynamics, 530. Chemical elements, 465. Chemical energy, transformation of radiant energy into, 493. Chemical equilibrium, 565. Chemical reactions, why do they take place? 530. Chromosphere of the sun, 81. Clark element, 443. Clausius' theory of electrolysis, 210, 356. Clausius, theory of solutions, 525. Coagulation of colloidal suspensions, 286. Coagulation of colloids by ions, 286. Coexistence of reactions, principle of the, 558. Cohen, on allotropic modifications of tin, 165. Colloidal solutions, 282. Colloidal suspensions, 282. Colloidal suspensions, coagulation of, 286. Colloidal suspensions, properties of, 284. Colloids and crystalloids, 282. Colloids coagulated by ions, 286. Color, change in with electrical charge, 290. Color demonstration of the disso- ciating action of water, 295. Color of solutions, 287. Color of solutions of electrolytes, 288. Combining numbers and atomic weights, 4. Combining numbers, chemical methods of determining, 5. Combining power, chemical prop- erties and atomic weights, 24. Combining weights, law of, 3. Combustion, heat of, 341. Common ion, solubility as affected by an electrolyte with a, 594. Complex reactions, 561. Composition and constitution, effect of on chemical activity, 611. Composition as conditioning acidity, 611. Composition as conditioning basicity, 623. Concentration, effect on migration velocity, 372. Concentration elements of the first type, 455. Concentration elements of the second type, 457. Concentration element, sources of potential in a, 464. Conduction of heat and electricity, 358. Conductivities at high temperatures, results obtained by Noyes, 411. Conductivities of different sub- stances, demonstration of the different, 388. Conductivities, relative, of different substances, 388. Conductivity as a measure of disso- ciation, compared with freezing- point lowering, work of Pearce, 396. Conductivity at high temperatures, 409. Conductivity, determination of the maximum molecular, 394. Conductivity, effect of pressure on, 408. Conductivity, increase in molecular with increase in dilution, 390. Conductivity, is it an accurate measure of dissociation? 395. Conductivity measurement, 381. Conductivity measurements, con- ditions which must be fulfilled in making, 381. INDEX 63a Conductivity method of measuring chemical activity, 609. Conductivity, molecular, 378. Conductivity of fused electrolytes, 416. Conductivity of fused electrolytes, general relations, 417. Conductivity of organic acids and the determination of dissociation constants, 403. Conductivity of organic bases and their dissociation constants, 405. Conductivity of solutions, method of measuring, 378. Conductivity of solutions of electro- lytes, 377. Conductivity, specific, 378. Conductivity, temperature coeffi- cients of, 383. Conservation of energy applied to thermochemistry, 322. Conservation of mass, law of, 1. Constant cells, 454. Constant heat of neutralization of strong acids and bases, 334. Constant pressure, specific heats of gases at, 68. Constant proportion, law of, 2. Constants, determination of the conductivity of organic bases and their dissociation, 405. Constants, the conductivity of organic acids and the determina- tion of dissociation, 403. Constant volume, specific heat of gases at, 68. Constitution and composition, effect of, on chemical activity, 611. Constitution as conditioning acidity, 617. Constitution as conditioning basicity, 627. Constitution, effect of, on heat of combustion, 345. Continuity of passage from liquid to gas, 93. Coolidge and Noyes, conductivity at high temperatures, 409. Cooper, conductivity at high tem- peratures, 411. Coppet, on freezing-point lowering, 223. Corona of the sun, 81. Corpuscle, 39. Coulomb's law, 359. Counter reactions, 560. Crafts and Meier, vapor-density of iodine, 63. Critical density, 92. Critical point, 97. Critical pressure, 91. Critical temperature, 91. Critical temperature of a gas, 87. Critical volume, 92. Crookes discovers uranium X, 508. Crum-Brown and Walker, electro- synthesis, 490. Cryohydrates, 251. Crystallographic form and chemical composition, 165. Crystallography, importance for chemistry and physical chem- istry, 160. Crystalloids- and colloids, 282. Crystals, properties of, 161. Crystals, thermal properties of, 163. Crystal systems, 158. Curie, M., and Dewar measure heat produced by radium, 504. Curie, M., and Laborde discover that radium produces heat, 504. Curie, Mme., discovers radium, 501. Curie, Mme., on the atomic weight of radium, 502. Curies discover induced radio- activity, 507. Daguerre, action of light on silver salts, 493. Dale and Gladstone, formula, 116. Dalton, law of multiple proportions, 3. Dalton's laws, 4. Daniell element, 466. Davy's electrochemical theory, 349. Davy, work of, 349. De Chancourtois and Cannizzaro, work of, 20. Decomposition values, 485. De La Rive, investigation of mag- netic rotation, 136. Densities and molecular weights of gases, 57. Densities of gases used to determine molecular weights, 6. Density and refractivity, 116. Deville, Sainte-Claire, dissociation by heat, 522. 634 INDEX De Vries, measurement of relative osmotic pressures, 197. De Vries, on the relation between osmotic pressure and vapor-ten- sion, 270. De Vries, relative osmotic pressure, 252. Dewar, liquefaction of gases, 88. Dewar, on the solidification of hydro- gen, 90. Diamagnetic bodies, 138. Dielectric constants of liquids, 154. Difference in potential between metal and solution, calculation of, 453. Differences of potential between metals and electrolytes, 471. Diffusion, 273. Diffusion, cause of, 277. Dilution law of Ostwald, 398. Dilution law of Ostwald, testing the, 399. Dilution law of Rudolphi, 401. Discharging potential of ions, 488. Dissociated solutions, chemical prop- erties of completely, 299. Dissociated solutions, physical prop- erties of completely, 300. Dissociating power and other prop- erties of solvents, relation be- tween, 437. Dissociating power of different sol- vents, 421. Dissociation and chemical activity, 438. Dissociation and fluorescence, 296. Dissociation and solubility of eleetro- \ lytes, 593. "* Dissociation as measured by change in solubility, 597. Dissociation by heat, 522. Dissociation constants, the conduc- tivity of organic acids and the determination of, 403. Dissociation decreases with rise in temperature, 412. Dissociation from conductivity com- pared with dissociation from \ freezing-point lowering, 396. Dissociation, is conductivity an v accurate measure of, 395. ** Dissociation measured by the boiling- . point method, 268. ^ Dissociation measured by the freez- ing-point method, 232. Dissociation of electrolytes, 393. Dissociation of fused salts, 418. Dissociation of the base, effect of, 544. Dissociation of vapors diminished by an excess of one of the products, 68. Dissociation theory and freezing- point lowering, 227. Distance, chemical action at a, 476. Distance, experiment illustrating chemical action at a, 476 Distance, experiment to demonstrate chemical action at a, 477, 480. Distillation of liquid mixtures, 181. Dobereiner's triads, 19. Double salts in solution, condition of, 415. Draper, on the hydrogen-chlorine aetinometer, 494. Drude, dielectric constants of liquids, 154. Dulong and Petit, law of, 11, 171. Dulong showed the action of mass in double decomposition, 518. Dumas, method of, 57. Dutoit and Aston, dissociating power and association of solvents, 437. Dutoit and Aston, work in non- aqueous solvents, 428. Dynamical method of measuring chemical affinity, 602. Dynamics and equilibrium, 514. Dynamics, chemical, 530. Dynamics, earlier views on, 514. Dynamics, fundamental equation of, 529. Earlier views on chemical dynamics, 514. Eastman, conductivity at high temperatures, 411. Edwards, formula for refractivity, 117. Ekaaluminium, 33. Ekaboron, 33. Ekasilicium, 33. Electrical charge, change in color with change in, 290. Electrical conductivity of crystals, 164. Electrical energy, 358. Electrical method of studying radio- active radiations, 502. INDEX 635 Electrical energy, transformation of intrinsic energy into, 445. Electrical units, 360. Electricity and heat, conduction of, 358. Electricity, passage of through elec- trolytes, 482. Electricity, relation between quan- tity of and amount of decompo- sition, 362. Electrochemistry, 347. Electrochemistry, development of, 347. Electrochemical equivalent, 364. Electrochemical nomenclature, 361. Electrolysis, 353, 366. Electrolysis and' polarization, 482. Electrolysis, evidence for the pri- mary decomposition of water in, 486. Electrolysis of water, 348. Electrolysis, primary decomposition of water in, 486. Electrolysis, products of, 482. Electrolytes, dissociation of, 393. Electrolytes, equilibrium of, in solu- tions, 593. Electrolytes, properties of solutions of, 299. Electrolytic dissociation, theory of, 208, 211. Electrolytic separation of the metals, 488. Electrolytic solution-tension, 449. Electromagnetic system of units, 361. Electromotive force calculated from osmotic pressure, 446. Electromotive force, measurement of, 444. Electromotive force of primary cells, 442. Electron, 40. Electron and Faraday's law, 364. Electrons, arrangements of, and chemical relations, 42. Electrons within the atom, arrange- ment of, 41. Electron theory and the periodic system, 41. Electron theory of Thomson, radio- activity in terms of, 512. Electrostatic system, 361. Electrosynthesis of organic com- pounds, 490. Elements, concentration, of the first type, 455. Elements, normal, 443. Elements predicted by the periodic system, 31. Emanation from radium, 506. Emanation from radium discovered by Rutherford, 506. Emanation from radium, molecular weight of, 506. Emanation induces radioactivity, 507. Emanation yields helium, 506. Emanium, 510. Emden measured the lowering of vapor-tension, 257. Endosmose, 190. Endothermic reaction, 325. Energy unchanged in chemical re- actions, 322. Engler and Wohler, absorption of oxygen by platinum black, 535. Equations, fundamental, of dynamics and equilibrium, 529. Equilibrium and dynamics, 514. Equilibrium between phases of three substances, 387. Equilibrium between phases of two substances, 582. Equilibrium between two compo- nents and four phases, 584. Equilibrium between two phases of same substance — three condi- tions variable, 581. Equilibrium, chemical, 565. Equilibrium, condition of a reaction when established, 565. Equilibrium, effect of pressure on, 592. Equilibrium, effect of temperature on, 591. Equilibrium, fundamental equation of, 529. Equilibrium in condensed systems, 587. Equilibrium in first order, heteroge- neous reactions, 568. Equilibrium in first order, homoge- neous reactions, 566. Equilibrium in second order, hetero- geneous reactions — one sub- stance solid, 571. Equilibrium in second order, hetero- geneous reactions — two sub- stances solid, 572. 636 INDEX Equilibrium in second order, hetero- geneous reactions — three sub- stances solid, 573. Equilibrium in second order, homo- geneous reactions, 569. Equilibrium in solutions of elec- trolytes, 593. Equilibrium methods of measuring relative activities, 606, 609. Equilibrium, summary of the discus- sion of, 600. Equivalent, electrochemical, 364. Ester, saponification of an, 542. Esters, saponification by bases, 605. Ethylene hydrocarbons, thermo- chemical measurements with, 342. Eutectic, 251. Eutectic alloys, 251. Evidence for hydrate theory of Jones, 239. Excess of one of the products diminishes dissociation, 68. Exothermic reaction, 325. Explosion bomb of Berthelot, 327. Extinction photochemical, 496. Fanjung, on conductivity at high pressure, 408. Faraday, law of, 352, 362. Faraday, liquefaction of gases, 85. Faraday, meaning of the law of, 363. Faraday measured the lowering of vapor-tension, 256. Faraday, observation on magnetic rotation, 135. Faraday, on gases absorbed by solids, 534. Faraday, on the passive state, 441. Faraday, second work on the lique- faction of gases, 86. Faraday's law for fused electrolytes, 417. Faraday, testing the law of, 362. Favre and Silbermann, work of, 319. Ferments act catalytically, 536. Fick's law of diffusion, 274. Fick, testing the law of, 275. Finkelstein, on the passive state, 441. First law of thermodynamics, 72. First order reactions, 531. Fitzpatrick, conductivity in methyl alcohol, 427. Fluorescence and dissociation, 296. Fluoroscopic method of studying radioactive radiations, 502. Flusin, on osmotic pressure, 222. Foreign substances, effect on the velocity of reactions, 556. Formation, heat of, 339. Franklin and Cady, velocity of ions in liquid ammonia, 423. Franklin and Kraus, conductivity in liquid ammonia, 423. Fraunhofer, spectrum lines, 81. Frazer and Morse, method of measur- ing osmotic pressure, 214. Free ions in solutions, evidence fur- nished for the existence of, 212. Freezing-point determinations, erro- neous conclusions from, 232. Freezing-point lowering, 222. Freezing-point lowering and osmotic pressure, relations between, 252, 253. Freezing-point lowering and the dis- sociation theory, 227. Freezing-point lowering, comparison of dissociation from conductivity with dissociation from, 396. Freezing-point, lowering of, relation between rise in boiling-point and, 272. Freezing-point method as a measure of dissociation, 232. Freezing-point method of determin- ing molecular weights, 230. Freezing-point method of measuring osmotic pressure, 255. Freezing-points, more accurate methods of measuring, '233. Freudenberg, electrolytic separation of the metals, 489. Frowein's tensimeter, 583. Fuch's method of measuring polariza- tion, 484. Fused electrolytes, conductivity of, 416. Fused electrolytes, conductivity of, general relations, 417. Fused salts, dissociation of, 418. Fusibility and volatility, 30. Galvani's discovery, 347. Gamma rays, 503. Gas-battery, 468. Gases, 46. INDEX 637 Gases, absorption spectra of, 80. •Gases, densities and molecular weights of, 57. Gases in gases, solutions of, 176. Gases in liquids, solution of, 177. Gases, kinetic theory of, 54. Gases, liquefaction of, 85. Gases, properties of, 46. - Gases, specific heat of, 68. Gases, spectra of, 79. Gas-laws apply to osmotic pressure, exceptions, 207. Gas-pressure and osmotic pressure, causes of, 206. Gas-pressure and osmotic pressure, relations between, 202. Gas-pressure, laws of, 46. Gay-Lussac, deviations from the law of, 51. Gay-Lussac, law of, 50. Gay-Lussac, method of, 59. Gay-Lussac, on the hydrogen- chlorine actinometer, 494. Gay-Lussac's generalization, 6. Gay-Lussac's law for osmotic pres- sure, 203. ■Geoffroy's and Bergmann's tables, 515. Gibbs' phase rule, 574. Gibbs' thermodynamics of the pri- mary cell, 445. Giesel discovers emanium, 510. Gladstone and Dale, formula, 116. Gladstone, effect of constitution on refractivity, 122. Gladstone, on refractive power, 301. Godlewski, on osmotic pressure, 222. Goodwin and Thomson, conductivity in liquid ammonia, 423. Goodwin and Wentworth, conduc- tivity of fused salts, 419. Graham, on crystalloids and colloids, 282. Graham, work of on diffusion, 274. Grotrian, on double salts in solution, 415. Grotthuss' theory of electrolysis, 354. Groups of the periodic system, rela- tions within, 26. Guldberg and Waage, work of, 526. Gutbier, method of preparing col- loidal suspensions, 284. Guthrie, work on cryohydrates, 252. Guye, hypothesis of, 133. Halogen substitution products of the paraffines, thermochemical results with, 343. Hamburger measures relative osmotic pressures by means of red blood corpuscles, 200. Hampson, liquefaction of gases, 89. Hantzsch's view as to the strength of ammonia, 627. Hardin, liquefaction of gases, 90. Hardy, on colloidal suspensions, 285. Hartley and Berkeley, method of measuring osmotic pressure, 217. Heat and electricity, conduction of, 358. Heat, dissociation by, 522. Heat liberated by radium, applica- tion to cosmic problems, 505. Heat liberated the same under the same conditions, 323. Heat of combustion, 341. Heat of combustion, effect of con- stitution on, 345. Heat of formation, 339. Heat of fusion, latent, 170. Heat of neutralization, 333. Heat of neutralization of strong acids and bases constant, 334. Heat of vaporization, 109. Heat of vaporization at the critical point, 111. Heat produced by radium, 503. Heat tone of a reaction, 325. Helium produced from the radium emanation, 506. Helmholtz assumed that the intrinsic energy that disappeared all passed over into electrical energy, 445. Helmholtz double layer, 449. Helmholtz element, 444. Helmholtz, on the electron, 364. Hemihedrism, 160. Henry's law, 177. Hess, thermochemical work of, 318. Heterogeneous reaction of the first order, 562. Heterogeneous reaction of the second order, 564. Heterogeneous reactions, 561. 638 INDEX Hexagonal crystal system, 159. Heycock and Neville, on solutions of metals in sodium, 251. Heydweiller and Kohlrausch, method of purifying water, 382. Hittorf, on the passive state, 441. Hittorf's theory, 367. Hofmann's modification of Gay- Lussac's method, 59. Holohedrism, 16,0. Hughes, dry hydrochloric acid does not decompose carbonates, 439. Humphreys, on solution and diffusion of metals in mercury, 31. Hydrate theory of Jones, evidence for, 239. Hydrate theory of Jones, how it differs from that of Mendeleeff, 249. Hydrates, a fifth argument for the existence of, based on tempera- ture coefficients of conductivity, 385. Hydrates, approximate composition of, 246. Hydrates, a sixth argument for the existence of, 396. Hydrates, bearing of on the tempera- ture coefficients of conductivity, 385. Hydrates formed by molecules or ions? 248. Hydrocyanic acid, dissociating power of, 422. Hydrogen-chlorine actinometer, 494. Hydrogen ions, catalytic action of, 537. Hydrolysis at elevated temperatures, 304. Hydrolytic dissociation, 303. Ice calorimeter of Bunsen, 112. Ice, correction for separation of, in the freezing-point method, 230. Ignition pressure, 557. Ignition temperature, 557. Inconstant cells, 454. Index of refraction, 115. Indicators, theory of, 292. Induction photochemical, 496. Influences which affect the velocities of reactions, 553. Inorganic solvents which dissociate, 426. Inorganic solvents which do not dis- sociate, 426. Intrinsic energy into electrical, trans- formation of, 445. Inversion of cane sugar, 531. Ion formation, modes of, 419. Ionization, effect of rise in tempera- ture on, 412. Ions, absolute velocities of, 375. Ions, experimental methods for de- termining the relative velocities of, 368. Ions form hydrates, 248. Ions in solution, evidence furnished for the existence of free, 212. Ions, velocities of, 366. Isohydric solutions, 413. Isomeres and polymeres, action of light in the formation of, 498. Isomeres, optically active, separation from racemic modifications, 132. Isomorphism, 166. Isomorphism an aid in determining atomic weights, 12. Isotropic crystal system, 162. Jahn, on magnetic rotation, 302. Joly concludes that radium does not exist in quantity deep down be- low the earth's surface, 505. Jones and Bassett, hydrate work, 240. Jones and Bassett, method for deter- mining the relative velocities of ions, 370. Jones and Chambers, abnormal freez- ing-point lowerings, 235. Jones and Getman, on hydrates, 235. Jones and Knight, abnormal freezing- point lowerings, 235. Jones and Mackay, method of purify- ing water, 382. Jones and McMaster, solvates, 249. Jones and Ota, abnormal freezing- point lowerings, 235. Jones and Rouiller, method for de- termining the relative velocities of ions, 370. Jones and Stine, law of mass action applied to hydration, 250. Jones and Uhler, spectroscopic work, 241. Jones and West, on the temperature coefficients of conductivity, 385. INDEX 639 Jones, boiling-point apparatus, 265. Jones, color demonstration of the dissociating action of water, 295. Jones, dissociation in the alcohols as measured by the boiling-point method, 427. Jones, freezing-point measurements, 599. Jones, freezing-point method, 233, 423. Jones, work in mixed solvents, 431. Joule's law, 359. Kablukoff , conductivity in the hydro- carbons, small, 427. Kablukoff, conductivity of hydro- chloric acid in ether, 430. Kalmus, 305. Kaufmann, experiment of, 39. Kayser and Runge, relations be- tween spectral lines, 83. Kelvin assumed that the intrinsic energy that disappeared all passed over into electrical energy, 445. Kelvin, on the size of molecules, 44. Khanikof and Longuinine, 177. Kier, on the passive state, 441. Kinetic theory employed to deduce the ratio between the specific heats of a gas, 76. Kinetic theory of gases, 54. Kinetic theory of liquids, 94. Kirchhoff, law of, 80. Kistiakowsky, method for deter- mining the relative velocities of ions, 370. Kistiakowski, on double salts in solution, 415. Knight, on double salts in solution, 415. Knoblauch, on counter reactions, 561. Kohlrausch and Heydweiller, method of purifying water, 382. Kohlrausch, law of, 391. Kohlrausch, method of measuring conductivity, 379. Kohlrausch, on the conductivity of the fused salts of silver, 419. Kohlrausch's law used to determine the relative velocities of ions, 392. Konowalow, on mixtures with con- stant boiling-points, 184. Konowalow, on the vapor-pressure of liquid mixtures, 182. Kopp, on specific heats of solids, 172. Kopp, work on boiling-points, 102. Kopp,work on molecularvolumes, 140. Kraus and Franklin, conductivity in liquid ammonia, 423. Kraus, conductivity at high tem- peratures, 409. Kiister, on counter reactions, 560. Kiister, on the molecular weights of solids, 312. Landolt compares molecular refrac- tivities, 119. Landolt, on optical activity, 302. Landolt tests the formula of Glad- stone and Dale, 116. Landsberger, boiling-point appa- ratus, 266. Laplace and Lavoisier, law of, 318. Larmor, on the electron, 364. Latent heat of fusion, 170. Latent heat of fusion, determina- tion of, 170. Lavoisier and Laplace, law of, 318. Law of mass action, 526. Le Bel and Van't Hoff, on optical activity, 129. Le Blanc, electrolytic separation of the metals, 489. Le Blanc, measurements of "decom- position values," 485. Le Blanc, method of measuring polar- ization, 484. Le Blanc, on refractive power, 301. Le Blanc, solution-tension of anions, 451. Le Blanc, source of the electrical energy in a concentration element, 465. Le.Chatelier, law of equilibrium, 593. Le Chatelier, specific heats of gases depend upon the temperatures,69. Leclanche' cell, 491. Lecoq de Boisbaudran discovers gallium, 33. Lecoq de Boisbaudran, relations be- tween spectral lines, 83. Lewis, work in liquid iodine as the solvent, 424. Liebermann, action of light in the formation of stereoisomers acids, 498. 640 INDEX Light, action of in the formation of isomeres and polymeres, 498. Light on certain silver salts, action of, 498. Linde, liquefaction of gases, 89. Lindsay, work in mixed solvents, 431. Liquefaction of gases, 85. Liquid element, theory of, 461. Liquid elements, 460. Liquids, 84. Liquids and gases, relations be- tween, 84. Liquids, general properties of, 84. Liquids in gases, solutions of, 176. Liquids in liquids, solutions of, 178. Liquids, kinetic theory of, 94. Liquids, vapor-pressure and boiling- points of, 99. Lobry de Bruyn and van Calcar, centrifugal experiment, 213. Lodge, method of, for determining absolute velocities of ions, 375. Loeb and Nernst, apparatus for determining relative velocities of ions, 369. Longinescu's method of determining molecular weights of pure liquids, 150, 154. Longinescu's method of determining the molecular weights of solids, 153. Loomis, freezing-point method, 234, 235, 423. Lorentz and Lorenz, formula for refractivity, 117. Lorenz, on fused electrolytes, 417. Lorenz, on the electron, 364. Lowering of vapor-tension of solv- ents by dissolved substances, 256. Mackay, on double salts in solution, 415. Magnetic property, 138. Magnetic property, recent work, 139. Magnetic rotation of the plane of polarization, 135. Marckwald, actinium produced from emanium, 510. Marignac, work on atomic weights, 16. Marsh, dry sulphuric acid does not decompose carbonates, 439. Mass action, law of, 526. Mass, law of the conservation of, 1. Mass of the cathode particle, 38. Mass unchanged in chemical re- actions, 322. Mayer, on the mechanical equivalent of heat, 71. McCoy, on the origin of radium, 510. Mcintosh and Archibald, work in liquid halogen acids, 426. McMaster, on solvates, 249. McMaster, work in mixed solvents, 434. Mechanical equivalent of heat, 71. Mechanical theory of heat, 71. Medium, nature of, on the velocity of reactions, 556. Melcher, conductivity at high tem- peratures, 411. Melting-point a criterion of purity, 169. Melting-points of solids, 167. Melting-points, relations between, 168. Membrane, effect of the nature of on osmotic pressure, 195. Membranes, semipermeable, made under pressure, 220. Mendeleeff hydrate theory, how it differs from that of Jones, 249. Mendeleeff, periodic system, 21. Mendeleeff predicted new elements from the periodic system, 33. Mendeleeff's table, modification of by Brauner, 35. Metabolons, 511. Metals, catalytic action of finely divided, 538. Metals in mercury, solution and diffusion of, 30. Methane hydrocarbons, thermo- chemical measurements with, 341. Method of determining the order of a reaction, 550. Methods of determining combining numbers,. 5. Methylacetate, saponification of, 603. Meyer and Freyer, effect of the walls of the containing vessel on the reaction, 535. Meyer, Lothar, periodic system, 21. Migration velocities, a periodic func- tion of atomic weights, 374. Migration velocities of ions, 366. Mitscherlich, on isomorphism, 167. INDEX 641 Mixed solvents, conductivity and viscosity in, 431. Mohler and Humphreys, 270. Moisson and Dewar, on the lique- faction of fluorine, 89. Moisture, effect of traces on the velocity of reactions, 556. Molecular and specific rotation, 126. Molecular conductivity, 378. Molecular conductivity, determina- tion of the maximum, 394. Molecular conductivity, increase in with increase in dilution, 390. Molecular latent heat of fusion, 170. Molecular refraction, additive, 124. Molecular refractivity, 117. Molecular volume of liquids, 139. Molecular weight of a pure homo- geneous solid, 315. Molecular weights and Avogadro's hypothesis, 7. Molecular weights and densities of gases, 57. Molecular weights, atomic weights from, 8. Molecular weights by the freezing- point method, 230. Molecular weights determined by the lowering of vapor-tension, 261. Molecular weights determined from the densities of gases, 6. Molecular weights of pure liquids, 149. Molecular weights of pure liquids determined by means of. their surface-tension, 145. Molecular weights of solids, 310. Molecules and atoms, 1. Molecules form hydrates, 248. Molecules, size of, 44. Monoclinic crystal system, 159. Monomolecular, or first order re- actions, 531. Monomolecular reactions, other, 541. Moore and Roaf, on osmotic pressure, 222. Morley, work on atomic weights, 16. Morse and Frazer, method of measur- ing osmotic pressure, 214. Morse, Black, and Olsen, solubility of certain permanganates, 186. Morse, method of preparing semi- permeable membranes, 190. 2 T Moser, measurements of electro- motive force, 457. Multiple proportions, law of, 3. Murray, effect of associated solvents on each other, 431. Natterer, liquefaction of gases, 86. Nature of the' ester and of the base on the velocity of saponification, 543. Neccari, on osmotic pressure, 222. Negative catalyzers, 536. Negative temperature coefficients of conductivity, 434. Nernst and Abegg, freezing-point method, 234, 235, 423. Nernst and Loeb, apparatus for de- termining the relative velocities of ions, 369. Nernst and Tammann, effect of press- ure on the action of acids on metals, 554. Nernst and Wartemburg, dissocia- tion of water-vapor, 149. Nernst, dielectric constants of liquids, 154. Nernst, dissociating power and di- electric constants, 437. Nernst, on electrolytic solution- tension, 449. Nernst, solubility deduction of, 595. Nernst's theory of diffusion, 278. Nernst, theory of the liquid element, 461. Neumann, work on differences of potential between metals and normal solutions of their salts, 473. Neutralization of acids and bases from the thermochemical stand- point, 333. Neutralization of weak acids and bases, heat of, 336. Newlands, octaves of, 20. Newton, theory of affinity, 514. Nilson discovers scandium, 33. Nitric acid, dissociating power of, 423. Nitro group, effect on acidity, 617. Non-reversible cells, 454. Normal electrode, 472. Normal elements, 443. Noyes and Blanchard, demonstra- tion of the different conductivities of different substances, 388. 642 INDEX Noyes and Coolidge, bomb for con- ductivity at high temperatures, 409. Noyes and Coolidge, conductivity at high temperatures, 409. Noyes and Coolidge, on the tempera- ture coefficients of conductivity, 385. Noyes and Wason, study of third order reactions, 547. Noyes furnishes evidence for the existence of free ions in solution, 213. Noyes, on hydrolysis at elevated temperatures, 304. Noyes' solubility experiments, 596. Octaves of Newlands, 20. Offer, work on cryohydrates, 252. Ohm's law, 360. Olsen and Morse, method of prepar- ing permanganic acid, 186. Optically active isomeres, separation from racemic modifications, 132. Optically active substances, 125. Optical activity and chemical con- stitution, 127. Optical method of measuring relative osmotic pressures, 200. Optical properties of crystals, 161. Order of a reaction, methods of de- termining the, 550. Order, reactions of higher than the third, 549. Organic acids and their substitution products, 614. Organic acids, conductivity of and the determination of dissociation constants, 403. Organic anions, velocities of the complex, 406. Organic bases, strengths of, 624. Organic compounds, electrosynthesis of, 490. Organic solvents, 427. Origin of radium, 510. Orthorhombic crystal system, 159. Osmotic apparatus of Berkeley, 218. Osmotic pressure, 188. Osmotic pressure and diffusion, 277. Osmotic pressure and freezing-point lowering, relations between, 252, 253. Osmotic pressure and gas-pressure, causes of, 206. Osmotic pressure and gas-pressure, relations between, 202. Osmotic pressure and vapor-tension, relation between, 270, 271. Osmotic pressure, Avogadro's law for, 205. Osmotic pressure, demonstration of, 188. Osmotic pressure, effect of the nature of the membrane on, 195. Osmotic pressure, electromotive force calculated from, 446. Osmotic pressure, exceptions to the applicability of the gas-laws to, 207. Osmotic pressure, laws of Boyle and Gay-Lussac apply to, 203. Osmotic pressure measured by the freezing-point method, 255. Osmotic pressure measurements by Pfeffer, 191. Osmotic pressure partly overcome by centrifugal force, 213. Osmotic pressure, results of Berkeley's measurements, 221. Osmotic pressures, measurement of the relative, 197. Osmotic pressures, relative, measured by animal cells, 200. Ostwald and Nernst tested the law of Faraday, 363. Ostwald applies the theory of Nernst to the gas-battery, 468. Ostwald, change in volume in neu- tralization, 301. Ostwald, classes of catalytic re- actions, 534. Ostwald, conception of matter, 40. Ostwald determined the conductivity of organic acids, 403. i Ostwald dilution law, 398. Ostwald dilution law, testing the, 399. Ostwald dilution law, why it does not apply to strong electrolytes, 403. Ostwald, electromotive force of con- centration elements, 457. Ostwald, experiment to illustrate chemical action at a distance, 476. Ostwald explains the action of the Becquerel actinometer, 495. INDEX 643 Ostwald, method of determining the order of a reaction, 552. Ostwald, modification of Kohl- rausch's law, 392. Ostwald, on diffusion, 281. Ostwald, one volt element, 444. Ostwald, on the action of acids on acetamide, 546. Ostwald, on the color of solutions, 288. Ostwald, on the conductivity of acetic acid and derivatives, 615. Ostwald, on the effect of oxygen on the strength of benzene acids, 621. Ostwald, on the inversion of cane sugar by different acids, 602. Ostwald, on the principle of the coexistence of reactions, 559. Ostwald, on the saponification of an ester, 543. Ostwald, on the strength of stereoiso- meres, 619. Ostwald studied the effect of oxygen on acidity, 616. Ostwald, thermoregulator, 383. Ostwald, volume-chemical method, 607. Ostwald, volume-chemical method of determining chemical equilibrium, 570. Ota, on double salts in solution, 415. Oxidation, 421. Oxidation and reduction elements, 467. Oxidizing agent, electrical, 467. Oxygen and sulphur, effect on acidity, 612. Ozone and oxygen, from the thermo- chemical standpoint, 331. Palmaer demonstrates the solutlon- ' tension of metals, 452. Paramagnetic bodies, 138. Passive state of the metals, 440. Pasteur, on optical activity, 128. Pebal, dissociation by heat, 523. Pebal, vapor-density of ammonium chloride, 66. Periodic system and the electron theory, 41. Periodic system of Mendel^eff and Lothar Meyer, 21. Perkin, on magnetic rotation, 302. Perkin, work on magnetic rotation, 137. Petit and Dulong's law, 11, 171. Pfaundler, on chemical equilibrium, 525. Pfeffer, measurements of osmotic pressure, 191. Pfeffer's results, 194. Phase rule applied to sulphur, 579. Phase rule applied to water, 575. Phase rule of Gibbs, 574. Phosphorus from the thermochemical standpoint, 333. Photochemical action, law of, 499. Photochemical action of newly dis- covered forms of radiation, 499. Photochemical extinction, 496. Photochemical induction, 496. Photochemical measurements, 496. Photochemistry, 493. Photographic method of studying radioactive radiations, 502. Physical properties and atomic weights, 27. Pictet liquefied oxygen, 87. Plane of polarization, magnetic rota- tion of, 135. Plane of polarized light, rotation of the plane of, 125. Poggendorff, method of measuring electromotive force, 444. Polarization, 483. Polarization and electrolysis, 482. Polarization, method of measuring, 483. Polarization, results of the measure- ments of, 484. Polarized light, rotation of the plane of, 125. Polonium, 510. Polymeres, action of light in the formation of, 498. Polymorphism, 165. Ponsot, freezing-point method, 234, 235. Ponsot, on osmotic pressure, 222. Potential between metal and solu- tion, calculation of the difference in, 453. Potential differences between metals and electrolytes, 471. Potential differences, measurement of individual, 471. Potential in a concentration element, sources of, 464. Potential of ions, discharging, 488. 644 INDEX Poynting, on osmotic pressure, 222. Precht and Runge, on the atomic weight of radium, 502. Pressure, effect of on chemical equilibrium, 592. Pressure, effect of on conductivity, 408. Pressure, influence of on velocity of reactions, 553. Priestly, ammonia decomposed by the electric spark, 515. Primary cells, 491. Primary cells, electromotive force, 442. Primary decomposition of water in electrolysis, 486. Primary decomposition of water in electrolysis, evidence for, 486. Primary products of electrolysis, 482. Principles used in measuring chemical activity, 601. Pringsheim explains photochemical induction, 498. Pringsheim, explanation of photo- chemical extinction, 496. Proportion, law of constant, 2. Proportions, law of multiple, 3. Proust and Berthollet, discussion, 517. Proust, discussion with Berthollet, 3. Proust, hypothesis of, 18. Pulfrich refractometer, 115. Purity, melting-point a criterion of, 169. Racemic modifications, separation of optically active isomers from, 132. Radiant energy into chemical, trans- formation of, 493. Radiations from radioactive sub- stances, 502. Radioactivity, 499. Radioactivity induced by the emana- tion, 507. Radioactivity in terms of the electron theory of Thomson, 512. Radioactivity of thorium, 501. Radioactivity, theory to account for, 511. Radiothorium, 511. Radium, discovery of, 501. Radium, origin of, 510. Radium produces heat, 503. Radium produces heat, application to cosmic problems, 505. Ramsay and Shields, work on surface- tension, 146. Ramsay and Soddy show that the radium emanation produces heat, 507. Ramsay and Young, vapor-pressures, 101. Ramsay discovers radiothorium, 511. Ramsay, on the vapor-pressure of amalgams, 269. Raoult, freezing-point method, 234, 423. Raoult, law of, dealing with the lowering of vapor-tension, 260. Raoult, on freezing-point lowering, 224. Raoult, on the lowering of vapor- tension, 258. Raoult's law for different solvents, 226. Ratio between the specific heats of gases as calculated, 72. Reactions, chemical, why do they take place? 530. Reactions, velocity of, 531. Reaction velocity, law of, enunciated by Wilhelmy, 519. Reducing agent, electrical, 467. Reduction, 421. Reduction and oxidation elements, 467. Refraction atomic, of some of the more common elements, 124. Refraction, index of, 115. Refraction molecular, additive, 124. Refractive power of liquids, 115. Refractivities, relations between the molecular, 118. Refractivity and density, 116. Refractivity, effect of constitution on, 120. Refractivity, molecular, 117. Refractivity, specific, 117. Refractometer, Pulfrich, 115. Regnault determines the specific heats of gases, 69. Regnault, on the vapor-pressure of liquid mixtures, 181. Regnault, work of on the law of Dulong and Petit, 171. Regular crystal system, 159. INDEX 645 Reicher, on the saponification of an acid, 543. Relative conductivities of different substances, 388. Relative osmotic pressures, measure- ment of, 197. Resistance box, 443. Resistance, specific, 378. Results of conductivity measure- ments at high temperatures, 412. Reversible cells, 454. Richards, T. W., work on atomic weights, 16. Rodger and Thorpe on viscosity of liquids, 142. Rodger and Watson, on magnetic rotation, 138. Roloff concludes that light trans- forms from the malenoid to the fumaroid form, 498. Rontgen discovers the Rontgen rays, 499. Rontgen, effect of pressure on the inversion of cane sugar, 554. Rontgen explains the nature of the Rontgen rays, 500. Rontgen rays, 499. Roozeboom, hydrates of ferric chlo- ride, 585. Roscoe and Bunsen, on the hydrogen- chlorine actinometer, 494. Roscoe, on mixtures of constant composition, 186. Rose, observation of, as bearing on mass action, 518. Rotation, magnetic, of the plane of polarization, 135. Rotation, measurement of, 126. Rotation of the plane of polarized light, 125. Rothmund, effect of pressure on the inversion of cane sugar, 554. Rouiller, work in mixed solvents, 433. Rowland, on the specific heat of water, 112. Rudolphi, dilution law, 401. Rudolphi dilution law applies to strongly dissociated electrolytes, 402. Rtidorff, on freezing-point lowering, 222. Runge and Precht, on the atomic weight of radium, 502. Rutherford and Barns show that most of the heat comes from the radium emanation, 507. Rutherford and Soddy discover tho- rium X, 509. Rutherford and Soddy, theory of radioactivity, 511. Rutherford discovers the radium emanation, 506. Rutherford, on the Becquerel rays, 501. Rutherford, on the decomposition products of radium, 508. Rutherford, on the emanation from radium, 506. Rutherford, on the heat liberated by radium as affecting the calculated age of the earth, 505. Rutherford, on the origin of radium, 510. Saint-Claire Deville, dissociation by heat, 522. Saint Gilles and Berthelot, bearing of their work on mass action, 520. Salts, electrolysis of, 487. Saponification, effect of the nature of the ester and of the base on the velocity of, 543. Saponification of an ester, 542. Saponification of esters by bases, 605. Saturated solution, 187. Schall, work in isobutyl alcohol, 428. Scheele showed that different wave- lengths of light produce different effects on silver salts, 493. Scheffer, work on diffusion, 276. Schiff, on the relation between com- position and specific heats, 114. Schiff, work on surface-tension, 145. Schlamp, conductivity in the higher alcohols, 427. Schlundt, on the dielectric constant of liquid hydrocyanic acid, 422. Schmidt, on the radioactivity of thorium, 501. Schonbein, on the passive state, 441. Schultze, action of light on silver salts, 493. Secondary batteries, 492. Secondary cells, 491. Secondary products of electrolysis, 482. Second law of thermodynamics, 78. Second order reactions, 541. 646 INDEX Second order reactions where the masses are not equivalent, 546. Semi-permeable membranes, 219. Semi-permeable membranes prepared by J. Traube, 189. Separation, electrolytic, of the metals, 488. Shields and Ramsay, work on surface- tension, 146. Shields, on hydrolytic dissociation, 303. Side reactions, 559. Silbermann and Favre, work of, 319. Silver salts, action of light on cer- tain, 498. Size of molecules, 44. Smale, work on the gas-battery, 470. Smits, on osmotic pressure, 222. Solids, general properties of, 157. Solids in gases, solutions of, 177. Solids in liquids, solutions of, 186. Solid solutions formed by certain compounds, 311. Solid solutions, properties of, 307. Solids, molecular weights of, 310. Solids, solution of liquids in, 306. Solids, solution of solids in, 306. Solids, solutions of gases in, 305. Solubility and dissociation of electro- lytes, 593. Solubility as affected by an electro- lyte with a common ion, 594. '\f* Solubility deduction of Nernst, 595. Solubility, dissociation as measured by change in, 597. Solubility experiments of Noyes, 596. Solutions, 176. Solutions in solids, 305. Solutions, kinds of, 176. Solutions of gases in gases, 176. Solutions of gases in liquids, 177. Solutions of liquids in gases, 176. Solutions of liquids in liquids, 178. Solutions of solids in gases, 177. Solutions of solids in liquids, 186. Solution-tension, constancy of, 476. Solution-tension, electrolytic, 449. Solution-tension of metals, calcula- tion of the, 474. Solution-tension of metals, demon- stration of, 452. Solution-tensions of metals, difference in, 476. Solvates in general, 249. Solvents, dissociating power of dif- ferent, 421. Solvents, inorganic, which dissociate, 426. Solvents, inorganic, which do not dissociate, 426. Solvents, mixed, conductivity and viscosity in, 431. Solvents, organic, 427. Soret, principle of, 204. Sources of potential in a concentra- tion element, 464. Specific and molecular rotation, 126. Specific gravity of liquids, 139. Specific gravity of liquids, methods of determining, 139. Specific heat of gases, 68. Specific heat of liquids, 111. Specific heat of solids, 171. Specific heat of water, 112. Specific heats, atomic weights from, 10. Specific heats of a gas, determination of the relation between, 75. Specific heats of a gas, ratio between, deduced from the kinetic theory, 76. Specific heats of gases at constant pressure and constant volume, 68. Specific heats of gases, determination of, 69. Specific heats of gases, ratio between, as calculated, 72. Specific heats, relation between com- position and constitution and, 113. Specific refractivity, 117. Specific resistance and specific con- ductivity, 378. Specific volume of liquids, 139. Spectral lines of the elements, rela- tions between, 81. Spectra of gases, 79. Spohr, on the saponification of an ester, 543. Spring, heterogeneous reactions of the first order, 562. Stas, work on atomic weights, 16. Stefan, work on diffusion, 276. Stereoisomerism, effect on acidity, 618. Stieglitz, on the theory of indicators, 293. INDEX 647 Stine, law of mass action applied to hydration, 250. Stokes' equation, 38. Stokes' theory of the RSntgen rays, 500. Strength of current, effect on migra- tion velocity, 372. Strengths of acids and bases, thermo- chemical method of determining the relative, 338. Strong electrolytes, why the Ostwald dilution law does not apply to them, 403. Strouhal and Barus, method of cali- brating a wire, 381. St. v. Laszczynski, work in acetone as the solvent, 428. . Substitution, 420. Substitution an electrical act, 420. Substitution products, organic acids and their, 614. Sulphur and oxygen, effect on acidity, 612. Sulphur dioxide, work of Walden on, as a solvent, 424. Sulphur, from the thermochemical standpoint, 332. Sulphuric acid, dry, does not act on dry sodium, 440. Summary of chemical dynamics, 564. Summary of discussion of equilib- rium, 600. Supersaturated solution, 187. Surface-tension and composition, re- lations between, 143. Surface-tension method of determin- ing molecular weights of pure liquids, 145. Surface-tension, method of measur- ing, 143. Surface-tension of liquids, 143. Symbols, thermochemical, 329. Table of atomic weights, 17. Tammann and Nernst, effect of press- ure on the action of acids on metals, 554. Tammann measured the lowering of vapor-tension, 257. Tammann, on the freezing-points of amalgams, 251. Tammann's method of measuring relative osmotic pressures, 200. Temperature coefficient of conduc- tivity, zero, 435. Temperature coefficients of conduc- tivity, 383. Temperature coefficients of conduc- tivity, bearing of hydrates on, 385. Temperature coefficients of conduc- tivity for a number of substances, magnitude of, 384. Temperature coefficients of conduc- tivity, negative, 434. Temperature, conductivity at high, 409. Temperature, effect of on chemical equilibrium, 591. Temperature, effect of rise in, on ionization, 412. Temperature, effect of rise in, on solubility, 188. Temperature, effect on migration velocities of ions, 373. Temperature, influence of on veloci- ties of reactions, 553. Tensimeter, 583. Tension series, 475. Tetartohedrism, 160. Tetragonal crystal system, 159. Tetrahedral carbon atom, 130. Than, dissociation by heat, 523. Than, vapor-density of ammonium chloride, 66. Thenard, on the hydrogen-chlorine actinometer, 494. Theories to account for catalysis, 534. Theory of electrolytic dissociation, 208. Theory to account for radioactivity, 511. Thermal change, 523. Thermal properties of crystals, 163. Thermochemical measurements, im- portance of, 324. Thermochemical method, 606. Thermochemical methods, 325. Thermochemical results, 331. Thermochemical results with organic compounds, 339. Thermochemical units and symbols, 329. Thermochemistry, 318. Thermochemistry and the conserva- tion of energy, 322. Thermochemistry of benzene, 344. 648 INDEX Thermodynamics, first law of, 72. Thermodynamics, second law of, 78. Thermoneutrality of salt solutions, law of, 319. Thermoneutrality of solutions of salts, explanation of the law of, 337. Thilorier, liquefaction of carbon dioxide, 86. Thilorier's mixture, 86. Third order reactions, 547. Thomsen, Julius, thermochemical measurements, 523. Thomsen, Julius, thermochemical method, 606. Thomsen, Julius, thermochemical method of determining chemical equilibrium, 570. Thomsen, Julius, thermochemical work of, 320. Thomson, dissociating power and dielectric constants of solvents, 437. Thomson, electron theory, radio- activity in terms of, 512. Thomson, on the coagulation of colloids by ions, 287. Thomson overthrows the objection to the electrochemical theory of Berzelius, 351. Thomson shows the arrangement of the electrons within the atom, 42.. Thomson's theory of the relation between the elements, 37. Thorium also radioactive, 501. Thorium and uranium produce radio- active forms of matter, 508. Thorpe and Rodger on viscosity of liquids, 142. Thwing, dielectric constants of liquids, 154. Tolman, on the existence of free ions in solution, 212. Transformation element with meta- stable phase, 590. Transformation element without metastable phase, 590. Transformation of intrinsic energy into electrical, 445. Transformation temperature, deter- mination of, 588. Traube J., densities of solutions, 300. Traube J., prepares semi-permeable membranes, 189. Trevor, on the inversion of cane sugar, 534. Triads of Dobereiner, 19. Triclinic crystal system, 160. Trimolecular reactions, 547. Trimolecular, reactions which are apparently, 548. Tripler, liquefaction of gases, 89. Troost and Hautefeuille, on the sta- bility of silicon tetrachloride, 592. Troost and Hautefeuille, transfor- mations of cyanogen and paro- cyanogen, 568. Trouton's law, 109. Types of cells, 454. Uhler and Jones, spectroscopic work, 241. Uniaxial crystal system, 162. Units in thermochemistry, 329. Unsaturated solution, 187. Uranium and thorium produce radio- active forms of matter, 508. Uranium X, 508. Valence, bearing of Faraday's law on, 481. Van der Waal's equation, 55. Van Marum, electrochemical work of, 347. Van't Hoff and Le Bel, on optical activity, 129. Van't Hoff deduced relation between osmotic pressure and freezing- point lowering, 253. Van't Hoff, method of determining the order of a reaction, 551. Van't Hoff, on condensed systems, 587. Van't Hoff, on solid solutions, 306. Van't Hoff, on the applicability of the gas-laws to osmotic pressure, 208. Van't Hoff, on the saponification of an ester, 543. Van't Hoff, transformation of di- bromsuccinic acid, 541. Vapor-densities, abnormal, 64. Vapor-densities, abnormal, explana- tion of, 65. Vapor-density measurements, results of, 63. INDEX 649 Vaporization, heat of, 109. Vaporization, heat of, at the critical point, 111. Vapor-pressure and-boiling-point of liquids, 99. '•/ Vapor-pressure of amalgams, 269. Vapor-pressure of liquid mixtures, 181. Vapor-pressures of different sub- stances; 100. ' Vapor-tension and osmotic pressure, relations between, 270, 271. Vapor-tension, molecular weights de- termined by the lowering of, 261. Vapor-tension of solvents, lowering of by dissolved substances, 256. Veazey, work in mixed solvents, 435. Vegetable cells used in measuring osmotic pressure, 197. Velocities of ions, 366. Velocities of ions, absolute, 375. Velocities of ions, causes which may affect the relative, 372. Velocities of ions, experimental methods for determining, 368. Velocities of reactions, influences which affect the, 553. Velocities of the complex organic cations, 407. Velocities of the complex organic ions, 406. Velocity of ions, the law of Kohl- rausch used to determine, 392. Velocity of reactions, 531. Velocity of reactions, influence of temperature and pressure on, 553. Victor Meyer, gas-displacement method of, 60. Viscosity, explanation of the increase in, on mixing alcohol and water, 435. Viscosity of liquids, 141. Viscosity of water, why certain salts lower the, 436. Voigtlander, on diffusion in jelly, 276. Volatility and fusibility, 30. Volhard, on equilibrium in first order, homogeneous reactions, 567. Vollmer, conductivity in the alcohols, 427. Voltameter, 365. Volta's discovery of the primary cell, 348. Volume-chemical method, 607. Volumes, atomic, 28. Von der Waals' equation applied to the continuous passage from gas to liquid, 95. Waage and Guldberg, work of, 526. ' Waals, Von der, equation, 55. Walden and Centnerszwer, on sulphur dioxide as a solvent, 425. Walden, on "abnormal electrolytes," 425. Walden, work in non-aqueous sol- vents, 424, 429. Walker and Crum-Brown, electro- synthesis, 490. Walker and Lumsden, boiling-point apparatus, 266. Walker measured the lowering of vapor-tension, 257. Walker, on amphoteric electrolytes, 298. Wanklyn and Robinson, vapor-den- sity of phosphorus pentachloride, 67. Wanklyn showed that dry chlorine does not act on dry sodium, 439. Warburg, cations in fused quartz move, 417. [ester, 543. Warder, on the saponification of an Washburn, on hydration, 250. Water, color demonstration of the dissociating action of, 295. Water, conductivity of, 382. Water, specific heat of, 112. Watson and Rodger, on magnetic rotation, 138. Weak acids and bases, explanation of the results with, 336. Weber; on specific heat of solids, 173. Weber's method of measuring diffu- sion, 274. "*■, Weights combining, law Of* 3. Wentworth and Goodwin, conduc- tivity of fused salts, 419. Wenzel, on the effect of mass, 516. Werner, work in pyridine as the solvent, 429. Weston element, 443. Whetham, method for determining absolute velocities of ions, 377. Wiedemann, E., determines the specific heat of gases, 69. Wiedemann, G., on electrical conduc- tivity of crystals, 164. 650 INDEX Wiedemann, G., work on magnetic property, 138. Wilhelmy enunciates law of reaction velocity, 519. Williamson, on chemical equilibrium, 524. Williamson's theory of electrolysis, 356. Williamson, theory of solutions, 210. Wilson, observation of, 37. Winkler discovers germanium, 34. Wire, calibration of, 381. Wislicenus, light transforms maleiic into fumaric acid, 498. Wislicenus, on citraconic and mesa- conic acids, 619. Wladimiroff measures relative osmotic pressures by means of bacteria, 200. Wroblewski and Olszewski, on the liquefaction of gases, 87. Wurtz shows that an excess of one of the products diminishes dissocia- tion, 68. Zanninovich-Tessarin, work in formic acid, 428. Zelinsky and Krapiwin, conductivity in mixed solvents, 430. Zelinsky and Krapiwin, work in methyl alcohol, 427. Zero temperature coefficient of con- ductivity, 435. Introduction to Physical Chemistry By JAMES WALKER, D.Sc, Ph.D. Professor of Chemistry in University College, Dundee Cloth. 8vo. $3.00, net " This volume by Dr, Walker might well be made the basis of a course of lectures, intended to give students who do not mean to specialize in physical chemistry, a general idea of the subject, while the same course might be taken with profit as an introductory one by those who expect to go farther in the subject. The author has been very successful along the lines that he has laid down, and his book can be recommended heartily." — Journal of Physical Chemistry. Chemical Lecture Experiments By FRANCIS GANO BENEDICT, Ph.D. Instructor in Chemistry in Wesleyan University I 1 2 mo. Cloth. $2.00, net EXTRACTS FROM THE PREFACE The object of this book is primarily to furnish teachers with a large number of reliable lecture experiments. That these experiments require in many cases different treatment from those performed in the laboratory will be obvious when it is considered that the demonstrations on a lecture table must be of sufficient magnitude, and of a character marked enough, to enable the phenomena to be observed at as great a distance as possible. THE MACMILLAN COMPANY 66 FIFTH AVENUE, NEW YORK CHICAGO BOSTON SAN FRANCISCO ATLANTA The Theory of Electrolytic Dissociation AND SOME OF ITS APPLICATIONS By HARRY C. JONES Associate Professor in Physical Chemistry, Johns Hopkins University Cloth. i2mo. $1.60, net "I have tried several of the German works, small and large, and I have no hesitation in saying that Professor Jones' presentation is the simplest, clearest, and most adequate in any language." — Professor S. F. Barker, Johns Hopkins University. " It is a text-book which will supply a long-felt want to teachers who have to do with students unfamiliar with the German language. . . . The examples chosen are apt, well described, and clearly explained. With this book and Professor Walker's Introduction to Physical Chemistry our students have now a remarkably good presentation of the subject in English." — Professor J. W. Walker, McGill University. Outlines of Industrial Chemistry A TEXT-BOOK FOR STUDENTS By FRANK HALL THORP, Ph.D. Massachusetts Institute of Technology New Edition, Fully Revised. Cloth. 8vo. $3.50 " I have examined it carefully and think it a most excellent book, meeting a want I have long felt in my higher classes. I have introduced it in this year's classes." — Professor Chas. E. Coates, Louisiana State University. " I feel no hesitation in saying that it is the best book for the purpose intended that it has been my good fortune to examine. It fills a very great need for a compact text-book in Technological Chemistry, and I am sure its use will be extensive. It reaches the standard of Dr. Thorp's usual excellent work in chemistry." — Professor Charles Baskerville, Univ. of North Carolina. THE MACMILLAN COMPANY 66 FIFTH AVENUE, NEW YORK BOSTON CHICAGO SAN FRANCISCO ATLANTA mm m 4 ■ ■