OUTLINES OF PHYSIGAL CHEMISTRY G. SENTER lEXT-BOOEa OF : SClfc^^.^ LIBRARY OF THE NEW YORK STATE COLLEGE OF HOME ECONOMICS CORNELL ITHACA, UNlVERSITf NEW YORK Cornell University Library QD 453.S47 Outlines of physical cliemistry 3 1924 002 980 054 M\\\ Cornell University WB Library The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002980054 OUTLINES OF PHYSICAL CHEMISTRY OUTLINES OF PHYSICAL CHEMISTRY G, SENTER, D.Sc. (Lond.), Ph.D. (Leipzig) LECTURER ON CHEMISTRY AT ST. MARY's HOSPITAL, UNIVERSITY OF LONDON LECTURER ON PHYSICAL CHEMISTRY, CASS TECHNICAL INSTITUTE, ALDGATE; FORMERLY EXAMINER IN CHEMISTRY TO THE ROYAL COLLEGE OF PHYSICIANS OF LONDON AND THE ROYAL COLLEGE OF SURGEONS OF ENGLAND SECOND EDITION, REVISED NEW YORK D. VAN NOSTRAND COMPANY 23 Murray and 27 Warren Sts. 1911 ri PREFACE TO FIRST EDITION THE present book is intended as an elementary in- troduction to Physical Chemistry. It is assumed that the student taking up the study of this subject has already an elementary knowledge of chemistry and phy- sics, and comparatively little space is devoted to those parts of the subject with which the student is presumed to be familiar from his earlier work. Physical chemistry is now such an extensive subject that it is impossible even to touch on all its important applications within the limits of a small text-book. I have therefore preferred to deal in considerable detail with those branches of the subject which usually present most difficulty to beginners, such as the modern theory of solutions, the principles of chemical equilibrium, elec- trical conductivity and electromotive force, and have devoted relatively less space to the relationships between physical properties and chemical composition. The prin- ciples employed in the investigation of physical proper- ties from the point of view of chemical composition are illustrated by a few typical examples, so that the student should have little difficulty in understanding the special works on these subjects. Electrochemistry is dealt with iv OUTLINES OF PHYSICAL CHEMISTRY rather more fully than has hitherto been usual in ele- mentary works on Physical Chemistry, and the book is therefore well suited for electrical engineers. From my experience as a student and as a teacher, I am convinced that one of the best methods of familiarising the student with the principles of a subject is by means of numerical examples. For this reason I have, as far as possible, given numerical illustrations of those laws and formulae which are likely to present difficulty to the be- ginner. This is particularly important with regard to cer- tain formulae — more particularly those in the chapter on Electromotive Force — which cannot easily be proved by simple methods, but which even the elementary student must make use of. The really important thing in this connection is not that the student should be able to prove the formula, but that he should thoroughly understand its meaning and applications. I have throughout the book used only the most ele- mentary mathematics. In order to make use of some of the formulae, particularly those in the chapters on Velo- city of Reaction and Electromotive Force, an elementary knowledge of logarithms is required, but sufficient for the purpose can be gained by the student, if necessary, from a few hours' study of the chapter on " Logarithms " in any elementary text-book on Algebra. The experiments described in the sections headed " Practical Illustrations " at the conclusion of the chap- ters can in most cases be performed with very simple apparatus, and as many as possible should be done by the student. The majority of them are also well adapted for lecture experiments. The more elaborate experi- PREFACE V merits which are usually performed during a course of practical Physical Chemistry are also mentioned for the sake of completeness ; for full details a book on Practical Physical Chemistry should be consulted. In drawing up my lectures, which have developed into the present book, I have been indebted most largely to the text-books of my former teachers, Ostwald and Nernst, more particularly to Ostwald's Allgemeine Chemie (2nd Edition, Leipzig, Engelmann) and to Nernst's Theo- retical Chemistry (4th Edition, London, Macmillan).^ The following works, among others, have also been consulted : Van't Hoff, Lectures on Physical Chemistry ; Arrhenius, Theories of Chemistry ; Le Blanc, Electrochemistry; Dan- neel, Elektrochemie (Sammlung Goschen) ; Roozeboom, Phasenlehre ; Findlay, The Phase Rule; Mellor, Chemi- cal Statics and Dynamics; Abegg, Die elektrolytische Dissociationstheorie. In these books the student will find fuller treatment of the different branches of the subject. References to other sources of information on particular points are given throughout the book. The importance of a study of original papers can scarcely be overrated, and I have given references to a number of easily accessible papers, both in English and German, some of which should be read even by the beginner. In the summarising chapter on " Theories of Solution" references are given which will enable the more advanced student to put himself abreast of the pre- sent state of knowledge in this most interesting subject. In conclusion, I wish to express my most sincere thanks to Assistant-Professor A. W. Porter, of University ' The fifth German edition of Nernst's text-book has now appeared. vi OUTLINES OF PHYSICAL CHEMISTRY College, London, for reading and criticising the sections on osmotic pressure and allied phenonmena, and for valu- able advice and assistance on many occasions ; also to Dr. H. Sand, of University College, Nottingham, and Dr. A. Slator, of Burton, for criticising the chapters on Electromotive Force and on Velocity of Reaction respec- tively. Lastly, I wish to acknowledge my indebtedness to my assistant, Mr. T. J. Ward, in the preparation of the diagrams and for reading the proofs. G. S. November, 1908 PREFACE TO SECOND EDITION AS less than two years have elapsed since the appear- ance of the first edition, only a few slight altera- tions have been rendered necessary by the progress of the subject in the interval. The opportunity has, how- ever, been taken to revise the text thoroughly ; in one or two places the wording has been slightly altered for the sake of greater clearness, and some misprints have been corrected. A few additions of some importance have also been made. In conformity with the elementary character of the book, the mathematical proofs of the connection be- tween osmotic pressure and the other properties of solu- tions which can be made use of for molecular weight determinations were omitted from the first edition. The book has, however, been more largely used by advanced students than was anticipated, and at the request of several teachers the proofs in question have now been inserted — as an appendix to Chapter V. The section dealing with the relationship between physical properties and chemical constitution has been rendered more com- plete by the insertion of brief accounts of absorption spectra and of viscosity. viii OUTLINES OF PHYSICAL CHEMISTRY I am again indebted to Professor Porter for much kind advice and assistance, and take this opportunity of expressing to him my grateful thanks. I wish also to acknowledge my indebtedness to a number of friends and correspondents, more particularly to Dr. A. Lapworth, F.R.S., Dr. J. C. Philip, Dr. A. E. Dunstan, Dr. W. Maitland and Mr. W. G. Pirie, M.A., for valuable sug- gestions. G. S. December, igio. TABLE OF CONTENTS {The numbers refer to pages) CHAPTER I PAGE FUNDAMENTAL PRINCIPLES OF CHEMISTRY. THE ATOMIC THEORY . . . . i Elements and compounds, i — Laws of chemical combination, 3 — Atoms and molecules, 5 — Fact. Generalisation or natural law. Hypothesis. Theory, 6 — Determination of atomic weights. General, 8 — Volumetric method. Gay-Lussac's law of volumes. Avogadro's hypothesis, 9 — Dulong and Petit's law, 11 — Isomorphism, 13 — Determination of atomic weights by chemical methods, 14 — Relation between atomic weights and chemical equivalents. Valency, 15 — The values of the atomic weights, 16 — The periodic system, 20. CHAPTER II GASES 25 The gas laws, 25 — Deviations from the gas laws, 28 — Kinetic theory of gases. General, 29 — Kinetic equation for gases, 30 — Deduction of gas laws from the equation pv = Imnc^, 31 — Van der Waals' equation, 33 — Avogadro's hypothesis and the molecular weight of gases. General, 36 — Density and molecular weight of gases and vapours, 36 — Results of vapour density determinations. Abnormal molecular weights, 40 — Association and dissociation in gases, 41 — Ac- curate determination of molecular and atomic weights from gas densities, 42 — Specific heat of gases. General, 43 — ix X OUTLINES OF PHYSICAL CHEMISTRY PAGE Specific heat at constant pressure, Cy, and constant volume, C„, 44 — Specific heat of gases and the kinetic theory, 46 — Experimental illustrations, 47. CHAPTER III LIQUIDS 49 General, 49 — Transition from gaseous to liquid state. Critical phenomena, 49 — Behaviour of gases on compression, 51 — Application of Van der Waals' equation to critical pheno- mena, S3 — Law of corresponding states, 56 — Liquefaction of gases, 58 — Relation between physical properties and chemi- cal composition of liquids. General, 59 — Atomic and mole- cular volumes, 60 — Additive, constitutive, and coUigative properties, 62 — Refractivity, 63 — Rotation of plane of polarization of light, 66 — Absorption of light, 6g — Viscosity, 73 — Practical illustrations, 77 CHAPTER IV SOLUTIONS 80 General 80 — Solution of gases in gases, 81 — Solubility of gases in liquids, 82 — Solubility of liquids in liquids, 84 — Distilla- tion of homogeneous mixtures, 87 — Distillation of non- miscible or partially miscible liquids ; steam distillation, go — Solution of solids in liquids, gi — Effect of change of tem- perature on the solubility of solids in liquids, 92 — Relation between solubility and chemical constitution, 94 — Solid solutions, 94 — Practical illustrations, 95. CHAPTER V DILUTE SOLUTIONS 97 General, 97 — Osmotic pressure. Semi-permeable membranes, 97 — Measurement of osmotic pressure, 99 — Van't Hoff's theory of solution, loi — Recent direct measurements of osmotic pressure, 104 — Other methods of determining osmo- tic pressure, 105 — Mechanism of osmotic pressure, 106 — Osmotic pressure and diffusion, 108 — Molecular weight of dissolved substances. General, 109 — Molecular weights TABLE OF CONTENTS xi PAGE from osmotic pressure measurements, no — Lowering of vapour pressure, in — Elevation of boiling-point, 114 — Ex- perimental determination of molecular weights by the boiling-point method, 116 — Depression of the freezing-point, iig — Experimental determination of molecular weights by the freezing-point method, lao — Results of molecular weight determinations in solution. General, 121 — Abnormal mole- cular weights, 123 — Molecular weight of liquids, 125 — Col- loidal solutions, 127 — Practical illustrations, 129. Mathema- tical deduction of formulae, 131. CHAPTER VI THERMOCHEMISTRY 139 General, 139 — Hess's law, 141 — Representation of thermo- cheraical measurements. Heat of formation, 143 — Heat of combustion, 145 — -Thermochemical methods, 145 — Results of thermochemical measurements, 147 — Relation of chemi- cal affinity to heat of reaction, 148 — Practical illustrations, 153- CHAPTER VII EQUILIBRIUM IN HOMOGENEOUS SYSTEMS. LAW OF MASS ACTION . . . .154 General, 154 — Law of mass action, 155 — Strict proof of the law of mass action, 160 — Decomposition of hydriodic acid, 161 — Dissociation of phosphorus pentachloride, 163 — Equili- brium in solutions of non-electrolytes, 164 — Influence of temperature and pressure on chemical equilibrium. General, 166 — Le Chatelier's theorem, iSg — Relation between chemi- cal equilibrium and temperature. Nernst's views, i6g Practical illustrations, 170. CHAPTER VIII HETEROGENEOUS EQUILIBRIUM. THE PHASE RULE 172 General, 172 — Application of law of mass action to hetero- geneous equilibrium, 172 — Dissociation of salt hydrates, 174 xii OUTLINES OF PHYSICAL CHEMISTRY PAGE — Dissociation of ammonium hydrosulphide, 176 — Analogy between solubility and dissociation, 177 — Distribution of a solute between two immiscible liquids, 177 — The phase rule. Equilibrium between water, ice and steam, 179 — Equilibrium between four phases of the same substance. Sulphur, 183 — Systems of two components. Salt and water, 186 — Freezing mixtures, iSg — Systems of two components. General, igo — Hydrates of ferric chloride, 194 — Transition points, 197 — Practical illustrations, 197. CHAPTER IX VELOCITY OF REACTION. CATALYSIS . . 200 General, 200 — Unimolecular reaction, 202 — Other unimolecular reactions, 205 — Bimolecular reactions, 207 — Trimolecular reactions, 2og — Reactions of higher order. Molecular- kinetic considerations, 211 — Reactions in stages, 212 — Determination of the order of a reaction, 213 — Complicated reaction velocities, 215 — Catalysis. General ,217 — Charac- teristics of catalytic actions, 217 — ^Examples of catalytic action. Technical importance of catalysis, 2ig — Biological importance of catalysis. Enzyme reactions, 221 — Mechan- ism of catalysis, 222 — Nature of the medium, 224 — Influence of temperature on the rate of chemical reaction, 225 — Formulae connecting reaction velocity and temperature, 228 — Practical illustrations, 229. CHAPTER X ELECTRICAL CONDUCTIVITY . . . .234 General, 234 — Electrolysis of solutions. Faraday's laws, 236-— Mechanism of electrical conductivity, 238 — Freedom of the ions before electrolysis, 240 — Dependence of conductivity on the number and nature of the ions, 242 — Migration velocity of the ions, 243 — Practical determination of the relative migration velocities of the ions, 246 — Specific, molecular and equivalent conductivity, 249 — Kohlrausch's law. Ionic velocities, 251 — Absolute velocity of the ions. Internal TABLE OF CONTENTS xiii PAGE friction, 253 — Experimental determination of conductivity of elect'olytes, 254 — Experimental determination of molecular conductivity, 257 — Results of conductivity measurements, 258 — Electrolytic dissociation, 260 — Degree of ionisation from conductivity and osmotic pressure measurements, 261 — Effect of temperature on conductivity, 263 — Practical illustrations, 264. CHAPTER XI EQUILIBRIUM IN ELECTROLYTES. STRENGTH OF ACIDS AND BASES. HYDROLYSIS . 266 The dilution law, 266 — Strength of acids, 269 — Strength of bases, 274 — Mixture of two electrolytes with a common ion, 276 — Isohydric solutions, 277 — Mixture of electrolytes with no common ion, 278 — Dissociation of strong electrolytes, 279 — Electrolj^ic dissociation of water. Heat of neutrali- sation, 283 — Hydrolysis, 285 — Hydrolysis of the salt of a strong base and a weak acid, 287 — Hydrolysis of the salt of a weak base and a strong acid, 290 — Hydrolysis of the salt of a weak base and a weak acid, 292 — Determination of the dissociation constant for water, 293 — Theory of indica- tors, 296 — The solubility product, 298 — Applications to analytical chemistry, 300 — Experimental determination of the solubility of difficultly soluble salts, 301 — Complex ions, 303 — Influence of substitution on degree of ionisation, 304 — Reactivity of the ions, 306 — Practical illustrations, 307- CHAPTER XII THEORIES OF SOLUTION 313 General, 313 — Evidence in favour of the electrolytic dissociation theory, 315 — Ionisation in solvents other than water, 317 — The old hydrate theory of solution, 319 — Mechanism of electrolytic dissociation. Function of the solvent, 322 — Hydration in solution, 325. XIV OUTLINES OF PHYSICAL CHEMISTRY CHAPTER XIII PAGl ELECTROMOTIVE FORCE 32S The Daniell cell, 328 — Relation between chemical and electrical energy, 331 — Measurement of electromotive force, 334 — Standard of electromotive force. The cadmium element, 336 — Solution pressure, 338 — Calculation of electromotive force at a junction metal/salt solution, 340. Differences of potential in a voltaic cell, 342 — Influence of change of con- centration of salt solution on the E.M.F. of a cell, 345 — Concentration cells, 347 — Cells with different concentrations of the electrode materials (substances producing ions), 351 — Electrodes of the first and second kind. The calomel elec- trode, 353 — Single potential differences. The capillary electrometer, 358 — Potential differences at junction of two liquids, 362 — Gas cells, 364 — Potential series of the ele- ments, 366 — Cells with different gases, 369 — Oxidation- reduction cells, 370 — Electrolysis and polarization, 373 — Separation of ions (particularly of metals) by electrolysis, 375 — The electrolysis of water, 376 — Accumulators, 377 — The electron theory, 378 — Practical illustrations, 381, DEFINITIONS AND UNITS^ In this section the centimetre-gram-second (C.O.S.) system of units is used throughout, length being measured in centimetres (cms.), mass in grams, and time in seconds. Density is mass per unit volume : unit, gram per c.c. (cubic centi- metre). Specific Volume (i/density) is volume per unit mass : unit, c.c. per gram. Velocity is rate of change of position : unit, cm. per sec. or cm./sec. Acceleration is rate of change of velocity : unit, cm. per sec. per sec. or cm./sec.''. Momentum is mass x velocity : unit, gram-cm. per sec. Force is mass x acceleration (rate of change of momentum). Unit, the dyne, is that force which is required to produce an acceleration of i cm. per sec. per sec. in a mass of i gram. As a gram-weight, falling freely, obtains an acceleration of g8o'6 cm. per sec. (owing to the attraction of the earth) the force represented by the gram-weight = g8o'6 dynes at a latitude of 45° and at sea-level. Energy may be defined as that property of a body which diminishes when work is done by the body ; and its diminution is measured by the amount of work done. Work Done is force x distance (the work done by a force is measured by the product of the force and the distance through which the point of application moves in the direction of the force). The unit of work ' The more important constants made use of in physical chemistry are collected here for convenience of reference. b XV xvi OUTLINES OF PHYSICAL CHEMISTRY (which is also the unit of energy) is the dyne-centimetre or erg. The gram-centimetre unit is sometimes used; i gram-centimetre = g8o'6 ergs ; also the joule (= lo' ergs) is frequently used, especially in electrical work (see below). Power is rate of doing work, unit, erg per second. There are six chief forms of energy: (i) mechanical energy, (2) volume energy, (3) electrical energy, (4) heat, (5) chemical energy, (6) radiant energy. These forms of energy are mutually convertible, and according to the law of conservation of energy, there is a definite and invariable relationship between the quantity of one kind of energy which disappears and that which results. The unit of energy, the erg, has already been defined. It is some- times convenient to express certain forms of energy in special units, heati for example, in calories ; in the following paragraphs the equivalents in ergs of these special units are given. Volume Energy is often measured in litre-atmospheres. When a volume, »!, of a gas expands to the volume v^ against a constant pressure p, say that of the atmosphere, the external work done by the gas (gained) is p (^2 - fj. The (average) pressure of the atmosphere on unit area (i sq. cm.) supports a column of mercury 76 cm. high and i sq. cm. in cross-section. Hence the pressure on i sq. cm. = 76 x I3'596 = I033'3 grams weight (as the density of mercury is I3'596), or I033'3 x 980-6 = 1,013,200 dynes. As the work done is the product of the constant pres- sure and the increase of volume, i litre-atmosphere (the work done when the increase in the volume of a certain quantity of a gas is i litre or 1000 c.c.) = 1,013,200 X 1000 = 1,013,200,000 ergs. Electrical Energy is the product of electromotive force and quantity of electricity, and is usually measured in volt-coulombs or joules. The practical unit of quantity of electricity is the coulomb ; it is that quantity of electricity which under certain conditions liberates o'ooiiiS grams of silver from a solution of silver nitrate. If a coulomb passes through a conductor in i second, the strength of current is i ampere ; the latter is therefore the practical unit of strength of current. The practical unit of resistance is the ohm, which is the resistance at 0° offered by a column of mercury io6-3 cm. long and weighing I4'452i grams. The practical unit of electromotive force is the volt; when a current of r ampere passes in I second through a conductor of resistance i ohm, the electromotive force is I volt. DEFINITIONS AND UNITS xvii The definitions of the C.G.S. units of electromotive force, current strength and resistance are to be found in text-books of physics, and cannot be given here. It can be shown that i ohm = lo' C.G.S. units and i ampere = i/io C.G.S. unit; hence, by Ohm's law, i volt = lo' C.G.S. units. Further, t volt-coulomb or i joule = lo' x lo-i = lo' C.G.S. units or lo' ergs. Heat Energy is measured in calories. The mean calorie is i/ioo of the amount of heat required to raise i gram of water from o to ioo° and does not differ much from the amount of heat required to raise i gram of water from 15° to 16°. i calorie = 42,650 gram-centimetres = 41,830,000 ergs (the mechanical equivalent of heat) = 4"i83 joules. One joule = o'23gi calories. There is no special unit for chemical energy ; it is usually measured in volt-coulombs or calories. The value of R, in the general gas equation (p. 27) for a mol of gas = 84,760 gram-centimetres = 83,150,000 ergs = i-gg calories approximately. OUTLINES OF PHYSICAL CHEMISTRY CHAPTER I FUNDAMENTAL PRINCIPLES OF CHEMISTRY. THE ATOMIC THEORY Elements and Compounds — Definite chemical substances are divided into the two classes of elements and chemical com- pounds. Boyle, and later Lavoisier, defined an element as a substance which had not so far been split up into anything simpler. The substances formed by chemical combination of two or more elements were termed chemical compounds. This definition proved to be a very suitable one, and retained its value even when many of the substances classed as ele- ments by Lavoisier proved to be complex. In course of time it came to be recognised that the substances which resisted further decomposition possessed certain other properties in com- mon, for example, the so-called atomic heat of solid elements proved to be approximately 6*4 (p. 12), and it was found possible to assign even newly-discovered elements with more or less certainty to their appropriate positions in the periodic table of the elements p. 21). There are, therefore, conclusive reasons, apart from the fact that they have so far resisted decomposi- tion, for regarding elements as of a different order from chemical compounds, and these reasons remain equally valid when full allowance is made for the remarkable discoveries of the last few years in this branch of knowledge. 2 OUTLINES OF PHYSICAL CHEMISTRY Until lately no case of the transformation of one element into another was known, but recent work on radium, by Ramsay and Soddy and others, has shown that this element is continuously undergoing a series of transformations, one of the final products of which is the inactive gas helium. It might at first sight be supposed that the old view of the impossibility of transforming the elements could be maintained, radium being looked upon as a chemical compound of helium with another element, but further consideration shows that this suggestion is not tenable, as radium fits into the periodic table, and, so far as is known, possesses all those other properties which have so far been con- sidered characteristic of elements as distinguished from chemical compounds. Evidence is gradually accumulating which indicates that the slow disintegration, with final production of other elements, is not confined to radium alone, but is shown more particularly by certain elements of high atomic weight such as uranium and thorium. It is true that the change is spontaneous, as so far there is no known means of initiating it or even of influencing its rate, but further progress in this direction is doubtless only a matter of time. As the phenomenon in question is probably a general one, it seems desirable to retain the term " element " to indicate a substance which has a definite position in the periodic table, and has the other properties usually regarded as characteristic of elements. From what has been said, it will be evident that it is difficult to define an element in a few words, but in practice there will probably not be much difficulty in drawing the distinction .between elements and compounds. Ostwald i ( 1 907) defines an element as a substance which only increases in weight as the result of a chemical change, and which is stable under any attainable conditions of temperature and pressure, but in this definition the question of radio-active substances is left out of account. ' Prinzipien der Chemie, Leipzig, 1907, p. 266. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 3 Laws of Chemical Combination — Towards the end of the eighteenth century, Lavoisier established experimentally the law of the conservation of mass, which may be expressed as follows: When a chemical change occurs, the total weight {or mass) of the reacting substances is equal to the total weight {or mass) of the products. As the weight is proportional to the mass or quantity of matter, the above law may also be stated in the form that the total quantity of matter in the uni- verse is not altered in consequence of chemical (or any other) changes. It is, of course, impossible to prove the law with absolute certainty, but the fact that in accurate atomic weight determinations no results in contradiction with it have been obtained shows that it is valid at least within the limits of the unavoidable experimental error. The enunciation of the law of the conservation of mass by Lavoisier, and the extended use of the balance, facilitated the investigation of the proportions in which elements combine, and soon afterwards the first law of chemical combination was estab- lished by the careful experimental investigations of Richter and Proust. This law is usually expressed as follows : — A definite compound always contains the same elements in the same proportions. The truth of this law was called in question by the famous French chemist Berthollet. Having observed that chemical processes are greatly influenced by the relative amounts of the reacting substances (p. 155), he contended that when, for example, a chemical compound is formed by the combination of two elements, the proportion of one of the elements in the compound will be the greater the more of that element there is available. This suggestion led to the famous controversy between Berthollet and Proust (1799- 1807), which ended in the firm establishment of the law of constant proportions. All subsequent work has shown that the law in question is valid within the limits of experimental error. In certain cases, elements unite in more than one proportion 4 OUTLINES OF PHYSICAL CHEMISTRY to form definite chemical compounds. Thus Dalton found by analysis that two compounds of carbon and hydrogen — methane and ethylene — contain the elements in the ratios 6 : 2 and 6 : i by weight respectively ; in other words, for the same amount of carbon, the amounts of hydrogen are in the ratio 2 : i. Similar simple relations were observed for other compounds, and on this experimental basis Dalton (1808) formulated the Law of Multiple Proportions, as follows : — When two elements unite in more than one proportion, for a fixed amount of one element there is a simple ratio between the amounts of the other element. Dalton's experimental results were not of a high order of accuracy, but the validity of the law was proved by the subsequent investigations of Berzelius, Marignac and others. Finally, there is a third comprehensive law of combination, which includes the other two as special cases. It has been found possible to ascribe to each element a definite relative weight, with which it enters into chemical combination. The Law of Combining Proportions, which expresses this conception, is as follows : — Elements combine in the ratio of their combining weights, or in simple multiples of this ratio. The combining weights are found by analysis of definite com- pounds containing the elements in question. When the com- bining weight of hydrogen is taken as unity, the approxi- mate values for chlorine, oxygen and sulphur are 3S"Si 8 and 16 respectively. These numbers also represent the ratios in which the elements displace each other in chemical com- pounds. Water, for example, contains 8 parts by weight of oxygen to i of hydrogen, and when the former element is dis- placed by sulphur (forming hydrogen sulphide) the new com- pound is found to contain 16 parts by weight of the latter element. 16 parts of sulphur are therefore equivalent to 8 parts of oxygen, and the combining weights are therefore often termed chemical equivalents. The chemical equivalent of an element is FUNDAMENTAL PRINCIPLES OF CHEMISTRY 5 that quantity of it which combines with, or displaces, one part (strictly i-oo8 parts) by weight of hydrogen {cf. p. 18). It must be clearly understood that the above generalisations or laws are purely experimental ; they express in a simple form the results of the investigations of many chemists on the com- bining powers of the elements, and are quite independent of any hypothesis as to the constitution of matter. As they have been established by experiment, we are certain of their validity only within the limits of the unavoidable experimental error, and cannot say whether they are absolutely true. It is possible that when the methods of analysis are greatly improved, it will be possible to detect small variations in the composition of definite compounds, but up to the present the most careful investigations, in the course of atomic weight determinations, have failed to show any deviation from the results to be expected according to the laws. Atoms and Molecules — The question now arises as to whether a theory can be suggested which allows of a convenient and consistent representation of the laws enunciated above. The atomic theory, first brought forward in its modern form by Dalton (1808), answers these requirements. Following out an idea of the old Greek philosophers, Dalton suggested that matter is not infinitely divisible by any means at our disposal, but is made up of extremely small particles termed atoms ; the atoms of any one element are identical in all respects and differ, at least in weight, from those of other elements. By the association of atoms of different kinds, chemical compounds are formed. The laws of chemical combination find a simple explanation on the atomic theory. Since a chemical compound is formed by the association of atoms, each of which has a definite weight, it must be of invariable composition. Further when atoms combine in more than one proportion, for a fixed amount of atoms of one kind the amount of the other must in- crease in steps, depending on the relative atomic weight — which is the law of multiple proportions. It is here assumed that 6 OUTLINES OF PHYSICAL CHEMISTRY the ultimate particles of a compound are formed by the associa- tion of comparatively few atoms, and this holds in general for inorganic compounds. Finally, the law of combining weights is also seen to be a logical consequence of the atomic theory, the empirically found combining weights, or chemical equiva- lents, bearing a simple relation to the (relative) weights of the atoms (p. is). When Dalton brought forward the atomic theory, the number of facts which it had to account for was comparatively small. As knowledge has progressed, the atomic theory has proved capable of extension to represent the new facts, and its applica- tion has led to many important discoveries. At the present day, the great majority of chemists consider that the atomic theory has by no means outgrown its usefulness. Fact. Generalisation of Natural Law. Hypothesis. Theory^ — Chemistry, like most other sciences, is based on facts, established by experiment. A few such facts have already been mentioned, for example, that certain chemical compounds, which have been investigated with the greatest care, always contain the same elements in the same proportions. A mere collection of facts, however, does not constitute a science. When a certain number of facts have been established, the chemist proceeds to reason from analogy as to the behaviour of systems under conditions which have not yet been investigated. For example, Proust showed by careful analyses that there are two well-defined oxides of tin, and that the composition of each is invariable. From the results of these and a few other investigations, he cotx\\xA&A from analogy that the composition of all pure chemical compounds is invariable, although of course very few of them had then been investigated from that point of view. To proceed in this way is to generalise, and the short statement of the conclusion arrived at is termed 9. generalisation 1 H. Poincar6, ha Science et I'Hypothese, Paris, Flammarion ; Ostwald, Vorlesungen iiber Naturphilosophie, Leipzig, 1902; Alexander Smith, General Inorganic Chemistry, London, igo6. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 7 or law. It will be evident that a law is not in the nature of an absolute certainty ; it comprises the facts experimentally estab- lished, but also enables us (and herein lies its value) to foretell a great many things which have not been, but which if necessary could be, investigated experimentally. The greater the number of cases in which a law has been found to hold, the greater is the confidence in its validity, until finally a law may attain practically the same standing as a statement of fact. We may confidently expect that however greatly our views regarding natural pheno- mena may change, such generalisations as the law of constant proportions will remain eternally true. Natural laws can be discovered in two ways : (i) by corre- lating a number of experimental facts, as just indicated ; (2) by a speculative method, on the basis of certain hypotheses as to the nature of the phenomena in question. The meaning to be at- tached to the term " hypothesis " is best illustrated by an example. In the previous section we have seen that the laws of chemical combination are accounted for satisfactorily on the view that matter is made up of extremely small, discrete particles, the atoms. Such a mechanical representation, which is more or less inaccessible to experimental proof, is termed a hypothesis A hypothesis may then be defined as a mental picture of an unknown, or largely unknown, state of affairs, in terms of some- thing which is better known. Thus, the state of affairs .in gases, which is and will remain unknown to us, is represented, according to the kinetic theory, in terms of an enormous number of rapidly moving perfectly elastic particles, and on this basis it is possible, with the help of certain assumptions, to deduce certain of the laws which are actually followed by gases (p. 25). There does not appear to be any fundamental distinction in the use of the terms hypothesis and theory. A theory may be defined as a hypothesis, many of the deductions from which have been confirmed by experiment, and which admits of the con- venient representation of a large number of experimental facts. There is some difference of opinion as to the value of 8 OUTLINES OF PHYSICAL CHEMISTRY hypotheses and theories for the advancement of science.^ The majority of scientists, however, appear to consider that the advantages of hypotheses, regarded in the proper light and not as representing the actual state of affairs, are much greater than the disadvantages. Boltzmann,^ indeed, maintains that "new discoveries are made almost exclusively by means of special mechanical conceptions". DETERMINATION OF ATOMIC WEIGHTS General — After the laws of chemical combination had been established, the next problem with which chemists had to deal was the determination of the relative atomic weights of the elements. This might apparently be done by fixing on one element, say hydrogen, as the standard ; a compound containing hydrogen and another element may then be analysed, and the amount of the other element combined with one part of hydrogen will be its atomic weight. It is clear, however, that this will be the case only when the binary compound contains one atom of each element, and it was just this difficulty of deciding the relative number of atoms of the two elements present that rendered the decision between a number and one of its multi- ples or sub-multiples so difficult. It has already been pointed out that the amount of an ele- ment which combines with, or displaces, part by weight of hydrogen (strictly speaking, 8 parts by weight of oxygen) is termed the combining weight or chemical equivalent of an ele- ment. The first step in determining the atomic weight of an element is to find the chemical equivalent as accurately as pos- sible by analysis and then to find the relation between the atomic weight and chemical equivalent by one of the methods described below. The atomic weight may be equal to, or a simple multiple of, the chemical equivalent. ' In one or two recent books, Ostwald has treated certain branches of chemistry on a system free from hypotheses. " Gas Tkeorie, Leipzig, 1896, p. 4. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 9 Dalton, working on the assumption that when two elements unite in only one proportion one atom of each is present, drew up the first table of atomic weights. Water was found by analysis to contain i part of hydrogen to 8 parts of oxygen by weight ; the atomic weight of oxygen was therefore taken as 8. In the same way, since ammonia contained i part of hydrogen to 4"6 parts of nitrogen, the atomic weight of the latter element was taken as 4"6. Great advances in this subject were then made by the Swedish chemist Berzelius. For fixing the pro- portional numbers, he depended to some extent, like Dalton, on the assumption of simplicity of composition, but was able to check the numbers thus obtained by the application of Gay- Lussac's law of volumes and Dulong and Petit's law. Later still, the discovery of isomorphism by Mitscherlich afforded yet another means of checking the atomic weights. Besides these physical methods, chemical methods may also be used for fixing the atomic weights of the elements. Each of these methods will now be shortly referred to. {a) YolametFic Method. Gay-Lussac's Law of Yolumes. Avogadro's Hypothesis — Gay-Lussac, on the basis of an extensive series of experiments on the combining volumes of gases, established the law of gaseous volumes, which may be expressed as follows : — Gases combine in simple ratios by volume, and the volume oj the gaseous product bears a simple ratio to the volumes of the re- acting gases, when measured under the same conditions. A few years before, the same chemist had discovered that all gases behave similarly with regard to changes of pressure and temperature, and this fact, taken in conjunction with the law of volumes and the atomic theory, seemed to point to some simple relation between the number of particles in equal volumes of different gases. Berzelius suggested that equal volumes of different gases, under corresponding conditions of temperature and pressure, contain the same number of atoms. It was soon found, however, that this assumption was untenable, and the lo OUTLINES OF PHYSICAL CHEMISTRY view held at the present day was first enunciated by the Italian physicist Avogadro. He drew a distinction between atoms, the smallest particles which can take part in chemical changes, and molecules, the smallest particles which can exist in a free con- dition, and expressed his hypothesis as follows : — Equal volumes of all gases, under the same conditions of temperature and pressure, contain the same number of molecules. In expressing the results of determinations of the densities of different gases, hydrogen, as the lightest gas, is taken as standard, and the number expressing the ratio of the weights of equal volumes of another gas (or vapour) and hydrogen, measured under the same conditions, is the density of the gas (or vapour density in the case of a vapour). From Avogadro's h)rpothesis it follows at once that the ratio of the vapour densities of another gas and hydrogen, being a comparison of the relative weights of an equal number of molecules, is also the ratio of the molecular weights. It is usual to refer both atomic and mole- cular weights to the atom of hydrogen as unity,i and therefore the molecular weight, being referred to a standard half that to which the vapour density is referred, is double the vapour density. When the molecular weight is known, it is a comparatively simple matter to establish the atomic weight. As an example, we may employ the volumetric method to fix the atomic weight of beryllium, a matter of great historical interest. It was found by analysis that beryllium chloride contains 4^55 parts of beryllium to 35 '5 parts of chlorine by weight; in other words, the chemi- cal equivalent of beryllium is 4"S5. If beryllium be regarded as a bivalent metal (p. 16), the formula for the chloride will be BeClg, and its atomic weight 2 x 4-55 = 9"i. If, however, it is trivalent, the formula for the chloride must be BeClj, and, to obtain the ratio for Be : CI found experimentally, its atomic weight must be 4'55 X 3 = i3'6S- "The vapour density of the chloride was de- termined by Nilson arid Petterson, and from the result the mole- cular weight calculated as 8o'i. The molecule of beryllium 1 Strictly speaking, to the atom of oxygen as 16 (p. 18). FUNDAMENTAL PRINCIPLES OF CHEMISTRY ii chloride cannot therefore contain more than 35-5 x 2 = 71 parts of chlorine, the formula for the chloride is BeClj, and the atomic weight of beryllium 9-1. The determination of atomic weights by the volumetric method thus reduces to finding the smallest quantity of an element present in a molecule, referred to the atom of hydrogen as unity. If the molecular weights of a large number of vola- tile compounds containing a particular element are determined, it is practically certain that at least some of the compounds will contain only one atom of the element in question, and the pro- portion in which the element is present in these compounds is its atomic weight. In the above example, for instance, it has been assumed that only one atom of beryllium is present in the molecule of beryllium chloride of weight Sot, and the justification for this assumption is that no compound is known the molecule of which contains less than 9-1 parts of beryllium. It is clear that the numbers thus obtained are maximum values, and the possibility is not excluded that the true values may be fractions of those thus arrived at. The values generally accepted are, however, confirmed by so many independent methods that every confidence can be placed in their trustworthiness. {b) Dulong and Petit's Law — In 1818, the French chemists Dulong and Petit enunciated the important law that for solid elements the product of the specific heat and atomic weight is constant, amounting to about 6'4. This law is a very striking one when the great differences in the magnitude of the atomic weights are taken into account. Thus, the specific heat of lead — the ratio of the quantity of heat required to raise i gram of the metal 1° in temperature to that required to raise the temperature of the same weight of water 1° — ^is 0^03 r, and its atomic weight 207, the product being 6'4 ; whilst for lithium, with a specific heat of o'g and an atomic weight of 7, the product is 6'3. Since quantities of the different elements in the proportion of their atomic weights require the same amount 12 OUTLINES OF PHYSICAL CHEMISTRY of heat to raise the temperature by a definite number of degrees, the law may also be expressed as follows : The atoms of all ek- ments have the same capacity for heat. It is clear that this law can be used to determine the atomic weight of an element when the specific heat is known, the quotient of the constant by the specific heat giving the re- quired value. Dulong and Petit's law was largely used by Berzelius in fixing the values of the atomic weights. Like many other empirical laws, that of Dulong and Petit is only approximately true, the " constant " varying from about 6"o to 67. This degree of concordance is, of course, quite sufficient for fixing the values of the atomic weights, as it is only necessary for this purpose to choose between a number and a simple multiple or submultiple. Moreover, the specific heat varies with the allotropic form of the element and with the temperature, and there is much uncertainty as regards the proper conditions for comparison. Regnault, who made a series of very careful determinations of specific heats, showed that most elements of small atomic weight, more particularly carbon, silicon and boron, have exceptionally small atomic heats. Later, how- ever, it was found that the specific heats of these elements increase rapidly with rise of temperature, and at high tempera- tures their behaviour is in approximate accordance with Dulong and Petit's law. This is clear from the accompanying table, showing the behaviour of carbon (diamond) and boron. Carbon (Diamond). Boron. Temp. Sp. Heat. Atomic Heat. Temp. Sp. Heat. Atomic Heat. 10° 206° 600° 1000° 0-1128 0-2733 0-4408 0-4589 1-33 3-25 5-28 5-51 27° 126° 177° 233° 0-2382 0-3069 0-3378 0-3663 2-61 3-40 370 4-02 The few elements which show this abnormal behaviour are of FUNDAMENTAL PRINCIPLES OF CHEMISTRY 13 low atomic weight, but the converse does not hold, as the atomic heat of lithium is normal. Some years after the introduction of Dulong and Petit's law, a similar law for compounds was enunciated by Neumann. He showed that, for compounds of similar chemical character, the product of specific heat and molecular weight is constant — in other words, the molecular heats of similarly constituted com- pounds in the solid state are equal. In 1864, Kopp extended Neumann's law by showing that the molecular heat of solid compounds is an additive property, being made up of the sum of the atomic heats of the component atoms. It follows that in certain cases atoms have the same capacity for heat before and after entering into chemical combination. For ex- ample, the specific heat of calcium chloride is o'i74, the mole- cular heat is therefore 0-174 x iii = i9"3, and the atomic heat of each atom 6-4. This law may be used to estimate the atomic heats of sub- stances which cannot be readily investigated in the solid form. The atomic heat of solid oxygen in combination is about 4*0, and of solid hydrogen 23. (t) Isomorphism — Mitscherlich observed that the corre- sponding salts of arsenic acid, H3ASO4, and phosphoric acid, H3PO4, crystaUize with the same number of molecules of water, are identical, or nearly so, in crystalline form, and can be obtained firom mixed solutions in crystals containing both salts, so-called mixed crystals. On the basis of these and similar observations, Mitscherlich established the Law of Isomorphism, according to which compounds of the same crystalline form are of analogous constitution. Thus, when one element replaces another in a compound without altering the crystalline form, it is assumed that one element has displaced the other atom for atom. The replacing quantities of the different elements are therefore in the ratio of their atomic weights, and if the atomic weight of one of them is known, that of the other can be calculated. This principle was largely used by Berzelius for fixing atomic 14 OUTLINES OF PHYSICAL CHEMISTRY weights before the establishment of Dulong and Petit's law, and afforded a welcome corroboration of those obtained by the use of the law of volumes. The converse to the law of isomorphism does not hold, as elements may displace one another atom for atom with complete alteration of crystalline form. The principle of isomorphism is, however, somewhat in- definite, inasmuch as even the most closely related compounds are not completely identical in crystalline form, and it is difficult to decide where the line between similarity and want of similarity is to be drawn. Thus the corresponding angles for the naturally-occurring crystals of the carbonates of cal- cium, strontium and barium are: Aragonite, ii6° lo'; Stron- tianite, 117° 19' ; Witherite, 118° 30'. Tutton,i from a carefiil comparative study of the sulphates and selenates of potassium, rubidium and caesium, has shown that each salt has its own specific interfacial angle, but the differences produced by dis- placing one metal of the alkali series by another does not exceed i'^ of arc, and is usually much less. The three most important characteristics for the establishment of isomorphism are : — (i) The capacity of forming mixed crystals. The miscibUity must be complete, or within fairly wide limits of concentration. (2) Similarity of crystalline form, which must include at least approximate agreement in the values of the geometrical con- stants. (3) The capacity of crystals of one substance to increase in size in a saturated solution of the other. {d) Detepmination of Atomic Weights by Chemical Methods — It is evident from the considerations advanced in the section on the determination of atomic weights by volu- metric methods (p. 10) that if the composition of a binary compound containing one or more atoms of an element such as hydrogen or chlorine for each atom of an element of unknown atomic weight has been determined by analysis, and if further the relative number of atoms of hydrogen or chlorine present is ' Science Progress, 1906, i, p. 91. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 15 known, the atomic weight of the other element can at once be calculated. In the case of beryllium chloride, it has been shown that the number of chlorine atoms present can be deter- mined by a physical method (p. 10), but such determinations can sometimes be made by purely chemical methods. As an illustration, we will consider the determination of the atomic weight of oxygen. Analysis shows that water contains approxi- mately I part of hydrogen to 8 parts of oxygen by weight. If the molecule of water contains one atom each of hydrogen and oxygen, its formula must be HO and the atomic weight of oxygen will be 8 ; if, on the other hand, two atoms of hydrogen are present, the formula must be HjO and the atomic weight of oxygen must be 16 in order to obtain the ratio between the weights of the elements found experimentally. It has been found that by the action of metallic sodium half the hydrogen in water can be displaced, and as by definition atoms are indi- visible, this indicates that the molecule of water contains two (or a multiple of two) atoms of hydrogen. The (probable) formula for water is therefore H2O and the atomic weight of oxygen 16. It will be evident that, as in the case of the volumetric method, the value thus obtained for the atomic weight is a maximum and further experiments are necessary to fix the value definitely. Relation between Atomic Weights and Chemical Equivalents. Yalency — The exact proportions in which the elements enter into chemical combination are determined by analysis, and the numbers thus obtained, referred to a definite standard, represent, according to the atomic theory, the atomic weights, or simple multiples or sub-multiples of the atomic weights, of the respective elements; The choice between several possible numbers is based on the methods discussed in the foregoing paragraphs, more particularly on Avogadro's hypo- thesis, and the fact that these independent methods give the same values affords strong evidence that the numbers thus ob- tained are the true ones — a view which obtains still further 1 6 OUTLINES OF PHYSICAL CHEMISTRY support from the periodic classification of the elements due to Mendeleeff (1869). The ordinary chemical formulae with which the student is familiar are based on the atomic weights thus obtained. For example, the formulae of a number of compounds containing only hydrogen and one other element are as follows : HCl, HjO, NHg, CH4. It is evident from these formulae that the power of different elements to combine with hydrogen is very different ; whilst one atom of chlorine combines with only one atom of hydrogen, one atom of carbon can become associated with no less than four atoms of hydrogen. The combining capacity of an element for hydrogen or other univalent element is termed the valency of an element, chlorine being a univalent and carbon a quadrivalent element. A little consideration of the above formulae will make clear the relationship between the atomic weight and the chemical equivalent of an element. It is clear that an amount of one element equivalent to its atomic weight may combine with (or displace) i, 2, 3 or more parts of hydrogen by weight, depending on its valency. Since the chemical equivalent of an element is that amount of it which can combine with or displace one part by weight of hydrogen it follows that ^ ° = Chemical equivalent. Valency As has been indicated in the foregoing paragraphs, the atomic weight and the chemical equivalent are often deter- mined more or less independently and the quotient of the two values is the valency. In other cases, however (for example, the volumetric method and the chemical method), the chemical equivalent and the valency are determined, and the product of the two is the atomic weight. The Values of the Atomic Weights— After the establish- ment of the law of multiple proportions and the formulation of the atomic theory by Dalton, it became a matter of the utmost ' importance for chemists to determine the atomic weights of FUNDAMENTAL PRINCIPLES OF CHEMISTRY 17 le elements with the greatest possible accuracy. This task as undertaken by Berzelius, who, in the course of about six sars (18 10- 18 16), fixed the combining weights of most of le known elements. Since then, the determination of atomic eights has proceeded regularly, but on two occasions a )ecial impulse was given to these investigations. The first xasion was a suggestion by Prout that the atomic weights :e exact multiples of that of hydrogen. The idea under- ing this assertion was that hydrogen is the primary element, le other elements being formed from it by condensation, he results of Berzelius were incompatible with Prout's j?pothesis, but as the atomic weights of certain elements un- Dubtedly approximated to whole numbers, Stas made a number [atomic weight determinations with a degree of accuracy which IS only been improved upon in quite recent times. The results btained by Stas completely disposed of Prout's hypothesis in s original form. The second event which stimulated atomic weight investiga- Qns was the development of the periodic classification of the [ements. In certain cases, the order of the elements, arranged :cording to their atomic weights, did not correspond with their lemical behaviour, and Mendeleeff asserted that in these ises the commonly accepted atomic weights were inaccurate, he investigations undertaken to test these suggestions afforded riking confirmation of Mendeleeffs views in some cases, but Dt in others. As regards recent progress in this branch of ivestigation special mention should be made of the determina- on of the combining ratios of hydrogen and oxygen by Morley 1 id of the comprehensive and masterly investigations of T. W. ichards and his co-workers.^ As the combining weights are relative, it is necessary to fix 1 a standard to which they may be referred. Dalton took the omic weight of hydrogen, the lightest element, as unit, but 1 Smithsonian Contributions to Knowledge, 1895. 2 See, for example, J. Amer. Chem. Soc, 1907, 29, 808-826. 2 iS OUTLINES OF PHYSICAL CHEMISTRY Berzelius, from practical considerations, proposed oxygen as standard, putting its atomic weight = loo. The justification for this procedure is that very few elements form compounds with hydrogen suitable for analysis ; the majority of determina- tions have been made with compounds containing oxygen, and . until comparatively recently the ratio of the atomic weights of hydrogen and oxygen was not accurately known. Although the hydrogen standard again came into use after the time of Berzelius, mainly because hydrogen was taken as a standard for other properties, yet in more recent times the oxygen standard has again come most largely into use, the atomic weight of that element being taken as i6-oo. The unit to which atomic weights are referred is therefore ^ of the atomic weight of oxygen, and is rather less than the atomic weight of hydrogen.^ Besides the advantage already mentioned, the atomic weights of more of the elements approximate to whole numbers when the oxygen standard is used, which is a distinct advantage, smce round numbers are generally used in calculations. Chemical equivalents, like atomic weights, should be referred to the oxygen standard, and the chemical equivalent of an element is a number representing that quantity of it which combines with, or displaces, 8 parts by weight of oxygen. The arguments in favour of the oxygen standard seem con- clusive, and as it is very confusing to have two standards in general use, it is very satisfactory that the International Com- mittee on Atomic Weights now use the oxygen standard only. ' According to the recent determinations of Morley, Rayleigh and others the atomic weight of oxygen is about 15-88 when hydrogen is taken as unit. It follows that on the oxygen standard, O = i6*oo, the atomic weight of hydrogen is about i-ooS. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 19 INTERNATIONAL ATOMIC WEIGHTS (1911) Elements. Sym- bols. At. Wt. = 16. Elements. Sym- bols. At. Wt. = 16. Aluminium Al 27-1 Molybdenum Mo 960 Antimony . Sb I20'2 Neodymium Nd 144-3 Argon A 39-88 Neon Ne 20-2 Arsenic As 74-96 Nickel Ni 58-68 Barium Ba 137-37 Nitrogen . N 14-01 Bismuth Bi 208 -o Osmium Os 190-9 Boron B ii-o Oxygen 16-00 Bromine . Br 79-92 Palladium . Pd 106-7 Cadmium . Cd II2'40 Phosphorus P 31-04 Caesium . Cs 132-81 Platinum . Pt 195-2 Calcium Ca 40-09 Potassium . K 39-10 Carbon C 1200 Praseodymium . Pr 140-6 Cerium Ce 140-25 Radium Rd 226-4 Chlorine . CI 35-46 Rhodium . Rh 102-9 Chromium . Cr 52-0 Rubidium . Rb 85-45 Cobalt Co 58-97 Ruthenium Ru 101-7 Columbium Cb 93-5 Samarium . Sa 150-4 Copper Cu 63-57 Scandium . Sc 44-1 Dysprosium Dy 162-5 Selenium . Se 792 Erbium Er 167-4 Silicon Si 28-3 Fluorine . F 19 -o Silver . Ag 107-88 Gadolinium Gd 157-3 Sodium Na 23-00 Gallium Ga 69-9 Strontium , Sr 87-63 Germanium Ge 72-5 Sulphur S 32-07 Glucinum . Tantalum . Ta 181-0 {beryllium) . Gl 9-1 Tellurium Te 127-5 Gold . Au 197-2 Terbium . Tb 159-2 Helium He 3-99 Thallium . Tl 204-0 Hydrogen . H I -008 Thorium . Th 232-4 Indium In 114-8 Thulium . Tm 168-5 Iodine I 126-92 Tin . Sn 1 19-0 Iridium Ir 193-1 Titanium . Ti 48-1 Iron . Fe 55-85 Tungsten . W 184-0 Krypton Kr 82-9 Uranium . U 238-5 Lanthanum La 139-0 Vanadium . V 51-06 Lead . Pb 207-10 Xenon Xe 130-2 Lithium Li 6-94 Ytterbium Lutecium . Lu 174-0 {Nieoytterbiutn) . Yb 172-0 Magnesium Mg 24-32 Yttrium Yt 89-0 Manganese Mn 54-93 Zinc . Zn 65-37 Mercury Hg 200-0 Zirconium . Zt 90-6 Only significant figures are given in the table. Where no figure follows the decimal point, the value of the first decimal i. g> 1 1 m II c5 in II & H s II 5 1 II K H II 01 O 1 o r^ 1 1 t> "n 00 N 1 1 > k9 M !l W in tn II O in II ,r, II II m c H jl 1 1 1 1 > H ■ o m II en II CO 5 Jl 'I II z J 00 H II 5= in 00 ro N II D XO H H II 8 o^ll II -Q 1' "1 > II 2 H 11^ > II H « II II 1 jn Ot 1 I^ in > ffio" WW H 11 o db « II CO N =^ir &II II - ij >< Th ,-^ •^ 1 o K g,w II 3 If II IS U1 II a 92 " II II -a M II 11 II ip 00 1 t^ PO ^11 m Ol -• WW II II w> J3< H II Oi H II a , < 1 M « o 1 ■* o o N ^ 1 II II Ti- 00 M 1 d w iS U ll II II 1 z ^ 0) 1 < M > Heat, p. 239 46 OUTLINES OF PHYSICAL CHEMISTRY For diatomic molecules, the average value of the molecular heat at constant volume is about 4-8 calories in the neighbour- hood of 100°; but chlorine and bromine are exceptions. For triatomic molecules the average value of MC„ is 6-5 cal. and the value increases with the complexity of the compound, as is illustrated in the table. Specific Heat of Gases and the Kinetic Theory- Much light is thrown on the question of the specific heat of gases by the kinetic theory. According to this theory the energy-content of a gas is made up of three parts: (i) the energy of rectilineal (progressive motion of the molecules), the so-called kinetic energy (p. 32) ; (2) the energy of intramolecular motion; (3) the potential energy due to the mutual action of the atoms ; ^ and when heat is supplied to a gas at constant volume all three factors of the energy may be affected. For monatomic gases, however, such as mercury vapour, the factors (2) and (3) are presumably absent, and the heat supplied must simply be employed in increasing the kinetic energy of the molecules. We have already learnt (p. 3 2) that the kinetic energy of I mol of any gas = f PV = 3T if expressed in thermal units. When a gas is raised at constant volume from the absolute temperature T^ to Tj we have for the kinetic energies at the two temperatures the equations fPiV = 3Tj and f P^V = 3T„, where Pj and Pj are the pressures at Tj and Tg respectively. Subtracting the first equation from the second, we obtain I (^2-^1)^ = 3(T2-Ti) and for a rise of temperature of 1° f (P3 - Pi)V = 3 (calories). Therefore the molecular kinetic energy of a monatomic gas is increased by 3 calories for a rise of 1° in temperature, or, in other words, the molecular heat MC, of a monatomic gas at constant volume is 3 calories. As the specific heat at constant pressure is 3-1-2 = 5 calories, the ratio, MCy/MC„ for a monatomic gas must be i-66, if the assumptions we have made on the basis of the kinetic theory are justified. As has already been mentioned, C„ is somewhat difficult to ' Boltzmann, he. cit., p. 54, GASES 47 determine directly, and to test the above deduction from the kinetic theory it is simpler to determine the ratio Cp/C, in- directly, which can be done in various ways, for example, by measuring the velocity of sound in a gas. Kundt and Warburg (1876) therefore determined the velocity of sound in mercury vapour and obtained for the above ratio the value i'66, in exact accord with the theoretical value, undoubtedly one of the most striking triumphs of the kinetic theory. Conversely, a gas for which the ratio Q,/C„ is i"66 must be monatomic, and by this method Ramsay showed that the rare gases argon and helium are monatomic. For gases containing two or more atoms in the molecule, the heat supplied is employed not only in accelerating the rectilinear motion of the particles, but also in performing internal work in the molecule. As the former effect alone requires 3 calories, the total molecular heat of a polyatomic gas will be 3 + « calories, where a is a positive quantity, constant for any one gas. The value of MQ, will be 5 + a calories, and the ratio of the • specific heats will be MC„ S + a M#=3"T^<'-67>i less than i'67 but greater than i. A comparison of the numbers given in the table shows that this deduction is in complete accord with the experimental facts. It may be expected that the more complex the molecule the greater will be the amount of heat expended in performing internal work and therefore the greater will be the specific heat. In accordance with this, MC„ for i mol of ether vapour is 33-5 calories, and for turpentine (CjoHig) 66'8 calories. The specific heat of monatomic gases is independent of temperature, that of polyatomic gases usually increases slowly with temperature. Experimental Illustrations— Experiments with gases are usually somewhat difficult to perform, and require special ap- paratus. Experimental illustrations of the simple gas laws are 48 OUTLINES OF PHYSICAL CHEMISTRY described in all text-books on physics, and need not be con- sidered here. The determination of the density ^ and hence the molecular weight of such a gas as carbon dioxide by Regnault's method may be performed as follows : One of the bulbs is first exhausted as completely as possible by means of a pump, the stop-cock closed, and the bulb weighed. It is then filled with water by opening the stop-cock while the end of the tube dips under the surface of water and again weighed. The volume of the bulb is obtained by dividing the weight of the water by its density at the temperature of the experiment. The water is removed from the bulb by means of a filter-pump, the interior of the bulb is dried (by washing out with alcohol and ether and warming), placed nearly to the stop-cock in a bath at constant temperature, the end is then connected to a T piece by means of rubber tubing ; one of the free ends of the T piece is connected, through a stop-cock or rubber tube and clip, to a pump, the other, also through a stop-cock or rubber tube and clip, to an apparatus generating carbon dioxide. The bulb is evacuated by means" of the pump, the stop-cock connecting it with the latter is then closed, that connecting it with the carbon dioxide apparatus opened, the bulb filled with carbon dioxide, disconnected and weighed. As the apparatus fills it with carbon dioxide at rather more than atmospheric pressure, the stop-cock is opened for a moment to adjust it to atmospheric pressure before weighing. The weight of a known volume of the gas at known temperature and pressure having thus been determined, its density and molecular weight can readily be calculated. The determination of vapour densities by Victor Meyer's method is fully described on page 38, and may readily be perfprmed by the student with ether or chloroform, steam being used as jacketing vapour. 1 For full details as to the manipulation of gases, consult Travers' Experimental Study of Gases (Macmillan, igoi). CHAPTER III LIQUIDS General — Liquids, like gases, have no definite form, but, unlike the latter, they have a definite volume, which is only altered to a comparatively small extent by changes of tempera- ture and pressure. In contrast to the simple gas laws, the formulae connecting temperature, pressure and volume of liquids are very compli- cated and empirical in character, and depend also on the nature of the liquid. This is, of course, connected with the fact that liquids represent a much more condensed form of matter than gases. I c.c. of liquid water at ioo°, when converted into vapour at the same temperature, occupies a volume of over 1600 c.c. It seems plausible to suggest that the main reason why the formulae representing the behaviour of liquids are so much more complicated than the gas laws is that the mutual attraction of the particles, which is almost negligible in the case of gases (p. 34), is of predominant importance for liquids. As is well known, gases can be liquefied by increasing the pressure and lowering the temperature ; and, conversely, by raising the temperature and diminishing the pressure a liquid can be changed to a gas. It is shown in the next section that there is no difference in kind, but only a difference in degree, between liquids and gases. Transition from Gaseous to Liquid State. Critical Phenomena — If gaseous carbon dioxide, below 31°, is con- fined in a tube and the pressure on it gradually increased, a point will be reached at which liquid makes its appearance in 4 49 so OUTLINES OF PHYSICAL CHEMISTRY the tube, and the whole of the gas can be liquefied without appreciable increase of pressure. If, however, carbon dioxide above 31° is continuously compressed, no separation into two layers (liquid and gas) occurs, no matter how high the pressure applied. Similarly, if carbon dioxide is contained in a sealed tube, under such conditions that both liquid and gas are present, and the temperature is gradually raised, it will be noticed that when the temperature reaches 31° the boundary between liquid and vapour disappears, and the contents of the tube become homogeneous. Other liquids show the same remarkable phenomena, but at tem- peratures which are characteristic for each sub- stance. This temperature is known as the critical temperature; above its critical temperature no pressure, however great, will serve to liquefy a gas, below its critical temperature any gas can be liquefied by pressure. That pressure which is just sufficient to liquefy a gas at the critical tem- perature is termed the critical pressure, and the specific volume under these conditions is called the critical volume. The critical phenomena may be observed, and rough measurements of the constants obtained, with an apparatus (Fig. 3) used by Cagniard de la Tour, who discovered these phenomena in 1822. The upper part of the branch A contains a suitable volume of the liquid to be examined, the branch B, the upper part of which is gradu- ated, contains a little air to act as a manometer, the remainder of the apparatus (the shaded part in the figure) is filled with mercury. The tube at first contains both vapour and liquid, but on gradually raising the temperature, a point is ultimately reached at which the boundary between liquid and vapour becomes faint, and finally disappears ; the tube is momentarily filled with peculiar flicker- FlG. 3. LIQUIDS 51 ing striae, and then the contents become quite homogeneous. On allowing to cool, a mist suddenly appears in the tube at a certain temperature, and separation into liquid and vapour again occurs. The temperature at which the boundary dis- appears on heating or reappears on cooling approximates to the critical temperature, and the critical pressure can be cal- culated from the volume of air in B. Accurate measurements of the constants may be made by methods described by Young ^ and others. As the temperature rises, the density of the liquid in the sealed tube naturally decreases, whilst that of the vapour increases, and it has been shown that at the critical temperature the densities of liquid and vapour are equal. The critical temperatures and pressures of a few substances are given in the accompanying table : — Critical Critical Pressure Temperature, C. (Atmospheres). Helium - 267-268° 2-3 Hydrogen -238° 15 Nitrogen . - 149° 27 Oxygen . -119° 58 Carbon dioxide 31° 72 Ethyl ether . 195° 35 Ethyl alcohol . 243° 63 Behaviour of Gases on Compression — We have already learnt that if gaseous carbon dioxide is compressed at a tem- perature below 31° it can be liquefied, but if the compression is carried out above 31° no separation into two layers occurs. These relations are best shown diagrammatically, as in Fig. 4, in which the ordinates represent the pressures and the abscissEe the corresponding volumes at constant temperature. If the gas in question obeys Boyle's law, the curves obtained by plotting the pressures against the corresponding volumes at constant temperature (the so-called isothermals) are hyperbolas, corresponding with the equation /» = constant, and this condi- tion is approximately fulfilled by air, as shown in the upper right- 1 Phil. Mag., 1892, [v.], 33, 153. 52 OUTLINES OF PHYSICAL CHEMISTRY hand corner of the diagram. An examination of the isothermals for carbon dioxide shows that the same is nearly true of this gas at 48-1°, but at 3S*S, and still more at 32-5, the isothermals deviate from those of an ideal gas. At the latter temperature it is very interesting to observe that the compressibility at 75 Y atmospheres is very great for a short part of the curve, and beyond that point extremely small ; in the latter respect the highly compressed gas resembles a liquid. At the critical point, 31 '1°, the curve is for a short distance practically hori- zontal, thus representing a great decrease of volume for a small change of pressure — in other words, a high compressibility. Finally, at 2i'i° and i3'i°, separation of liquid takes place, the LIQUIDS S3 curves run horizontal whilst the gas is changing to liquid at constant pressure, and then the curves run almost vertical, indicating a small decrease of volume with increase of pres- sure {i.e., a small compressibility), characteristic of liquids. It is evident from the foregoing that at any point within the dotted line ABC both vapour and liquid are present ; at any point outside only one form of matter, either vapour or liquid. The above considerations serve to show that there is no fundamental distinction between gases and liquids: a highly- compressed gas above its critical point cannot be definitely classified either as liquid or gas. It is evident from the figure that as regards compressibility, highly compressed carbon dioxide behaves more like a liquid than a gas. It is, in fact, possible to pass from the typically liquid to the gaseous form, and vice versd, without a separation into two layers. Thus liquid carbon dioxide below 31°, under the conditions represented by the point x-^ in Fig. 5, may be compressed above its critical pressure along «i_}'i and then warmed above its critical temperature whilst the pressure is kept constant at y-^. During this process no separation into two layers will be noticed, and by now re- ducing the pressure the fluid can be obtained in as dilute a form as desired (what is ordinarily termed a gas), say the con- dition represented by x, whilst remaining quite homogeneous. Similarly a gas can be completely converted to a liquid without discontinuity, along xyy-^x-^. Application of van der Waals' Equation to Critical Phenomena — We have already learnt that no actual gas follows the gas laws quite strictly, and, further, that the behaviour of actual gases can be represented with fair ac- curacy, even up to high pressures, by van der Waals' equation, ( P + v^j (V - ^) = RT. If this equation is arranged in descending powers of V it becomes 54 OUTLINES OF PHYSICAL CHEMISTRY This is a cubic equation, V being treated as the variable and P and T, as well as a, b, and R, as constants. Ac- cording to the values of these constants the equation has either three real roots or one real and two imaginary roots. Otherwise expressed, the magnitudes of a and b may be such that at one temperature and pressure, the volume V has three real values, whilst at another temperature and pressure it may have only one real value. We will now compare these theo- retical deductions with the actual case of car- bon dioxide. It is clear from Fig. 4 that at i3*i° and 48 atmo- spheres, carbon dioxide has two volumes, as a gas (represented by the point D) and as a liquid (the point E), but the third volume demanded by the equation is not shown. At 48* 1°, on the other hand, there is only one volume for each pressure, corres- ponding with one real root of the equation under these conditions. Some light is thrown on the question of the missing third real volume when the isothermal curves for carbon dioxide are plotted by substituting the values of a and b, found experi- mentally (p. 34) in equation (i). The wavy curve ABCDE shown in Fig. 5 was obtained in this way ; on comparison with the experimental curve for carbon dioxide (Fig. 4), it will be Volume- Fig. 5. LIQUIDS 55 seen that whereas the points D and E in the latter isothermal for 13° are joined by a straight line DE, in the former the corresponding points E and A are joined by the dotted line ABCDE, which represents a change from the gaseous to the liquid form without discontinuity. The point C, at which the line of constant pressure cuts the isothermal, represents the third of the volumes required by the above cubic equation, but it probably cannot be realised in practice, as the part DCB of the curve on which it occurs represents decrease of volume with diminishing pressure, quite contrary to our usual experi- ence. On the other hand, the sections AB and ED have a real meaning. When a vapour is compressed till saturated, it does not necessarily liquefy; in the complete absence of liquid it may be compressed considerably beyond the point at which liquefaction occurs in the presence of traces of liquid ; in other words, a part of the curve ED may be experimen- tally realised. Similarly, water may be heated in a carefully cleaned vessel several degrees above its boiling point, that is, it does not necessarily pass into vapour when the superincum- bent pressure is less than its vapour pressure, and a part of the curve AB may thus be experimentally realised. Similar phenomena will be met with later ; it often happens that when a system is under such conditions that the separation of another phase (form of matter) is possible, the change does not occur in the absence of the new phase. Van der Waals' equation can also be employed to obtain important relations between the critical constants and the other characteristic constants representing the behaviour of gases. It has already been pointed out that the densities and consequently the volumes of liquid and gas become equal at the critical temperature, and as this must also be true for the intermediate third volume, it follows that the three roots of the equation V«-(^+^V^ + |V-^ = o(r) become equal under these conditions. If, in this general 56 OUTLINES OF PHYSICAL CHEMISTRY equation, we call the three roots Vj, V^ and V,, then the equation (V- Vi)(V-V2)(V-V3) = o, must hold, which, when the roots are equal, becomes (V - YiY = V - 3VftV2 + jVa^V - Va' = o (2), where Vj is the critical volume. Equating the coefficients of the identical equations (i) and (2), we have ^ + ^ = 3V* (i) ; 1^ = 3V? (ii) ; Ij = V? (iii). From the last three equations, the values of the critical con- stants can readily be obtained in terms of R, a and l>. We have Critical volume V^ = 3^ (from ii and iii), Critical pressure P* = — ^ (from ii), Critical temperature Tj = — ^ (from i). We thus reach the interesting result that the critical constants may be calculated from the deviations from the gas laws, when the latter are expressed in terms of the constants a and 6 of Van der Waals' equation. As an illustration of the satisfactory agreement between the observed and calculated values, we will take the data for ethylene, for which a = o'oo786, d = o"oo24, R = 0*0037. Vj = 0*0072 (observed value o'oo6), Pj = j-^ Tj- = 50*5 (observed value 51 atmospheres), Ti = = 262° Abs. (observed value 282°). " 27 X o"oo24 X 0-0037 ' Law of Corresponding States — ^Van der Waals has further pointed out that if the pressure, volume and temperature of a substance are expressed as multiples of the critical values, that is, if we put P = aPft, V = /JV^, T = yT^, and then substitute in the equation (P + fl/V2)(V - d) = RT, Pj, Vj and Tj being LIQUIDS 57 replaced by their values in terms of a, b and R, the equation simplifies to {^ + |)(3^ - I) = 8y. This equation does not contain anything characteristic of the behaviour of an individual substance, and ought therefore to hold for all substances in the gaseous and liquid state. Experiment shows, however, that it is only to be regarded as a first approximation, the deviation in many cases being much greater than the experimental error. For our present purpose, these considerations are chiefly of importance as affording information regarding the proper con- ditions for comparison of the physical properties of liquids. If we wish, for example, to compare the molecular volumes of ether and benzene, it would probably not be satisfactory to compare them at the ordinary temperature of a room, as this would be near the boiling-point of ether, 35°, but much below that of alcohol, 78°. According to van der Waals, the proper temperatures for comparison, the so-called " corresponding tem- peratures," are those which are equal fractions of the respective critical temperatures. Thus, if we choose 20°, or 293° Abs., as the temperature of experiment for ether, the critical tem- perature of which is 195°, or 468° Abs., the proper temperature, t, for comparison with alcohol (critical temperature, 243° C.) will be given by -^^-gg — = ^^^ , whence ^=51 . The same considerations apply to the pressures. The theoretical basis for this method of comparison is that, as mentioned above, the choosing of pressures, volumes or tem- peratures which for different substances bear the same proportion to their respective critical constants leads, when substituted in van der Waals' equation, to an equation which is the same for all substances, and the practical justification for choosing these as corresponding conditions is that more regularities are actually S8 OUTLINES OF PHYSICAL CHEMISTRY observed by this method than when the comparison is made under other circumstances. Liquefaction of Gases — As already indicated, all gases can be liquefied by cooling them below their respective critical temperatures and applying pressure. The methods employed for this purpose by Cailletet, Pictet, Wroblewski and others are fully described in text-books of physics. In recent years the older methods have been almost completely displaced, in the case of the less condensible gases, such as air and hydro- gen, by a method introduced almost simultaneously by Linde and by Hampson. The principle of the method is that when a gas is allowed to pass from a high to a low pressure through a porous plug without performing external work it becomes cooled (Joule-Thomson effect). The cooling effect is due to the performance of internal work in overcoming the mutual attrac- tion of the particles, and is therefore only observed for " im- perfect " gases (p. 34). The effect is the greater the lower the temperature at which the expansion takes place, and the greater the difference of pressure on the two sides of the plug. The cooling effects thus obtained are summed up in a very ingenious way by the principle of " contrary currents," the same quantity of gas being made to circulate through the apparatus several times, and after passing through the plug being caused to flow over and cool the tube through which a further quantity of gas is passing on its way to the plug (or small orifice). The apparatus employed is represented diagrammatically in Fig. 6. By means of the pump A, the gas is compressed in B to (say) 100 atmospheres, the heat given out in this process being absorbed by surrounding B with a vessel through which a continuous current of cold water is passed. The cooled, com- pressed gas then passes down the central tube G, towards the plug E, being further cooled on the way by the gas passing up the wide tube D, which has just expanded through the plug. After passing through E and thus falling to its original pressure, the gas passes upwards over the central tube G and again LIQUIDS 59 B reaches A by the tube C and the left-hand valve at the bottom of A. The direction of the circulating stream of gas is indicated by the arrows. In course of time, the temperature becomes so low that part of the gas is liquefied and collects in the vessel F. More air is drawn into the appar- atus as required, and the process is continuous. By means of an apparatus con- structed on this principle Dewar, and, somewhat later, Travers, succeeded in obtaining liquid hydrogen in quantity. All known gases have now been liquefied. The liquefaction of helium was effected quite recently by Kam- merlingh Onnes. RELATION BETWEEN PHYSI- CAL PROPERTIES AND CHEMICAL CONSTITUTION General — ^The foregoing para- graphs of this chapter represent an introduction to the relation- ship between the physical pro- perties of liquids and their chemi- cal composition, inasmuch as in- formation has been gained as to the conditions under which measurements should be made with different liquids in order to obtain comparable results (theory ^"'- ^• of corresponding states). Although in this chapter we are mainly concerned with the physical properties of pure liquids, it is convenient to include also some observations with solu- r J A_ I ~r *"^~" \ t 1 i 1- k 1] 1° G i_ L F 6o OUTLINES OF PHYSICAL CHEMISTRY tions. We will deal shortly with the following physical pro- perties: (i) Atomic and molecular volumes; (2) refractivity ; (3) rotation of plane of polarization of light; (4) absorption of light ; (s) viscosity. Atomic and Molecular Yolumes — In the case of gases, we have seen that simple relations are obtained when the volumes occupied by different substances in the ratio of their molecular weights are compared ; at the same temperature and pressure, the volumes are equal. The justification for taking the molecular weights (in grams, for instance) as comparable quantities is that, according to the molecular theory, equal numbers of molecules of different substances are thus compared. Similarly, in dealing with liquids, it is usual to determine the molecular volume of the liquid, i.e., the volume occupied by the molecular weight of the liquid in grams, which is, of course, ob- tained by dividing the molecular weight in grams by the density of the liquid at the temperature of experiment. As the specific volume, V, of a liquid is inversely as the density, the molecular volume may also be defined as molecular weight in grams x sp. volume. Similarly, the atomic volume = (atomic weight in grams) -=- density, or, (atomic weight in grams) x sp. volume. Kopp was the first chemist to carry out an extended series of observations on this subject, and he found that the most regular results were obtained when molecular volumes were determined, not at the same temperature, but at the boiling-points of the respective liquids under atmospheric pressure. It is interesting to observe that this purely empirical method of procedure was found much later to be theoretically justifiable, as the boiling- points of most liquids are approximately two -thirds of their respective critical temperatures (both measured on the absolute scale). The boiling-points are therefore corresponding tempera- tures, (p. 57). Kopp found that as a first approximation the molecular volume could be regarded as the sum of numbers representing LIQUIDS 6 1 the volumes of the component atoms. The atomic volumes of the commoner elements occurring in organic compounds are as follows : — C H CI Br I S 0(0-H)0(0 = ) II s'5 22"8 27'8 37'5 22"6 7"8 i2'2 In some cases the atomic volume depends on the way in which the element is bound, thus oxygen joined to hydrogen (hydroxyl oxygen) has the atomic volume 7 "8, whilst for oxygen doubly linked to carbon (carbonyl oxygen) the volume is 12' 2. As an illustration the calculated and observed volumes of acetic acid may be compared as follows : — 2C = 22 4H = 22 (Carbonyl) O = 12-2 (Hydroxyl) O = 7-8 64-0 As the molecular weight of acetic acid is 60 and its density at the boiling-point is 0-942 the observed molecular volume M/rf = 63-7- It should be mentioned that the atomic volumes given above are not obtained directly, but by comparison of chemical compounds with definite differences of composition {e.g., the difference in the molecular volumes of the compounds C^Hjo and C^Hg gives the volume of two atoms of hydrogen), and are therefore not necessarily the same as those for the free elements. In some cases, however, the two values coincide, thus the atomic volumes of the free halogens, chlorine and bromine, at their boil- ing-points are 23-5 and 27- 1 respectively, whilst their values in combination are 22-8 and 27-8, so that the halogens have ap- proximately the same volume in the free and combined condi- tion. The same is approximately true for certain other elements for which comparison is possible. The extended investigations of Thorpe, Lossen and Schiflf 62 OUTLINES OF PHYSICAL CHEMISTRY afford a general confirmation of Kopp's conclusions ; the cal- culated and observed values generally agree within about 4 per cent. Although, strictly speaking, the consideration of the mole- cular volume of a substance in solution does not belong to this section, it is convenient to refer to it here. The molecular solu- tion volume, M», of a substance may readily be calculated from the formula M» = — 3 5-, where M is the molecular weight da of the solute in grams, n the weight of the solvent containing M grams of solute, d the density of the solution, and d that of the solvent. This formula is derived on the assumption, which is certainly not justifiable, that the density of the solvent itself is not affected by dissolving a substance in it, and therefore M» is only the " apparent " solution volume. The molecular volume is sometimes nearly the same in the free state and in solution* {e.g., bromine in carbon tetrachloride), but is often much less (e.g., many salts in water). Additive, Constitutive and CoUigative Properties — The molecular volume is a good example of what is termed an additive property, since it can be represented as the sum of volumes pertaining to the component atoms. It is not, how- ever, strictly additive, since it is influenced somewhat by the arrangement of the atoms in the molecule, and therefore the atoms to some extent influence each other. Properties which depend largely on the constitution of the molecule, in other words, on the arrangement of the atoms in the molecule, are termed constitutive ; a typical constitutive property is the rota- tion of the plane of polarization of light (p. 66). The only strictly additive property is weight. Other properties, such as the refractivity, the molecular volume, heat of combustion, etc., are more or less additive, but are to some extent complicated by constitutive influences, probably due largely to the mutual influence of the atoms. There is a third class of properties, which always retain the 'Lumsden, Trans. Chem. Soc, 1907, 91, 24; Dawson, ibid., igio, 97, 1041. LIQUIDS 63 same value independent of the number and nature of the atoms in a molecule or of their arrangement, and depend only on the number of molecules. A good illustration of these properties has already been met with in connection with gases. When these are taken in quantities which, according to the atomic theory, are proportional to their molecular weights, they all exert the same pressure when occupying equal volumes at the same tempera- ture. Such properties have been termed colligative by Ostwald. Many illustrations of these three classes of properties will be met with in the course of our work. Befractivity — The velocity with which light is propagated through different substances is very different. The relative velocities in two media can be deduced when the change in [ direction of a ray of light in I j. passing from one medium to "^'^^^ I another is known. When the ray passes from one medium to \ the other, the incident ray, the I _ _ _ refracted ray (in the second r; £ E. z Vr:iSF_t."-lI" medium) and the normal to : -"r~r"J~r-i'*__-£r--5V^ the boundary between the two --^—^ =:^:--_t-.r-.r^^-:r-_:^^ media (a line drawn perpen. Fig. 7. dicular to the boundary where the incident ray meets it) are in one plane. If i is the angle of incidence (the angle between the incident ray and the normal) (Fig. 7) and r is the angle of refraction (the angle between the normal and the refracted ray) and z/j and z/j the respective velo- cities of light in the two media, it can be shown that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, and is equal to the ratio of the velocity of light in the two media. The ratio in question is termed the index of refraction, and is usually represented by the symbol n. We have therefore the relation n = —. — = — . sm r Vo 64 OUTLINES OF PHYSICAL CHEMISTRY If the first medium is a vacuum, n is always greater than i — in other words, light attains its greatest velocity in a vacuum, and is retarded on passing through matter. The refractive index is, however, often referred to air as unity, and to convert the values thus found to a vacuum they must be multiplied by 1-00029, giving what is termed the "absolute refractive index". An instrument employed for the determination of refractive indices is termed a refractometer. Among the more convenient forms of refractometer, those due to Ahh6 and to Pulfrich may be specially mentioned. Ordinary white light cannot be employed for refractivity measurements, as the component rays are refracted or retarded to a different extent on passing through matter, the rays thus scattered or dispersed giving rise to a spectrum. This difficulty is avoided by using light of the same wave-length (so-called monochromatic light), and for this purpose sodium light, the wave-length of which is represented by the letter D, is con- venient. Measurements of the refractive index referred to sodium light are represented by the symbol «],. The refractive index of a given substance, like any other property, depends on the conditions of temperature, pressure, etc., under which the measurements are made. It has been found convenient to express the results of measurements not simply in terms of n-o, but in terms of the function — -7— where d is the density of the liquid or gas (Gladstone and Dale, 1858). This purely empirical function has the great advantage of being, for any given substance, practically in- dependent of the temperature. In 1880, Lorenz and Lorentz arrived simultaneously, from theoretical considerations, at the rfi — \ I somewhat more complicated formula, -j-v — ' > and showed that, for the same substance, it remained fairly constant, not only for widely differing temperatures, but even for the change from Uquid to gaseous form. Thus Eykman found that the LIQUIDS 65 value of this function for isosafrol, CioHj^Og, amounted to 0-2925 and 0-2962 at 17-6° and 141° respectively, and Lorenz obtained for water at 10° and water vapour at 100° the values o-2o68 and 0-2061 respectively. For comparative purposes, it is usual to employ the atomic refraction (atomic weight x refraction constant) and the mole- cular refraction (molecular weight x refraciion constant); the latter, if we employ the second form of the refraction constant, . . , n^ - 1 M. IS given by -j-— — • -j, where M is the molecular weight. In this case also it has been found, from measurements on many organic liquids, that the molecular refraction may be represented to a first approximation as the sum of the refrac- tions of the component atoms, so that the refractive power is largely an additive property. Just as in the case of molecular volumes, however, there are certain deviations from this additive behaviour (constitutive influences) which may be connected with the arrangement of the atoms in the molecule. Briihl,i who has been particularly prominent in investigating this question, points out that the molecular refraction of compounds containing double and triple bonds is greater than the calculated value, and he takes account of this constitutive influence by ascribing definite refractivities to these bonds. The values given by Briihl for a few of the elements are as follows^ : — C H 0(in OH) 0(in CO) CI I ^-^le TnpJ 2-48 1-04 1-58 2-34 6-02 13-99 I'?^ 2'l8 Later investigations show that neighbouring double or triple bonds exert a mutual influence, so that the matter becomes somewhat complicated. Conversely, it is sometimes possible, from measurements of the refractive index (or other physical property), to draw con- clusions as to the constitution of chemical compounds, but as ' For a short summary of Briihl's work, by himself, see Proc. Royal Institution, igo6, 18, 122. 2 The number? are referred to the a ray of hydrogen. 5 66 OUTLINES OF PHYSICAL CHEMISTRY our knowledge of the relations between physical properties and chemical constitution is very imperfect, this method should only be employed with great caution. It is evident that no conclu- sions as to chemical constitution can be drawn from additive properties, but only from constitutive properties. Rotation of Plane of Polarization of Light — The pro- perties of liquids so far dealt with have been mainly additive, the magnitude of properties such as volume, effect on the speed of light, etc., being much the same in the free state and in combination. We have now to deal with the property pos- sessed by a few liquids (and dissolved substances) of rotating the plane of polarized light — a property which depends entirely upon the arrangement of the atoms in the molecule. Isomeric substances have in general nearly equal molecular refractivity and molecular volume, but it often happens that of two isomeric substances, such as the two lactic acids, one rotates the plane of polarized light and the other does not. Plane polarized light (light in which the vibrations are all in one plane) is obtained by passing monochromatic light through a polarizing prism (Nicol prism or tourmaline plate) which cuts off all the rays except those vibrating in one plane. A prism of this type is mounted at some distance from another similar prism in such a way that light which has been polarized in the first prism may be examined after it has passed through the second prism, which is termed the analyser. If now the analyser is rotated until it is perpendicular to the polarizer, all the light which passes through the former will be cut off by the analyser, and on looking through the eyepiece the field will appear dark. If now, while the prisms are in this relative posi- tion, a tube filled with turpentine is placed between them, the field again appears clear, but becomes dark on rotating the analyser through a certain angle. This observation is readily accounted for on the view that the plane of polarization is twisted through a certain angle whilst the light is traversing the turpentine, and the analyser must therefore be rotated in ordei LIQUIDS 67 to bring it into the former relative position with regard to the polarized ray. The angle through which the analyser has been turned is read og^^oa-a graduated scale. The instrument used for measuring the rotation of liquids, which consists essentially of the two prisms and graduated scale, as described above, is termed a polarimeter. The observed angle of rotation depends on the nature of the liquid, on the wave-length of the light employed in the measurements, and on the temperature, and is proportional to the length of liquid traversed. For purposes of comparison, the results are usually expressed in terms of the specific rotation [a] for a fixed temperature t and a particular wave-length of light (for example, sodium light) by means of the formula where a is the observed angle, / is the length of the column of liquid in decimetres, and d is the density of the liquid at the temperature i. The molecular rotation m\o\ is obtained by multiplying the specific rotation by the molecular weight of the liquid. The specific rotation of substances in solution is represented by the analogous formula ^ ,( lOOa where ^ is the number of grams of solute in 100 grams of the solution, d is the density of the solution at the temperature t, and a and / have the same significance as before. The liquids and dissolved substances which possess this re- markable property are almost exclusively compounds containing carbon. Further, only compounds containing an asymmetric carbon atom, that is, a carbon atom joined to four different groups, have the power of rotating polarized light (Van't Hoff and Le Bel, 1874). For example, the graphic formula of ordinary lactic acid, which is optically active, may be written as follows : — 68 OUTLINES OF PHYSICAL CHEMISTRY CH3 I H— C— OH COOH showing that no two of the groups attached to the central carbon atom are identical. A further remarkable fact is that when one form of a substance, such as lactic acid, can rotate the plane of polarized light to the right, a second modifica- tion can always be obtained which, although identical with the first in all other physical properties, rotates polarized light to the left to the same extent as the first modification rotates it to the right. The first is termed the dextro or d modi- fication, the second the laevo or / modification. Van't Hoff and Le Bel account for this on the hypothesis that the four different groups are not in the same plane as the carbon atom, but are arranged in the form of a tetrahedron with the carbon atom in the centre. It can be shown, most readily by means of a model,' that when all four groups are different there are two arrangements which cannot be made to coincide by rotating one of the models. These two arrangements behave to each other as object and mirror image, or a right- and left-hand glove, which cannot be brought into the same relative position, and, according to the theory, correspond with the dextro and laevo modifications respectively. If any two of the groups become identical, however, the two arrangements can always be brought to coincidence, and there is no possibility of optical isomerism. In calculating the specific rotation of a dissolved substance, it is implicitly assumed that it is not affected by an indifferent solvent. As a matter of fact, however, the molecular rotation of a dissolved substance often differs considerably from its value ' Models for this purpose can be bought for a few pence, or can be made by the student with a piece of cork and four pins provided with differently coloured balls at the ends. LIQUIDS 69 in the pure state. This is well shown by the following results obtained by Patterson' for /-menthyl-i^-tartrate in the pure state, and in 1-2 per cent, solution. Molecular Rotation of /-menthyl-^-tartrate. Solvent. Molecular Rotation at 20°, None - 284* Ethyl alcohol - 306-2° Benzene - 296'i° Nitrobenzene -245-3° So far, no definite connection has been found between any other property of the solvent and its effect on the rotation of a solute. Almost the only regularity which has yet been dis- covered in this branch of the subject is that the rotatory power of the salt of an optically active acid (or base) in dilute solution is independent of the nature of the base (or acid) with which it is combined. This important result is further referred to at a later stage. All transparent substances, when placed in a magnetic field, rotate the plane of polarized light, and the late Sir William Perkin, who devoted many years to the systematic investigation of this subject, showed that this magnetic rotation is, like refrac- tivity, largely an additive property. Absorption of Light " — ^When a ray of white light passes through matter a greater or less amount of absorption invari- ably occurs, and the spectrum of the issuing ray shows dark bands corresponding with the rays which have been absorbed. This spectrum is termed an absorption spectrum. Absorption may be general or selective. In the former case there is a general weakening throughout whole regions of the spectrum ; in the latter case, there are independent relatively narrow bands in different regions of the spectrum. 'See Trans. Chem. Soc, 1905, 87, 128. ^Smiles, Chemical Constitution and some Physical Properties (Long- mans, 1910), pp. 324-423. 70 OUTLINES OF PHYSICAL CHEMISTRY The absorption spectrum is one of the most characteristic properties of a given substance or class of substances under definite conditions. Thus, for instance, the absorption spectra of permanganates in dilute solution are characterised by the presence of five dark bands in the green. In the case of liquids or solutions, absorption is most conveniently measured in the transmitted light, as already indicated. In the case of solids, however, observations may be made with reflected light, as part at least of the reflection takes place from layers a little below the surface, and the short distance traversed is usually sufficient to produce some absorption. The method which is most largely employed in the case of liquids is to use as a source of illumination the electric arc or spark passing between metallic (preferably iron) poles, the spectrum of the light being photographed after the latter has passed through the liquid. Substances which have high ab- sorbing power are usually examined in solution, and the solvent chosen should not itself show absorption in the part of the spectrum studied. Ethyl alcohol is most largely used as solvent. A very important question in such measurements is the effect of dilution on the persistence and intensity of a band — it very often happens that a band appears only within certain limits of dilution. For this reason, it is usual to carry out measurements with varying thicknesses of the absorbing layer and with varying concentrations. The solutions are made more and more dilute till absorption is no longer observed. For purposes of comparison, the solutions to be examined are usually made up to contain simple fractions of a mol per litre. The method usually employed in representing the results graphically requires some explanation. It is illustrated in Fig. 8, which shows the absorption in the ultra-violet region of a solution of the amino derivative of dimethyldihydroresorcin in ethyl alcohol. The diagram shows the presence of one band. The principle of the method is that the oscillation frequencies of the limits of the absorption band are plotted LIQUIDS 71 Oscillation Frequencies. 000 against the logarithms of the relative thicknesses referred to the thinnest layer of the most dilute solution examined. It is more convenient to use the logarithms of the relative thicknesses than the thicknesses them- selves as ordinates. The latter are shown on the right-hand side of the figure, and it is evident that if equal increments of thickness were used, the curve would become inconveniently long. The space above the curve shows the wave lengths of the light absorbed at different dilutions, and the curve itself represents the limits of the absorption. The lowest part of the curve, usually termed the " head," is that point at which the strongest ab- sorption takes place ; in the diagram it occurs at an oscillation frequency of 3600 units. The so- called " persistence " of the band is the difference of the logarithms of the thicknesses at which the band makes its appearance and dis- appears respectively, and is indicated on the diagram by its depth (in the present case extending from i to 23 units). 34 32 a 30 d '?ft u [/3 26 1—1 24 'Z 22 ^4-1 rn 20 11 <1) 18 I A ■s 14 h) ,>; \/ (Tl V. 10 8 (/} y 6 Xi i-l 4 rA hn °, 2 2 4 0000 C C^ Tf CD CO Cq -q CO CO CO CO ■* -rr T t I 1 A ' 1 / \ / / 1 / 1 / \ / \ V y V. y 2000 1.50Q 1000 a 500 ■a 'n !400 w 250 200 J?; 1(10 (4-1 W a u 30 a tn 20 tn lb a 10 tI 5 J3 -4-> 9) > 3 ^ (1) 2 !A 0-6 Fig. 8. 72 OUTLINES OF PHYSICAL CHEMISTRY It may be mentioned that most of the measurements have been made in the ultra-violet region of the spectrum, but a certain number of observations have also been made in the visible and ultra-red regions. A great deal of discussion has taken place as to the mechanism of light absorption, and a dynamical explanation has found most favour. According to Drude, absorption in the ultra-violet and visible regions is connected with the presence of negative electrons (valency electrons), and there is doubtless some intimate connection between the rate of vibration of the electrons and the frequency of the light waves absorbed. It appears, however, that absorption in the ultra-red region is due, not to electrons, but to particles of much greater magnitude, probably atoms or even groups of atoms. As already indicated, the absorption spectra of chemical compounds are closely related to their constitution, and in recent years this method of elucidating chemical constitution has come increasingly into use. The progress made in this branch of investigation is mainly due to Hartley, and within the last few years to Baly and his co-workers.^ It is impossible here to do more than to indicate in the briefest way the broad differences between the absorption spectra of the main groups of organic compounds. According to Hartley,^ all compounds which exert selective absorption are of aromatic character, for example, benzene, pyridine, and their derivatives. Those showing strong general absorption have also a cyclic structure, but are not typical aro- matic compounds ; examples, thiophene, piperidine, etc. Finally, compounds which exert only a weak general absorption are open chain compounds; examples, fatty alcohols, esters, etc. Although recent investigation has led to the discovery of one or two exceptions to these generalisations, they remain sub- stantially accurate. Apart from these broad differences in the absorption curves ^ Trans. Chem. Soc. from 1904 onwards. ' British Association Report, 1903. LIQUIDS 73 of different groups of organic compounds, it has been shown by Hartley that substances of closely allied constitution have absorption curves of similar type. The recent progress in the establishment of the chemical constitution of organic compounds from measurements of their absorption spectra is entirely due to the application of this important rule. Thus if the con- stitution of one compound is known with certainty from its chemical behaviour, and a second compound can be represented by alternative formulae, of which one is analogous to that of the compound of known constitution, a comparison of absorp- tion spectra often enables a decision to be made. Like the other physical methods of determining chemical constitution, the one under discussion should be used with considerable caution in the present very imperfect state of our knowledge of absorption phenomena. As a supplement to purely chemical methods of determining constitution, however, especially when such methods lead to contradictory results, it is rendering valuable service. As regards the additive character of absorption spectra, comparatively little is known with certainty. The determina- tion of the effect of different groups of atoms on the character of the absorption spectrum is attended with considerable diflS- culty, but some progress has been made in this direction. Ultra-red absorption spectra have a pronounced additive char- acter ; this is probably connected with the generally accepted view that absorption in this case is connected with the vibrations of the atoms themselves. Viscosity — The measurement of internal friction, or vis- cosity, gives information as to the work done in the relative displacement of the particles of a solid, liquid, or gas. In the case of liquids, for which the property has been most fully investigated, the viscosity is most conveniently studied by observing the rate of flow through capillary tubes. We may assume that the layer of liquid in contact with the wall of the tube is at rest, that the layer next to it is moving slowly parallel to the axis of the tube, and that the rate of movement gradually 74 OUTLINES OF PHYSICAL CHEMISTRY increases towards the interior, attaining its maximum at the centre of the tube. It is evident that the rate of displacement of the layers with regard to each other must be mainly deter- mined by the amount of friction between them, and hence measurements of the rate of flow afford information as to the viscosity of liquids. The converse of viscosity is X&xu^&A. fluidity ; a liquid of small viscosity, such as ether, is said to have a high degree of fluidity. The magnitude of the viscosity depends greatly on the nature of the liquid. Thus the viscosity of warm ether is very small, whereas that of treacle and of pitch is so great that they approximate to the behaviour of solids, the internal friction of which is extremely high. The internal friction of gases is very small (p. 25). The coefficient of viscosity, -q, is usually defined as the force required to move a layer of unit area through a distance of unit length past an adjacent layer unit distance away. For water at 15°, 17 = o'oi34 in absolute units; for glycerine at the same temperature, 17 = 2-34. The coefficient of viscosity of a liquid can be calculated from the rate of outflow from a cylindrical tube by means of the equation pTvr^t '' = ^^' where v is the volume of liquid discharged in the time t, p the pressure under which the outflow takes place, r the radius and / the length of the tube. In practice, however, the rate of flow of the liquid is compared with that of a standard liquid, usually water, under the same experimental conditions, and its absolute viscosity, rf, calculated by means of the formula y)h„ = tlt^, where -q^ is the absolute viscosity of water at the temperature of the experiment, and / and t^ are the times required for the discharge of equal volumes of the liquid and water respectively. The viscosity of liquids diminishes rapidly as the temperature LIQUIDS 75 rises, but so far no simple relationship of general applicability connecting change of viscosity and temperature has been dis- covered. Measurement of Yiscosity — The determination of vis- cosity by the comparative method may be conveniently carried out with the apparatus described by Ostwald and illustrated in Fig. 9. It consists essenti- ally of a capillary tube, db, connected at its upper part with a bulb k, and at its lower end with a wider tube, bent into U-shape and provided with a bulb e. Marks are etched on the capillary tube at c and d above and \( below the bulb k. The apparatus is filled at/ with a definite volume of the liquid, which is then sucked into the other limb till the surface rises above the mark c. The time required for the level of the liquid to fall from c to ^ is then noted. Observations have previously been made with water under similar conditions. As the pressures under which the discharge takes place are in the ratio of the density, d, of the liquid to that of water, the relative viscosity, x = i;/?;^ is given by the equation X = dtjd^i^. On account of the great influence of _ . . , Fig- 9- temperature on the viscosity, the measure- ments must be made at constant temperature, and for this purpose the apparatus is so constructed that it can conveniently be immersed in a thermostat. Results of Yiscosity Measurements^ — Reference has already been made to the enormous differences in the viscosity of liquids, and also to the fact that temperature has a great influence on the magnitude of the viscosity. In comparing 'Smiles, loc. cit. pp. 51-105. 76 OUTLINES OF PHYSICAL CHEMISTRY different liquids with regard to viscosity, we are again confronted with the difficulty of deciding at what temperatures the measure- ments should be made. The choice of the boiling-points as corresponding temperatures (p. 57) did not in this case lead to very satisfactory results, and most regularities were observed by using the data for points at which the rate of change of viscosity with temperature is the same (Thorpe and Rodger). A comparison of substances of allied chemical constitution shows that viscosity is to some extent an additive property, but is greatly affected by constitutive influences. The absolute viscosity of a number of pure liquids at 0° and at 25° is given in the accompanying table (Walden) : — Liquid. ij at 0°. r, at 25". Acetone Methyl alcohol Acetic anhydride Water Ethyl alcohol Benzonitrile 0-00397 0-00846 0-0130 0-0178 0-0179 0-0194 0-00316 0-00580 o-oo86o 0-00891 0-0108 0-0125 Nitrobenzene 0-0307 0-0182 In recent years the viscosity of mixtures of liquids has been the subject of a good deal of investigation. If for simplicity we confine our attention to mixtures of two components only, three classes may be distinguished : — (i) The viscosity of the mixture lies between those of the pure components. Example, ethyl alcohol and carbon disul- phide. (2) The viscosity of the mixture in certain proportions is greater than that of either component. Example, pyridine and water. (3) The viscosity of the mixture in certain proportions is less than that of either constituent. Example, benzene and acetic acid. A few numbers illustrating the behaviour of the mixtures LIQUIDS 77 cited as examples of classes (2) and (3) are given in the accompanying table. Pyridine and Water.i Benzene and Acetic Acid.s Per cent. Pyridine. ij at 25°. Per cent. Benzene. 1) at 25°. 0-00 19-28 39-84 59-70 66-65 80-15 100-00 0-00890 0-01336 0-01833 0-02187 0-02225 0-01894 0-00885 o-oo 34-93 48-29 77-26 89-73 97-25 100-00 O-0II74 0-00734 0-00666 0-00597 0-00591 0-00594 0-00598 The results are very similar to those for the vapour pressures of binary mixtures, described later (p. 87). No general agreement has so far been reached as to the explanation of these remarkable differences in the behaviour of binary mixtures (compare p. 322). Measurements of the viscosity of salt solutions (solutions which conduct the electric current) have also led to interesting results, but they cannot be usefully considered at the present stage. Practical Illustrations, {a) Critical Phenomena — The critical phenomena can be observed in an apparatus, con- structed like that of Cagniard la Tour, but more simply as fol- lows : A tube 3-4 mm. internal diameter and 3-4 cm. long is constructed out of a piece of glass tubing, the walls of which are o-y-cS mm. thick, by closing one end in the blow-pipe and drawing out the other at a distance 3-4 cm. from the closed end into a fairly long (5-6 cm.) thick-walled capillary tube. The capillary is then bent, at a point about i cm. from the commence- ment of the wide part of the tube, at right angles to the latter and then partly filled with ether as follows. The tube is warmed and the capillary end dipped into ether, which is drawn into the tube ' Hartley, Thomas and Appleby, Trans, Chem. Soc, 1908, 94, 538. 'Dunstan, ibid., 1905, 87, 16. 78 OUTLINES OF PHYSICAL CHEMISTRY as the latter cools. The ether in the tube is then boiled gently to expel all the air, the end of the capillary dipping all the time in ether, and on again allowing to cool, ether is drawn in so as practically to fill the tube. The excess of ether is then boiled off till the tube is about three-quarters full, the end of the capillary being in ether throughout, and then allowed to cool till the liquid just begins to rise up the capillary tube, showing that the pressure inside is somewhat less than atmospheric ; the capillary is then rapidly sealed off near the bend on the side remote from the tube. In order to observe the capillary phenomena in the tube thus prepared, the latter is suspended by a wire and heated by means of a Bunsen burner held in one hand, the face being protected, in the event of an explosion, by a large plate of glass held in the other hand. In this way, the complete dis- appearance of the liquid above a certain temperature, and its reappearance on cooling, may be observed without the least danger. When practicable, the tube may be heated in an iron or copper vessel provided with mica windows, and the critical temperature may be read off on a thermometer placed side by side with the tube in the air bath. {d) Determination of Molecular Volume — The determination of the molecular volume of a liquid reduces to a determination of its density at a definite temperature compared with that of water as unity, and any of the well-known methods for deter- mining the density of liquids may be employed for this purpose. A direct method for determining the density, and hence the mole- cular volume, of a liquid at its boiling-point has been described by Ramsay. A tube is drawn out to a long neck and the latter bent in the form of a hook. The vessel is then filled with liquid, heated in the vapour of the same liquid till equilibrium is reached and then weighed. If the volume of the vessel and its coefficient of expansion are known, the molecular volume of the liquid can at once be calculated. LIQUIDS 79 Measurements of the refractive index of liquids (water alcohol, benzene) and of the rotation of the plane of polarization of light by liquids or solutions (cane sugar in water) should be made by the student ; the methods are fully described in text- books of physics. The experiments on rotation of the plane of polarization may conveniently be made in connection with the hydrolysis of cane sugar in the presence of acids (p. 230). CHAPTER IV SOLUTIONS General — Up to the present, we have dealt only with the properties of pure substances which may exist in the gaseous, liquid or solid state, or simultaneously in two or all of these states. We now proceed to deal with the properties of mixtures of two or more pure substances. When these mixtures are homogeneous, they are termed solutions^ There are various classes of solutions, depending on the state of the components. The more important are : — (i) Solutions of gases in gases ; (ii) Solutions of (a) gases, (B) liquids, (c) solids in liquids ; (iii) Solutions of solids in solids, so-called solid solutions ; and each of these classes wDl be briefly considered. A distinction is often drawn between solvent and dissolved substance, but, as will appear particularly from the sections dealing with the mutual solubility of liquids, there is no sharp distinction between the two terms. The component which is present in greater proportion is usually termed the solvent. The dissolved substance is sometimes called the solute. When one of the compounds is present in very small pro- portion, the system is termed a dilute solution, and as the laws ^The term solution is also applied to mixtures which appear homo- geneous to the naked eye but heterogeneous when examined with a micro- scope or ultramicroscope, e.g., colloidal solution of arsenic sulphide. The usual definition of a solution is "a homogeneous mixture which cannot be separated into its components by mechanical means," but the last part of this definition is open to objection. 80 SOLUTIONS 8i representing the behaviour of dilute solutions are comparatively simple, they will be dealt with separately in the next chapter. Solution of Gases in Gases — This class of solution differs from the others in that the components may be present in any proportion, since gases are completely miscible. If no chemical change takes place on mixing two gases, they behave quite in- dependently and the properties of the mixture are therefore the sum of the properties of the constituents. In particular, the total pressure of a mixture of gases is the sum of the pressures which would be exerted by each of the components if it alone occupied the total volume — a law which was discovered by Dalton, and is known as Dalton' s law of partial pressures. Dalton's law is of the same order of validity as Avogadro's hy- pothesis ; it is nearly true under ordinary conditions, and would in all probability become strictly true at great dilution. Dalton's law can of course be tested by comparing the sum of the pressures exerted separately by two gases with that after admixture, but it is of interest to inquire into the possibility of measuring the partial pressure of one of the components in the mixture itself. It was pointed out by van't Hoff that this is always possible if a membrane can be obtained which allows only one of the gases to pass through. This suggestion was experimentally realised by Ram- say 1 in the case of a mixture of nitrogen and hydrogen as follows: P (Fig. I o.) is a palladium vessel containing nitrogen, the pressure of which can be determined from the difference of level between A and B in the manometer, which contains mercury. P is enclosed in another vessel, which can be filled 1 PUl. Mag., 1894, [v.], 38, ao6. Fig. 10. §2 Outlines of physical chemistry with hydrogen at any desired pressure. The vessel P is heated and a stream of hydrogen at known pressure passed through the outer vessel. As palladium at high temperatures is permeable for hydrogen, but not for nitrogen, the former gas enters P till its pressure outside and inside are equal. The total pressure in P, as measured on the manometer, is greater than the pressure in the outer vessel, and it is an experimental fact that the excess pressure inside is approximately equal to the partial pressure of the nitrogen. If, on the other hand, we start with a mixture of hydrogen and nitrogen, and wish to find the partial pressure of the latter, all that is necessary is to put the mixture inside a palladium bulb, keep the latter at a constant high temperature and pass a current of hydrogen at known pressure through the outer vessel till equi- librium is attained, as shown on the manometer. The difference between the external and internal pressure is then the partial pressure of the nitrogen. This very instructive experiment will be referred to later in connection with the modern theory of solutions (p. loi). Solubility of Gases in Liquids — In contrast to the com- plete miscibility of gases, liquids are only capable of dissolving gases to a limited extent. When a liquid will not take up any more of a gas at constant temperature it is said to be saturated with the gas, and the resulting solution is termed a saturated solution. The amount of a gas taken up by a definite volume of liquid depends on {a) the pressure of the gas, {b) the tem- perature, {c) the nature of the gas, {d) the nature of the liquid. The greater the pressure of a gas, the greater is the quantity of it taken up by the solvent. For gases which are not very soluble, and do not enter into chemical combination with the solvent, the relation between pressure and solubility is expressed by Henry's law as follows : The quantity of gas taken up by a given volume of solvent is proportional to the pressure of the gas. Another way of stating Henry's law is that the volume of a gas taken up by a given volume of solvent is independent of the SOLUTIONS 83 pressure. This is clearly equivalent to the first statement, be- cause when the pressure is doubled the quantity of gas absorbed is doubled, but since its volume, by Boyle's law, is halved, the original and final volumes dissolved are equal. The question may be regarded from a slightly different point of view, which is instructive in connection with later work. When a definite volume of liquid is saturated with a gas at a certain pressure, there is an equilibrium between the dissolved gas and that over the liquid, and Henry's law may be expressed in the alternative form : The concentration of the dissolved gas is proportional to that in the free space above the liquid. We may consider that the gas distributes itself between the solvent and the free space in a ratio which is independent of the pressure. The solubility of gases in liquids diminishes fairly rapidly with rise of temperature. For purposes of comparison, the solvent power of a liquid for a gas is best expressed in terms of the " coefficient of solubility," which is the volume of the gas taken up by unit volume of the liquid at a definite temperature. ^ The so-called "absorption coefficient " of Bunsen, in which solubility measurements are still often expressed, is the volume of a gas, reduced to 0° and 76 cm. pressure, which is taken up by unit volume of a liquid at a definite temperature under a gas pressure equal to 76 cm. of mercury. With regard to the influence of the nature of the gas on the solubility, it may be said in general that gases which have distinct basic or acidic properties, for example, ammonia and hydrogen chloride, are very soluble, whilst neutral gases, such as hydrogen, oxygen and nitrogen, are comparatively insoluble. Further, gases which are easily liquefied, for example, sulphur dioxide and hydrogen sulphide, are fairly soluble. As regards the relation between solvent power and the nature of the liquid, very little is known. In general, the order of the solubility of gases in different liquids is the same, and the solvent power -of a liquid therefore appears to be to soma extent a specific property. ' Alternatively : the ratio of the concentration in liquid and in gas space. 84 OUTLINES OF PHYSICAL CHEMISTRY The above remarks are illustrated by the following table, in which the coefficients of solubility of some typical gases in water and in alcohol are given : — Gas. Water. Alcohol. Ammonia Hydrogen sulphide Carbon dioxide Oxygen . Hydrogen 1050 80 1-8 0-04 0'02 18 4-3 0-28 0-07 It may be mentioned that the solubility of gases in water is greatly diminished by the addition of salts, and to a much smaller extent by non-electrolytes. The interpretation of these results has given rise to considerable difference of opinion.^ Solubility of Liquids in Liquids — As regards the mutual solubility of liquids, three cases may be distinguished : (i) The liquids mix in all proportions, e.g., alcohol and water ; {2) the liquids are practically immiscible, e.g., benzene and water ; (3) the liquids are partially miscible, e.g., ether and water. (i) and (2) Complete miscibility and non-miscibility — Very little is known as to the factors which determine the miscibility or non-miscibility of liquids. The separation of the compon- ents by fractional distillation is discussed in succeeding sections. (3) Partial miscibility — If ether, in gradually increasing amounts, is added to water in a separating-funnel, and the mix- ture well shaken after each addition, it will be noticed that at first a homogeneous solution is formed, but when sufficient ether has been added, a separation into two layers takes place on standing. The upper layer is a saturated solution of water in ether, the lower layer a saturated solution of ether in water. As long as the relative quantities of ether and water are such that a separation into two layers takes place on standing, the ' Compare Philip, Trans. Chem. Soc, igoy, 91, 711 ; Usher, ibid., irgio, 97, 66. SOLUTIONS 8s composition of these layers is independent of the relative amounts of the components present, since the composition is determined by the solubility of ether in water and of water in ether at the temperature of experiment. In the majority of cases, the solubility of two partially miscible liquids increases with the temperature, and it may therefore be anticipated that liquids which in certain propor- tions form two layers at the ordinary temperature may be com- pletely miscible at higher temperatures. Several such cases are known, for example, phenol and water, and aniline and water, which have been investigated by Alexieeff. He took the components in varying proportions, and gradually raised the temperature till the mixture became homogeneous. The results with phenol and water are represented graphically in Fig. II, the composition of the mixture being measured on the horizontal axis and temperatures along the vertical axis. The point D represents o per cent, phenol (loo per cent, water), E represents loo per cent, phenol. At all points outside the curve ABC there is complete miscibility, at points inside the curve two layers exist. The maximum represents the tem- perature, 68'4'', above which phenol and water are miscible in all proportions. If, therefore, we start with a homogeneous solution of phenol in water of the composition represented by the point x, and gradually add phenol at constant tem- perature, the composition of the solution will alter along the dotted line xx' until the curve AB is reached at z. This point represents a saturated solution of phenol in water, and on further addition of phenol a separation into two layers takes place, the compositions of which are represented by the points z and z' respectively. As more phenol is added, the composition of the layers remains unaltered, but the relative amount of the second layer increases until at the point z' only this layer is present, and its composition then alters along zx' . If, however, phenol is added to the same solution at the tem- perature corresponding with the point y the composition alters 86 OUTLINES OF PHYSICAL CHEMISTRY along yy' but no separation into two layers takes place. It is evident that there is a striking analogy between the miscibility of two liquids and the critical phenomena represented in Fig. 5. In both cases there is only one phase outside the curves 210' Miscibility of Phenol and Watfir. Fig, II. 60 0% Nicotine Miscibility of Nicotine and Water. Fig. 12. 100% Nicotine AOE and ABC respectively, and two phases at points inside the curves. Further, above a certain temperature only one phase can exist in each case, and the temperature of com- plete miscibility for binary mixtures may therefore be termed the critical solution temperature. Moreover, just as we carj SOLUTIONS 87 pass without discontinuity from a gas to a liquid (p. 53), we can pass from a solution containing excess of water to one contain- ing excess of phenol without discontinuity. Starting with a mixture represented by the point x, the temperature is raised above the critical solution temperature along xy, phenol is then added till the point j is reached and the homogeneous mixture then cooled along y'x. In some cases, however, the solubility of one liquid in another diminishes with rise of temperature, thus if a saturated solution of ether in water, prepared at the ordinary temperature, is gently warmed, it becomes turbid, indicating partial separation of the ether. An interesting example of this behaviour is seen in nicotine and water, which are miscible in all proportions at the ordinary temperature, but separate into two layers when the temperature reaches 60°. If a temperature can be reached beyond which the mutual solubility again begins to increase with rise of temperature, the components may again become miscible in all proportions. This has been experimentally realised so far only for nicotine and water, which again be- come completely miscible when the temperature exceeds 2ro°. The remarkable solubility relations of these two liquids are therefore represented by a closed curve (Fig. 12), which will be readily understood by comparison with Fig. 11. Distillation of Homogeneous Mixtures — A very impor- tant matter with reference to binary homogeneous mixtures is the possibility of separating them more or less completely into their components by distillation. Much light is thrown on this question by the investigation of the vapour-pressure of the mix- ture as a function of its composition at constant temperature. Experimental investigation shows that the curve representing the relation between vapour pressure and composition at constant temperature usually belongs to one of the three main types a, b and c represented in Fig. 1 3, in which the abscissae represent the composition of the mixture and the ordinates the corres- ponding vapour pressures. 88 OUTLINES OF PHYSICAL CHEMISTRY («) The vapour-pressure curve of the mixture may have a minimum, as represented by the point U in the curve RUS ; example, hydrochloric acid and water. (In the diagram the ordinate PR represents the vapour-pressure of B, and QS that of the other pure substance A.) (6) The vapour-pressure curve may show a maximum, repre- sented by the point T on the curve RTS ; example, propyl alcohol and water. P(o''/„ A) Composition Fig. 13. Q (100 °/„ A) (f) The vapour-pressure of the binary mixture may lie between those of the pure components A and B, as repre- sented by the curve RWS ; example, methyl alcohol and water. In considering these three typical cases with regard to their bearing on the separation of two liquids by fractional distilla- tion, the important question is the relation between the com- position of the boiling liquid and that of the escaping vapour. For a pure liquid, the composition of the escaping vapour is necessarily the same as that of the liquid, but this is not in general the case for a, mixture of liquids, and therefore th? SOLUTIONS 89 composition of the mixture may alter continuously during dis- tillation. Case {a). Since a liquid boils when its vapour pressure is equal to the external pressure, it is clear that if a mixture the vapour-pressure curve of which has a minimum (as in the curve RUS) be boiled, the composition of the liquid will alter in such a way that it tends to approximate to that represented by the point U, since all other mixtures have a higher vapour pressure, and will consequently pass off first. When finally only the mixture U remains, it will distil at constant tempera- ture like a homogeneous liquid, since the composition of the vapour is then the same as that of the liquid. The best- known example of such a constant-boiling liquid is a mixture of hydrochloric acid and water, which boils at 110°. If a mixture containing the components in any other proportion be heated, either hydrochloric acid or water will pass off, and the com- position of the liquid will move along the curve to the point of minimum vapour pressure, beyond which it distils as a whole, without further change of composition. Case {b). When, on the other hand, there is a maximum in the vapour-pressure curve, the mixture which has the highest vapour tension will pass over first, and the composition of the residue in the retort will tend towards the component which was present in excess in the initial mixture. In the case of propyl alcohol and water, for example, the mixture which has the highest vapour tension contains from 70 to 80 per cent, alcohol (the maximum being very flat) ; a mixture of this com- position would boil at constant temperature, whilst for one con- taining more water, some of the latter would finally remain in the retort. Case {c). In this case the composition of the vapour, and therefore the composition of the liquid remaining, alter continu- ously on distillation. The vapour, and therefore the distillate, will contain the more volatile liquid, A, in greater proportion, and the residue excess of the less volatile liquid, a partial separation 90 OUTLINES OF PHYSICAL CHEMISTRY being thus effected. If the distillate rich in A is again distilled a mixture still richer in A is at first given off, and the process may be repeated again and again. The more or less complete separation of liquids by this method is termed fractional dis- tillation. It was long thought that constant-boiling mixtures were definite chemical compounds of the two components — for example, HCl, SHjO in the case of hydrochloric acid and water, but this view was shown by Roscoe to be untenable. He found that the composition of the mixtures does not correspond with simple molecular proportions of the com- ponents, and, further, that the composition alters con- tinuously with alteration of the pressure under which the distillation is conducted, which is not likely to be the case if definite chemical compounds are present. Distillation of Non-Miscible or Partially Miscible Liquids. Steam Distillation — If two immiscible liquids are distilled from the same vessel, since one does not affect the vapour pressure of the other, they will pass over in the ratio of the vapour pressures till one of them is used up. The tem- perature at which the mixture boils is that at which the sum of the vapour pressures is equal P(o=>;oB) Composition Q loo °/o B) to the superincumbent Fig. 14. pressure. The curve re- presenting the relation between vapour pressure and composition of the mixture is therefore a straight line (UU', Fig. 14) parallel to the axis of composition, PU representing the sum of the vapour pressures SOLUTIONS 91 RP and QT, of the two components at the temperature in question. These considerations are very important in connection with steam-distillation. This process is usually employed for the separation of substances with a high boiling-point, such as aniline, and will be familiar to the student. The relative volumes of steam and the vapour of the liquid which pass over are in the ratio of the vapour pressures, f-^ and p^, at the tem- perature of the experiment, and the relative weights which pass over are therefore in the ratio p-^d-^ : p:^d^, in which d-y and d^ are the densities of steam and of the other vapour respectively. Assuming that the system aniline-water boils at 98°, at which temperature the vapour pressure of water is 707 mm. (/j), the partial pressure of the aniline (/j) wUl be 760- 707 = 53 mm., and the weights of aniline and water which pass over are in the ratio S3 x 93 : 707x18 or 4929 : 12,726. This shows that under ideal conditions the ratio of water to aniline in the distillate is approximately 2-5 : i, the comparatively small vapour pressure of aniline being partially compensated for by its rela- tively high molecular weight. Finally, we consider the distillation from the same vessel of partially miscible liquids. The relation between vapour pressure and composition of the mixture in this case is repre- sented by the curve RSST (Fig. 14), RP representing the vapour pressure of the pure component A, and QT that of the other component B. In general, the vapour pressure of one liquid is lowered by the addition of another. It follows that the vapour pressure of partially miscible liquids, as long as two layers are present, will be represented by a straight line parallel to the axis of composition, but lower than the line UU' repre- senting the sum of the separate vapour pressures. The pressures when only one phase is present are represented by RS and ST respectively. Solution of Solids in Liquids— In this case the solubility is always limited, and depends on the nature of the solvent 92 OUTLINES OF PHYSICAL CHEMISTRY and solute and on the temperature. As in the other case; of solubility we are really dealing with an equilibrium, in this case between the dissolved salt and the solid. Two principal methods are employed for determining the solubility of solids in liquids, (i) Excess of the finely-divided solid is shaken continuously with a definite quantity of the solvent at a definite temperature till equilibrium is attained; (2) the solvent is heated with excess of the solute to a tem- perature higher than that at which the solubility is to be determined, and then cooled to the desired temperature in contact with the solid. The second method is to be recom- mended when sufficient time is allowed for the attainment of equilibrium at the temperature of experiment, but with suitable precautions the methods give identical results. It is of interest to note that the solubility depends somewhat upon the state of division of the solids ; the more finely divided the solid the greater is the solubility. For fairly soluble salts the difference is negligible, but for slightly soluble salts it may be relatively very considerable. Thus Ostwald has shown that the solubility in water of yellow oxide of mercury is about 14 per cent, greater than that of the coarser-grained red modification. The results of solubility measurements may be expressed in various ways, for example, as the number of grams of solute in 100 grams of the solvent, in 100 grams of the solution, or in 100 c.c. of the solution. When a solution saturated at a high temperature is allowed to cool in the complete absence of the solid solute, the excess of dissolved substance may not separate (cf. p. 55), and the solution is then said to be supersaturated. Effect of Change of Temperature on the Solubility of Solids in Liquids — The variation of the solubility in water of certain salts with change of temperature is shown in Fig. 15, the solubilities being represented as ordinates and the tempera- tures as abscissas. The curves are not drawn to scale, but represent diagrammatically the effect of change of temperature. SOLUTIONS 93 The solubility of most solids in water increases fairly rapidly with the temperature, e.g., potassium nitrate; but sodium chloride is only slightly more soluble in hot than in cold water. Calcium hydroxide and certain other calcium salts are less soluble in hot than in cold water; a solution of calcium hydroxide (lime water) saturated at the ordinary temperature, Temperature-^ Fig. 15. becomes turbid on warming. In the case of calcium sulphate, the solubility increases at first with rise of temperature and then diminishes, so that there is a maximum in the solubility curve, as shown in the figure. Solubility curves are usually continuous, but that representing the solubility of sodium sulphate shows a distinct change of direction at 33°. This is owing to the fact that we are dealing 94 OUTLINES OF PHYSICAL CHEMISTRY with the solubility curves of two distinct substances. Below 33°, the dissolved salt is in equilibrium with the solid deca- hydrate Na2S04, loHjO, but the latter splits up into the anhydrous salt and water at 33°, so that the solubility curve at .higher temperatures is that of the anhydrous salt. That this explanation of the phenomenon is correct is shown by the fact that the solubility of the anhydrous salt can be determined for a few degrees below 33° in the complete absence of crystals of the decahydrate ; the part of the curve thus obtained, repre- sented by the dotted line, is continuous with the right-hand curve. It is important to remember that the change to which the break in the solubility curve of sodium sulphate is due takes place in the solid phase and not in the solution. No well- defined case is known of a sharp break in a curve representing the variation of a physical property in a homogeneous system with temperature or composition. Relation between Solubility and Chemical Constitution — Very little is known as to causes influencing the mutual solubility of substances and its variation with temperature. In general, it may be said that substances of similar chemical com- position are mutually soluble, thus the parafifins are mi^cible with each other in all proportions, and organic compounds containing the hydroxyl group are all fairly soluble in water. In these cases it does not seem probable that the solubility is connected with anything in the nature of ordinary chemical combination. Phenomena of an apparently different nature are met with in the solubility of gases in liquids^ already referred to (p. 83), where it was pointed out that the solvent power is in general a specific property of the solute, and to some extent independent of the nature of the gas. The solubility of indifferent gases appears in the first instance to depend upon the relative ease with which they can be liquefied. Solid Solutions^ — In general, when the temperature of a dilute solution is lowered until partial solidification takes place, ' Compare Bruni, Feste Losungen und Isomorphismus, Leipzig, 1908. SOLUTIONS 95 the solvent separates in the solid form, practically uncontami- nated with the solute. When, however, a solution of iodine in benzene is partially frozen, crystals containing both substances separate, and when solutions of varying concentration are used, there is a constant ratio between the iodine remaining in solution and that in the solidified benzene. This is illustrated in the accompanying table ; in the top line is given the concentration Cj of the iodine in the liquid benzene, in the second line the iodine concentration Cg in the solid benzene, and in the third line the ratio of the concentrations in solid and liquid, which is approximately constant : — Cj 3-39 2-587 0-945 per cent. Cj I '2 7 9 o'92S o'3i7 per cent. C7C1 0-377 0-358 0-336 This phenomenon exactly corresponds with Henry's law regard- ing the solubility of gases in liquids (p. 82), and as the crystals containing the two substances are .quite homogeneous, they may be regarded as a solid solution of iodine in benzene. Similar phenomena have been observed for many other pairs of sub- stances, more particularly for certain metals (p. 192). Besides crystalline solid solutions, of which an example has just been given, non-crystalline or amorphous solid solutions are known. The hydrogen absorbed by palladium appears to be in solid solution in the metal, but the phenomenon is com- plicated, and is not yet thoroughly understood. Van't Hoff suggests that two solid solutions are present, hydrogen dissolved in palladium and palladium dissolved in solid hydrogen, corre- sponding with the two liquid layers formed by phenol and water. There is evidence that in some cases the dissolved substances can diffuse slowly through the solid solvent, which indicates that the solute exerts osmotic pressure (p. 97). Practical Illustrations. («) Partial Miscibility — The fact that certain liquids, such as phenol and water, are only 96 OUTLINES OF PHYSICAL CHEMISTRY partially miscible at ordinary temperatures, but completely miscible above 69°, may be illustrated as follows : 5-6 grams of crystals of phenol are placed in a small separating funnel, and on adding a little water and shaking it will be found that a clear solution is formed, mainly due to the effect of water in lowering the freezing-point of phenol. On further addition of water two layers will be formed, which only disappear when a large excess of water has been added. If, on the other hand, phenol is warmed to 75° in a test tube, and water at the same temperature is gradually added, no separation into two layers will occur, corresponding with the fact that the critical solution temperature has been exceeded. {b) Solubility and Temperature — The solubility in water of a salt such as sodium chloride may conveniently be determined as follows. A large test tube is partially filled with distilled water and excess of powdered sodium chloride, and partially immersed in a bath kept at constant temperature. The tube is closed by means of a rubber cork through which passes a glass stirrer, driven by means of a motor. At intervals samples of the solution are removed by means of a pipette, a weighed portion of the solution evaporated to dryness, and the residue weighed. When the concentration of the solution no longer alters, it is saturated. Observations should be made at differ- ent temperatures at intervals of 10° and the results plotted on squared paper, the temperatures being plotted as abscissae, and the solubility expressed as grams of the salt in 100 grams of solvent, as ordinates (Fig. 15). (c) Supersaturated Solutions — A supersaturated solution of sodium sulphate may be prepared by heating the salt with half its weight of water in a flask till a perfectly clear solution is obtained; the flask is then plugged with cotton wool and set aside to cool. If a small crystal of the sulphate is added to the cold solution, crystallization at once starts, but crystals not isomorphous with sodium sulphate {e.g., sodium chloride crystals) are not efficient in starting crystallization. CHAPTER V DILUTE SOLUTIONS General — So far, we have dealt in a general way with the properties of solutions, mainly on the lines of the older methods of investigation, as they were practised up to about twenty years ago. In 1885, however, a new turn was given to the subject by the enunciation of the modern theory of solution by van't HofF. Many of the experimental facts on which this theory is based had previously been established by the work of Ostwald, Raoult and others, and these results were correlated, and many fresh avenues opened for investigation, by van't Hoff's theory, the most important point in which is the conception of osmotic pressure, which will now be considered. It has already been shown that the laws applicable to gases are very simple and that these laws are most strictly followed in the rarefiedcondition ; on the molecular theory this is accounted for by assuming that the particles are then so far apart as to exert little or no mutual influence, and that the space filled by the material of the particles is negligible in comparison with the space occupied. Similarly, we may reasonably anticipate that the laws expressing the behaviour of dissolved substances will be most simple in dilute solution, in other words, when one of the components (the solvent) is present in large propor- tion compared with the other (the solute), and this is quite borne out by the facts. Osmotic Pressure. Semi-permeable Membranes — When a few drops of bromine are carefully placed by means 7 97 98 OUTLINES OF PHYSICAL CHEMISTRY of a pipette at the bottom of a jar full of hydrogen or air, and the jar is covered and allowed to stand, it will be found after some time that the heavy bromine vapour has distributed itself uniformly throughout the confined space against the force of gravity. We may say that the bromine vapour exerts a pressure in virtue of which it diffuses into those parts of the confined space where the pressure is less, and equilibrium is only attained when the pressure is equal throughout. In an exactly similar way, if a sugar solution is carefully covered with a layer of water, the dissolved sugar exerts a pressure with the result that it ultimately becomes uniformly distributed in the solution. This pressure cannot be determined directly, since the external pressure is the sum of this and the pressure of the liquid, but the principle of the method used for measuring it will be under- stood from its analogy with the method already described for measuring the partial pressure of a gas in a mixture (p. 8i). In the latter case, it will always be possible to determine the partial pressure of a gas, A, mixed with another gas, B, when a membrane is known which allows B, but not A, to pass through. Such a membrane is said to be semi-permeable, and for a mixture of nitrogen and hydrogen heated palladium answers the purpose. It is clear that, if we could find a membrane which allows water, but not dissolved sugar, to pass through, the pressure exerted by the latter in solution, its so-called osmotic pressure, could be measured. Such membranes were discovered by Traube, in the course of his experiments on so-called artificial vegetable cells. The most suitable membrane for the purpose was found to be copper ferrocyanide, and the formation of this membrane and its im- permeability for certain dissolved salts may be illustrated as follows. A glass tube, provided with a rubber tube and clip at one end and open at the other, is partly filled by suction with an aqueous solution of copper acetate (about 2-8 per cent.) and ammonium sulphate (0-5 per cent.), and the open end, in which the surface of the liquid has been made parallel by DILUTE SOLUTIONS 99 adjustment, is then dipped carefully into a 2 -4 per cent, aqueous solution of potassium ferrocyanide, containing a little barium chloride, and the tube supported in that position. A thin membrane of copper ferrocyanide forms across the lower end of the tube, and if the experiment has been carefully performed, it will be found that even after standing some hours there is no white precipitate (of barium sulphate) in the lower solution, showing that the membrane is impervious to ammonium sul- phate. Traube tried many other membranes, but none proved so efficient as copper ferrocyanide. Measurement of Osmotic Pressure — The semi-permeable membranes prepared by Traube were much too weak to with- stand fairly large pressures, and their use for actual measurements was only ren- dered possible by PfefTer's idea of deposit- ing them in the walls of a porous pot A (Fig. 16) such as are used for experiments on gas diffusion. The pot is first carefully washed, soaked in water for some timei then nearly filled with a solution of copper sulphate (2-5 grams per litre), dipped nearly to the neck in a solution of potas- sium ferrocyanide (2'i grams per litre) and allowed to stand for some hours. The salts diffuse through the walls of the pot and at their junction form a membrane of copper ferrocyanide, which, since it is im- permeable for the salts from which it is formed, remains quite thin but is capable of withstanding fairly large pressures, owing to its being supported by the walls. The cell is then taken out, washed, filled with a strong solution of sugar, and closed with a well-fitting rubber cork through which an open glass tube, B, passes. To ensure the tightness of the apparatus, it is of I Z2S s^a Sugar 5fllulial Fig. 16. loo OUTLINES OF PHYSICAL CHEMISTRY advantage, before forming the membrane, to dip the upper part of the pot, to the depth of about two inches, into melted paraffin, and after the pot is filled and the cork and tube placed in position, the upper surface should be covered with melted paraffin. When a: cell thus prepared is placed in water, the water passes in, the pressure inside slowly increases (as shown by the rise in level of the solution in the tube), and finally reaches a point at which, when the cell has been properly prepared, it remains constant for days. The maximum pressure thus attained, in other words, (^ excess of pressure which must prevail inside the cell in order to prevent more water flowing in through the semipermeable membrane, is termed the osmetic pressure of the solution. In accurate measurements, it is preferable to close the cell with a cork carrying a closed manometer, containing a definite volume of air confined over mercury. Dilution of the solution by the entry of a large volume of water is thus avoided. This arrangement was used by Pfeffer in his original experiments. The osmotic pressures measured in this way are very con- siderable — thus a I per cent, solution of cane sugar exerts a pressure of more than half an atmosphere, and a i per cent, potassium nitrate solution over two atmospheres. The question as to the relation between osmotic pressure and concentration of the solution was investigated by Pfeffer, and the results obtained for aqueous solutions of sugar and of potassium nitrate at room temperature are given in the ac- companying table, in which C represents the concentration of the solution (in grams per loo c.c. of solution) and P the osmotic pressure (in cm. of mercury). Cane Sugar. Potassium Nitrate. C P P/C C P P/C 1 S3'S S3'5 0-8 130-4 163 2 IOI-6 50-8 1-43 218-5 153 4 208-2 S2-I 3-33 436-8 133 6 3o7'S Si'3 It is clear from these results that the ratio P/C is approximately DILUTE SOLUTIONS loi constant for any one solution, in other words, the osmotic pres- sure of a solution is proportional to its concentration. It will be observed that the ratio is somewhat less for potassium nitrate at the higher pressures, a result due in part to the slight per- meability of the membrane for the salt under these conditions. It was also shown by Pfeifer that the osmotic pressure at constant concentration increases with the temperature ; some of the results obtained in this connection are quoted on the next page. The magnitude of the osmotic pressure observed with different membranes was not quite the same, but this must be ascribed to the imperfection of most of the membranes, as it can be shown theoretically that the numerical value of the osmotic pressure is independent of the nature of the membrane, provided the latter is perfectly semi-permeable. Yan't Hoff's Theory of Solutions — Pfeffer's investiga- tions were undertaken for botanical purposes, and their great general importance was only recognised in 1885 by van't Hoff, who used them as the experimental basis of a new theory of solution. We have already seen that osmotic pressure may be regarded as in some respects analogous to gas pressure, and as the former can be measured as described in the previous section we are now in a position, following van't Hoff, to investigate the relationship between osmotic pressure, volume and tem- perature as has already been done for gases. As regards the relation between osmotic pressure and volume at constant temperature, we have seen in the previous section that P/C is constant for any one substance, and as the concen- tration is inversely as the volume in which a definite weight of substance is dissolved, we obtain, by substituting i/V for C, the equation PV = constant, the exact analogue for solutions ot Boyle's law for gases. With reference to the relation between osmotic pressure and temperature at constant concentration, van't Hoff showed from Pfeffer's observations that the osmotic pressure, P, like the gas I02 OUTLINES OF PHYSICAL CHEMISTRY pressure, is proportional to the absolute temperature, T. Some of the observations on which this conclusion is based are given in the accompanying table : — Cane Sugar. Sodium Tartrate. / T P / T P 14-2° 287-2 51-0 13-3° 285-3° 90"8 32-0° 305-0 54-4 (54-6) 37-0° 310-0° 98-3 (98-2) The observed values are given in the third column, with the calculated values in brackets ; the agreement is within the limits of experimental error. From these two equations, PV = const, and P oc T, we can derive an equation for dilute solutions corresponding to that already obtained for gases (p. 26), PV = ^T, in which P represents the osmotic pressure of a solution con- taining a definite weight of a solute in the volume, V, of solution, and r is a constant. It remains to calculate the numerical value of r for a definite amount, say a mol of a dissolved substance, as has already been done for gases. This can readily be done from Pfeffer's observa- tion that a I per cent, solution of cane sugar at 0° exerts an osmotic pressure of 49-3 cm. of mercury. The molecular weight of cane sugar is 342, the volume in which it is contained 34,200 c.c, the pressure is 49-3 x i3'S9 gram/cm.^, and the absolute temperature 273°. Hence PV 49-3 X 13-59 X 34,200 o /• • X r = -=r =r ^^^ ^-^^ — ^^ — = 83,900 (m gram-cm. units), 1 273 a value which almost exactly corresponds with that obtained for gases. As the same value for r is obtained for a mol of other organic compounds, such as urea and glucose, we will represent it by R, to indicate that it is a factor of general im- portance. We have thus obtained two results of the greatest importance : (i) the equation PV = RT is valid for dilute solu- DILUTE SOLUTIONS 103 dons ; (2) the numerical value of R is the same for dissolved substances as for gases. The latter statement implies, as is clear from the general equation, that the osmotic pressure of a definite quantity of cane sugar or other substance in solution is equal to the gas pressure which it would exert if it occupied the same volume in the gaseous form. We may therefore say with van't Hoff that " tM osmotic pressure exerted by any substance in solution is the same as it would exert if present as gas in the same volume as that occupied by the solution, provided that the solution is so dilute that the volume occupied by the solute is negligible tn comparison with that occupied by the solvent". This statement holds for all temperatures, as is at once clear from the fact that the solution obeys the gas laws. Certain important exceptions to the above rule, more particularly in the case of solutions which conduct the electric current, will be discussed in a later chapter. Some important consequences of the validity of the general equation, PV = RT, for dissolved substances will be dealt with in detail later. In particular, the molecular weight of a dis- solved substance is the quantity in grams which, when dissolved in 2 2 '4 litres at 0°, exerts an osmotic pressure of i atmosphere, a definition almost exactly analogous to that for gases (p. 36). The same fact may be expressed somewhat differently as fol- lows : Quantities of different substances in the ratio of their molecular weights, when dissolved in equal volumes of the same solvent, exert the same osmotic pressure. So far, we have considered only the experimental basis of the theory of solution. It has, however, been shown theoretically by van't Hoff, by thermodynamical reasoning, that the osmotic pressure and gas pressure must have the same absolute value, if the solution is suflficiently dilute, and this conclusion has been confirmed by Lord Rayleigh and by Larmor, among others. The latter writer puts the matter as follows : " The change of available energy on further dilution, with which alone we are concerned in the transformations of dilute solu- I04 OUTLINES OF PHYSICAL CHEMISTRY tions \cf. p. 150], depends only on the further separation of the particles . . . and so is a function only of the number of dissolved molecules per unit volume and of the temperature, and is, per molecule, entirely independent of their constitution and that of the medium," ^ the assumption being rnade that the particles are so far apart that their mutual influence is negligible. "The change of available energy " is thus brought into exact correlation with that which occurs in the expansion of a gas. Recent direct Measurements of Osmotic Pressure — It is a remarkable fact that, although Pfeffer's osmotic pres- sure measurements were made as early as 1877, the degree of accuracy attained by him has not been improved upon until quite recently. Accurate measurements are, however, very desirable, because although the relation between osmotic pres- sure and concentration can be calculated from the gas laws in dilute solution, there is still much uncertainty as to how far the gas laws are applicable, or what is the exact relationship between osmotic pressure and concentration, in concentrated solutions. In particular, it is, or was until quite recently, uncertain whether V in the general equation, PV = RT, should represent the volume of the solvent or that of the solution. This uncertainty has been to some extent removed by the very careful measurements carried out by Morse and Frazer ^ since 1 903 by Pfeffer's method with slight modifications. Their results show that, if V in the general equation be taken as the volume of the solvent, aqueous solutions of cane sugar approximately follow the gas laws up to a concentration of 342 grams of the solute in 1000 grams of water. A few of their results, illustrating the above statement, are given in the accompanying table; the numbers under "gaseous" are calculated on the assumption that the sub- stance as gas occupies the same volume as the solvent in the solution. 'Larmor, Encyc. Britannica, loth ed., vol. xxviii., p. 170. ^Amer. Chem. J., 1905, 34, i ; 1906, 36, i, 39; 1907, 37, 324, 425, 558, 381 175 ; 1908, 39, 667 ; 40, I, 194 ; 1909, 41, I, 257. DILUTE SOLUTIONS I OS Concentration of Solution. Pressure at constant temp. (20°) (atmospheres). Gaseous. Osmotic. Ratio of osmotic pres- sure to gas pressure. viols per looo grams of water. Mols per litre oi solution. o-io 0-09794 2-39 2-522 i-°S5 0-20 0-40 0-19192 0-36886 4-78 9-56 5-023 9-96 I -05 1 1-038 o"6o o-8o 0-53252 0-68428 i4"34 19-12 15-20 20-60 1-060 1-077 i-oo 0-82534 23-90 26-12 1-093 The table shows that only when concentrations are referred to a definite weight (or volume) of solvent is there proportionality between concentration and osmotic pressure ; if they are re- ferred to a constant volume of solution ("column 2) the osmotic pressure increases faster than the concentration. The numbers in the fifth column show, however, that the osmotic pressure at 20° is on the average about 6 per cent, greater than the gas pressure. Curiously enough, the ratio is about the same at all temperatures from 0° to 25°. Other Methods of Determining Osmotic Pressure — The difificulties inherent in the direct determination of osmotic pressure can often be avoided by determining it indirectly by comparison with a solution of known osmotic pressure. Solutions which have the same osmotic pressure are said to be isotonic or isosmotic. One such method, used by de Vries, depends on the use of plant cells as semi-permeable membranes. The protoplasmic layer which surrounds the cell-sap is permeable to water, but impermeable to many substances dissolved in the cell-sap, such as glucose and potassium malate. If such a cell is placed in contact with a solution of higher osmotic pressure than the cell-sap, water is withdrawn from the cell (just as a sugar solution absorbs water through a semi-permeable membrane) and the protoplasm shrinks away from the cell-wall ; a pheno- menon which is termed plasmolysis. If, however, the solution has a smaller osmotic pressure than that of the cell-sap, water enters the cell, the protoplasm expands and lines the cell-wall. The behaviour of the protoplasm, especially if coloured, can be ' Zeitsch. physikal. Chem., 1888, 2, 415. io6 OUTLINES OF PHYSICAL CHEMISTRY followed under the microscope, and by trial a solution can be found which has comparatively little effect upon the appearance of the cell, and is therefore isotonic with the cell contents. A method depending on the same principle, in which red blood corpuscles are used instead of vegetable cells, has been described by Hamburger,^ and the cell-walls of bacteria may also be used as semi-permeable membranes. The following table contains some " isotonic coefficients " as given by de Vries and by Hamburger ; the numbers represent the ratio of the osmotic pressures of equimolecular or equimolar solutions of the compounds mentioned. Substance. Cane sugar . Potassium nitrate . Isotonic Coefficients. Plasmolytic With Red Blood Method. Corpuscles. . l-8l 172 • 3'o 3-0 Sodium chloride . • 3'o 30 Calcium chloride . ■ 4-33 4"oS It will be observed that, although the results obtained by the two methods agree fairly well, the osmotic pressures for equi- valent solutions are not equal, as would be expected according to Avogadro's hypothesis. The deviation from the expected result is such that potassium nitrate, for example, exerts an osmotic pressure about 17 times greater than that due to an equimolar solution of cane sugar. This observation is of fundamental importance in connection with modern views as to salt solutions. The Mechanism of Osmotic Pressure — The foregoing considerations are quite independent of any hypothesis as to the exact nature of osmotic pressure, and so far no general agreement has been reached on this point. Van't Hoff inclines to the view that the pressure is to be accounted for on kinetic grounds,^ perhaps as being due to the bombardment of the ^ Zeitsck. physikcU. Chem., 1890, 6, 319. 2 For a discussion between van't Hoff and Lothar Meyer on this point, see Zeitsch. physikal. Chem., 1890, 5, 23, 174. DILUTE SOLUTIONS 107 walls of the vessel by solute particles, in the same way as the pressure of a gas is produced according to the kinetic theory, and the fact that the osmotic pressure is proportional to the absolute temperature appears rather to support this suggestion. Other views are that it is connected with attraction between solvent and solute, or perhaps with surface tension effects. It may be pointed out that the equivalence of osmotic pressure and gas pressure in great dilution is no evidence that they arise from the same cause. As regards semi-permeable membranes, their efficiency does not depend, as might at first sight be sup- posed, on anything in the nature of a sieve action, only the smaller molecules being allowed to pass, but rather upon a difference in their solvent power for the two components of the mixture. The action of the palladium in Ramsay's experiment (p. 81) is very probably to be accounted for in this way, and that the same is true for solutions is well illustrated by an in- structive experiment due to Nernst and illustrated in Fig. 17. The wide cylin- drical glass tube A is closed at the bottom with an animal membrane (bladder) which has previously been thoroughly soaked in water; it is then filled with a mixture of ether and benzene and fitted with a cork and narrow tube, as shown in the figure. The cell is supported on a piece of wire gauze in a beaker partly filled with moist ether and loosely closed .by a cork, B. After a time it will be observed that the liquid has risen to a considerable height in the narrow tube. What occurs in this case is that the ether dissolves in the water with which the membrane is soaked, and in this way is transferred inside the cell, whilst the benzene, being insoluble in water, is unable to pass out. Fig. 17. io8 OUTLINES OF PHYSICAL CHEMISTRY Similarly, the efficiency of the copper ferrocyanide membrane may depend on its solvent power for water but not for sugar. Osmotic Pressure and Diffusion — It has already been pointed out that there is a close connection between osmotic pressure, as defined above, and diffusion ; it is the difference in the osmotic pressure of cane sugar in different parts of a system which causes it in time to be uniformly distributed through that system. The diffusion of dissolved substances was very fully investigated by Graham, but the general law of diffusion was first enunciated by Fick. Fick's law is comprised in the equation ds =■ - T>K^dt, dx which states that the amount of solute, ds, which passes through the cross-section of a diffusion cylinder is proportional to the area. A, of the cross-section, to the difference of concentration, dc, at two points at a distance dx from one another, to the time, dt, and to a constant, D, characteristic for the substance, and termed the diffusion-constant. As an illustration of the above formula, it was found that when dc=\ gram per c.c, dx=i cm., A= 1 sq. cm.and(//=one day, that 075 grams of sodium chloride passed between the two surfaces. This is excessively slow, in comparison with the high osmotic pressures set up even by dilute solutions, and the explanation is to be found in the great friction due to the smallness of the particles. As the driving force — the osmotic pressure — ^and the rate of diffusion are known, the resistance to the movement of the particles can be obtained. It has been calculated that the enormous force of four million tons weight is needed to force i gram mol of cane sugar through water at a velocity of i cm. per sec. The more rapid diffusion in gases may plausibly be ascribed to the much smaller resistance to the movement of the particles. The rate of diffusion is much influenced by temperature and, curiously enough, to about the same extent for all solutes DILUTE SOLUTIONS 109 the average increase is about :^ of the value at 1 8° for every degree C. MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. General — It has already been pointed out (p. 103) that since Avogadro's hypothesis is valid for solutions, the molecular weight of a dissolved substance can readily be calculated when the osmotic pressure exerted by a solution of known concentration at known temperature and pressure is known. An illustration of this is given on the next page. As, however, the direct measure- ment of osmotic pressure is a matter of considerable difficulty, it has been found more convenient for the purpose to measure other properties of solutions, (Ae relationship of which to the osmotic pressure is known. The only three methods which can be dealt with here are : — (i) The lowering of vapour pressure ; (2) The elevation of boiling-point ; (3) The lowering of freezing-point, brought about by adding a known weight of solute to a known weight or volume of solvent. It can be shown by thermodynamical reasoning (p. 1 3 1) that un- der certain conditions the lowering of vapour pressure, the eleva- tion of the boiling-point and the lowering of the freezing-point due to the addition of a definite quantity of solute to a definite volume of solvent are each proportional to the osmotic pressure of the solution. Further, the equations expressing the exact relation- ships between these three factors and the osmotic pressure have also been established,^ and all these theoretical deductions have been fully confirmed by experiment. It follows that just as equimolecular quantities of different substances in equal volumes of the same solvent exert the same osmotic pressure, so equimole- cular quantities of different substances in equal volumes of the same solvent raise the boiling-point, lower the freezing-point, and lower the vapour tension to the satne extent. These statements find a very simple representation on the molecular theory. Since 1 Appendix, pp. 131-138. no OUTLINES OF PHYSICAL CHEMISTRY equimolecular quantities of different substances contain the same number of molecules, it follows that the magnitude of the osmotic pressure, lowering of vapour pressure, etc., depends only on the number of particles present and is independent of their nature (colligative properties, p. 63). The molecular weight of the solute could, of course, be obtained by determining one of the factors (i), (2), (3) and then calculating the value of the osmotic pressure, but it is much simpler to obtain the molecular weight by comparison with a substance of known molecular weight. It may be mentioned that besides the methods just indicated, there are other analogous methods for determining molecular weights which, from considerations of space, cannot be referred to here. Nernst has pointed out that any process involving the separation of solvent and solute can be used for determining molecular weights, and a little consideration will show that the four methods just mentioned come under this heading. Moreover, the osmotic effect of the solute is to diminish the readiness with which part of the solvent may be separated from the solution, and the effect of the solute on the boiling- and freezing-points of the solvent must therefore be in the direction already indicated. The mathematical proof of the connection between these four properties depends upon the equivalence of the work done in removing part of the solvent from the solu- tion (Appendix). The four different methods for determining molecular weights in solution and the general nature of the results obtained will now be considered in detail. Molecular Weights &om Osmotic Pressure Measure- ments, {a) Iirom absolute values of the osmotic pressure — The principle of this method has already been discussed (p. 103). If g grams of substance, dissolved in v c.c. of solvent, gives an osmotic pressure of/ cm. at T° abs., the molecular weight,. m, will be that quantity which, when present in 22,400 c.c. of solvent, will give an osmotic pressure of 76 cm. Hence, since pvIT is proportional to the amount of substance used (p. 26), g- DILUTE SOLUTIONS pv _ 22,400 X 76 273 + ' ■ ■■ 273 or ... S X 22,400 X 76 X (273 + f) 2-iipv As an example, we will take an experiment of Morse and Frazer (p. 105) in which a solution containing 34-2 grams of sugar in 1000 c.c. (really 1000 grams) of water gave an osmotic pressure of 2-522 atmospheres = 191-6 cm. at 20°. Hence _ 34-2 X 22,400 X 76 X 20-? , m = iz i!i I. z± = 326-0 273 X 191-6 X 1000 as compared with the theoretical value of 342. (b) By comparison of osmotic pressures — Since equimolecular solutions in the same solvent have the same osmotic pressure, it is only necessary to find the strengths of two solutions which are in osmotic equilibrium (isotonic), and if the molecular weight of one solute is known that of the other can be calculated. De Vries found that a 3-42 per cent, solution of cane sugar was isotonic with a 5-96 per cent, solution of raffinose, the molecular weight of which was then unknown. If it be re- presented by X, then 3-42 : 5-96 : : 342 : : x, whence «=596. This result has since been confirmed by chemical methods. Lowering of Vapour Pressure — It has long been known that the vapour pressure of a liquid is diminished when a non- volatile substance is dissolved in it, and that the diminution is proportional to the amount of solute added. In 1887 Raoult, on the basis of a large amount of experimental work, established the following important rule : Equimolecular quantities of differ- ent substances, dissolved in equal volumes of the same solvent, lower the vapour pressure to the same extent. On comparing the relative lowering (i.e., the ratio of the observed lowering and the original pressure) in different solvents, the same observer discovered another important rule, which may be expressed as follows : The relative lowering of vapour pressure is equal to the ratio of the number of mokcules of solute and the total number of 112 OUTLINES OF PHYSICAL CHEMISTRY molecules in the solution. Putting p-^ and p^ for the vapour pressures of solvent and solution respectively, the rule may be put in the form A -A _ " /i N + « in which n and N represent the number of molecules of solute and solvent respectively, In order to illustrate the validity of this rule, some results given by Raoult are quoted in the ac- companying table ; the relative lowering is that due to the addition of i mol of solute to loo mols of the various sol- vents : — Solvent. HjO PCI3 CSa CCI4 CH3I (CaHsJaO CH3OH Relative lowering o-oio2 o-oio8 o'oios o'oibs 0-0105 0-0096 0-0103 The results agree excellently among themselves, and fairly well with the calculated value, i/ioi = 0-0099. About the same time van't Hoff introduced the conception of osmotic pressure, and showed by a thermodynamical method that the relation between the relative lowering of vapour pres- sure and the osmotic pressure is given by the equation AzA=_M /i jRT • ^ • ■ ■ ^^^ where M = molecular weight of solvent, in the form of vapour, s is its density, and the other symbols have their usual significance. The expression M/sRT is therefore constant, since it depends only on the nature of the solvent, and consequently the relative lowering of vapour-pressure is proportional to the osmotic pres- sure P. By using the general equation, PV = «RT (where n is the number of mols of solute), P in equation (i) can be elimin- ated,^ and we finally obtain mRT 1 P = -Tj—, where V is the volume of the solvent. If N represents the number of mols of solvent, M its molecular weight and j its density, the volume V of the solvent = MN/s. Hence P = itm" > ^"^ when this value is substituted in equation (i) we obtain (^j- ^2)/^! =*!/N. DILUTE SOLUTIONS ri3 A -A _ Si A ~ N- This equation differs from that of Raoult in that the de- nominator on the right-hand side is N instead of N + «, but they become identical " at infinite dilution " when the volume of the solute is negligible in comparison with that of the solvent. By substituting for n and N gfrn and W/M, where g and W are the weights of solute and solvent respectively, in is the (unknown) molecular weight of the solute and M that of the solvent in the form of vapour, we obtain the equation A -A ^ g^ /i Vim which enables us to calculate the molecular weight of a dissolved substance when the relative lowering produced by a known weight of solute in a known weight of solvent is known. As an illustration, an experiment of Smits may be quoted. He found that at o° the lowering of vapour pressure produced by adding 29-0358 grams of sugar to 1000 grams of water is 0-00705 mm., the vapour pressure of water at that temperature being 4-62 mm. Hence 70s 29-0358 X 18 J 1—^ = ^ •■'•' , and m = 342, 4-62 in exact agreement with the theoretical value. As the lowering of vapour pressure is very small and not very easy to determine accurately by a statical method, it has not been very largely used for molecular weight determinations, the closely allied method depending on the elevation of the boiling-point being preferred. It has, however, one great advantage, inasmuch as, unlike the boiling-point and freezing- point methods, it can be used for the same solution at widely different temperatures. For this purpose, a dynamical method suggested by Ostwald and worked out by Walker ^ has certain advantages. A current of air is drawn in succession through (i) two sets of Liebig's bulbs containing the solution of vapour 1 Zeitsch. physikal. Chem., 1888, 2, 602. 8 114 OUTLINES OF PHYSICAL CHEMISTRY pressure p^ (2) similar bulbs containing the pure solvent vapour pressure p-^ (3) a U-tube containing concentrated sulphuric acid. In the first two sets of bulbs it becomes saturated up to /^ with the vapour of the solvent, in the third set up to /j, in the U-tube the moisture is completely absorbed. The loss of weight in the second set of bulbs is proportional to p^ -p.^ and the gain in the U-tube to/i (cf. p. 91).! Elevation of Boiling-point — A little consideration shows that there is a close connection between this method of deter- mining molecular weights and that depending on the lowering of vapour pressure. A liquid boils when its vapour pressure is equal to that of the atmosphere. The presence of a solute lowers the vapour pressure, and to reach the same pressure as before we require to raise the temperature a little; it is evident that, to a first approximation, this elevation must be proportional to the lowering of vapour pressure. It follows that, in this case also, equimolecular quantities of different solutes, in equal volumes ^f the same solvent, raise the boiling- point to the same extent. The molecular weight of any soluble substance may therefore be found by comparing its effect on the boiling-point of a solvent with that of a substance of known molecular weight. For this purpose, it is convenient to determine the molecular elevation constant, K, for each solvent, that is, the elevation of boiling-point which would be produced by dissolving a mol of any substance in 100 grams or 100 c.c. of the solvent. Actually, of course, the elevation is determined in fairly dilute solution, and the value of the constant calculated on the assumption that the rise of boiling-point is proportional to the concentration. Then the weight in grams of any other compound which, when dissolved in 100 grams ot 100 c.c. of the solvent, produces a rise of K degrees in the boiling-point is the molecular weight. If g grams of substance, of unknown molecular weight, ot, dissolved in L grams of solvent raises the boiling-point 8 ' A modification of this method has recently been used by Lord Berkeley and Hartley for the indirect determination of the osmotic pressure of con- centrated solutions of cane sugar (Proc. Roy. Soc, 1906, 77A, 156. DILUTE SOLUTIONS 115 degrees, whilst m grams in 100 grams of solvent give a rise of K degrees, it follows that I OOP- . _- , ioopK -- ; S : : w : ; K, whence m = ^ g — • Li LO In the course of the last few years, the constants for 100 grams and 100 c.c. have been very carefully determined for a large number of solvents, and some of the more important data are given in the accompanying table : — Solvent. iviuiecuictr £. 0'4II 144 I2'll 149 1-253 143 23-12 152 2-791 145 26-59 154 5-897 147 The observed molecular weights depend not only on the nature of the solute and on the concentration, but also very largely on the nature of the solvent. Examples will be given in the follow- ing pages showing that in certain solvents the observed mole- ' Concentration in grams per 100 grams of benzene, DILUTE SOLUTIONS 123 cular weights are often higher than those deduced from the chemical formula of the solute. The solute is then said to form complex molecules or to be associated, and the solvent is termed an associating solvent. In other solvents, on the contrary, the molecular weight may be equal to or less than that deduced from its chemical formula. In the latter case the solute is said to be dissociated, and the solvents in question are termed dissociating solvents. Abnormal Molecular Weights — In order to illustrate the results of molecular weight determinations from a slightly differ- ent point of view, the following table contains the values for the molecular freezing-point depression, K, for three typical sol- vents, water, acetic acid and benzene. The data are mainly due to Raoult, and in calculating K it is assumed that the molecular weight corresponds with the ordinary chemical formula of the solute : — Solvent — Benzene. Solute. K. Methyl iodide . 50*4 Ether . . . 49-7 Acetone . . 49-3 Aniline . . .46-3 Methyl alcohol 25-3 Phenol . . . 32'4 Acetic acid . 25-3 Benzoic acid . 25-4 This very instructive table shows that, for all three solvents, there are two sets of values for K, one of which is approximately double the other. The question now arises as to which of these are the normal values, obtained when' the solute exists as single molecules in solution. This can at once be settled by using van't Hoff's formula, K = (o'02T^)/H (p. 120), and we find that the normal depressions are i8-6, 39*0 and 51 '2 for water, acetic acid and benzene respectively. This means that acetic acid, phenol and some other compounds dissolved in Solvent— Water. Solvent — Acetic Acid. Solute. K. Solute. ■ K. Cane sugar 186 Methyl iodide . 38-8 Acetone . 17-1 Ether . . . 39-4 Glycerol . 17-1 Acetone . .38-1 Urea . . i8-7 Methyl alcohol 35-7 HCl . . 39'i HCl. . . . 17-2 HNO3 . 35-8 H2SO4 . . . i8-6 KNO3. . 35-8 (CHaCOOjjMg 1 8- 2 NaCl . . 36-0 124 OUTLINES OF PHYSICAL CHEMISTRY benzene produce only half the depression, in other words, exert only about half the osmotic pressure that would be expected ac- cording to their formulae, whilst in water certain acids and salts have an abnormally high osmotic pressure. The osmotic pressure of certain mineral acids in acetic acid is abnormally low. On the molecular theory, an abnormally small osmotic pressure shows that the number of particles is smaller than was anticipated. The experimental results can be satisfactorily accounted for on the view that acetic acid and benzoic acid exist as double molecules in benzene solution, and that phenol is polymerized to a somewhat smaller extent. This explanation seems the more plausible inasmuch as acetic acid contains com- plex molecules in the form of vapour (p. 41). It is mainly compounds containing the hydroxyl and cyanogen groups which are polymerized in non-dissociating solvents ; in dissociating solvents, such as water and acetic acid,^ these com- pounds have normal molecular weights. It may be anticipated that the molecular complexity of solutes will be greater in concentrated solutions, and the avail- able data appear to show that such is the case. The results are, however, somewhat uncertain, inasmuch as in concentrated solution the gas laws are no longer valid (p. 122). Solvents such as benzene are sometimes termed associating solvents, but this probably does not mean that they exert any associating effect. There is a good deal of evidence to show that the substances existing as complex molecules in benzene and chloroform solution are complex in the free condition, and that the complex molecules are only partly broken up in so-called associating solvents. The explanation of the behaviour of solutes in water is by no means so simple, and can only be dealt with fully at a later stage. The data in the table indicate that cane sugar, urea, acetone, etc., are present as single molecules in solution, but hydrochloric acid, potassium nitrate, etc., be- have as if there were nearly double the number of molecules to ' That acetic acid is in some cases at least a dissociating solvent is evident from the fact that the molecular weight of methyl alcohol in it is almost normal. DILUTE SOLUTIONS 125 be anticipated from the formulae. When van't Hoff put forward his theory of solutions he was quite unable to account for this behaviour, and contented himself with putting in the general gas equation a factor, /, to represent the abnormally high os- motic pressure, so that for salts and the so-called " strong " acids and bases in aqueous solution the equation became PV = «-RT. The factor i can of course be obtained for aqueous solutions by dividing the experimental value of the molecular depression by the normal constant, i8'6, so that for potassium nitrate, for example, i = 35'8/i8"6 = i'92. Van't Hoff recalled the fact that ammonium chloride, in the form of vapour, exerts an abnormally high pressure, which is simply accounted for by its dissociation according to the equa- tion NH^Cl = NHg -1- HCl, but it did not appear that the results with salts, etc., could be explained in an analogous way. We shall see in detail later that the elucidation of the signifi- cance of the factor / was of the highest importance for the further development of the theory of solution. According to our present views, the substances which show abnormally high osmotic pressures are partially dissociated in solution, not into ordinary atoms, but into atoms or groups of atoms associated with electrical charges. The equation representing the partial splitting up of potassium nitrate, for example, may be written + . — KNO3 = K + NO3, which indicates that the solution contains potassium atoms associated with positive electricity, and an equal number of NO3 groups, associated with negative elec- tricity. These charged atoms, or groups of atoms, are termed ions. Molecular Weight of Liquids — Our knowledge as to the molecular weight of pure liquids is due mainly to the investi- gations of Eotvos (1886) and of Ramsay and Shields (1893), and is based on the remarkable rule, discovered by Eotvos, that the rate of change of ike ' ' molecular surface energy " of many 126 OUTLINES OF PHYSICAL CHEMISTRY liquids with temperature is the same. If y represents the sur- face tension and s the " molecular surface," the rule in question may be written where c is a constant.^ The molecular surface, s, can be ex- pressed in terms of readily measurable quantities as follows : The molecular volume of any liquid is represented by Mw where M is the molecular weight and v the specific volume. If the molecular volume is regarded as a cube, one edge of the cube will measure (Mw)^, and the area of one side of it (Mw)l (M»)l may therefore be called the molecular sur- face, s, and just as the relative molecular volumes of different liquids contain an equal number of molecules so the relative molecular surfaces for different liquids are such that an equal number of molecules lie on them. Equation (i) then becomes d\y{M.vf\ _ y^v^^ - y,(Mz># _ It "'• ""^ ^^T^ ~' ' ^^ ^ The student should make himself familiar with this method of repre- senting rate of change, as it is largely used in physical chemistry. It is perhaps most readily understood by considering the rate of change of position of a body as discussed in mechanics. If a body is moving with uniform velocity, the velocity can at once be found by dividing the distance, s, traversed by the time, t, taken to traverse it, hence velocity = -!■. The velocity may, however, be continually altering, and it is often desirable to express the velocity at any instant. It is not at first sight evident how this can be done, as it requires some time for the particle to traverse any measurable distance, and the velocity may be altering during that time. The nearest approach to the real velocity at any instant will be obtained by taking the time, and therefore the distance traversed, as small as possible. We might then imagine an ideal case in which j and t are taken so small that any error due to the variation of speed during the time t can be neglected. If we represent these values of s and t by ds and dt respectively, the speed of the particle at any instant will be given by ds\dt. In the example given in the text d{ys)ldt represents the rate of change of the product with temperature, and the equation shows that the rate of change is constant. DILUTE SOLUTIONS 127 where yj and y^ are the surface tensions of a liquid at the temperatures t^ and i'j respectively. From equation (2) we obtain, for the molecular weight M, M={^(^^}^ . . (3) The surface tension of a large number of pure liquids at different temperatures has been measured by Ramsay and Shields by observing the height to which they rose in capillary tubes. The results show that, if M is taken as the molecular weight corresponding with the simplest formula of the liquid, the value off for the majority of substances is about - 2'i2. The method may be illustrated ' by a determination of the molecular weight of liquid carbon disulphide. The experi- mental data are that y = 33"6 (dynes per sq. cm.) at i9"4°, and 29*4 dynes at 46t° : the specific volume (i/density) of carbon disulphide at i9"4° is i/i'264; at 46'i° it is i/i'223. Hence M = r - 2-i2(i9-4 - 46-i) \^^ 8 \33-6/(r264)i-29-4/(i-223)*/ ^ as compared with the value 76 calculated from the formula. Colloidal Solutions — Strictly speaking, the consideration of colloidal solutions belongs to Chapter IV., but as they cannot be adequately discussed without referring to osmotic pressures, it is more convenient to deal with them here. Thomas Graham, in the course of his investigations on the velocity of diffusion in solution, was led to draw a distinction between two classes of substances, which he termed crystalloids and colloids respectively. Crystalloids can easily be obtained in the form of crystals, and include most acids, bases and salts ; colloids, on the other hand, cannot as a rule be obtained in crystalline form. Starch, gum, caramel and albumen are typical colloids. The chief differences between the two forms of substance, however, lie in the physical properties of their ^ Ramsay and Shields, Trans, Chem. Soc, 1893, 63, 1096. 128 OUTLINES OF PHYSICAL CHEMISTRY solutions. It was shown by Graham that crystalloids diffuse much more quickly than colloids. This is illustrated by the following numbers, valid for io°, the time of diffusion of hydro- chloric acid being taken as unity. Crystalloids. Colloids. Substance Relative times of \ equal diffusion / HCl NaCl Sugar I 2-3 7 Albumen Caramel 49 98 As under equivalent conditions the rate of diffusion is proportional to the osmotic pressure of the solute, it follows that the osmotic pressure of colloids is very small, and therefore that their molecular weights are very high. Many attempts have been made to determine the molecular weights of t)^ical colloids, but the results are not very conclusive. The indirect methods do not give very satisfactory results for such colloids as albumen and starch, as it is very difficult to free them from traces of salts, which have a high osmotic pressure. This difficulty is to some extent overcome by determining the osmotic pressures directly, another colloid, such as parchment paper, being used as semi-permeable membrane. It is a remarkable fact that one colloid, while usually allowing crystalloids to pass, is impervious to other colloids. Hence, as parchment paper is permeable for dissolved salts, the latter cannot set up an osmotic pressure, and any pressure observed must be due to the colloid only. Direct measurements of the osmotic pre- sure of colloidal solutions with parchment paper and with collodion membranes have not, however, led to very con- clusive results. The conclusion above indicated, that colloids have very complex molecules, is abundantly confirmed by direct observa- tion. Thus a colloidal solution of mercuric sulphide can readily be obtained by passing hydrogen sulphide through a neutral solution of mercuric chloride. Although this solution after filtration appears quite clear by transmitted light, examination DILUTE SOLUTIONS 129 of a drop under a high power of the microscope shows that it is full of small particles of the sulphide in rapid motion — the so-called Brownian movement. Moreover, many colloidal solu- tions which appear homogeneous even under a high magnifica- tion can be shown to be in fact heterogeneous by examination with the ultramicroscope. A remarkable property of most colloidal solutions is that although stable in the presence of non-electrolytes, they are precipitated or coagulated by traces of electrolytes. This can be shown very well with a colloidal solution of arsenic sulphide, obtained by passing hydrogen sulphide through a cold, neutral solution of arsenious oxide. Many colloids {e.g., aluminium hydroxide) are precipitated by electrolytes in a gelatinous form, termed a hydrogel, the soluble form is termed a hydrosol. The precipitation of colloids by electrolytes is doubtless connected with the fact that they are electrically charged, either positively {e.g., arsenious sulphide) or negatively {e.g., ferric hydroxide) with regard to the solvent. This may be illustrated by placing at some distance apart in the solution two plates connected with the terminals of the lighting circuit, when it will be observed that certain colloids (those positively charged) move towards the negative plate, and others towards the positive plate. Although some plausible suggestions have been made as to the mechanism of the coagulation of colloids by electro- lytes, the phenomenon has not yet been thoroughly elucidated. Practical Illustrations. Osmotic Pressure — The nature of semi-permeable membranes may readily be illustrated by Traube's experiment, described on page 98, and also by allowing drops of a fairly concentrated solution of potassium ferrocyanide to fall into a moderately dilute solution of copper sulphate in such a way that the drops, which are immediately surrounded by a film of copper ferrocyanide, remain suspended at the surface of the solution. It will be observed that the cells grow fairly rapidly owing to passage inwards of water from the copper sulphate solution, and, further, that in consequence 9 I30 OUTLINES OF PHYSICAL CHEMISTRY of the increased concentration of the copper sulphate solution round the drop, the concentrated solution slowly flows down through the less concentrated solution. The stream of con- centrated solution can readily be recognised by the difference of refractivity, especially if a bright light is placed behind the vessel Selective Action of Semi-permeable Membrane — This can be illustrated by Nernst's experiment, which is fully described and figured on page 107. A simple experiment illustrating the same principle has been described by Kahlenberg.^ At the bottom of a cyli' drical jar is placed a layer of chloroform, above that a layer of water, and at the top a layer of ether and the jar is then corked. After some time it will be noticed that the chloroform layer has increased in depth, the water layer having moved higher up the tube. This phenomenon depends on the fact that ether is much more soluble in water than chloroform. The water there- fore acts like a semi-permeable membrane, absorbing the ether and giving it up to the chloroform. At the same time the chloroform is dissolving in the water and passing through to the ethereal layer, but owing to its much smaller solubility, the current upwards is negligible in comparison with that downwards. In the same paper, Kahlenberg describes a- number of experi- ments with rubber membranes, which are in many respects instructive. Separation of Solvent and Solute in Freezing-point Experi- ments — This point, which is of fundamental importance for the applicability of the freezing-point method of determining mole- cular weights, can be illustrated by partially freezing an aqueous solution of a highly coloured substance such as potassium permanganate (o'l per cent, solution). When the solution is poured off, it will be found that the ice which has separated is practically colourless. The determination of molecular weights by the boiling-point method (p. 116) and by the freezing-point method (p. 120) are fully described in the course of the chapter. ' y. Physical Ckem., 1906, 10, 141. APPENDIX. MATHEMATICAL DEDUCTION OF IMPORTANT FORMULA. In the course of the present chapter, several formulje of fundamental importance have been made use of, and their meaning has been fully illustrated by numerical examples. For the sake of the more advanced student, simple deductions of these formulae are given. It must be understood that the deductions are not mathematically strict, as certain of the assumptions on which they are based are only approximately true. The fundamental equation (p. 1 1 2), A -A M /i sRT ■ ■ ■ (I) which gives the connection between the relative lowering of vapour pressure and the osmotic pressure, and the Raoult-van't Hoff formula (p. 113), A -A ^ ^ . . /i N • • • ■ (^> which is readily derived from equation (i) by means of the gas laws, can be deduced by a statical-thermodynamical method due to Arrhenius and also by a cyclical thermodynamical method due to van't Hoff. These deductions will now begiven. (i) TAe Statical Method — A long tube R containing a solution of n mols of a non-volatile solute in N mols of solvent,^ is closed at its lower end by a semi-permeable membrane and placed upright in a vessel C which contains pure solvent (fig. 20). The arrangement is covered by a bell-jar and all air is removed from the interior. When equilibrium between solvent 1 In calculating the number of mols of solvent, its molecular weight, M, is taken as that in the form of vapour (p. 112). 131 132 OUTLINES OF PHYSICAL CHEMISTRY and solution is established through the semi-permeable mem- brane it is evident that the osmotic pressure is measured by the hydrostatic pressure of the column of liquid (height K) in the tube. Now the pressure of vapour at the level, a, of the surface of the solution must be the same inside and outside the tube. If this were not the case, evaporation or condensation of vapour would take place at the surface, a, and in either case the con- centration of the solution would be altered and the equilibrium between solution and solvent disturbed, which is contrary to the original postulate that the system is in equilibrium. If p-^ is the vapour pressure of the solvent and p^ that of the solution, the difference /j - p^ is the difference of pressure at the —J surface of the solvent and at P'° 20. tjig level a. This difference is due to the weight of a column of vapour of height h on unit area, therefore P\-Pi = hd . . . . (a) where d is the density of the vapour. We have now to express d and ^ in a different form. If »j is the volume of i mol of the vapour, and M the molecular weight of the vapour in the gaseous form, we have d = M/^j. When this value of d is substituted in the general gas equation, /jWj = RT, we obtain a - j^^. Further, as the osmotic pressure, P, is measured by the weight of the column h, therefore P = hs' where / is the density of the solution. If very dilute solutions are used, no appreciable APPENDIX 133 error will be committed by substituting s, the density of the solvent, for s', the density of the solution. Substituting these values of d and /i in equation (a) we obtain or Px - P'l _ _M p /i ~ 5Rf ■ ^' which is equation (i), p. iiz. From this equation, we obtain the formula, A -A _ « " /i " N as already described (p. 112). (2) The Cyclical Method — This thermodynamical proof of the above formula depends upon the performance of a cyclic process — in which the system is finally brought back to its initial condition — reversibly at constant temperature. The fundamental point to bear in mind in connection with such processes is that they must be conducted throughout under equilibrium conditions. It has already been pointed out (p. no) that the thermodynamical proof of the connection between osmotic pressure and the lowering of vapour pressure depends on the work done in removing solvent reversibly from a solution. There are two principal methods by which removal (or addition) of solvent can be accomplished : — (a) If the solution is brought into contact with its own saturated vapour at constant temperature, the slightest diminu- tion of the external pressure will effect the removal of part of the solvent ; on the other hand, the slightest increase of the external pressure will bring about condensation of vapour. If the change of volume of the solution is in each case very small compared with the total volume, the change in concentration can be neglected. {U) A solution is placed in a cylinder closed at the bottom with a semi-permeable membrane, the cylinder is immersed in the pure solvent, and a movable piston rests on the upper surface. The solution and solvent will be in equilibrium through the semi-permeable membrane when the pressure on the piston is equal to the osmotic pressure. If the pressure is diminished ever so slightly by raising the piston, solvent will 134 OUTLINES OF PHYSICAL CHEMISTRY. enter ; if the pressure oa the piston is slightly increased, solvent will pass out through the membrane. We have, there- fore, a second method by which solvent can be separated from a solution in a reversible manner, equilibrium being maintained throughout. The cyclic process, in which both these methods are used, will now be described. (i) From a solution containing n mols of solute to N mols of solvent, a quantity of solvent which originally contained i mol of solute is squeezed out reversibly by means of the piston and cylinder arrangement ; the quantity thus removed is N/« mols. As the original quantity of solution is supposed to be very great, its concentration, and therefore its osmotic pressure, are not appreciably altered in the process. As the volume removed is that which contained i mol of solute, the work done in the process, which is the product of the volume and the osmotic pressure, is equal to -RT .... (i) (p. 2 7) if the gas laws apply. (2) The quantity of solvent is now converted reversibly into vapour by expansion at the pressure, /p of the solvent ; the work gained is approximately /jOj for i mol of vapour (the volume of the liquid being regarded as negligible in comparison), or -/i»i .... (u) altogether, (3) The vapour is now allowed further to expand till its pressure falls to p^ the vapour pressure of the solution : in this process, an amount of work is gained represented approximately by A +A/- \ per mol of vapour, where (/j + Pi)!^ is the mean pressure during the small expansion. The quantity of vapour actually used is N/w mols, hence the total work gained is !(^') (».-■) ^ . .o«) (4) The vapour, at the pressure p^, is now brought into contact with the solution, with which it is in equilibrium, and condensed reversibly, so that the system regains its initial state. The work done on the system in condensing the gas to liquid APPENDIX 135 at the pressure p^ is approximately - -/2»2 .... (IV) As the entire cycle is carried through at constant temperature, there has on the whole been no transformation of heat into work or vice versA ; as the system is finally brought back to its initial condition, the work expended must on the whole be equal to the work gained; in other words (i) + (ii) + (iii) + (iv) must be zero when due regard is had to the signs. Combining in the first place (iij, (iii), and (iv), we have which reduces to N /z n \ + »l\ / . . ^ N where v is the mean volume of i mol of vapour. Substituting for v its value from the general gas equation, V = RT//, we have finally ^ as the work gained in the last three stages of the cycle. This must be equal to the work done on the system during the osmotic removal of solvent, hence ^ . RT^^LJlAa _ RT = o n /i Pi N as before. The same result may be obtained still more simply by integration. The work gained in step (ii) is exactly balanced by that done on the system in (iv), as is evident from the factors themselves, if the gas laws hold. In (iii) both the pressure and the volume change during the expansion, hence work gained for i mol of vapour is equal to RT— = RT loge -2 = RT log,-a (since /iWj ^p^v.^) I />civ= I J ' When the Eolution is dilute, p in the denominator may be put equal to /l w''hout sensible error. 136 OUTLINES OF PHYSICAL CHEMISTRY. = - RT log„^2 = - RT log, (x J^\ = RT approximately,^ or, for the total volume of vapour, N^^ /i -. The remainder of the proof is as above. Lowering of Freezing-point — The above formula has been deduced by an isothermal cyclic process, but the cyclic process by which the freezing-point formula is deduced cannot be carried through at constant temperature. We are therefore concerned with a new question, that of the relationship between heat and work. The law which applies in this case is the second law of thermodynamics, the deduction of which is to be found in any advanced book on Physics, and which states that the maximum work, dK, obtainable from a given quantity of heat Q, in a reversible cycle is given by dK = Q^I where the symbols have the usual significations (p. 151). A solution containing n mols of solute in N mols (W grams) of solvent is contained in the cylinder with semi-permeable membrane and movable piston already described. The freezing- point of the solvent is taken as T and that of the solution as T — dT. The stages in the cyclic process are as follows : — (i) At the temperature T - dT an amount of solvent which originally contained i mol of solute is frozen out ; the amount in question is N/« mols or MN/« grams. The separation can be carried out at constant temperature provided that the amount of solution is so great that its concentration is not thereby appreciably affected. The solidified solvent is then separated from the solution and the temperature of both raised to T. MN (2) The solidified solvent is fused, in which process H . calories are taken up, H being the heat of fusion per gram. (3) The fused solvent is then brought into contact with the ^ RT -^-T — -^ is the first term of the expansion of the logarithmic function. 1 he more accurate form of the van't Hoff-Raoult formula is n loge pilpi = jj, to which the usual form approximates in dilute solution. APrENDIX 137 solution through the semi-permeable membrane under equi- librium conditions, that is, when the pressure on the piston is equal to the osmotic pressure of the solution (p. 133) and is allowed to mix reversibly with the solution. The work done in this process is represented by the product of the osmotic pressure, P, and the volume, v, in which i mol of solute was dissolved and is, therefore, according to the gas laws, equal to RT. (4) The system is finally cooled to the original temperature, T - dT, in order to complete the cycle. We have now to consider the work done in the different stages of the cycle. The heat expended in warming solution and solvent in (i) is practically compensated ^ by the heat given out in (4). Further, an amount of heat HW/« is taken in at the higher temperature T and a somewhat less amount given out at T — dT ; hence, by the second law of thermodynamics, the work gained is W ^ n T The only work done by the system is that expended in the osmotic readmission of the solvent, hence W dT RT = H . - . -^ n 1 or (fT = -jj- . ^ . . . . (i) If instead of H we use the molecular heat of fusion, A., we have X = MH, and, further, N = W/M. Substituting these values in equation (i), the latter reduces to ^T = ^- . j^. . . . . (2) From this it is evident that the lowering of the freezing-point, like the relative lowering of vapour pressure, is proportional to the ratio of the number of mols of solute to the number of mols of solvent. From the above formula, or more readily from equation (i), above, an expression for K, the depression produced when i mol of solute is dissolved in 100 grams of solvent, can readily be obtained. R is approximately = 2 when expressed in calories, 1 The two amounts are not exactly equal, but the difference can be made negligible in comparison with the heat taken up in the second stage of the cycle. 138 OUTLINES OF PHYSICAL CHEMISTRY n = 1 and W = 100. Hence we obtain, for this ' particular value of dT, 2T^ I 0'02T^ ^T = K=^.— =^j-, . . (3) which is the formula given on p. 120. Elevation of Boiling-point — By means of a cyclic process exactly corresponding with that already used in establishing the freezing-point formula, the formula connecting the elevation of the boiling-point with the latent heat of vaporisation of the solvent is obtained in the form 0-02T2 where H is the heat of vaporisation of i gram of solvent at the temperature of the experiment, and T is the boiling-point of the solvent on the absolute scale. Summary of Formulae — [a) Osmotic pressure and relative lowering of vapour-pressure. From formula (i) (p. 112) we obtain by substitution P = — —^ —- — ^^ atmospheres ; where P is the osmotic pressure, expressed m atmospheres, s is the density of the solvent at the absolute temperature T, M is the molecular weight of the solvent in the form of vapour, and /i and/2 ^re the vapour-pressures of solvent and solution respectively. {b) Osmotic pressure and lowering of freezing-point — P'rom formula (i) (p. 137), by substitution „ loooH.? dT ^ , r = ■■ . -— - atmospheres ; 24'22 1 where H is the latent heat of fusion of the solvent in calories per gram, T is the freezing-point of the solvent on the absolute scale and dT is the freezing-point depression. Osmotic pressure and elevation of boiling-point — The formula, which corresponds exactly with that for the freezing-point depression, is loooHj rfT "~ 24-22 T where H is the latent heat of vaporisation for i gram of solvent at its boiling-point, T is the boiling-point of the solvent on the absolute scale, and dT is the boiling-point elevation. CHAPTER VI THERMOCHEMISTRY General — It is a matter of every-day experience that chemical changes are usually associated with the develop- ment or absorption of heat. When substances enter into chemical combination very readily, much heat is usually given out (for example, the combination of hydrogen and chlorine to form hydrogen chloride), but when combination is less vigorous, the heat given out is usually much less, and, in fact, heat may be absorbed in a chemical change. These facts, which were noticed very early in the history of chemistry, led to the suggestion that the amount of heat given out in a chemical change might be regarded as a measure of the chemical affinity of the reacting substances. Although, as will be shown later, this is not strictly true, there is, in many cases, a parallelism between chemical affinity and heat liberation. In thermochemistry, we are concerned with the heat equivalent of chemical changes. Heat is a form of energy, and therefore the laws regarding the transformations of energy are of importance for thermo- chemistry. It is shown in text-books of physics that there are different forms of energy, such as potential energy, kinetic energy, electrical energy, radiant energy and heat, and that these different forms of energy are mutually convertible. Further, when one form of energy is converted completely into another, there is always a definite relation between the amount which has disappeared and that which results. The 139 I40 OUTLINES OF PHYSICAL CHEMISTRY best-known example of this is the relation between kinetic energy and heat, which has been very carefully investigated by Joule, Rowland and others. Kinetic energy may be measured in gram-centimetres or in ergs, and heat energy in calories (see p. xvii). The investigators just referred to found that I calorie = 42,650 gram-centimetres = 41,830,000 ergs, an equation representing the mechanical equivalent of heat. From the above considerations it follows that when a certain amount of one form of energy disappears an equivalent amount of another form of energy makes its appearance. These results are summarised in a law termed the Law of the Conservation of Energy, which may be expressed as follows : The energy of an isolated system is constant, i.e., it cannot be altered in amount by interactions between the parts of the system. The proof of this law lies in the experimentalimpossihility of perpetual motion — it has been found impossible to construct a machine which will perform work without the expenditure of energy of some kind. In dealing with chemical changes, it has been found con- venient to employ the term chemical energy, and when two substances combine with liberation of heat, we say that chemical energy has been transformed to heat. To make this clear, we will consider a concrete case, the burning of carbon in oxygen with formation of carbon dioxide, a reaction which, as is well known, is attended with the liberation of a considerable amount of heat. The reaction can be carried out under such condi- tions that the heat given out when a definite weight of carbon combines with oxygen can be measured, and it has been found that when 12 grams of carbon and 32 grams of oxygen unite, 94,300 calories are liberated. This result may conveniently be represented by the equation C + Oj = COg + 94,300 cal. in which the symbols represent the atomic weights of the reacting elements in grams. The above equation is an illus- tration of the conversion of chemical energy into heat — 12 THERMOCHEMISTRY 141 grams of free carbon and 32 grams of free oxygen possess 94,300 cal. more energy than the 44 grams of carbon dioxide formed by their union. From these and similar considerations it follows that the free elements must have much intrinsic energy, but the absolute amount of this energy in any par- ticular case is quite unknown. Fortunately, this is a matter of secondary importance, as chemical changes do not depend on the absolute amounts of energy, but only on the differences of energy of the reacting systems. So far, we have implicitly assumed that the increase or de- crease of internal energy when a system A changes to a system B is measured by the heat absorbed or given out during the reactions ; but this is not necessarily the case. In particular, external work may be done during the change, by which part of the energy is used up, or heat may be produced at the expense of external work (cf. p. 27). If the total diminution of internal energy in the change A -> B is represented by U, the heat given out by - Q, and the external work done by the reacting sub- stances during the transformation by A, we have, by the prin- ciple of the conservation of energy, U = A - Q. The factor A is only of importance when gases are involved in the chemical change ; the method of calculating the work done in changes of volume of gases has already been given (p. 27). Hess's Law — It is an experimental fact that when the same chemical change takes place between definite amounts of two substances under the same conditions the same amount of heat is always given out provided that the final product or products are the same in each case. Thus when 12 grams of carbon combine with 32 grams of oxygen with formation of carbon dioxide, 94,300 cal. are always liberated, quite independently of the rate of combustion or of the nature of the intermediate pro- ducts. This law was first established experimentally by Hess in 1840, and may be illustrated by the conversion, by two different methods, of a system consisting of i mol of ammonia and of 142 OUTLINES OF PHYSICAL CHEMISTRY hydrochloric acid respectively and a large amount of water, each taken separately, into a system consisting of i mol of ammonium chloride in a large excess of water. By the first method we measure (a) the heat change when i mol of gaseous ammonia and I mol of gaseous HCl combine, (A) the heat change when the solid ammonium chloride is dissolved in a large excess of water ; by the second method we measure the heat changes when [c) i mol of ammonia, (d) i mol of hydrochloric acid are dissolved separately in excess of water, and (e) when the two solutions are mixed. The results obtained were as follows : — First Way. (a) NHj gas + HCI gas = +42,100 cal. (i) NH4CI + aq = - 3,900 cal. 38,200 cal. Second Way. (c) NHjgas + aq = + 8,400 cal. (d) HCl gas + aq = + 17,300 cal. (e) HClaq + NHjaq = + 12,300 cal. 38,000 cal. As will be seen, a + 6 = {: + d+e within the limits of ex- perimental error. It can easily be shown that Hess's law follows at once from the principle of conservation of energy. This law is of the greatest importance for the indirect deter- mination of the heat changes involved in certain reactions which cannot be carried out directly. For example, we cannot determine directly the heat given out when carbon combines with oxygen to form carbon monoxide. The heat given out when 12 grams of carbon burn to carbon dioxide is 94,300 cal., which is, by Hess's law, equal to that produced when the same amount of carbon is burned to monoxide and the latter then converted to dioxide. The latter change gives out 68,100 THERMOCHEMISTRY 143 caL, and the reaction C + O = CO must therefore be associated with the liberation of 94,300 - 68,100 = 26,200 cal. Representation of Thermochemical Measurements. Heat of Formation — As has already been pointed out, the results of thermochemical measurements may be conveniently represented by making the ordinary chemical equation into an energy equation, for example, C + O2 = COj + 94,300 cal. 94,300 cal. is termed the heat of formation of carbon dioxide from its elements. This equation is, however, not complete, inasmuch as we do not know the intrinsic energy associated with free carbon and oxygen respectively, nor do we know the differences of energy between the various elements, as they are not mutually convertible by any known means. We may there- fore choose any arbitrary value for the intrinsic energies of the elements, and it has been found most convenient to put them all equal to zero. On this basis the complete energy equation for the formation of carbon dioxide can be written + = CO2 + 94,300 cal., whence CO2 = — 94,300 cal., that is, the energy of i mol of carbon dioxide is -94,300 calories. Therefore, in writing an energy equation, the formula of a compound is replaced by the heat of formation with its sign reversed, which represents its intrinsic energy. We can make use of this simple rule in two ways : (i) to calculate the heat set free in a chemical change when the heats of formation of the reacting substances are known ; (2) to calculate an unknown heat of formation when all the other heats of formation and the heat given out in the chemical change are known. As an example of the first application, we may calculate the heat change, x, when copper is displaced from copper sulphate in dilute solution by metallic zinc according to the equation CuSO^aq + Zn = ZnSO^aq + Cu. 144 OUTLINES OI^ "PHYSICAL CHEMISTRY The heat of formation (from its elements) of copper sulphate in dilute solution is 198,400 cal. and of zinc sulphate under the same conditions 248,500 cal. The energy equation for the chemical change is therefore Zn + CuSO^ aq = Cu + ZnS04 ^^ o + (-198,400) = o + (-248,500) + a; cal., the intrinsic energies of the elements and compounds being written below the respective formulae. As 248,500 cal. are given out in the formation of zinc sulphate and 198,400 cal. absorbed when copper sulphate yields metallic copper, x, the total heat liberated in the reaction is 248,500 - 198,400 = 50,100 cal. As an example of the second application, the heat of forma- tion of methane from its elements, which cannot be determined directly, will be calculated. The heat given out when i mol of this compound is burned completely in oxygen is 213,800 cal., and the heat of formation of the products, carbon dioxide and liquid water, are 94,300 and 68,300 cal. respectively. Re- presenting the heat of formation of methane by x, its intrinsic energy therefore by - x, we have the equation CH^ + 2O2 = CO2 + 2H2O — x + o = -94,300 + (-2 X 68,300) + 213,800 cal. Whence x = 17,100 cal. A compound such as methane, which is formed with libera- tion of heat, is termed an exothermic compound, whilst one which is formed with absorption of heat is termed an endo- ihermic compound. The majority of stable compounds are exothermic. Among the best-known endothermic compounds are carbon disulphide, hydriodic acid, acetylene, cyanogen and ozone. It is not always easy to determine directly whether a compound is exothermic or endothermic, but this may be done indirectly by carrying out a chemical change with the compound itself and with the components separately and comparing the heat THERMOCHEMISTRY 145 changes in the two cases. The method may be illustrated by reference to carbon disulphide. When burnt completely in oxygen, the gaseous compound gives out 265, roo cal. accord- ing to the equation CSg + 3O2 = COg + 2SO2 -I- 265,100 cal. Hence, representing the intrinsic energy of the compound by - X, we have, for the energy equation, — X + o = +(— 94,300) + ( - 2 X 71,000) + 265,100, and — X = + 28,800 cal. The intrinsic energy of carbon disul- phide is therefore 28,800 cal. ; that is, the compound has 28,800 cal. more energy than the elements from which it is formed. Heat of Combustion — Whilst a great many inorganic re- actions are suitable for thermochemical measurements, this is not in general the case for organic reactions ; in fact, the only reaction which is largely used for the purpose is combustion in oxygen to carbon dioxide and water. The heat given out in such a reaction is termed the /leai of combustion, and from this, by application of Hess's law, the heats of formation can be cal- culated, as has been done for methane and carbon disulphide, in the preceding section. Further, the heat given out in a chemical change can readily be calculated by Hess's law when the heats of combustion of the reacting substances are known — it will clearly be equal to the sum of the heats of combustion of the substances which disappear less the sum of the heats of combustion of the substances formed. As an example, the heat of formation of ethyl acetate from ethyl alcohol and acetic acid may be calculated. The heat of combustion of ethyl alcohol is 34,000 cal., of acetic acid 21,000 cal., and of ethyl acetate 55,400 cal., whence the heat of formation of ethyl acetate is 34,000 -H 21,000 - 55,400 = - 400 cal. Thermochemical Methods — Two principal methods are employed in measuring the heat changes associated with chemical reactions. If the reaction takes place in solution, the water calorimeter, so largely used for purely physical measure- ments, may be employed. For the determination of heats of 146 OUTLINES OF PHYSICAL CHEMISTRY combustion, on the other hand, in which solids or liquids are burned completely in oxygen, special apparatus has been de- signed by Thomsen, Berthelot, Favre and Silbermann and others. (a) Reactions in Solution — The change (chemical reaction, dilution or dissolution), the thermal effect of which is to be measured, is brought about in a test-tube deeply immersed in a large quantity of water, and the rise of temperature of the water is measured with a sensitive thermometer. When the weight of the water and the heat capacity of the calorimeter are known, the heat given out in the reaction can readily be calculated. Allowance must, of course, be made for the heat capacity of the solution in the test-tube. A simple modification of Berthelot's calorimeter, used by Nernst, is shown in Fig. 21. It consists of two glass beakers, the inner one being supported on corks, as shown, and nearly filled with water. Through the wooden cover, X, of the outer beaker pass a thin-walled test-tube. A, in which the reaction takes place, an accurate thermometer B, and a stirrer C of brass, or, better, of platinum. The water in the calorimeter is stijrred during the reaction, which must be rapid, and the heat of reaction can then be calculated in the usual way when the weight of water in the calorimeter and the rise of temperature are known. Experiments on neutralization and on heat of solution are conveniently made in the inner beaker, the solution itself serving as calorimetric liquid. For dilute aqueous solutions, it is sufficiently accurate to assume that the heat capacity of the solution is the same as that of water. The chief source of error in the measurements is the loss of heat by radiation, which is minimised (a) by choosing for investigation reactions which are complete in a comparatively short time ; {S) by making the heat capacity of the calorimeter system large. It is of advantage so to arrange matters that the temperature of the calorimeter liquid is 1-2° below the atmospheric temperature before the reaction, and 1-2° above it after the reaction. THERMOCHEMISTRY 147 t (U mnn-- B TTmr nsTOix {6) Combustion in Oxygen — This may conveniently be carried out in Berthelot's calorimetric bomb, a vessel of steel, lined with platinum and provided with an air-tight lid. The sub- stance for combustion is placed in the bomb, which is filled with oxygen at 20-25 atmo- spheres' pressure. The whole apparatus is then sunk in the water of the calorimeter, and the combustion initiated by heating electrically a small piece of iron wire placed in contact with the solid. Results of Thermoohemi- cal Measurements — Some of the more important results of thermochemical measure- ments have already been inci- dentally referred to in the preceding paragraphs. In stating the results of thermo- chemical measurements, the condition of the substances taking part in the reaction must always be clearly stated. This applies not only to the physical state, in connection with which allowance must be made for heat of vaporization, heat of fusion, etc., but also to the different allotropic modifications of the solid. Thus mono- clinic sulphur has 2300 cal. more internal energy than rhombic sulphur, and yellow phosphorus 27,300 cal. more than the red modification. The correction for change of state is often very great. For the transformation of water to steam at 100°, it amounts to Fio. 21. 148 OUTLINES OF PHYSICAL CHEMISTRY about 537 x 18 = 9566 calories per mol. If, instead of the heat of formation of liquid water, which is 68,300 cal., the heat of formation of water vapour is required, it is 68,300 - 9570 = 58,730 cal. in round numbers.* As regards the thermochemistry of salt solutions, one or two experimental results may be mentioned which will find an interpretation later. When dilute solutions of two salts, such as po'assium nitrate and sodium chloride, are mixed, heat is neither given out nor absorbed. This important result is termed the Law of thermoneutrality of salt solutions (p. 279). Further, when a mol of any strong monobasic acid is neutralized by a strong base, the same amount of heat, 13,700 cal., is always liberated (p. 284). The heat of formation of salts in dilute aqueous solution is obtained by the addition of two factors, one pertaining to the positive, the other to the negative part of the molecule; in other words, the heat of formation of salts in dilute solution is a distinctly additive property. The same is true to some axtent for the heat of combustion of organic compounds. For example, the difference in the heat of combustion of methane and ethane is 158,500 cal., and in general, for every increase of CHj, the heat of combustion increases by about 158,000 cal. From these and similar results, we can deduce the general rule that equal differences in composition correspond to approxi- mately equal differences in the heat of combustion. We may go further, and obtain definite values for the heat of combustion of a carbon atom and a hydrogen atom as has already been done for atomic volumes ; the molecular heat of combustion is then the sum of the heats of combustion of the individual atoms. Experience shows that when allowance is made for double and triple bindings, the observed and calculated values for the heats of combustion of hydrocarbons agree fairly well. Relation of Chemical AflQnity to Heat of Reaction — Very early in the study of chemistry, it becomes evident that chemical actions may be divided into two classes : (i) those ^ The connection to be applied for changes in the volume of gases has already been discussed (p. 27) : it amounts to 2 T cal. per mol. THERMOCHEMISTRY 149 which under the conditions of the experiment are spontaneous or proceed of themselves, once they are started, e.g., the com- bination of carbon and oxygen ; (2) those which only proceed when forced by some external agency, e.g., the splitting up of mercuric oxide into mercury and oxygen. In this section we are concerned only with spontaneous changes. The direction in which a chemical change takes place in a system depends on the energy relations of the system. We are accustomed to say that the direction of the change is determined by the chemical affinity of the reacting substances, and it is a matter of the utmost importance to obtain a numerical expression for the chemical affinity or driving force in a chemical system, the driving force being defined in such a way that the chemical change proceeds in the direction in which it acts, and comes to a standstill when the driving force is zero. Most reactions in which there is a considerable transformation of chemical energy, and therefore a considerable development of other forms of energy, such as heat or electrical energy, proceed very rapidly (for example, the combination of hydrogen and chlorine), whilst reactions in which less chemical energy is transformed are usually much less vigorous (for example, the combination of hydrogen and iodine). It seems, therefore, at first sight plausible to measure the chemical affinity in a system by the amount of heat liberated in the reaction (Thomsen, Berthelot). As, however, chemical affinity has been defined as acting in the direction in which spontaneous chemical change takes place, it would follow that only reactions in which heat is given out can take place spontaneously. This deduction is contrary to experience. Water can spontaneously pass into vapour, although in the process heat is absorbed, and many salts, such as ammonium chloride, dissolve in water with absorption of heat. It is clear, therefore, that chemical affinity, as above defined, cannot be measured by the total heat liberated in the reaction. ISO OUTLINES OF PHYSICAL CHEMISTRY The importance for technical purposes of such a reaction as the burning of coal in oxygen is not so much the total heat obtainable by the change as the amount of work which the change may be made to perform. In a similar way, it has been found convenient to' measure the chemical affinity of a system by the maximum amount of external work which, under suitable conditions, the reaction may be made to perform. This is a special case of a very comprehensive natural law, which may be expressed as follows : All spontaneous reactions (in the widest sense, including neutralization of electrical charges, falling of liquids to a lower level, etc.) can be made to perform work, and all reactions which can be made to per- form work are spontaneous, i.e., can proceed of themselves without the application of external forces. The available energy of a chemical reaction, that is, that part of the total energy which at constant temperature and under suitable condi- tions can be made to perform an equivalent of work, has been termed " free energy " by Helmholtz. The chemical affinity or driving force of a reaction is not proportional to the total change of energy, but to the change in the available ox free energy. The total energy, U, of a chemical change can be obtained in the form of heat by carrying out the reaction under such conditions that no external work is done (p. 141). We have now to consider what is the connection between the total decrease of energy, U, and the decrease of available or free energy, which may be termed A. This question is closely connected with the conditions under which heat can be con- tinuously transformed into work. We have to find an expres- sion for the maximum work performed in a cycle in which the heat is taken in at the temperature T, and given out at the slightly lower temperature T - rfT. The principle to be used for this purpose is that employed in the theory of the steam-engine, but it has universal applicability. According to this, the maxi- mum work, dh, obtainable from a given quantity of heat Q is given by THERMOCHEMISTRY 151 2NaCl + CaCOj, yet the sodium carbonate found on the shores of certain lakes in Egypt is produced according to the equation 2NaCl + CaCOg -^ NajCOg + CaCl2, the converse of the first equation. In the latter case, the sodium chloride is present in solution in such large excess that the re- action proceeds in the direction indicated by the arrow, so that, according to BerthoUet, an excess in quantity can compensate for a weakness in specific affinity. An important step forward was made in this subject by Berthelot and Pean de St. Gilles in 1862, in the course of an investigation on the formation of esters from acids and alcohol. For acetic acid and ethyl alcohol, the reaction may be repre- sented by the equation C2H5OH + CHjCOOH ^ CH3COOC2H5 -I- HjO. If one starts with equivalent amounts of acid and alcohol. iS6 OUTLINES OF PHYSICAL CHEMISTRY the reaction proceeds till about 66 . per cent, of the reacting substances have been used up, and then comes to a standstill. Similarly, if equivalent quantities of ethyl acetate and water are heated, the reaction proceeds in the reverse direction (indicated by the lower arrow) until 34 per cent, of the compounds have been used up and the mixture finally obtained is of the same composition as when acid and alcohol are the initial substances. A reaction of this type is termed a reversible reaction, and the facts are conveniently represented by the oppositely-directed arrows. When, however, for a fixed proportion of acid, varying amounts of alcohol are taken, the equilibrium point is greatly altered, as is shown in the accompanying table. The first and third columns show the proportion of alcohol present for i equivalent of acetic acid, and the second and fourth columns the proportion of acid per cent, converted to ester. Equivalents of Alcohol. 0-2 o-S I'O 1-5 We here measure the amount of chemical action by the extent to which the acid is converted into ester, and the table shows very clearly the influence of the mass of the alcohol on the equilibrium. The influence of the relative proportions of the reacting substances on chemical action was thus clearly recognised, but was not accurately formulated till 1867. In that year, two Nor- wegian investigators, Guldberg and Waage, enunciated the Law of mass action, which may provisionally be expressed as follows : The amount of chemical action is proportional to the active mass of each of the substances reacting, active mass being defined as the molecular concentration of the reacting substance. The im- portant part of this statement is that the chemical activity of Ester Formed. Equivalents of Alcohol. Ester Formed. 19-3 2'0 82-8 42'0 4-0 88-2 66-s 12-0 93"2 77-9 50-0 lOQ-Q EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 157 a substance is not proportional to the quantity present, but to its concentration, or amount in unit volume of the reaction mixture. The law applies in the first instance more particularly to gases and substances in solution ; the active mass of solids will be considered later. The " amount of chemical action " exerted by a certain sub- stance can be measured (a) from its influence on the equilibrium, as in the formation of ethyl acetate, just referred to ; {d) from its influence on the rate of a chemical action, such as the inver- sion of cane sugar. The law of mass action can therefore be deduced from the results of kinetic or equilibrium experiments. Conversely, once the law is established, it can be employed both for the investigation of rates of reaction and of chemical equilibria, and it is the fundamental law in both these branches of physical chemistry. In the above form, the law of mass action cannot readily be applied, and it will therefore be formulated mathematically. For purposes of illustration, we choose a reversible reaction between two substances in which only one molecule of each reacts ; a typical case is the formation of ethyl acetate and water from ethyl alcohol and acetic acid, already referred to. Calling the molecular concentrations of the reacting substances a and i, the rate at which they combine is, according to the law of mass action, proportional to a and to d separately, and there- fore proportional to their product. We may therefore write for the initial velocity of reaction at the time t^ — Rate^ oc ai or Rate, = kai, where /5 is a constant — an affinity constant — depending only on the nature of the substances, the temperature, etc. As the re- action proceeds, the active masses gradually diminish, since the original substances are being used up in producing the new substances. If, after an interval of time f, x equivalents of the ester and water have been formed, the rate of the original reaction will be 158 OUTLINES OF PHYSICAL CHEMISTRY Rate, = A{a-x){i-x). That this must be so is clear when one bears in mind that a and d represent molecular concentrations, and that for every molecule of ester and of water which are formed, an equal number of molecules of acid and alcohol must be used up. We have now to take into account the fact that the substances formed react to produce the original substances. At the time /, when the concentration of the ester and water is x, the rate of the reverse reaction will be : Rate, = k^x\ where i^ is another affinity constant. We then have two reactions pro- ceeding in opposite directions, the velocity of the direct reaction is continually diminishing owing to diminishing concentration, that of the reverse reaction is continually increasing owing to increasing concentration of the reacting substances. A point must ultimately be reached when the velocity of the direct • is equal to that of the reverse reaction, and the system will no longer change ; this is the condition of equilibrium. If the particular value of x under these conditions is acj we have the equations Rate direct = ^{a - Xi){l> - X^) and rate reverse = ^I'^i^ and since these are equal k{a - x-^{b - Xj) = k-^x^, which may be written (a - x^)(b - X i) _K _y- The facts are made still clearer if we represent the reaction as follows, the initial concentrations being represented on the upper, and the equilibrium concentrations on the lower line : — Commencement a b 00 C2H5OH + CHjCOOH^iCHgCOOCaHs + H^O Equilibrium a - x-^ b - x^ x-^ x-^ It is important to note that, since K, which is usually termed the equilibrium constant, is the ratio of the two velocity con- EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 159 slants, which are independent of the concentration, the above equation holds for all concentrations. Hence, if the equilibrium consta^nt for any chemical change is obtained from one experi- ment, the equilibrium conditions can be calculated for any value of the original concentrations. Numerous applications of this equation are given in the succeeding paragraphs. When more than one molecular equivalent of a compound takes part in a chemical change, each equivalent must be con- sidered separately, as far as the law of mass action is concerned. In order to illustrate this statement, we will consider the com- bination of hydrogen and iodine to form hydriodic acid. The reaction is reversible, and may therefore be represented by the equation Hj + I^^HI-t-HI. The rate of the inverse reaction = ^S^'m, since it is propor- tional to the concentration of each of the two mols of hydriodic acid and therefore to their product. As the velocity of the direct reaction = kQ-R^i^, we obtain for the conditions at equilibrium the equation The general equation for a reversible reaction may be written in the form i^j^Aj -f «2-^2 + ■ ■ • ? '^I'-Ai' + "a'Aj' + . . . where n-^ molecules of the substance Aj react with n^ molecules of the substance A2 . . . to form n-[ molecules of the substance Aj' and n^ molecules of the substance Aj'. The rates of the direct and reverse actions are represented by the equations : Rate direct ='^C"'C"j . . . and rate inverse = -^iC^SC^^ .... and in equilibrium K = ^ /Vi At An An Ao The above is the strict mathematical form of the law of mass i6o OUTLINES OF PHYSICAL CHEMISTRY action. To illustrate the meaning of the symbols, we may consider the reaction 2FeCl3 + SnClg = SnCl^ + 2FeCl2 Aj' Ag Ai' A/ In this case n-^ = 2, n^ = i, n^'-^ i, and Wg' = 2. The final equation then becomes -rr _ CpeGla CsnCla CsnCU CpeCIa Strict Proof of the Law of Mass Action — The law of mass action, the meaning of which has been illustrated in the previous paragraphs, may be strictly proved by a thermo- dynamical method (Guldberg and Waage, 1867), or by a molecular-kinetic method (van't Hoff, 1877). The latter proof is comparatively simple, and depends on the assumption that the rate of chemical change is proportional to the number of collisions between the reacting molecules, which, in sufficiently dilute solution, will be proportional to the respective concen- trations. Taking again ester formation as an example, the velocity of the direct change = /iCaicohoi Cacid and that of the reverse change = /ijCester Cwater. At equilibrium, the rates will just balance, and therefore As before, this equation may be put in the form ^alcohol ^acid *i -j^ P C ~ i ^ ' ^-^ester *^water '^ where the respective concentrations are those under equilibrium conditions, and K is the equilibrium constant. It follows from the assumptions made both in the thermo- dynamical and kinetic proofs that the law of mass action holds strictly only for very dilute solutions, but the experimental results show that it often holds with a fair degree of accuracy even for moderately concentrated solutions. EQUILIBRIUM IN HOMOGENEOUS SYSTEMS i6i EQUILIBRIUM IN GASEOUS SYSTEMS (a) Decomposition of Hydriodic Acid — A typical example of equilibrium in a gaseous system is that between hydrogen, iodine and hydriodic acid, investigated by Bodenstein.^ The reaction, which is represented by the equation H.^ + Ij^ 2HI, is a completely reversible one, the concentration at equilibrium being the same whether one starts with hydrogen and iodine or with hydriodic acid, if the conditions otherwise are the same. Applying the law of mass action, we get at once p2 = J^ . . . • (I) as shown in the previous paragraph. It is clear from the equation that if from one observation the respective molecular concentrations of iodine, hydrogen and hydriodic acid are known, K, the equilibrium constant at the temperature in question, can be calculated. The question now arises as to how the progress of the reaction can be followed, so that it may be known when equilibrium is attained. It is further necessary to find a method of measurement such that the equilibrium does not alter while the observations are being made. In this case it happens that both the direct and inverse reactions are extremely slow at room temperature, but are fairly rapid at 445°, the tem- perature of boiling sulphur. If then the mixture is heated for a definite time at a high temperature and then cooled rapidly, the respective concentrations at high temperatures can be deter- mined at leisure by analysis. The reacting substances, in varying proportions, are heated at a definite temperature in sealed glass tubes for definite periods, and the amount of hydrogen then present measured after absorption of the iodine and hydriodic acid by means of potassium hydroxide. For the present, only results will be considered in which the tubes were heated so long at 445° that equilibrium was attained. In one experiment, 20"S5 mols of hydrogen were heated with ^ Zeitsch. fhysikal. Chem., 1897, 22, i. 1 62 OUTLINES OF PHYSICAL CHEMISTRY 3 1 '89 tnols of iodine, and it was found that the mixture at equilibrium contained 2'o6 mols of hydrogen, i3'40 nn°ls of iodine and 36'98 mols of hydriodic acid in the same volume. Hence _ [H,][I,J _ (2-06 x 13-40) _ ^- [Hip - (36-98)2 -00200. Equation (i) could, of course, be tested by finding if the same value of K is obtained for different initial concentrations of the reacting substances, but it is in some respects preferable to calculate by means of the equation the proportion of hydriodic acid formed at equilibrium when different initial concentrations of the reacting substances are taken, and to compare the results with those actually observed. In the calculation, K is taken as 0-0200 at 445°. If I raol of hydrogen is heated with a mols of iodine, and 2x mols of hydriodic acid are formed, i - x mols of hydrogen and a - X mols of iodine will remain behind. Substituting in equation (i), (i - x){a - x) ^^2 = K = 0-0200 . . (2) The first and second columns of the accompanying table contain the initial concentrations of hydrogen and iodine respectively, and the fourth and fifth columns the observed and calculated concentrations of hydriodic acid at equilibrium, the latter values being obtained from the expression 2x = I + t^ - V(r + ay - 4«-f s where s = i - 4K = o'ga obtained by solving the quadratic equation (2) above. H, I, Ij/H, = a HI found 2x (calc.) 20-57 5-22 0-254 10-22 lo'ig 20-6 i4'45 0-702 25-72 25-54 20'5S 31-89 I-SS2 36-98 37-13 20-41 52-8 2-538 38-68 39-01 20-28 67-24 3-316 39-52 39-25 EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 163 The close agreement between observed and calculated values shows that the law of mass action applies in this case. It can easily be shown from the fundamental equation that in this case the position of equilibrium is independent of the pressure or of the volume. Calling a, b and c the amounts of hydrogen, iodine and hydriodic acid present at equilibrium, the concentrations are a/V, bjN and c/V respectively, where V is the volume occupied by the mixture. Substituting in the general equation, we obtain abl^ = K ; in other words, K is independent of the volume. Bodenstein found that this re- quirement of the theory was also satisfactorily fulfilled. (3) Dissociation of Phosphorus Peutachloride — Another instructive example of equilibrium in a gaseous system is that between phosphorous pentachloride and its products of de- composition, represented by the equation PClj ^ PCI3 + Clj. A decomposition of this type, in which a chemical compound yields one or more products, is termed dissociation, and the student will have met with many examples of dissociation in his earlier work. As before, on appl)ang the law of mass action, we obtain CpolB If we commence with a molecules of PCI5, and x molecules each of PCI3 and Clj are formed, the concentrations of PCI5, PCI3 and CI2 at equilibrium are (a — x)IY, xjV and xjY re- spectively, and, substituting in the above equation, ^2 = K. (a - x)y It will be observed that the equilibrium in this case depends on the volume, and the larger the volume the smaller is (a - x) — in other words, the greater is the dissociation. An important point in connection with chemical equilibrium in general is the effect of the addition of excess of one of the products of decomposition (dissociation) on the degree of 1 64 OUTLINES OF PHYSICAL CHEMISTRY decomposition. If, for example, a mols of PClj are vaporized in a volume V in which b mols of PCI3 are already present, and if acj is the degree of dissociation of the pentachloride under these conditions, the relative concentrations of trichloride, penta- chloride and chlorine will be b ■{ x-^, a - x-^, and x-^ respec- tively. The equilibrium equation is therefore - (aci) Q> + x^) _ {a - x^)\ where K has the same numerical value as for the pentachloride alone, provided that the volume V and the temperature are the same. If it is assumed that the degree of dissociation when PCI5 is heated alone under the same conditions is 1 not more than say 25 per cent., it is clear that the proportion of undis- sociated compound cannot be very seriously increased by the presence of excess of PCI3. Hence when b, the initial amount of PCI3, is made very large, x-^, the amount of chlorine present at equilibrium must become very small in order that the pro- duct K (a — x^ may retain approximately the same value ; in other words, the dissociation of PCI5 must then be very small. From these considerations we deduce the following important general rule : The degree of dissociation of a compound is diminished by addition of excess of one of the products of dissociation provided that the volume remains constant. Equilibrium in Solutions of Non-Electrolytes— As an illustration of an equilibrium in solution, that between acid, alcohol, ester and water (p. 156) may be considered rather more fully. For this equilibrium, according to the law of mass action, we have K. .tester ^water If at the commencement a, b and c mols of acid, alcohol and water respectively are present in V litres, and under equi- librium conditions x mols of water and ester respectively have been formed, the respective concentrations are EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 165 r - ^—^ ■ r - ^~^ . r =~.r _ i^^ ■ ^acid -y > ^alc. — -y" ' tester -tr ' ^water — "y ' whence, substituting in the above equation, {a-x){l>-x) ^ ^ x{c + x) In this case also, the position of equilibrium is independent of the volume. The value of K may be obtained from the observation already mentioned, that when acid and alcohol are taken in equivalent proportions, two-thirds is changed to ester and water under equilibrium conditions. Hence ^ ^ s This equation may now be employed, as in the case of hydriodic acid, to calculate the equilibrium conditions for varying initial concentrations of the reacting substances. As an example, we take the proportion of i mol of acetic acid converted to ester by varying proportions of alcohol, when the initial mixture contains neither ester nor water. The equation in this case simplifies to (i - x){li - x) X' = i. whence x = |(i + b— Jb^ — b + i). The observed and cal- culated values of x are given in the table, and it will be seen that the agreement is very satisfactory, although the solution is so concentrated that it is scarcely to be expected that the law of mass action will apply strictly. b X (found) X (calc.) b X (found) X (calc.) COS o'o5 0-049 0-67 0-519 0-528 o-o8 0-078 0-078 i-o 0-665 0-667 o-i8 o'lyi 0-171 i-S 0-819 0-785 0-28 0'226 0-232 2-0 0-858 0-845 o'33 0-293 0-31 1 2-24 0-876 0-864 0-50 0-414 0-423 8-0 0-966 0-945 1 66 OUTLINES OF PHYSICAL CHEMISTRY As regards the practical investigation of this equilibrium, the reacting substances are heated in sealed tubes at constant temperature (say ioo°) till equilibrium is attained, cooled, and the contents titrated with dilute alkali, using phenolphthalein as indicator. As the concentrations of acid and alcohol before the experiment are known and the acid concentration after the at- tainment of equilibrium is obtained from the results of the titration, the proportion of ester formed can readily be calcu- lated. The equilibrium in salt solutions will be more conveniently dealt with at a later stage (Chapter XL). Influence of Temperature and Pressure on Chemical Equilibrium. General — The equations for chemical equi- librium deduced by means of the law of mass action hold for all temperatures provided that all the components remain in the system : the only effect of change of temperature is to alter the value of the equilibrium constant. The displacement of equi- librium is connected with the heat liberated in the chemical change by the equation. = ■^> ^^^ ^^^ value z'oo x 10"^ at 1220° abs. and io"4 x io~' at 13 20° abs. Hence, substituting in equation (2), we have io'4 X 10"^ Q (1320 - 1220) 2'9o X io~* 4'58)i (1320 X 1220) and Q = 41,000 cal. approximately. A specially interesting case is that in which there is no heat change when the first system changes to the second. Since in this case Q = o, the right-hand side of equation (i) becomes zero, and therefore there should be no displacement of equili- logio i68 OUT'LllSfES OF PHYSICAL CHEMISTRY brium with temperature. The condition of zero heat of reaction is, as has already been pointed out (p. 145), approximately ful- filled in ester formation, and in accordance with this, Berthelot found that at 10° 65 '2 per cent, of the acid and alcohol change to ester and at 220° 66*5 per cent. ; the displacement of equilibrium with temperature is therefore slight. There are certain rules of great importance which show qualitatively how the equilibrium is displaced with changes of temperature and pressure. If Q is the heat developed when the system A changes to the system B, and is positive, then with rise of temperature A increases at the expense of B ; con- versely, if Q is negative, B increases with rise of temperature at the expense of A. These statements may be summarised as follows : At constant volume increase of temperature favours the system formed under heat absorption and conversely. As an example, we may take nitrogen peroxide, NjO^ ^ 2NO2, for which the change represented by the lower arrow is attended with the liberation of a large amount (12,600 cal.) of heat. Increase of temperature favours the reaction for which heat is absorbed, in this case the reaction represented by the upper arrow, so that as the temperature rises N^O^ is split up more completely into NO2 molecules. Another interesting example is the relationship between oxygen and ozone, represented by the equation 2O3 = 3O2 -I- 2 X 29,600 cal. The equilibrium for the reaction 203^303 is very near the oxygen side at the ordinary temperature, but increase of temperature must displace it in the direction repre- sented by the lower arrow, since under these circumstances heat is absorbed ; in other words, ozone becomes increasingly stable as the temperature rises. The experimental results so far obtained are in satisfactory agreement with the theory.* ' Compare Fischer and Marx, Berichte, 1907, 40, 443. At first sight this appears to be in contradiction to the well-known fact that when a mixture of oxygen and ozone is heated to 250° the ozone is practically destroyed. It must be remembered, however, that the mixture contains far too much ozone for equilibrium, but owing to the low temperature it attains its true equilibrium very slowly. At 250°, however, the attainment of equilibrium is fairly rapid. EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 169 From the above considerations we conclude that endothermic compounds, such as ozone, acetylene and carbon disulphide, become increasingly stable as the temperature rises, whilst exothermic compounds undergo further dissociation. A similar law can be enunciated for the effect of pressure on equilibrium as follows : On increasing the pressure at constant temperature the equilibrium is displaced in the direction in which the volume diminishes. Taking as an illustration the gaseous equilibrium, PClg^PClg + CI2 in which the upper arrow indicates the direction of increase of volume, the rule indicates that increase of pressure will displace the equilibrium to the left, whilst decrease of pressure will favour the reverse change. As is well known, these deductions are in complete accord with the experimental facts. For reactions not attended by any appreciable change of volume, such as the decomposition of hydriodic acid at high temperatures, the equilibrium should not be altered by change of volume, a conclusion borne out by experiment (p. 163). Le Chatelier's Theorem — Le Chatelier has pointed out that the rules above referred to with regard to the effect of changes of temperature and pressure on equilibria are special cases of a much more general law which may be enunciated as follows : When one or more of the factors determining an equi- librium are altered, the equilibrium becomes displaced in such a way as to neutralize, as far as possible, the effect of the change. A little consideration will show that this rule affords a satisfac- tory interpretation of all the phenomena just mentioned. Relation between Chemical Equilibrium and Tem- perature. Nernst's Yiews — Although the van't Hoff equation connecting equilibrium and temperature enables us to calculate the position of equilibrium at different tempera- tures when the position of equilibrium at one temperature and the heat of reaction are known, it has not until quite recently been possible to calculate chemical equilibria from thermal and thermochemical data alone. Within the last 170 OUTLINES OF PHYSICAL CHEMISTRY two or three years, the latter problem appears to have been to a great extent solved by Nernst.^ The fundamental as- sumption, on the basis of which it has been found possible to deduce formulse connecting the equilibrium in a system with the thermal data characteristic of the reacting substances, is that the free energy, A, and the total heat of reaction, Q, are not only equal at the absolute zero, as already pointed out (p. 1 5 2), but their values coincide completely in the immediate vicinity of that point. It is evident that this assumption cannot be tested directly, but the fact that the formulae deduced on this basis have been to a great extent confirmed by experiment ^ goes far to justify it. There can be no doubt that the results just described con- stitute one of the most important advances in physics and chemistry of recent years. It is beyond the scope of the present book to discuss the question more fully, but it may be mentioned that the theory not only admits of the calcula- tion of equilibria in homogeneous and heterogeneous systems from thermal data, but also gives a formula representing the variation of vapour pressure with temperature. Practical Illustrations — The law of mass action may be illustrated most conveniently by the action of water on bismuth chloride, represented by the equation BiClg + H20^BiOCl+ 2HCI. When dilute hydrochloric acid is added to a mixture of the salt and water, the equilibrium is displaced in the direction represented by the lower arrow, and a homogeneous solution is obtained. If excess of water is added to this solution, the equilibrium is displaced in the direction represented by the upper arrow, and a precipitate of bismuth oxychloride is formed. The law may also be illustrated qualitatively by the inter- action of ferric chloride and ammonium thiocyanate to form ' Nernst, Applications of Thermodynamics to Chemistry. London: Constable, 1907. Annual Reports, Chemical Society, igo6, pp. 20-22. ^ Nernst, loc. cit. EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 171 blood-red ferric thiocyanate.^ This reaction is of particular interest, as it was one of the first reversible reactions to be systematically investigated (J. H. Gladstone, 1855).^ The equation representing the reaction is as follows : — FeClg + 3NH^CNS^Fe(CNS)3 + 3NH4CI. Solutions of the salts are first prepared; the thiocyanate solution contains 37 grams of the salt to 100 c.c. of water, and the ferric chloride solution 3 grams of the commercial salt and 12 -5 c.c. of concentrated hydrochloric acid to 100 c.c. of water. 5 c.c. of each of the solutions are added to 2 litres of water and the solution divided between four beakers. The solutions are pale-red in colour, as the equilibrium lies considerably towards the left-hand side. To the contents of two of the beakers are added 5 c.c. of the ferric chloride and the thiocyanate solution respectively, and it will be observed that the solutions become deep red, owing to the displace- ment of the equilibrium in the direction of the upper arrow. On the other hand, the addition of 50 c.c. of a concentrated solution of ammonium chloride^ to the solution in the third beaker makes it practically colourless, the equilibrium being displaced in the direction of the lower arrow, in accordance with the law of mass action. ' Lash Miller and Kenrxck, y. Amer, Chem. Soc, 22, 291. 2 Phil. Trans. Roy. Soc, 1855, 179. 3 Strictly speaking, all the solutions should be made up to the same volume in each case, but for qualitative purposes the method described is sutificiently accurate. The deep-red colour is presumably due to ihe for- mation of non-ionised ferric thiocyanate (p. 260) ; it cannot be due to Fe-" or to CNS' ions, which are practically. colourless. CHAPTER VIII HETEROGENEOUS EQUILIBRIUM. THE PHASE RULE General — In contrast to homogeneous systems, in which the composition is uniform throughout, heterogeneous systems are made up of matter in different states of aggregation. The separate portions of matter in equilibrium are usually termed phases ; each phase is itself homogeneous, and is separated by bounding surfaces from the other phases. Liquid water in equilibrium with its vapour is a heterogeneous system made up of two phases, the equilibrium in this case being of a physical nature. Another heterogeneous equilibrium, formed by calcium carbonate with its products of dissociation, consists of three phases, two of which are solid, calcium carbonate and calcium oxide, and one gaseous. A still more complicated case is the equilibrium between a solid salt, its saturated solution, and vapour, made up of a solid, a liquid and a gaseous phase. It should be remembered that though each phase must be homogeneous, both as regards chemical and physical pro- perties, it may be chemically complex. For example, a mixture of gases only forms a single phase, since gases are miscible in all proportions. Further, a phase may be of variable composi- tion, thus a solution only constitutes one phase, although it may vary greatly in concentration. Application of Law of Mass Action to Heterogeneous Equilibrium — It has already been shown that equilibria in homogeneous systems may be dealt with satisfactorily by 173 HETEROGENEOUS EQUILIBRIUM 173 means of the law of mass action, provided that the molecular condition of the reacting substances is known. The matter is, however, somewhat more complicated for heterogeneous equi- libria, more particularly when solid substances are present, as in the equilibrium between calcium carbonate, calcium oxide and carbon dioxide already referred to. Debray, who investi- gated this system very carefully, showed that, just as water at a definite temperature has a definite vapour pressure, independent of the amount of liquid present, there is a definite pressure of carbon dioxide over calcium carbonate and oxide at a definite temperature, independent of the amount or the relative propor- tions of the solids present. The question now arises as to how the law of mass action is to be applied to systems in which solids are present. This problem was solved by Guld- berg and Waage, who found that the experimental results, such as those for the dissociation of calcium carbonate, were satis- factorily represented on the assumption that the active mass of a solid substance at a definite temperature is constant, i.e., inde- pendent of the amount of solid present. It was not at first clear what physical meaning is to be attached to this statement, but Nernst pointed out that for any such system it was sufficient to consider the equilibrium in the gaseous phase, the active mass of a solid being repre- sented as its concentration in the gaseous phase. In other words, a solid, like a liquid, may be regarded as having a definite vapour pressure at a definite temperature, independent of its amount. At first sight it may seem surprising to ascribe a definite vapour pressure to such a substance as calcium oxide, but it is well known that solids like bismuth and cadmium have definite vapour pressures at moderate temperatures, and there is every reason for supposing that the diminution of vapour pressure with fall of temperature is continuous. There is now no difficulty in applying the law of mass action to equilibria in which solid substances are concerned, for example, to the dissociation of calcium carbonate. For convenience, we will 174 OUTLINES OF PHYSICAL CHEMISTRY use the partial pressures, /, of the components in the gaseous phase as representing the active masses.^ We then obtain CaCOj^CaO + COj '^^CaCOs = ^i/CaO/cOai whence pco, = , / — -' = constant. «i;>Ca0 Otherwise expressed, since all the factors on the right-hand side of the equation are constant at constant temperature, the vapour pressure of carbon dioxide must be constant, which is in accordance with the experimental facts. It is clear from the form of the equation that the pressure remains constant only within limits of temperature such that both calcium carbonate and oxide are present. If the tem- perature is so high that no calcium carbonate is present, the pressure is no longer defined, but depends on the size of the vessel, etc. Dissociation of Salt Hydrates — Other interesting examples of heterogeneous equilibrium are those between water vapour and salts with water of crystallisation. If, for example, crystallised copper sulphate, CUSO4, sHjO is placed in a desiccator over concentrated sulphuric acid at 50°, it gradually loses water and finally only the anhydrous sulphate remains. If arrangements are made for continuously observing the pressure during dehyd- ration, it will be found to remain constant at 47 mm. until the salt has lost two molecules of water, it then drops to 30 mm. and remains constant until other two molecules of water have been lost, when it suddenly drops to 4^4 mm. and remains constant till dehydration is complete. The explanation of the successive constant pressures observed during dehydration is similar to that already given for the constant pressure of carbon dioxide over calcium carbonate and oxide. At 50° the hydrates CuSO^, sHjO and CUSO4, sH^O are in equilibrium with a 1 The partial pressure of a gas is proportional to the number of particles present per unit volurne and therefore to its molecular concentration or active mass (of. p. 156). HETEROGENEOUS EQUILIBRIUM 175 pressure of aqueous vapour = 47 mm., and as long as any of the pentahydrate is present, the pressure necessarily remains con- stant. When, however, all the pentahydrate is used up, the trihydrate begins to dehydrate, giving rise to a little of the monohydrate, CUSO4, HgO. As a new substance is then taking part in the equilibrium, the pressure of aqueous vapour neces- sarily alters, and remains at the new value until the trihydrate is used up. The successive equilibria are represented by the following equations: — I. CuSO^, sHjO^CuSOi, 3H2O + 2H2O. II. CuSOi, sHjjO^CuSOi, H2O + 2H2O. III. CuSO^, H^O^CuSO^ + HjO. By applying the law of mass action to any of the above equations, it may easily be shown that the pressure of aqueous vapour must be constant at constant temperature. Putting the partial pressures of the pentahydrate and the trihydrate as Pj and Pj respectively, we have from equation I. : — ^Pl = -iiPj/^HaO. whence /^HaO = t-^ = constant. It is important to realise clearly that the observed pressure is not due to any one hydrate, it is only definite and fixed when both hydrates are present. The tension of aqueous vapour over hydrates, like the vapour pressure of water, in creases rapidly with the temperature. This is illustrated in the following table, in which the vapour pressures (in mm.) over a mixture of NajHPO^, 7H2O and Na2HP04, and those of water at the same temperatures, are given : — Temperature . . I2'3° i6-3° 207° 249° 3I-5'' 36-4"' 40-0° Na2HP04 + o-7HjO , 4-8 6-9 9-4 I2'9 21-3 30-5 4i'2 Water .... io-6 13-8 i8-i 23-4 34-3 45-1 54-9 Ratio salt/water . . 0-46 0*50 0-52 0-55 0-62 o-68 0-75 The results throw light on the question of the efflorescence (giving up of water) and deliquescence (absorption of water) of 176 OUTLINES OF PHYSICAL CHEMISTRY hydrated salts in contact with the atmosphere. If a hydrate (in the presence of the next lower hydrate) has a higher vapour pressure than the ordinary pressure of aqueous vapour in the atmosphere, it will lose water and form a lower hydrate. For example, the salt Na2HP04, laHjO has a vapour pressure of over i8 mm. at 25", which is greater than the average pressure of aqueous vapour in the atmosphere at that temperature, though less than the saturation pressure (see table), and therefore the salt is efflorescent under ordinary conditions. On the other hand, the vapour tension of the heptahydrate at 25° is only 13 mm. and it is therefore stable in air. The table shows that the ratio of the vapour pressure of a hydrate to that of water increases rapidly with the temperature and ultimately it becomes greater than unity ; the vapour tension of the hydrate is then greater than that of water. Dissociation of Ammonium Hydrosolphide — Solid ammonium hydrosulphide partly dissociates on heating into ammonia and hydrogen sulphide, according to the equation NH^HSjiNHg + HjS. This equilibrium is of a different type to those already mentioned, as a solid dissociates into two gaseous components. Representing molecular concentrations as partial pressures, we obtain, on appl)dng the law of mass action, - ^^"'^"'^ =K,or/NH,/H3S= K/nh4Hs= constant, /NH4HS since the partial pressure of solid ammonium sulphide is constant at constant temperature. The equation indicates that the product of the partial pressures of the two gases is constant at constant temperature. When the gases are obtained by heating ammonium hydro- sulphide, they are necessarily present in equivalent amount and exert the same partial pressure. The above formula may, however, be tested by adding excess of one of the products of dissociation to the mixture. This was done by Isambert, with the result indicated in the following table, which holds for 25 -i"; the volume being kept constant throughout; — HETEROGENEOUS EQUILIBRIUM 177 ^NHs ^HaS /NHj/'HaS 250-5 250-5 62,750 2o8-o 294-0 60,700 4S3'o 143-0 64,800 In the first experiment the gases are present in equivalent proportions, in the second experiment excess of hydrogen sulphide, in the third excess of ammonia have been added. The results indicate that the product of the pressures is con- stant within the limits of experimental error, as the theory indicates, and, further, that addition of excess of one of the products of dissociation diminishes the amount of the other, as already shown for phosphorus pentachloride (p. 163). Analogy between Solubility and Dissociation — There is a very close analogy between the solubility of solids in liquids and the equilibrium phenomena just considered, more particularly the dissociation of salt hydrates. In both cases there is equilibrium between the solid as such and the same sub- stance in the other (gaseous or liquid) phase. We have already seen, in the case of the hydrates of copper sulphate, that the vapour pressure {i.e., the concentration of vapour in the gas space) depends on the composition of the solid phases, and it is then easy to see that the solubility of sodium sulphate (its concentration in the liquid phase) must also depend on the composition of the solid phase. The solubility alters when the solid decahydrate changes to the anhydrous salt, just as does the vapour pressure when copper sulphate pentahydrate disappears. A further analogy between the two phenomena is that just as the addition of an indifferent gas to the gas phase does not alter the equilibrium', except in so far as the volume is changed, so the addition of an indifferent substance to a solu- tion does not greatly affect the solubility of the original solute. Distribution of a Solute between two Immiscible Liquids — The distribution of a solute such as succinic acid between two immiscible liquids such as ether and water exactly corresponds with the distribution of a substance between the 13 178 OUTLINES OF PHYSICAL CHEMISTRY liquid and gas phase (p. 83), and therefore the rules already mentioned for the latter equilibrium apply unchanged to the former. The most important results may be expressed as follows (Nernst) : — (i) If the molecular weight of the solute is the same in both solvents, the distribution coefficient (the ratio of the concentra- tions in the two solvents after equilibrium is attained) is con- stant at constant temperature (Henry's law). (2) In presence of several solutes, the distribution for each solute separately is the same as if the others were not present (Dalton's law of partial pressures). The first rule may be illustrated by the results obtained by Nernst for the distribution of succinic acid between ether and water, which are given in the table : — Cj (in water) Cj (in ether) Cj/Cj 0-024 o"oo46 5*2 0-070 0-013 S'4 0-I2I o'022 5-4 The results were obtained by shaking up varying quantities of succinic acid with 10 c.c. of water and 10 c.c. of ether in a separating funnel, and determining the concentrations of acid in the two layers after they had separated completely. The fact that the ratio Cj/Cg is approximately constant shows that Henry's law applies. When the molecular weight of the solute is not the same in both solvents, the ratio of the concentrations is no longer constant, and, conversely, if the ratio of the concentrations is not constant at constant temperature, the molecular weight cannot be the same in both solvents. This is illustrated by the following results obtained by Nernst for the distribution of benzoic acid between water and benzene : — C, (in water) Cj (in benzene) Cj/'^s ^^S ijcl 0-0150 0-242 0-062 0-0305 0-0195 0-412 0-048 0-0304 0-0289 0*970 0-030 0-0293 HETEROGENEOUS EQUILIBRIUM 179 As the table shows, the ratio CJC2 is not even approximately constant, but on the other hand, the ratio CJ ^^/Cj is constant (fourth column). A little consideration shows that this is connected with the fact already mentioned, that whilst benzoic acid has the normal molecular weight in water, in benzene it is present almost entirely as double molecules (p. 1 24). In this case also we may assume that there is a constant ratio between the concentrations of the simple molecules in the two phases, and as it may easily be shown (p. 267) that the concentration of the simple molecules in benzene is proportional to the square root of the total concentration, the results are in accord with the theory. The Phase Rule. EquilibFium between Water, Ice and Steam — In the previous sections of this chapter, it has been shown that many heterogeneous equilibria can be dealt with satisfactorily by means of the law of mass action. This holds not only for phases of constant composition, but within limits also for phases of variable composition, such as solutions. With reference to dilute solutions there is, of course, no difficulty, as the active mass of the solute is proportional to its concentra- tion. This is not the case, however, for strong solutions, and the application of the law of mass action to these is attended with considerable uncertainty. As far back as 1874, a complete method for the representa- tion of chemical equiUbria was developed by the American physicist, Willard Gibbs, which has come to be known as the phase rule. The first point to notice with regard to this method is that it is entirely independent of the molecular theory ; the composition of a system is determined by the number of in- dependently variable constituents, which Gibbs terms components. He then goes on to determine the number of " degrees of free- dom" of a system from the relation between the number of components and the number of phases. It is for this reason that his method of classification is termed the phase rule. In order to make clear the meaning of the terms employed it will be well, before enunciating the rule, to illustrate them by Solid 1 80 OUTLINES OF PHYSICAL CHEMISTRY means of a very simple case, namely water. As regards the equilibrium in this case, we may, according to the conditions of the experiment, have one, two or more phases present. Thus, under ordinary conditions of temperature and pressure, there are two phases, water and water vapour, in equilibrium. This equilibrium is represented in the accompanying diagram by the line OA (Fig. 22), temperature being measured along the horizontal and pressure along the vertical axes. It is only at points on the curve that there is equilibrium. If, for example, the pressure is kept below that represented by a point on the curve OA (by continuously increasing the volume) the whole of the water will be converted to vapour ; if, on the other hand, it is kept at a point a little above the curve at a definite temperature, the •'y'O Vapour whole of the vapour will ulti- mately liquefy. When the temperature is a little below 0°, only ice and vapour are Temperature-s- present, and the equilibrium Fig. 22. between them is represented on the diagram by the line OC, which is not continuous with OA. The two curves meet at O, and O is the point at which ice and water are in equilibrium with water vapour. It is easy to see that at this point ice and water have the same vapour pressure. If this were not so, vapour would distil from the phase with the higher vapour pressure to that with the lower vapour pressure till the first phase was entirely used up, a result in contradiction with the fact that the two phases remain in equilibrium at this point. Since 0° is the temperature at which ice and water are in equilibrium with their vapour under atmospheric pressure, and as pressure lowers the melting-point HETEROGENEOUS EQUILIBRIUM i8i of ice, the point O, at which the two phases are in equilibrium under the pressure of their own vapour (about 4"6 mm.), must be a little above o° ; the actual value is + 0*007° C. The diagram is completed for stable phases by drawing the line OB, which represents the effect of pressure on the melting-point of ice ; the line is inclined towards the pressure axis because in- creased pressure lowers the melting-point. The point O is termed a triple point, because there, and there only, three phases are in equilibrium. At points along the curves two phases are in equilibrium, and under the con- ditions in the intermediate spaces only one phase is present, as the diagram shows. So far, only stable conditions have been considered, but unstable conditions may also occur. Thus water does not necessarily freeze at 0° ; if dust is carefully excluded, it is pos- sible to follow the vapour pressure curve for some degrees below zero. The part of the curve thus obtained is represented by the dotted line OA' which is continuous with OA and lies above OC, the vapour pressure curve for ice. These results illustrate two important rules : (i) there is no abrupt change in the properties of a liquid at its freezing-point when the solid phase does not separate ; (2) the vapour pressure of an unstable phase is greater than that of the stable phase at the same temperature. The last result may be anticipated, since it is then evident how an unstable phase may change to a stable phase by distillation. The phase rule may now be enunciated as follows : If P represents the number of phases in a system, C the number oj components and F the number of degrees of freedom, the rela- tion between the number of phases, components and degrees of. freedom is represented by the equation C - P -f- 2 =■ F. The meaning of the terms " component " and " degree of freedom " will become clear as we proceed. The former has already been defined as the smallest number of independent variables of which the system under consideration can be built 1 82 OUTLINES OF PHYSICAL CHEMISTRY up. Thus in the case of water, considered above, there is only one component, and the system calcium carbonate-calcium oxide-carbon dioxide can be built up from two components, say calcium oxide and carbon dioxide. Particular instances of the application of the phase rule will now be given. If the number of phases exceeds the number of components by 2, the system has no degrees of freedom (F = o), and is said to be non-variant. An illustration of this is the triple point O in the diagram for water (p. i8o), where there are three phases (liquid water, ice and water vapour) and one component (water). If one of the variables, the temperature or the pressure, is altered and kept at the new value, one of the phases disappears ; in other words, the system has no degrees of freedom. If the number of phases exceeds the number of components by one F = I, and the system is said to be univariant. As an illus- tration, we take the case of water vapour, where there are two phases and one component, say any point on the line OA. In this case the temperature may be altered within limits without altering the number of phases. If the temperature is raised, the pressure will increase correspondingly, and the system will thus adjust itself to another point on the curve OA. Similarly, the pressure may be altered within limits, the system will re-attain to equilibrium by a change of temperature at the new pressure. If, however, the temperature be kept at an arbitrary value and the pressure is then changed, one of the phases will disappear ; the system has therefore one, and only one, degree of freedom. If the number of phases is equal to the number of components, the system has two degrees of freedom, and is said to be divariant. The areas in the diagram (Fig. 2 2) are examples of this case — there is one phase (vapour, liquid or solid) and one component. If, for instance, we consider the vapour phase, the temperature may be fixed at- any desired point within the triangle AOC, and the pressure may still be altered within limits along a line parallel to the pressure axis without alteration in the number of phases, as long as the curves OA and OC are not reached. HETEROGENEOUS EQUILIBRIUM 183 If the number of phases is less than the number of com- ponents by one, the system is Invariant, and so on. This particular instance cannot occur in the case of water, but does so in a four-phase system, as described in the next section. Equilibrium between Four Phases of the same Sub- stance. Sulphur — The diagram for water represents the equi- librium between three phases of the same substance. We are now concerned with sulphur, which is somewhat more compli- cated inasmuch as there are two solid phases, monoclinic and rhombic sulphur, in addition to the usual liquid and vapour phases. Rhombic sulphur is stable at the ordinary temperature, and on heating rapidly melts at 115°. On being kept for some time in the neighbourhood of 100°, however, it changes completely to monoclinic sulphur, which melts at 120°. Monoclinic sulphur can be kept for an indefinite time at 100° without changing to rhombic ; it is therefore the stable phase under these conditions. Thus, just as water is the stable phase above 0° and ice is stable below 0°, there is a temperature above which monoclinic sulphur is stable, below which rhombic sulphur is stable, and at which the two forms are in equilibrium with their vapour. This tem- perature is termed the transttion point, and occurs at 95 '6°. The change of one form into another is under ordinary condi- tions comparatively slow, and it is therefore possible to determine the vapour pressure of rhombic sulphur up to its melting-point, and that of monoclinic sulphur below its transition point. Although the vapour pressure of solid sulphur is comparatively small, it has been measured directly down to 50°. The complete equilibrium diagram, which includes the fixed points just mentioned, is represented in Fig. 23 . O is the point at which rhombic and monoclinic sulphur are in equilibrium with sulphur vapour, and is consequently a triple point, analogous to that for water ; OB is the vapour-pressure curve of rhombic sulphur, and OA that of monoclinic sulphur. OA', which is continuous with OA, is the vapour-pressure cvirve of monoclinic 1 84 OUTLINES OF PHYSICAL CHEMISTRY sulphur in the unstable or metasiable condition ; OB' similarly represents the vapour-pressure curve of rhombic sulphur in the unstable condition, and B' its melting-point. It will be observed that in both cases the metastable phase has the higher vapour pressure (p. i8i). The line OC represents the effect of pressure on the transition point O and is therefore termed a transition curve ; since, contrary to the behaviour of water, pressure raises the transition point, the line is inclined away from the pressure 'C(131*400atmos.) A(i20') Vapour Temperature—^ Fig. 23. axis. Similarly, the curve AC represents the effect of pressure on the melting-point of monoclinic sulphur, and as it is less inclined away from the temperature axis than OC, the two lines meet at C at 131° under a pressure of 400 atmospheres. The curve AD is the vapour-pressure curve of liquid sulphur above 1 20°, where the liquid is stable, and AB', continuous with DA, is the vapour-pressure curve of metastable liquid sulphur. As already indicated, B' represents the melting-point of njetastable HETEROGENEOUS EQUILIBRIUM 185 rhombic sulphur ; in other words, it is a metastable triple point a^ which rhombic and liquid sulphur, both in the metastable condition, are in equilibrium with sulphur vapour. OB', as already indicated, represents the vapour-pressure curve of meta- stable rhombic sulphur, and the diagram is completed, both for stable and metastable phages, by B'C, which represents the effect of pressure on the melting-point of rhombic sulphur. Mono- clinic sulphur does not exist above the point C; when fused sulphur solidifies at a pressure greater than 400 atmospheres, the rhombic form separates, whilst, as is well known, the monoclinic form first appears on solidification under ordinary pressure. The areas, as before, represent each a single phase, as shown in the diagram. Monoclinic sulphur is of particular interest, because it can only exist in the stable form within certain narrow limits of temperature and pressure, represented in the diagram by OAC. The phase rule is chiefly of importance in indicating what are the possible equilibrium conditions in a heterogeneous system, and in checking the experimental results. To illustrate this, we will use it to find out what are the possible non-variant systems in the case of sulphur, just considered. From the formula C - P -t- 2 = F, since C = i, P must be three in order that F may be zero ; in other words, the system will be non-variant when three phases are present. As any three of the four phases may theoretically, be in equilibrium, there must be four triple points, with the following phases : — (a) Rhombic and monoclinic sulphur and vapour (the point O). {p) Rhombic and monoclinic sulphur and liquid (the point C). {c) Rhombic sulphur, liquid and vapour (the point B'). {d) Monoclinic sulphur, liquid and vapour (the point A). The phase rule gives no information, however, as to whether the triple points indicated can actually be observed. In this particular case they are all attainable, as the diagram shows, but only because the change from rhombic to monoclinic sulphur above the triple point is comparatively slow. If it 1 86 OUTLINES OF PHYSICAL CHEMISTRY happened to be rapid, the point B' could not be actually observed. Systems of Two Components. Salt and Water— The equilibrium conditions are somewhat more complicated on passing from systems of one component to those of two com- ponents, such as a salt and water. For simplicity, the equi- librium between potassium iodide and water will be considered, as the salt does not form hydrates with water under the con- ditions of the experiment. There will therefore be only four phases, solid salt, solu- tion, ice and vapour. There are three degrees of freedom, as, in ad- dition to the tempera- ture and pressure, the concentration of the solution may now be varied. The equilibrium in this system is repre- sented in Fig. 24, the ordinates representing temperatures and the abscissae concentra- tions. At 0° (A in the diagram) ice is in equilibrium with water and vapour, as has already been shown. If, now, a little potassium iodide is added to the water, the freezing-point is lowered, in other words, the temperature at which ice and water are in equilibrium is lowered by the addition of a salt, and the greater the proportion of salt present, the lower is the temperature of equilibrium. This is represented on the curve AO, which is the curve along which ice, solution and vapour are in equilibrium. On continued addition of potassium iodide, however, a point must be reached at which the solution is saturated with the salt, and on further addition of potassium 20 30 40 50 60 Fig. 24. HETEROGENEOUS EQUILIBRIUM 187 iodide, the latter must remain in the solid form in contact with ice and the solution. It is clear that, since the progressive lowering of the freezing-point depends upon the continuous increase in the concentration of the solution, the temperature corresponding with the point O must represent the lowest temperature attainable in this way under stable conditions. To complete the diagram, it is further necessary to determine the equilibrium curve for the solid salt, the solution and vapour. Looked at in another way, this will be the solubility curve of potassium iodide, which is represented by the curve OB. This curve is only slightly inclined away from the tempera- ture axis, corresponding with the fact that the solubility of potassium iodide only increases slowly with rise of temperature. The point O, which is the lowest temperature attainable with two components, is known as a eutectic point ; in the special case when the two components are a salt and water, it is termed a cryohydric point. The meaning of the diagram will be clearer if we consider what occurs when solutions of varying concentration are pro- gressively cooled. If, for example, we commence with a weak salt solution above its freezing-point {x in the diagram) and continuously withdraw heat, the temperature will fall (along xy) till the line OA is reached ; ice will then separate, and as the cooling is continued the solution will become more con- centrated and the composition will alter along the line AO until O is reached ; salt then separates as well as ice, and the solution will solidify completely at constant temperature, that of the point O. Similarly, if we start with a concentrated salt solution and lower the temperature until it reaches the curve OB, salt will separate and the composition will alter along the curve BO until it reaches the point O, when the mixture solidifies as a whole. Finally, if a mixture corre- sponding with the composition of the cryohydric mixture is cooled, the line parallel to xy representing the fall of tem- perature will meet the curve first at the point O, and the 1 88 OUTLINES OF PHYSICAL CHEMISTRY mixture will solidify at constant temperature. At the cryohydric temperature, the composition of the solid salt which separates is necessarily the same as that of the solution. Guthrie,^ who was the first to investigate these phenomena systematically, was of opinion that these mixtures of constant composition were definite hydrates, which were therefore termed cryohydrates. At first sight there seems much to be said for this view, as the separa- tion takes place at constant temperature, independent of the initial concentration, and the mixtures are crystalline. For the following reasons, however, it is now accepted that the cryo- hydrates are not chemical compounds : (a) the properties of the mixture (heat of solution, etc.) are the mean of the pro- perties of the constituents, which is seldom the case for a chemical compound; {U) the components are not usually present in simple molar proportions ; and (<:) the heterogeneous character of the mixture can be recognised by microscopic examination. The magnitude of the cryohydric temperature is of course con- ditioned by the effect of the salt in lowering the freezing-point of the solvent, and by its solubility at low temperatures. The eutectic temperatures of solutions of sodium and ammonium chlorides are - 22° and - 17° respectively, that of a solution of calcium chloride — 37°. The application of the phase rule to this system will be readily understood from what has been said above. When there are four phases, ice, salt, solution and vapour, and two com- ponents, we find, by substituting in the formula C - P -I- 2 = F, that F = o, that is, the four phases can only be in equilibrium at a single point, the point O in the diagram. When there are three phases, there is one degree of freedom, and the equi- librium is represented by a line (OA and OB in the diagram). If, for example, the condition of affairs is that represented by a point on the line OA, and the concentration of the solution is increased and kept at the new value (by further addition of salt when necessary) ice will dissolve, and the temperature will fall till it corresponds with that at which ice is in equilibrium ipAj7. Jl/ag-., 1884, [5], 17, 462. HETEROGENEOUS EQUILIBRIUM 189 with the more concentrated solution and vapour. If, then, while the concentration is still kept at the above value, the tempera- ture is altered and kept at the new value, one of the phases will disappear. The system is therefore univariant. If, instead of the concentration, one of the other variables is changed, corre- sponding changes in the remaining two variables take place, and the system adjusts itself till the three phases are again in equilibrium. If there are only two phases, for example, solution and vapour, the phase rule indicates that the system is bivariant, and it can readily be shown, by reasoning analogous to the above, that such is the case. Freezing Mixtures — The use of mixtures of ice and salt as "freezing mixtures'" for obtaining constant low temperatures, depends upon the principles just discussed. Suppose, for example, we begin with a fairly intimate mixture of ice and salt and a little water. When a little of the salt dissolves, the solution is no longer in equilibrium with ice. It will strive towards equilibrium by some more ice dissolving to dilute the solution, the latter, being now more unsaturated with regard to the salt, will dissolve more of it, more ice will go into solution and so on. As a consequence of these changes, heat must be absorbed in changing ice to water (latent heat of fusion of ice), and in connection with the heat of solution of the salt if, as is usually the case, the heat of solution is negative. The temperature, therefore, falls till the cryohydric point is reached, and then remains constant, since it is under these conditions that ice, salt, solution and vapour are in equilibrium. As the temperature of a cryohydric mixture is so much below atmospheric temperature, heat will continually be absorbed from the surroundings, but as long as both ice and solid salt are present, the heat will be used up in bringing about the change of state, and the temperature will remain constant. When, however, either ice or salt is used up, the temperature must necessarily begin to rise. I go OUTLINES OF PHYSICAL CHEMISTRY Systems of Two Components. General — The particular case of a two-component or binary system already considered — potassium iodide and water — is very simple, for two reasons : (i) the solid phases separate pure from the fused mass, in other words, the phases are not miscible in the solid state ; (2) the components do not enter into chemical combination. Com- plications occur when chemical compounds are formed, and when the solid phases separate as mixed crystals (p. 95) con- taining the two components in varying proportions. We will consider three comparatively simple cases of equilibrium in binary systems, the components being in all cases completely miscible in the fused state : — (a) The components do not enter into chemical combination, and are not miscible in the solid state. {b) The components do not enter into chemical combination, but are completely miscible in the solid state. (c) The components form one chemical compound, but are not miscible with each other or with the compound in the solid state. Case {a). One example of this case is potassium iodide and water which has just been discussed. Another, which will be briefly considered, is the equilibrium between the metals zinc and cadmium.^ To determine the equilibrium curves, mixtures of these metals in varying proportions are heated above the meltmg-point, and then allowed to cool slowly, the rate of cooling being observed with a thermocouple, one junction of which is placed in the mixture and the other kept at constant temperature. If the thermocouple is connected to a mirror galvanometer, the rate of cooling can be followed by the move- ment of a spot of light. It will be observed that at two points there are halts in the rate of cooling — so-called " breaks " — the first point varies with the composition of the mixture, whilst the second is practically constant at 270°. The curve obtained by plotting the temperatures of the first break against the ' Hiniichs, Zeitsch. anorg. Chem., 1907, 55, 415, HETEROGENEOUS EQUILIBRIUM 191 composition of the mixture is represented in Fig. 25. The analogy of the diagram with that for potassium iodide and water will be evident, as is its interpretation. The point A represents the freezing-point of zinc, B that of cadmium, the curve AC represents the effect of the gradual addition of cadmium upon the freezing-point of zinc, and BC the effect of zinc in lowering XoO/oCd Z ^ lOOO/oCd Equilibrium Diagram for Zinc and Cadmium FlQ. 25. the freezing-point of cadmium, C is the eutectic point at which solid zinc and cadmium are in equilibrium with the fused mass. Consider first a fused mixture rich in zinc. As the temperature falls, a point is ultimately reached at which pure zinc begins to separate, and as the change from liquid to solid is, as usual, attended with liberation of heat, the temperature will remain practically steady for a short time — ^this represents the first break on cooling. As zinc continues to separate, the composi- tion of the mixture moves along the curve AC, at C the solution 192 OUTLINES OF PHYSICAL CHEMISTRY is also saturated with regard to cadmium, and therefore at the temperature represented by C, both zinc and cadmium separate in a mixture of the same composition as the fused mass. This, as already mentioned, is the eutectic point, and as the mixture at that point behaves like a single substance, the temperature remains constant till the whole mass has solidified. This is the second break observed when the mixture cools. If, on the other hand, we commence with a mixture rich in cadmium, the latter separates along the curve BC till the point C is reached, and then the mixture solidifies as a whole. Finally, if a mixture is taken, the composition of which is that of the eutectic mixture, there is only one break in the cooling curve, at the eutectic point. The composition of the eutectic mixture is represented by the point Z on the axis of composition XY, and corresponds with 17 "4 per cent, of zinc and 8 2 "6 per cent, of cadmium by weight. Case {b). No chemical compound. Separation of mixed crystals. A good example of this case is the system palladium-gold,i the equilibrium diagram for which is repre- sented in Fig. 26. Here there is only one break in the cooling curve, and the temperature of the break gradually falls from B, the melting-point of the pure metal with the higher melting- point (in this case gold), to A, the melting-point of palladium. In this case, when the fused mass is allowed to cool, crystals containing both metals in varying proportions separate, and therefore the ordinary rule with regard to the lowering of melting-point of one substance by the addition of another does not apply, and there is no eutectic point (p. 187). Gold and palladium are miscible in all proportions in the solid state, but in many cases the miscibility is limited. As the composition of the crystals and the solution does not remain the same during solidification, there is in general an interval of tempera- ture, termed the crystallisation interval, between the beginning and end of crystallisation. ^ Ruer, Zeitsch. aiiorg. Chem., igo6, 51, 391. HETEROGENEOUS EQUILIBRIUM 193 XO°/oAu YlOCPSAu Compoaition Equilibrium Diagram for Palladium and Gold Fig. z6. 13 Composition Equilibrium Diagram for Mercury and Thallium Fig. 27. loo"^ Tl 194 OUTLINES OF PHYSICAL CHEMISTRY Case (c). One chemical compound. No miscibility in solia form. A typical freezing-point curve for a system of this type is given in Fig. 27, representing thallium-mercury amal- gams. It will be observed that there is a maximum on the curve, corresponding with the composition of a compound HgjTl, containing two equivalents of mercury to one of thallium. This compound melts at a definite temperature, and it is evident from the curve that the melting-point is lowered both by the addition of mercury (along CB) and of thallium (along CD). From this it is clear that the components of a chemical compound lower the freezing-point of the compound just as foreign substances do. The remainder of the curve will readily be understood from the previous paragraphs. A repre- sents the freezing-point of mercury, AB the lowering of the freezing-point of mercury by the progressive addition of the compound HgjTl, E the melting-point of thallium, and ED the effect on the melting-point of thallium produced by gradu- ally increasing amounts of the same compound. The points B and D are eutectic points, the eutectic mixtures containing mercury and HgjTl, and HgjTl and thallium, respectively. The occurrence of a maximum on the freezing-point curve is usually an indication of chemical combination, but, on the other hand, chemical compounds are sometimes present, although there are no maxima on the curve. This occurs more par- ticularly when the chemical compound decomposes before its melting-point is reached. The systematic investigation of the freezing-point curve of a binary mixture is one of the best methods for detecting chemical compounds and establishing theii formulae. This can be illus- trated by the equilibrium curve of ferric chloride and water, which is of great historical interest, inasmuch as, in the course of the investigation of this system by Roozeboom, many of the points we have been discussing were elucidated. The Hydrates of Ferric Chloride — The freezing-point curve of this system is represented in Fig. 28, and will be HETEROGENEOUS EQUILIBRIUM 195 readily understood by comparison with the previous diagrams, more particularly Fig. 27. For convenience, the concentrations in this case are expressed as the ratio of the number of mols of ferric chloride present to 100 mols of water. In interpreting the curve, we commence at the left-hand side of the diagram. A represents the freezing-point of water, and > <*^ 10 CO g- r' _« to (O f «i^ f* r- •* to ^- in l' m 6> CO in «™ 80° 70° I f of/ u. ^< 60° -> 1^ >/ 50° / 40° 0) 11 / 30° / ^^ f^ \ aaP / ' 10° A / 00 ( / 10° \ so" \ 300 40° V IB (-55") O 5 10 ' 15 20 S5 30 35 X Mo's.' Fe^Clg to 100 mols. HgO Fig. 28. AB the lowering of freezing-point produced by the progressive addition of ferric chloride. At the point B, - 55°, the solution is saturated with regard to ferric chloride, and B is therefore the eutectic point, at which ice, solution, a hydrate of ferric chloride (Fe^Clg, 12H2O) and vapour are in equilibrium. On adding more ferric chloride, the ice phase will disappear, and equilibrium will be attained at a point on the curve BC, at which the 196 OUTLINES OF PHYSICAL CHEMISTRY dodecahydrate, FcjClj, 12H2O, is in equilibrium with solution and vapour. The curve BC may therefore be regarded as the solubility curve of the dodecahydrate, and corresponds exactly with the curve OB (Fig. 24). On continued addition of ferric chloride, the equilibrium temperature continues to rise up to the point C at 37°, at which point the composition of the mixture corresponds with that of the dodecahydrate. Further addition of ferric chloride lowers the temperature along the line CD, so that C is a maximum on the curve. At this point, the solid dodeca- hydrate is in equilibrium with a liquid of the same composition ; in other words, C is the melting-point of the compound FcjClg, izHjO, just as the point C (Fig. 27) represents the melting-point of Hg^Tl. On addition of more ferric chloride, the melting-point is lowered, as represented by the section CD of the curve. At the point D, the curve reaches another minimum, or eutectic point, which corresponds with the point B, except that a new hydrate, Fe^Clg, 7H2O, takes the place of ice. On further addition of ferric chloride, another maximum is reached, which represents the melting-point of the hepta- hydrate. In an exactly similar way, the other two maxima at higher concentrations of ferric chloride indicate the existence of two other hydrates, Fe^Clg, sHjO and FcjClg, 4H2O, in the solid state. At the last eutectic point, K, the four phases in equilibrium are the tetrahydrate, anhydrous ferric chloride, solu- tion and vapour, and KL represents the effect of temperature on the solubility of the anhydrous chloride. The application of the phase rule to this system should be made by the student. As at the point D (and the other corre- sponding points) the solubility curves of the dodecahydrate and heptahydrate intersect, D may be termed the transition point for the two hydrates. Since at these points there are four phases in equilibrium, they are also termed quadruple points. In recent years, many other systems have been fully investi- gated on analogous lines to that indicated above. The chief experimental difficulty is to avoid supercooling, a source of HETEROGENEOUS EQUILIBRIUM 197 error which is much more troublesome in some systems than in others. Transition Points — In the preceding sections, mention has been made on several occasions of transition points. When a substance is polymorphic (/.«., exists in more than one form) it is often possible, as in the case of sulphur, to find a temperature — the so-called transition point — at which two forms are in equilibrium ; at higher temperatures one of the forms is stable, at lower temperatures the other. It has been shown that at the transition point the two modifications have the same vapour pressure, but at other temperatures the metastable form has the higher vapour pressure. By similar reasoning it can be shown that the metastable phase has the higher solubility and the lower melt- ing-point. It may happen, however, as in the case of benzophenone, that the modification stable at low temperatures melts before the transition point is reached. It is evident that in this case the transition can only take place in one direction, from the modification the existence of which is favoured by high tem- perature to that stable at low temperatures. Substances such as sulphur, for which there is a reversible transition, are termed enantiotropic, substances for which the transition is only in one direction are termed monotropic. It may be asked bow it is possible to obtain the metastable form of benzophenone, as it is necessarily unstable under all conditions. The explanation is that when a fused polymorphic substance is allowed to solidify, it is generally the most unstable form which separates first (e.g., sulphur). Similarly, the transition point of two hydrates is that tempera- ture at which they are in equilibrium, and at which they have the same solubility. Practical Illustrations. Distribution of a solute between two immisdble solvents — To a nearly saturated aqueous solu- tion of succinic acid (say 100 c.c.) in a stoppered bottle an 198 OUTLINES OF PHYSICAL CHEMISTRY approximately equal volume of ether is added, and the bottle kept at room temperature for half an hour, shaking it at intervals. When the separation into two layers is complete, part of the ethereal layer is pipetted off and titrated with barium hydroxide, and the same is done with the aqueous layer. Less concentrated solutions of succinic acid are then used, and the concentrations in the ethereal and aqueous layers determined as before. The value of the distribution constant Cj/Cj is then calculated from the results, and should be constant, as the molecular weight is the same in the two solvents (p. 178) In a similar way the distribution of benzoic acid between water and benzene may be investigated. In this case, as ben- zoic acid is unimolecular in water and bimolecular in benzene (p. 179), the ratio CJ VCj, where Cj represents the concentration in the aqueous layer, Cj the concentration in the benzene layer, should be approximately constant. Determination of transition points — Transition temperatures, such as that above which rhombic sulphur is unstable and monoclinic sulphur stable, can be determined in various ways, which depend in principle on the difference in properties of the two phases. The dilatometer method is largely used ; it depends on the fact that there is a more or less sudden change of volume when the transition takes place. Into a fairly wide glass tube, provided with a capillary tube and scale at the upper end and open at the lower end, is placed a mixture of the two modifications, e.g., monoclinic and rhombic sulphur, the lower end is then sealed up, and the vessel filled to the lower end of the scale with an indifferent liquid such as oil. The dilatometer is then placed in a bath the temperature of which is gradually raised, and readings made of the level of the liquid in the dilatometer. The rate of change of level will be more or less steady till the neighbourhood of the transition point is reached, when a relatively rapid change of level will be observed. The chief drawback to the method is that the change seldom takes place rapidly when the transition point is HETEROGENEOUS EQUILIBRIUM 199 reached. To facilitate the change as far as possible, some of the second phase should always be present, (p. 55). By solubility or vapour-pressure measurements — The fact that the two phases have the same solubility at the transition point may be employed to determine the latter. To determine the transition point in the system NajSO^jio HjO ^ NajSO^ + 10 HjO, it is only necessary to measure the solubility of the anhydrous salt and of the decahydrate in the neighbourhood of the transition point, and the point at which the solubility curves intersect will be the required point. Measurements of vapour pressure may be employed in a similar way. Thus Ramsay and Young determined the vapour pressures of solid and liquid bromine respectively and found that the curves intersected at - 7°, which is therefore the transition temperature for solid and liquid bromine ; in other words, the melting-point of bromine. CHAPTER IX VELOCITY OF REACTION. CATALYSIS General — In inorganic chemistry, the question as to the rate of a chemical change does not often arise, because in general the reactions are so rapid that it is impossible to measure the speed. The neutralization of an acid by a base, for instance, as shown by the change of colour of the indicator, is practically instantaneous. Howeverj some instances of slow inorganic re- actions in homogeneous systems are known. The rate of com- bination of sulphur dioxide and oxygen to form sulphur trioxide is very slow under ordinary conditions, and the mixture of gases has to be heated in contact with platinum as an accelerating agent in order to obtain a good yield of trioxide. In organic chemistry, on the other hand, slow chemical reactions are very frequently met with. Thus the combination of an organic acid and an alcohol to form an ester is very slow under ordinary conditions, and the mixture of acid and alcohol, saturated with hydrogen chloride, has to be boiled for a considerable time in order to obtain a good 5aeld of ester. In this chapter, as in the preceding one on chemical equili- brium, the law of mass-action is the guiding principle. It has already been pointed out (p. 158) that the rate of a chemical reaction at any instant may be regarded as the difference in the speeds of the direct and the reverse reaction at that instant. If we consider a simple reversible reaction, such as ester forma- tion, in which a, b, c and d are the initial equivalent concentra- tions of the reacting substances, and if x is the amount of 300 VELOCITY OF REACTION. CATALYSIS 201 ester formed in the time /, the equation for the reaction velo- city at that instant may be written ■j- = k(a - x){}> - X) - k-^{c + x){d + x) . (i) in which dx represents the small increase in the amount of x during the small interval of time, dt. This equation is a direct consequence of the application of the law of mass action to the reaction in question. It very often happens, however, that the equilibrium lies very near one side, which can only mean that the rate of the reverse reaction is small in comparison with that of the direct reaction. This is clear from the following considerations. The splitting up of hydrogen peroxide into water and oxygen is represented by the equation HgOg-^HjO + ^Oj, and the equilibrium be- tween this compound and its decomposition products by the equation HjOg^HjO + ^Oj. Applying the law of mass action, we have /^[HA]^^i[H20][0Ji and [H,OJ _ k^ = -^1 = K. [H,0] [OJ* k Now it is an experimental fact that the concentration of hydrogen peroxide in equilibrium with water and oxygen at atmospheric pressure is so small that it cannot be detected by analytical means. It follows, from the above equation, that ^j is small in comparison with k ; otherwise expressed, the rate of the con- verse reaction, represented by the lower arrow, is negligible in comparison with that of the direct reaction, represented by the upper arrow. The same considerations apply to the more general case re- presented by equation (i). If k^ is negligible in comparison with k, the expression k-^^c + x){d + x) in equation (i) is negligible in comparison with the remainder of the right-hand side of the equation, and the latter therefore simplifies to 202 OUTLINES OF PHYSICAL CHEMISTRY — = k{a - x){b - x). Reactions of this type, in which the rate of the inverse reaction is negligible, are by far the simplest from a kinetic standpoint, and will therefore be considered first. Unimolecular Reaction — The simplest type of chemical reaction is that in which only one substance is undergoing change, and there is practically no back reaction. Such a reaction, which can be readily followed, is the splitting up of hydrogen peroxide to water and oxygen in the presence of colloidal platinum or of certain enzymes. The reaction, which is usually carried out in dilute aqueous solution, may be repre- sented by the equation HjOj = HgO + O, and there is the advantage that the solvent does not appreciably alter during the reaction. As the colloidal platinum or the enzyme remains of constant activity during the reaction, the course of reaction is determined solely by the peroxide concentration (ef. p. 205). The reaction in the presence of haemase (blood-catalase) can conveniently be followed by removing a portion of the solution from time to time, adding to excess of sulphuric acid, which immediately stops the reaction, and titrating with permanganate solution. Some of the results obtained in this way are repre- sented in the accompanying table : — a-x X t (mins.). (C.C :. KMnOJ. (c.c. KMnO^). k 46-1 — s 37-1 9-0 0-0435 10 29-8 i6-3 0-0438 20 19*6 26-5 0-0429 30 12-3 33'8 0-0440 5° s-° 4I-I 0-0444 The numbers in the second column represent the number of c.c. of dilute permanganate solution equivalent to 25 c.c. of the reaction mixture when the times represented in the first VELOCITY OF REACTION. CATALYSIS 203 column have elapsed after mixing the peroxide and enzyme, and therefore represent the concentrations of peroxide in the mixture at the times in question. By subtracting these numbers from that representing the initial concentration of the peroxide, 46"i CO., the amounts of peroxide split up at the times t are obtained ; these numbers are given in the third column. The numbers illustrate very clearly the falling off in the rate of the reaction as the concentration of the peroxide diminishes. Thus in the first ten minutes an amount of peroxide equivalent to i6'3 CO. of permanganate is split up, whilst in the second interval of ten minutes only 26'S — i6"3 io"2 c.c. are de- composed. According to the law of mass action, the rate of the reaction at the time / should be proportional to the concentration of the peroxide, a — x, at that time, hence j-^= k[a-x) . . . (2) In this form, however, the equation cannot be applied directly to the experimental results, since dx, the amount of change of X in the time d^, would have to be taken fairly large in order to obtain accurate results, and during the interval a-x would naturally have diminished. Better results would be obtained if a — x were taken as the average concentration during the interval dt within which dx of peroxide is being decomposed, but even this method does not give accurate values for k. The diflSculty is got over by integrating the equation on principles described in books on higher mathematics. In this way, and bearing in mind that, when /= o, a; = o, we obtain from equation (2) above -;°g'^«; = ^ . ■ • (3) It is, however, much more convenient to work with ordinary logarithms (to the base 10) than with logarithms to the base e. Making the transformation in the usual way, we obtain 204 OUTLINES OF PHYSICAL CHEMISTRY l'°Si»J^ = 0-4343'* • • • (4) By substituting in the above equation corresponding values of a, a-x and t from the table (p. 202), we obtain the values of k given in the fourth column of the table, the average value being 0*0437. Since k is constant within the limits of experimental error, it follows that the assumption on which the equation is based, that the rate of the reaction is proportional to the concentration of the peroxide, is justified. It is instructive to compare the accurate value of k, obtained by means of the integrated equation (4), with that calculated from the differential equation (2), taking as the value oi a — x the average value during an interval. If we choose the interval between 5 and ro minutes, dx = 7-3 c.c, dt = t^ minutes, and the mean value of a - x'\& 33"4S c.c. Hence Y = -6 X 33-45. and k = o'o436, which is very close to the accurate average value 0-0437. A reaction of the above type, in which only one mol of a single substance is undergoing change, is termed a unimolecular reaction or a reaction of the first order, k is termed the velocity constant, and is, for unimolecular reactions, independent of the units in which the concentration is expressed, but increases con- siderably with rise of temperature. The meaning of k becomes clear when we consider the initial velocity of the reaction. Under these circumstances, the general equation dx\dt = k (a — X) becomes dxldt = ka =■ 0-043 7a for the example given above. Otherwise expressed, the initial velocity of the reaction = velo- city constant x initial concentration. If, by addition of fresh peroxide, the concentration is kept throughout at its initial value, then in unit time (i minute) 0-0437 of "■ o*" over 4 per cent, of a will be decomposed. VELOCITY OF REACTION. CATALYSIS 205 If the integrated equation (3) is written in the form log fl/(a ~ x) = kt, we see that the left-hand side of the equation only becomes in- finitely great (a = x) when t is infinitely great. Hence, for finite values of t, x is always less than a, in other words, a chemical reaction, even if irreversible, is never quite complete. Other Unimolecnlap Reactions — Many unimolecukr re- actions have been investigated, among the more interesting being the hydrolysis of cane sugar and of esters under the influence of acids. The hydrolysis of cane sugar to dextrose and laevulose is represented by the equation C12H22O11 -f- HjO = CgHijOg + CgHjgOg, and as the acid remains unaltered at the end of the reaction, it does not occur in the equation. The reaction can be con- veniently followed by measuring the change in rotation with a polarimeter (p. 66) ; as cane sugar is dextrorotatory and the mixture of dextrose and laevulose laevorotatory, the rotation diminishes steadily as the reaction progresses, and finally changes sign. As both sugar and water take part in the reaction, the velocity equation, according to the law of mass action, is ^^ - hr r J. — ^^sugar ^water* As, however, water is present in great excess, its concentra- tion, and therefore its active mass, remain practically constant throughout the reaction, and the equation therefore reduces to one of the first order, in satisfactory agreement with the ex- perimental results. Similar considerations enable us to understand why the acid does not appear in the velocity equation. It is true that he rate of the reaction depends upon the concentration of acid present, and this, if necessary, could be expressed by putting in a term Cadd on the right-hand side of the velocity equation. 2o6 OUTLINES OF PHYSICAL CHEMISTRY But as Cacid does not change in the course of the reaction, the only effect is to multiply the right-hand side of the equa- tion by a constant amount vphich, under ordinary circumstances, we may consider as included in the velocity constant k. In the same way, the enzyme concentration in the example quoted on the previous page is included in the velocity constant, and the course of the reaction is determined by the peroxide concentra- tion. The hydrolysis of an ester — for example, ethyl acetate — in the presence of excess of a strong acid, such as hydrochloric acid, is represented by the equation CH3COOC2H5 -1- HjO = CH3COOH -1- CjHgOH, and is also of the first order, as the active mass of the water is constant. The reaction may readily be followed by removing a portion of the reaction mixture from time to time and titrating with dilute alkali. The measurements may conveniently be made as follows : To 40 c.c. of 1/2 normal hydrochloric acid, previously kept in a 100 c.c. flask for some time at 25°, 2 c.c. of methyl acetate, warmed to the same temperature, is added, the mixture shaken, and the flask well corked and allowed to remain in the thermostat at constant temperature. At first every 20-30 minutes, and then at longer intervals, 2 c.c. of the mixture is removed with a pipette, diluted, and titrated rapidly with N/io barium hydroxide, using phenolphthalein as indicator. The results are calculated in the usual way by substitution in equa- tion (r). At 25° the value of k for this reaction is o'oo32. It should be mentioned that it is not necessary to take for the value of a the initial concentration of the reacting sub- stance ; the calculation of the velocity constant may be com- menced at any stage in the reaction. If, in the example quoted, 29'8 c.c. is taken as the starting-point, the first value of wUl be obtained from the equation i/io logi(,29'8/i9'6 = o"4343,4, the second from the equation 1/20 logio29'8/i2-3 = 0-4343^, and it will be found that the results thus obtained agree fairly VELOCITY OF REACTION. CATALYSIS 207 well with those already given, in which 46-1 c.c. was taken as the initial concentration. This method of calculation gives satisfactory results when, as is not infrequently the case, there are irregularities at the beginning of a reaction. Bimolecular Reactions — When two substances react and both alter in concentration, the reaction is said to be bimdle- cular, or of the second order. If the initial molar concentration of one substance is a, that of the other l>, and x the amount transformed in the time t, the velocity equation is ^^ = k{a - x)(6 - x) . . . (i) The simplest case is that in which the substances are present in equivalent quantities. The velocity equation then becomes g = /i(a - xY, which, on integration, gives the formula - -7 ;- = k . . , . (2) t a{a - x) ' As an illustration of a bimolecular reaction, the hydrolysis of an ester by alkali may be adduced, a reaction which has been thoroughly investigated by Warder, Ostwald, Arrhenius and others. For ethyl acetate and sodium hydroxide, the equation is as follows : — CH3COOC2H5 + NaOH = CHgCOONa + CjHgOH. In carrying out an experiment, 1/20 molar solutions of ethyl acetate and of sodium hydroxide are warmed separately in a thermostat at constant temperature (25°) for some time, equal volumes of the solutions are then mixed, and from time to time a portion of the reaction mixture is removed and titrated rapidly with dilute hydrochloric acid. In the following table are given some results obtained by Arrhenius : — 2o8 OUTLINES OF PHYSICAL CHEMISTRY 1/50 molar solution at 247''- 1/170 molar solution at 247°. t (min.) a-x k t (min.) a — x k 8-04 — 2-31 4 5-3° o-oi6o 6 1-87 00170 6 4-58 0-0156 12 1-57 0-0170 8 3'9i o'oi64 18 I-3S O-OI71 10 3-51 o"oi6o 24 I'20 0-0167 12 3-12 0"0l62 30 I'lO 0-0163 The numbers for a - a; in the second and fifth columns re- present the concentrations of sodium hydroxide (and of ethyl acetate) expressed as the number of c.c. of hydrochloric acid required to neutralize 10 c.c. of the reaction mixture. The reaction is very rapid, and therefore the experimental error is somewhat large but the values obtained for k in the third and sixth columns show that the assumptions on which formula (2) is based are justified. Another bimolecular reaction, which differs from the former inasmuch as two molecules of the same substance react, is the transformation of benzaldehyde to benzoin under the influence of potassium cyanide. The reaction is represented by the equation 2C6H5CHO = CgHgCHOHCOCeHg, the potassium cyanide remaining unaltered at the end of the reaction. When the reacting substances are not present in equivalent proportions, the calculation is somewhat more complicated. On integrating the equation dxfdt = k{a - x){6 - x), we obtain for this case , 1 , b{a - x) °-«43^ = ^(^3^1ogio^-J^ . . (3) In order to illustrate the application of this equation, some results obtained by Reicher for the saponification of ethyl acetate by excess of alkali may be adduced. The reaction was followed by titrating portions of the reaction-mixture from time to time with standard acid, as already described, and the excess VELOCITY OF REACTION. CATALYSIS 209 of alkali was determined by titration of a portion of the solution after the ethyl acetate was completely saponified (at the end of twenty-four hours). t (min.). a - X b -X k (alkali concentration). (ester concentration) 61-95 47-03 — 4-89 50-59 35-67 0-00093 11-36 42-40 27-48 0-00094 29-18 29-35 14-43 0-00092 00 14-92 — It is important to note that the value of k for a bimolecular reaction is not, as the case of a unimolecular reaction, indepen- dent of the units in which the concentration is expressed. If, for example, a unit i/«th of the first is chosen, the value of k = IX, 1 nx 1*1 _ becomes — ■ = . i a{a - x) t na. n(a - «) t a{a — x) n so that the value of k diminishes proportionally to the increase of the numbers expressing the concentrations. The truth of this statement can be tested by means of the data for ester saponification due to Arrhenius. If the titrations are made with acid of half the strength actually used, (« = 2), the numbers expressing the concentrations will be doubled, and it will be found by trial that the value of k becomes half that given in the table. Trimolecular Reactions — ^When three equivalents take part in a chemical change, the reaction is termed trimolecular, and several such reactions have been carefully investigated. If, as before, we represent the initial molar concentrations of the reacting substances by a, b and c respectively, and if a; is the proportion of each transformed in the time t, the rate of reaction at that time will, according to the law of mass action, be represented by the differential equation 14 2IO OUTLINES OF PHYSICAL CHEMISTRY — = k{a - x){6 - x){c — x). Such an equation is somewhat difficult to integrate, and we will therefore confine ourselves to the simple case in which the initial concentrations are the same. The equation then becomes dxfdt = k {a - x)^, which on integration gives for k — , _ I x(2a - X) ~ 1 2a.\a - xf Different cases arise according as the reactbg molecules are the same or different. The simplest case, in which the three re- acting molecules are the same, is illustrated by the condensation of cyanic acid to cyamelide, represented by the equation 3HCNO = HgCgNjOs. A case where two only of the reacting molecules are the same is the reaction between ferric and stannous chlorides, represented by the equation zFeClg + SnClj = SnCl^ + zFeClj: Finally, the reaction between ferrous chloride, potassium chlorate and hydrochloric acid, represented by the equation eFeClj + KCIO3 + 6HC1 = eFeCls + KCl + sH^O, has been shown by Noyes and Wason to be proportional to the respective concentrations of the three reacting substances, and is therefore of the third order. As an illustration of a trimolecular change, some of Noyes' results for the reaction between ferric and stannous chlorides are given in the table. The reacting substances were mixed together at constant temperature, and from time to time a measured quantity of the solution was removed with a pipette, the stannous chloride decomposed with mercuric chloride and the ferrous salt still remaining titrated with potassium per- manganate in the usual way. VELOCITY OF REACTION. CATALYSIS 211 SnCla = FeClg = 0-0625 normal = a. t (min.) u, - X X k o'o625 — I 0-04816 0-01434 88 3 0*03664 0-02586 81 7 o"o2638 0-03612 84 17 o'oi784 0-04502 89 25 0-01458 0-04792 89 Reactions of Higher Order. Molecular Kinetic Con- siderations — Whilst reactions of the first and second order are very numerous, reactions of the third order are compara- tively seldom met with, and reactions of a still higher order are practically unknown. This is at first sight surprising, as the equations representing many chemical reactions indicate that a considerable number of molecules take part in the change, and a correspondingly high order of reaction is to be expected. The oxidation of ferrous chloride by potassium chlorate in acid solu- tion, for example, is usually represented by the equation eFeClg -I- KCIO3 4- 6HC1 = 6FeCl3 + KCl -1- 3H2O. Applying the law of mass action (p. 143), we have therefore g = .S[FeClJ«[Ka03][HCl]», that is, the reaction should be of the thirteenth order, whilst it is actually of the third order (p. 210). To account for this result, it has been suggested by van't Hoff that complicated chemical reactions take place in stages, and that the reaction whose speed is actually measured is one in which only two or three molecules take part, the velocity of the other reactions being very great in comparison. This view is further considered in the next section. The molecular theory throws a good deal of light on this question. On the assumption that the rate of chemical reaction is proportional to the number of collisions between the reacting molecules (p. 160), it follows that in a trimolecular reaction the 212 OUTLINES OF PHYSICAL CHEMISTRY three reacting molecules must collide simultaneously to produce a chemical change. The probability of such a collision is ex- tremely small compared with that between two molecules ; there- fore, if at all possible, the reaction will take place between two molecules or by the change of a single molecule. The proba- bility of the simultaneous collision of four molecules is so small as to be almost negligible. Reactions in Stages — It has just been pointed out that many reactions which are represented by rather complicated equations prove on investigation to be of the second or third order, which seems to show that the reaction, the speed of which is being measured, is in reaUty a comparatively simple one. When a chemical change takes place in stages, a little consideration shows that it is the slowest of a series of reactions which is the determining factor for the observed velocity. This process has been fittingly compared by Walker to the sending of a telegram ; the time which elapses between dispatch and receipt is con- ditioned almost entirely by the time taken by the messenger between receiving-ofKce and destination, as that is by far the slowest in the successive stages of transmission. An instructive example of a reaction which takes place in stages is the burning of phosphorus hydride in oxygen, investi- gated in van't HofTs laboratory by van der Stadt. The change is usually represented by the equation 2PH3 -H 4O2 = PjOg + 3H2O, according to which it would be a reaction of the sixth order whilst the rate was actually found to be proportional to the respective concentrations of the two gases, the reaction being therefore of the second order. On allowing the gases to mix gradually by diffusion, it was then found that the first stage of the reaction is represented by the equation PH3 -H O2 = HPO2 + H2 — that of a bimolecular reaction — the subsequent changes by VELOCITY OF REACTION. CATALYSIS 213 which water and phosphorus pentoxide are produced being very rapid in comparison. Many other reactions proceed in stages, and in some cases evidence as to the nature of the intermediate compounds has been obtained* Thus the reaction between hydrobromic and bromic acid, usually represented by the equation HBrOj + sHBr = sH^O + sBr^, is bimolecular in the presence of excess of acid, and it is probable that the first stage (the slow reaction) is as follows : — HBrOg + HBr = HBrO + HBrO^, the subsequent changes, by which bromine and water are finally produced, being comparatively rapid. It is very probable that the equations which we ordinarily use represent only the initial and final stages in a series of changes, and the determination of the " order " of the reaction is one of the most important methods for elucidating the nature of the relatively unstable intermediate compounds. Determination of the Order of a Reaction — Three im- portant methods which are largely used in determining the order of reactions may be mentioned here. (a) The Method of Integration — According to this method, the values of k given by the integrated equations for reactions of the first, second and third order are calculated from the ex- perimental results, and the order of the reaction is that in which constant values are obtained for k. The method can be applied to the numbers obtained for the reaction between equivalent amounts of ethyl acetate and sodium hydroxide, when it will be found that the values for k, calculated from the equation k = i/^loga/(a — «), continually decrease throughout the reaction; the values obtained with an equation of the third order continu- ally increase, and only for the equation k = \lt.xja{a — oi)\s k actually constant. The disadvantage of this method is that disturbing causes, such as secondary reactions or the influence of the reaction products on the velocity, may so complicate the 214 OUTLINES OF PHYSICAL CHEMISTRY results that a decision as to the order of the reaction is impossible or an erroneous conclusion may be drawn. {6) Osiwald's " Isolation " Method — It has already been pointed out that if one or more of the reacting substances is taken in great excess, so that their concentration does not alter appreciably during the reaction, the velocity, as far as these substances is concerned, may be regarded as constant. It is on this principle that the " isolation " method is based. Each of the reacting substances in turn is taken in small concentra- tion and all the others in excess, and the relation between the reaction velocity and the concentration of the substance present in small amount determined experimentally. As an example, we will consider the reaction between potassium iodide and iodate in acid solution, investigated by Dushman.^ Regarding the action of the acid as due to H- ions (p. 125), the reaction velocity, according to the law of mass action, must be repre- sented by the equation g = /&[I03']»>[IT^[H-]'^. When iodide and acid are used in large excess, the velocity is proportional to the iodate concentration («j = i) ; with a large excess of iodate and acid it is proportional to the square of the iodide concentration («j = 2) ; and finally, when iodide and iodate are in large excess, it is proportional to the square of the acid concentration {n^ — 2). Hence the velocity equation becomes g = *[I03'][IT[Hf , and when neither of the reagents is present in great excess, is of the fifth order. {c) Time taken to Complete the same Fraction of the Reaction — Measurements are made with definite concentrations of the reacting substances, and with double and treble those con- jy. Physical Chem., 1904, 8, 453. As the rate of reaction does not depend upon the particular iodate or iodide used, we employ the formulae for the iodate ion IO3' and the iodide ion I'. VELOCITY OF REACTION. CATALYSIS 215 centrations, and the times taken to complete a certain stage (say one-third) of the reaction noted. The order of the reaction can then be determined from the following considerations (Ostwald) :— (i) For a reaction of the first order the time taken to com- plete a certain fraction of the reaction is independent of the initial concentration. (2) For a reaction of the second order, the time taken to complete a certain fraction of the reaction is inversely propor- tional to the initial concentration, e.g., if the concentration is doubled, the time taken to complete a certain fraction of the reaction is halved. (3) In general, for a reaction of the «th order, the times taken to complete a certain fraction of the reaction are inversely proportional to the {n - 1) power of the initial concentra- tion. In the experiments by Arrhenius, quoted on page 208, it will be noticed that in the second experiment, in which the con- centrations are less than J of those in the first experiment, the time taken to complete half the reaction is about three times as long in the former case as in the latter. Complicated Reaction Velocities — In the present chapter, it has so far been assumed that chemical reactions proceed only in one direction, and are ultimately complete, or practically . so, but in many cases these conditions are not fulfilled and the course of the reaction is complicated. The more im- portant disturbing causes are (a) side reactions; {p) counter reactions ; {c) consecutive reactions. Each of these will be briefly considered. (a) Side Reactions — In this case the same substances react in two (or more) ways with formation of different products ; in general the reactions proceed side by side without influencing each other. An example is the action of chlorine on benzene,^ which may substitute or form an additive product according to the equations ' Slator, Trans. Chem. Soc, 1903, 83, 729. 2i6 OUTLINES OF PHYSICAL CHEMISTRY (i) CeHg + CI2 = CgHjCl + HCl, (2) CeHg + 3CI2 = CgHgCle. The relative amounts of the products formed in side reactions depend on the conditions of the experiment, and it is usually possible so to choose the conditions that one of the reactions greatly predominates and can be investigated independently. (S) Counter Reactions — This term is applied when the pro- ducts of a reaction interact to reproduce the original substances, so that a state of equilibrium is finally reached, all the re- acting substances being present (p. 201). Using the same terminology as before, the rate of formation of an ester, for example, will be represented by the differential equation — = k{a - x)[b - x) - k-jj^c + x){d + x). The conditions can, however, usually be chosen in such a way that either the direct or the reverse reaction predominates, and the values of k and k-^ can thus be determined separately. In this way it has been shown experimentally by Knoblauch^ that the ratio kjk = K, the equilibrium constant, as the theory requires (p. 158). (tt = 0-5555 and (ft/ + io)/A« = 3-60 approximately. VELOCITY OF REACTION. CATALYSIS 227 Reaction. Velocity Constants. Quotient for loo. AsH3 = As + 3H . '^266 = °'°o°3S ,^367 = 0-0034 1-23 2NO = N2 + 02 . -^ess = 39-63 ^1347= 191800 1-17 CHjCOOCaHg + NaOH '^9-4= 2 '307 ^44-90 = 2 I '648 1-89 CH^ClCOONa + NaOH ^7Q=o"ooo89 ^102=0-015 z-S CHjClCOONa+HaO . '^70=O'OOOO42 kifj =0-00170 3-2 CjHgONa + CHgl /4o = 0-00336 '^30= 2-125 3-34 Inversion of cane sugar . '*26 = °'76S '^65=35-5 3-6 H202 = H20 + . /4(, = 0-OI20 ,4jg = 0-0180 I'S Fermentation by yeast . 10-20° — 3-8 »> ») 30-40° — 1-6 The quotient for 10° for reactions in solvents other than water is also between 2 and 3 in the majority of cases. According to the molecular theory, rise of temperature ought to increase the rate of chemical change, owing to the accelerating effect on molecular movements. This effect, however, would only increase proportionally to the square root of the absolute tempera- ture (p. 32), and it can easily be calculated on this basis that the quotient for 10° for a bimolecular reaction at the ordinary temperature would be about i -04, much too small to account for the large temperature coefficient actually observed. Up to the present, no plausible explanation of the great magnitude of the temperature coefficient of chemical reactions has been given. The only other property which appears to increase as rapidly with temperature is the vapour pressure, and it is not improbable that there is a close connection between vapour pressure and chemical reactivity. At moderate temperatures the temperature coefficients of enzyme reactions are approximately the same as those of chemical reactions in general, but at temperatures in the neigh- bourhood of 0°, the rate of change of k with the temperature is often abnormally high, as the table shows. It is interesting to note that the rate of development of organisms, for example, the rate of growth of yeast cells, the rate of germination of certain seeds, and the rate of develop- 2 28 OUTLINES OF PHYSICAL CHEMISTRY ment of the eggs of fish, is also doubled or trebled for a rise of temperature of io°, and it has therefore been suggested that these processes are mainly chemical. Formnlse connecting Reaction Velocity and Tempera- ture — As has already been pointed out (p. 167), the law con- necting the displacement of equilibrium with temperature is known. So far, however, no thoroughly satisfactory formula showing the relationship of rate of reaction and temperature has been established, although many more or less satisfactory empirical formulae have been suggested. If the relationship which has been shown to hold approximately for the rate of de- composition of dibromosuccinic acid — that the quotient for 10° is the same at high as at low temperatures — holds in general, the equation connecting k and T must be of the form 41og,>4)/^T A where A is constant. On integration, this becomes \ogk = AT -f- B, B being a second constant. This formula holds for the decom- position of nitric oxide and for certain other reactions, but is not generally valid. As a matter of fact, the quotient ^t+ij^t generally diminishes with rise of temperature. An equation which takes account of this has been proposed by Arrhenius ; in its integrated form the equation is as follows : — logyJ = - A/T -1- B. For two temperatures, Tj and Tg, for which the values of the velocity constant are ^j and i^ respectively, the above equation becomes loge/ij - loge/^i = A.(^Y - y)' and when A is known (from two observations) the velocity constant for any other temperature can be calculated. Arrhenius showed that the above empirical equation repre- sents satisfactorily the influence of temperature on the rate of hydrolysis of cane sugar and on certain other reactions, and it VELOCITY OF REACTION. CATALYSIS 229 has since been employed by many other observers with fairly satisfactory results. A is a constant for any one reaction, but differs for different reactions. Practical Illustrations — As the rate of chemical reactions alters so greatly with change of temperature, it is necessary in accurate experiments to work in a thermostat provided with a regulator to keep the temperature constant. For purposes of illustration, however, sufficiently accurate results can be obtained by using so large a volume of solution that the temperature does not alter appreciably during the reaction. Unimolecular Reaction. (a) Decomposition of Hydrogen Peroxide ^ — To 200 c.c. of a mixture of one part of defibrinated ox-blood and 10,000 parts of water, an equal volume of about i/ioo molar hydrogen peroxide (o"34 grams per litre) is added, and the mixture shaken. At first every ten minutes, and then at longer intervals, 25 c.c. of the reaction mixture is removed with a pipette, added to a little sulphuric acid, which at once stops the action, and titrated with i/ioo normal potassium permanganate. If pure hydrogen peroxide is not available, the commercial product should be neutralized with sodium hydroxide before use. Another portion of the original hydrogen peroxide solution should be titrated with permanganate, and if the reacting solutions have been measured carefully, the initial concentration in the reaction mixture may be taken as half that in the original solution. The observations should be calculated by substitution in the formula i// log aja — x = o'4343 k, valid for a unimolecular reaction. A corresponding experiment may be made with double the peroxide concentration, in order to illustrate the fact that the time taken to complete a certain fraction of the reaction is independent of the initial concentration. {b) Hydrolytic Decomposition of Cane Sugar in the Presence of Acids — Equal volumes of a 20 per cent, solution of cane ' Senter, Zeitsch. physikal. Chem., 1903, 44, 257. The amount of or- ganic matter is so small that the error in titration due to its reducing action on permanganate is negligible. 230 OUTLINES OF PHYSICAL CHEMISTRY sugar and of normal hydrochloric acid, previously warmed to 25°, are mixed, the observation tube of a polarimeter is filled with the mixture, and an observation of the rotation taken as quickly as possible. The polarimeter tube is then immersed in a thermostat at 25°, and kept in the latter except when readings of the rotation are being made. In order that it may be conveniently immersed in a thermostat, the polarimeter tube is provided with a side tube, through which it is filled, and the end of which is not immersed. To prevent alterations while readings are being made, the tube is provided with a jacket filled with water at the temperature of the thermostat. Several chemists have described arrangements according to which the tube remains in the polarimeter throughout an ex- periment, the temperature being kept constant by passing a stream of water at constant temperature through the jacket of the polarimeter tube.^ With rapid working, however, the simpler method described above gives excellent results. If it is convenient to make an observation after the reaction is complete (say 24 hours), the total change of reading is taken as a in the formula for a unimolecular reaction, and the differ- ence of the initial reading and that at the time t is proportional to X, the amount of sugar split up. If the reaction is not complete in a reasonable time, the final reading can be calculated from the fact that for every degree of rotation to the right in the original mixture, the wholly inverted mixture will rotate o"3is° to the left at 25°. {c) Hydrolysis of Ethyl Acetate in the Presence of Hydro- chloric Acid — The method of experiment in this case has already been described (p. 206). Bimolecular Reaction, (a) The rate of reaction is proportional to the concentration of each of the reacting substances — This state- ment can be illustrated very satisfactorily by a method described by Noyes and Blanchard, and depending upon the fact that the time taken to reach a certain stage of a reaction is inversely proportional to its rate. ' Cf. Lowry, Trans. Faraday Society, 1907, 3, 119. VELOCITY OF REACTION. CATALYSIS 231 In a two-litre flask a mixture of 1600 c.c. of water, 50 c.c. half-normal hydrochloric acid and 20-30 c.c. of dilute mucilage of starch is prepared, and 400 c.c. of this mixture is placed in each of 4 half-litre flasks of clear glass, standing on white paper. For comparison, a fifth half-litre flask contains 400 c.c. of water, 10 c.c. of starch solution, and sufficient of a «/ioo solution of iodine to give a blue colour of moderate depth. Half-normal solutions of potassium bromate (7 grams per half-litre) and of potassium iodide are also prepared. To the flasks I. and II. 5 c.c. of the bromate solution is added, and to III. and IV. 10 c.c. of the same solution. Then at a definite time, 5 c.c. of the iodide solution is added to flask I., the mixture rapidly shaken, and the time which elapses until the solution has the same depth as the test solution carefully noted. Then to flasks II., III. and IV. are added successively 10 c.c, 5 c.c. and 10 c.c. of the iodide solution, and the times required to attain the same depth of colour as the test solution carefully noted in each case. If x is the time required when 10 c.c. of each reagent is used, 2x will be the time required when 10 c.c. of one solution and 5 c.c. of the other is used, and 4a; when S c.c. of each solution is used. If for some reason the reactions are too rapid, the strengths of the bromate and iodide solutions should be altered till intervals convenient for measurement are observed. (i) Quantitative measurement of a bimolecular reaction — The rate of reaction between ethyl acetate and sodium hydroxide may be measured as described on a previous page. From a practical point of view, however, the measurement presents certain draw- backs because it is difficult to prepare a solution of sodium hy- droxide free from carbonate and also to prevent absorption of that gas from the air during the experiment. A reaction ^ free from these disadvantages, which is very rapid in dilute solution, is that between ethyl bromoacetate and sodium thiosulphate, represented by the equation CHgBrCOOCaH^ -1- Na^S^g = CH2(NaS203)COOC2H5 -h NaBr. 1 Slator, Trans. Cheni. Society, 1905, 87, 484. 232 OUTLINES OP' PHYSICAL CHEMISTRY The rate of the reaction can readily be followed by removing a portion of the reaction mixture from time to time and titrating with nj loo iodine, which reacts only with the unaltered thio- sulphate. 300 c.c. of an approximately 1/60 normal solution of sodium thiosulphate is added to an equal volume of a dilute aqueous solution of ethyl bromoacetate (2-2*i grams per litre) in a litre flask, the mixture shaken and the flask closed by a cork. At first every 5 minutes, and then every 10 or 15 minutes, 50 c.c. of the reaction mixture is removed with a pipette and titrated rapidly with «/ioo iodine, using starch as indicator. Seven or eight such titrations are made, and then, after an interval of 5-6 hours, when the reaction is presumably complete, a final titration is made in order to determine the excess of thiosulphate remaining. The initial concentration of thiosulphate, expressed in c.c. of the iodine used in titrating the mixture, can be obtained by titrating part of the original thiosulphate solution, and the initial concentration of bromo- acetate in the reaction-mixture is clearly equivalent to the amount of thiosulphate used up. The case is exactly analogous to that quoted on page 209, in which the sodium hydroxide is in excess, and the value of k may be obtained by substitution in equation (3), p. 208. Catalytic Actions — The decomposition of hydrogen per- oxide by blood and of cane sugar in the presence of acids are examples of catalytic actions. Hydrogen peroxide can also be decomposed by a colloidal solution of platinum, which may be prepared as follows (Bredig): Two thick platinum wires dip into ice-cold water, and a current of about 10 amperes and 4.0 volts is employed. When the ends of the wires are kept 1-2 mm. apart, an electric arc passes between them, particles of platinum are torn off and remain suspended in the water. The solution is allowed to stand for some time, and filtered through a close filter. It represents a dark-coloured solution in which the particles cannot be detected with the ordinary VELOCITY OF REACTION. CATALYSIS 233 microscope. A very dilute solution may be used to decompose hydrogen peroxide, and the reaction may be measured as* described above when blood is employed. Catalytic Action of Water — This may be illustrated by its effect on the combustion of carbon monoxide in air, which does not take place in the entire absence of water vapour. Carbon monoxide is prepared by the action of strong sulphuric acid on sodium formate and is carefully dried by passing through two wash-bottles containing strong sulphuric acid, and finally through a U tube containing phosphorus pentoxide. Some time before the experiment is to be tried, a little strong sulphuric acid is put in the bottom of a wide-mouthed bottle with a close-fitting glass stopper, and the bottle allowed to stand, tightly stoppered, for some time. The carbon monoxide issuing from the apparatus burns readily in air, but is immediately extinguished if the wide- mouthed bottle is placed over it. If, however, a small drop of water is placed in the tube whence the gas is issuing, the gas will continue to burn when the bottle is placed over it. CHAPTER X ELECTRICAL CONDUCTIVITY Electrical Conductivity. General — From very early times it was noticed that electricity can be conveyed in two ways : (i) In conductors of the first class, more particularly metals, without transfer of matter ; (2) in conductors of the second class — salt solutions or fused salts — with simultaneous decom- position of the conductor. We are here concerned only with conductors of the second class, but the use of the terms em- ployed in electrochemistry may be illustrated by reference to conduction in metals. For conductivity in general. Ohm's law holds, which may be enunciated as follows : The strength of the electric current passing through a conductor is proportional to the difference of potential between the two ends of the conductor, and in- versely proportional to the resistance of the latter. Strength of current is usually represented by C, difference of potential or electromotive force by E, and resistance by R ; Ohm's law may therefore be written symbolically as follows : — C = ^ ^ R- The practical unit of electrical resistance is the ohm, that of electromotive force the volt, and that of current the ampere. The strength of an electric current can be measured in various ways, perhaps most conveniently by finding the weight of silver liberated from a solution of silver nitrate in a de finite interval of time. An ampere is that strength of current which in one 234 ELECTRICAL CONDUCTIVITY 235 second will deposit o'ooiiiS grams of silver from a solution of silver nitrate under certain definite conditions. Quantity of elec- tricity is current strength x time; the amount of electricity which passes in one second with a current strength of i ampere is a coulomb. When there is a difference of potential of one volt between two ends of a conductor, and a current of i ampere is passing through it, the resistance of the conductor is I ohm. The resistance of a metallic conductor is proportional to its length and inversely proportional to its cross-section. Hence if / is the length and j' the cross section, the resistance R is given by R = /) -, where p is a constant depending only on the material of the conductor, the temperature, etc., and is termed the specific resistance. If both / and j are equal to unity (i cm.) the resistance is equal to p. The specific resistance, p, of a conductor is therefore the resistance in ohms which a cm. cube of it offers to the passage of electricity. If there is a difference of potential of i volt between two sides of the cube, and the current which passes is i ampere, the specific resistance of the cube is, by Ohm's law, = 1. A conductor of low resist- ance is said to have a high electrical conductivity, that is, it readily allows electricity to pass. Conductivity is therefore the converse of resistance, and specific conductivity, k = i/p, where p is specific resistance. Specific conductivity is measured in reciprocal ohms, sometimes termed mhos. In order to illustrate the magnitude of these factors, the specific resistance and the specific conductivity of a few typical substances at 1 8° are given in the table : — 30 per cent. Substance. Silver. Copper. Mercury. Gas carbon, sulphuric acid. Sp. resistance, p O'oooooi6 o'oooooi7 o'oooog 00050 0^74 Sp. conductivity, k 624,000 587,000 10,240 200 1-35 Silver has the highest conductivity of all known substances , 236 OUTLINES OF PHYSICAL CHEMISTRY gas carbon is a comparatively poor conductor; and 30 per cent, sulphuric acid, one of the best conducting solutions, is enormously inferior to the metals in this respect; Electrolysis of Solutions. Faraday's Lavs — ^We now consider the phenomena accompanying the conduction of electricity in aqueous solutions of salts. If, for example, two platinum plates, one connected to the positive, the other to the negative pole of a battery, are dipped into a solution of sodium sulphate, it will be observed that hydrogen is immediately given oiif at the plate connected to the negative pole of the battery, and oxygen at the plate connected to the positive pole. Further, if a few drops of litmus have previously been added to the solution, it will be noticed that the solution round the positive plate or pole becomes red, indicating the production of acid, and that round the negative pole becomes blue, showing the formation of alkali. An ammeter placed in the circuit will show that a current is passing through the solution, so that the chemical changes in question accompany the passage of the current. Even if the poles are far apart, the gases are liberated, and the acid and alkali appear immediately connection is made through the solution, and if the current is continued, the acid and alkali accumulate round the respective poles without any apparent change in the main bulk of liquid between the poles. These phenomena can scarcely be accounted for otherwise than by supposing that matter travels with the current, and that part travels towards the positive pole and part towards the negative pole. To these travelling parts of the solution Faraday gave the name of ions. It will be well to mention here the nomenclature used in this part of the subject. A solution or fused salt which con- ducts the electric current is termed an electrolyte. The plate in the solution connected to the positive pole of the battery is termed the positive pole, positive electrode or anode, that connected to the negative pole of the battery the negative pole, negative electrode or cathode. The ions which move ELECTRICAL CONDUCTIVITY 237 towards the anode are often termed anions, those travelling towards the cathode cations. We will now consider the relationship between the amount of chemical action and the quantity of electricity passed through a solution. The amount of chemical action might be estimated by measuring the volume of gas liberated at one of the poles, or by the amount of metal deposited on an electrode. This question was investigated by Faraday, and as a result he established a law which bears his name, and which may be enunciated as follows : For the same electrolyte, the amount 0/ chemical action is proportional to the quantity of electricity which passes.^ Further, Faraday measured the relative quantities of substances liberated from different solutions by the same quantity of electricity, and was thus led to the discovery of his so-called second law : The quantities of substances liberated at the elec- trodes when the same quantity of electricity is passed through different solutions are proportional to their chemical equivalents. The chemical equivalent of any element (or group of elements) is equal to the atomic weight (or sum of the atomic weights) divided by the valency. The second law, therefore, states that if the same quantity of electricity is passed through solutions of sodium sulphate, cuprous chloride, cupric sulphate, silver nitrate and auric chloride, the relative amounts of hydrogen and the metals liberated are as follows: — Electrolyte NaaSO^ CuCl CuSOj AgNO, AuClj Electrochem. ^g 63-4 ^ 63-4 . 108 197 equivalent H = I ; 0= ^ ! Cu = ^; Cu = ^; Ag = — ; Au=-^ The above result may also be expressed rather differently as follows : The electrochemical equivalents (the proportions of different elements set free by the same current) are proportional to the chemical equivalents. That quantity of electricity which passes through an electro- lyte when the chemical equivalent of an element (or group of 1 Faraday measured the amount of electricity by its action on a mag- netic needle. 238 OUTLINES OF PHYSICAL CHEMISTRY elements) in grams is being liberated will obviously be a quantity of very considerable importance in electrochemistry. Since i ampere in i second (a coulomb) liberates o'ooooio36 grams of hydrogen, it follows that when the chemical equivalent of hydrogen or any other element is liberated, i/o'ooooio36 = 96540 coulombs must pass through the electrolyte. The same quantity of electricity will liberate 35'4S x o'ooooio36 = o"ooo368 grams of chlorine, 127 x o'ooooio36 = o'ooi3i6 grams of iodine, and 108 x o"ooooio36 = o'ooiii8 grams of silver. It is often designated by the symbol F. Mechanism of Electrical Conductivity — It has already been pointed out (p. 236) that during the electrolysis of sodium sulphate the products of electrolysis appear only at the poles, the main bulk of solution between the poles being apparently unaffected. This is most readily accounted for on the view that part of the solute is moving towards the positive and part towards the negative pole, these moving parts being termed anions and cations respectively. We now assume further that the cations are charged with positive electricity, and move towards the negatively charged cathode owing to electrical attraction ; similarly, the negatively charged anions are attracted to the cathode. When the ions reach the poles, they give up their charges, which neutralize a corresponding amount of the opposite kinds of electricity on the anode and cathode respec- tively, and then appear as the elements or compounds we are familiar with. The process of electrolysis is illustrated in Fig. 29. Into the vessel containing sodium sulphate solution dip two electrodes (on opposite sides of the vessel) connected with the positive and negative poles of the battery respectively. The direction of motion of the ions to the oppositely-charged poles is illustrated by the arrows. It is not always an easy matter to say what the moving ions are. It is only rarely that they are set free as such, since secondary reactions often take place at the electrodes. When a strong solution of cupric chloride is electrolysed, copper ELECTRICAL CONDUCTIVITY 239 and chlorine are liberated at the cathode and anode respectively, and it is probable that these substances are the ions. In the case of sodium sulphate, however, for which hydrogen and oxygen are the products of electrolysis, secondary reactions must take place. The current is in all probability conveyed through the solution by Na and SO4 ions. When the former reach the cathode, they give up their charges and form metallic sodium, which immediately reacts with the water, forming sodium hydroxide and hydrogen. In the same way the SO4 ions, on reaching the anode, give up their charges, and the free SO4 group then reacts with the water according to the equation SO4 + HjO = HjSO^ + O, oxygen being liberated and sul- phuric acid regener- ated. In this way the phenomena al- ready described are readily accounted for. So far, we have assumed that the material of the elec- trodes is not acted on by the products of electrolysis. This is generally true when the electrodes are made of platinum or other resistant Fig. 29. metal, but in other cases secondary reactions take place between the discharged ions and the poles. Thus when a solution of copper sulphate is electrolysed between copper poles, the SO4 ions, after losing their charges, react with the anode according to the equation Cu -f- SO4 = CUSO4, so that the net result of the electrolysis of copper sulphate between copper poles is the trarisfgr of copper from the anode to the cathode, + —0 6k (^ ^^H 240 OUTLINES OF PHYSICAL CHEMISTRY We have assumed that in a solution of sodium sulphate the moving ions are Na and SO^. As the Na ion moves towards the negative electrode, it must already be positively charged ; + this may be indicated thus : Na (Fig. 29), or, more concisely, by a dot, thus : Na\ As neither positive nor negative elec- tricity accumulates in the solution during electrolysis, the amount of positive electricity neutralized on the anode must be equivalent to that neutralized on the cathode. Hence, since two sodium ions are discharged for every SO^ ion, the latter must carry double the amount of electricity that a sodium ion carries, and this is indicated by the symbols SO4 or SO4" (Fig. 29). According to our present views, the metallic components of salts in solution are positively charged, the number of charges corresponding with the ordinary valencies of the metals. Some important cations are K', Na", Ag', NH^-, Ca", Hgj", Hg", Fe", Fe-", etc. The remainder of the salt molecule constitutes the negative ion, which, like the positive ion, may have one, two or more (negative) electric charges. Among the more important anions are CI', Br', I', NO3', SO/', CO3", PO^'", etc. Acids and bases deserve special consideration from this point of view. Since salts are derived from acids by replacing the hydrogen by metals, it is natural to suppose that the positive ion in aqueous solutions of acids is H', and that the remainder of the molecule constitutes the negative ion. On the other hand, aqueous solu- tions of all bases contain the OH' group. These points are dealt with fully at a later stage. Freedom of the Ions before Electrolysis — The fact that the ions begin to move towards the respective electrodes im- mediately the current is made appears to indicate that they are electrically charged in the solution before electrolysis is com- menced. The questions therefore arise as to the state of such a salt as sodium chloride in dilute solution, and as to what occurs when the circuit is completed. The view long held was that the atoms are united to form a molecule, NaCl, at least ELECTRICAL CONDUCTlVlTV 241 partly owing to the electrical attraction of their contrary charges, and that the current pulls them apart during electrolysis. Careful measurements show, however, that Ohm's law holds for electro- lytes, from which it follows that the electrical energy expended in electrolysis is entirely used up in overcoming the resistance of the electrolyte, so that no work is done in pulling apart the components of the molecule. On the basis of this observation, and in agree- ment with certain views previously enunciated by Williamson as to the kinetic nature of equilibrium in general (cf. p. 160), Clausius showed that the equilibrium condition in electrolytes cannot be such that the ions of contrary charge are firmly bound together ; on the contrary, the equilibrium must be of a kinetic nature, so that the ions are continuously exchanging partners, and must, at least momentarily, be present in solution as free ions. The average fraction of the ions free under definite conditions of temperature and dilution was not estimated by Clausius, but he considered that the fraction was probably very small. Clausius's theory accounts for the qualitative phenomena of electrolysis, as during their free intervals the ions would be progressing towards the oppositely charged poles, and would finally reach them and be discharged. The views of Clausius were further developed in 1887 by Arrhenius.^who first showed how the fraction of the molecules split up into ions could be deduced from electrical conduc- tivity measurements, and independently from osmotic pressure measurements. This constitutes the main feature of the theory of electrolytic dissociation, which is dealt with in detail later fp. 260), and the fact that the two methods for determining the fraction of the molecules present as free ions gave results in very satisfactory agreement contributed much to the general acceptance of the theory. In a normal solution of sodium chlo- ride, then, there is an equilibrium between free ions and non- ionised molecules, represented by the equation NaCl 5t Na" + CI', in which, according to Arrhenius, about 70 per cent, of the salt is ionised and the remaining 30 per cent, is present as 1 Zeitsch. physikal. Chem., 1887, i, 631. 16 ^42 OUTLINES OF PHYSICAL CHEMISTRY NaCl molecules. According to this theory, the electrical con- ductivity is determined exclusively by the free ions, and not at all by the non-ionised molecules or by the solvent. Dependence of the Conductivity on the Number and Nature of the Ions — We are now in a position to form a picture of the mechanism of electrical conductivity in a solu- tion. Suppose there are two parallel electrodes i cm. apart (Fig. 29) with the electrolyte between them, and that the differ- ence of potential between the electrodes is kept constant, say at I volt. Before the electrodes are connected with the battery, the ions are moving about in all directions through the solution. When connection is made — in other words, when the electrodes are charged — they exert a directive force on the charged ions, which move towards the poles with the contrary charges. Those nearest the poles arrive first, give up their charges to the poles, thus neutralising an equivalent amount of electricity on the latter, and then either appear in the ordinary uncharged form (e.g., copper), react with the solvent {e.g., SO4 when platinum electrodes are used), with the electrodes {e.g., SO4 with copper electrodes), or with each other. It will be seen that the process does not consist in the direct neutralisation of the electricity on the positive electrode by that on the negative electrode, but part of the charge on the anode is neutralised by the anions, whilst an equivalent amount of charge on the cathode is neutralised by the cations — a process which has the same ultimate effect as direct neutralisation. On this basis it is clear that with a constant E.M.F. the rate at which the charges on our two plates are neutralised, in other words, the conductivity of the solution between them, depends on three things : (i) the number of carriers or ions per unit volume ; (2) the load or charge which they carry ; (3) the rate at which they move to the electrodes. Each of these factors will now be briefly considered. (i) The Number of Ions — Other things being equal, the conductivity of a solution will clearly be proportional to the ELECTRICAL CONDUCTIVITY 243 number of ions per unit volume. For the same electrolyte, the number of ions can, of course, be varied by varying the concentration of the solution. In general, it may be said that on increasing of concentration the ionic concentration also in- creases, but the exact relationship will be dealt with later. For different electrolytes of the same equivalent concentration, the conductivity will depend on the extent to which the solute is split up into its ions and on their speed. (2) The Charge Carried by the Ions — As has already been pointed out, there is a simple relationship between the capacity of different ions for transporting electricity, since the gram- equivalent of any ion (positive or negative) conveys 96,540 coulombs. Thus if in an hour ( = 3600 seconds) a gram-equiva- lent of sodium (23 grams) and of chlorine (3S"47 grams) are discharged at the respective electrodes, the current which has passed through the cell is 96,540 , „ , = 26-8 amperes. 3600 (3) Migration Velocity of the Ions — In this section we will for simplicity consider only univalent ions, but the same considerations apply to all electrolytes. Since positive and negative ions are necessarily discharged in equivalent amount (p. 240), and the number of positive and negative univalent ions discharged in a given time is therefore equal, it might be supposed that the ions must travel at the same rate. This, however, is by no means the case. Our knowledge of this subject is mainly due to Hittorf, who showed that the relative speeds of the ions could be deduced from the changes in concen- tration round the electrodes after electrolysis. The effect of the unequal speeds of the ions on the concen- trations round the poles is made clear by the accompanying scheme (Fig. 30), a modified form of one given by Ostwald. The vertical dark lines represent the anode and cathode respec- tively, and the dotted Unes divide the cell into three sections, those in contact with the electrodes being termed the anode 244 OUTLINES OF PHYSICAL CHEMISTRY and cathode compartments respectively. The positive ions are represented by the usual + sign, and the negative ions by the - sign. I. represents the state of affairs in the solution before connection is made ; the number of anions is the same as that of the cations, and the concentration is uniform throughout. The remaining lines represent the state of affairs in the solution after electrolysis on different assumptions as to the relative f -I- -(- -f + nr. u. -^ -I- 4- -1- + + + + + -I- + + + + + + + +; ++++++ + ■^ + f + +1 +- f + + + -f + f + f + + + +¥+++++ Fig. 30. speeds of the ions. Suppose at first that only the negative ions move. The condition of affairs in the solution when all the negative ions have moved two steps to the left is shown in 11. Each ion left without a partner is supposed to be dis- charged, and the figure shows that although the positive ions have not moved an equal number of positive ions is discharged. Further, whilst the concentration in the anode compartment has not altered during the electrolysis, the concentration in the cathode compartment has been reduced by half. Suppose now that the positive and negative ions move at the same rate. The state of affairs when each ion, positive or ELECTRICAL CONDUCTIVITY 245 negative, has moved two steps towards the oppositely-charged pole is represented in III. It is evident that four positive and four negative ions have been discharged, and that the con- centration of undecomposed salt has diminished in both com- partments, and to the same extent, namely by two molecules. Finally, let us assume that both ions move, but at unequal rates, so that the positive ions move faster than the negative ions in the ratio 3:2. The state of affairs when the positive ions have moved three steps to the right, and the negative ions two steps to the left, is shown in IV. It is clear that five positive and five negative ions have been discharged, and that whilst there is a fall of concentration of two molecules round the cathode, there is a fall of three round the anode. These results show that the fall of concentration round any one of the electrodes is proportional to the speed of the ion leaving it. In II., for example, there is a fall of concentration round the cathode, but not round the anode, corresponding with the fact that the anion moves, but not the cation. Similarly, in III., the fall of concentration round anode and cathode is equal, corresponding with the fact that the anion and cation move at the same. Finally, in IV., fall round anode : fall round cathode : : 3 : 2, corresponding with the fact that speed of cation : speed of anion = 3:2. From these examples we obtain the important rule that Fall of concentration round anode _ speed of cation - Fall of concentration round cathode speed of anion The student often finds a difficulty in understanding how, as in IV., five ions can be discharged at the anode when only two anions have crossed the partitions. To account for this, it must be assumed that there is always an excess of ions in contact with the electrodes, so that more are discharged than actually arrive by diffusion. The speed of the cations is often represented by u, and that of the anions by v. The total quantity of electricity (say, unit 246 OUTLINES OF PHYSICAL CHEMISTRY quantity) carried is proportional to {u + v), and, of this total n = v/{u + v) is carried by the anions and i - « = u/{u + v) by the cations, n, the fraction of the current carried by the anion, is termed the transport number of the anion ; similarly, I — « is the transport number of the cation. It is evident from the figure that there is a central section of the cell between the dotted lines in which no change of con- centration takes place when elec- trolysis is not carried too far. Therefore, in order to investigate the changes in concentration, it is simply necessary to remove the solutions round the electrodes after electrolysis and analyse them, but the experiment will only be successful if the intermediate layer has not altered in strength. Practical Determination of the Relative Migration Velo- cities of the Ions — The experi- ment may conveniently be made in the modified form of Hittorf's apparatus used in Ostwald's labo- ratory (Fig. 31). It consists of two glass tubes communicating towards the upper ends ; one of them is closed at the lower end, and the other provided with a stopcock, as shown. The elec- trodes, A and K, are sealed into glass tubes which pass up through the liquid, and communication with a battery is made in the usual way by means of wires which pass down the interior of the glass tubes. As an illustration, the determination of the transport numbers gKa: Fig. 31. ELECTRICAL CONDUCTIVITY 247 of the Ag' and NO3' ions in a solution of silver nitrate will be described. The anode A is of silver, and should be covered with finely-divided silver by electrolysis just before the experiment ; the cathode is of copper. The electrodes are placed in position, the anode compartment filled up to the connecting tube with r/20 normal silver nitrate, the cathode compartment up to B with a concentrated solution of copper nitrate, and finally the apparatus is carefully fiUed up with the silver nitrate solution in such a way that the boundary between the two solutions at B remains fairly sharp. The cell is then connected in series with a high adjust- able resistance, an ammeter, and a silver voltameter, and then joined to the terminals of a continuous current hghting circuit (no volts) in such a way that the silver pole becomes the anode. By means of the variable resistance, the current is so adjusted that a current of about o'oi ampere is obtained (to be read off on the ammeter), and the electrolysis continued for about two hours. Finally, a measured amount (about 3/4) of the anode solution is run off and titrated with thiocyanate in the usual way. The strength of the current can be read off on the ammeter, and from this and the time during which the current has passed, the total quantity of electricity passed through the solution can be calculated. It is, however, prefer- able to employ for this purpose the silver voltameter above referred to. It consists of a tube Avith stopcock similar to the left-hand part of the transport apparatus (Fig. 31), and is provided with a silver electrode (to serve as anode) similar to that in the other apparatus, and placed in a corresponding position (in the lower part of the tube). The tube is filled to 3/4 of its length with a 15-20 per cent, solution of sodium or potassium nitrate, and carefully filled up with dilute nitric acid so that the two solutions do not mix. The cathode, of platinum foil, dips in the nitric acid. During electrolysis, the NO3' ions dissolve silver from the anode, and by titrating the whole of the contents with ammonium thiocyanate after the experiment, the amount of silver in solution cap be determined, and frojn this 248 OUTLINES OF PHYSICAL CHEMISTRY the quantity of electricity which has passed through the solution can readily be calculated (p. 238). We now return to the transport apparatus. For our purpose it will be sufficient to deal only with the change of concentra- tion in the anode compartment. From this the transport number of the cation is obtained, and the transport number of the anion is then at once obtained by difference. During electrolysis, the silver concentration round the anode diminishes owing to migration of silver ions towards the cathode. The process may conveniently be illustrated by III. of Fig. 30 where the fall owing to migration is from 4 to 2. At the same time, however, NO3 ions reach the anode, and after being discharged dissolve silver from it, the silver concentration in the anode compartment therefore increasing. The latter effect is the same as that taking place simultaneously in the silver volta- meter, as described above, and therefore, if no silver migrated from the anode, the total increase of concentration in this com- partment would be equal to that in the silver voltameter, which, as explained above, is a measure of the total quantity of electricity which passes; we will term this a. If b is the (unknown) change in concentration due to the migration of the silver ions, the observed change in concentration at the anode will be a - ^. As a is known, and a - ^ is found by titrating the anode solution after the experiment, b can readily be obtained. In practice, the greater part of the anode solution after electrolysis is run into a beaker, it is then weighed or an aliquot part measured, and titrated. The calculation of the results will be rendered clear from the details of an experiment made in Ostwald's laboratory. Before the experiment 12 "31 grams of the silver nitrate solution re- quired 26-56 c.c. of a 1/50 « potassium thiocyanate solution, so that I gram of solution contained o'oo739 grams of silver nitrate. After the experiment, 23-38 grams of the anode solution required 69-47 c.c. of the thiocyanate solution, cor- ELECTRICAL CONDUCTIVITY 249 responding to o'236i grams of silver nitrate. The solution, therefore, contained 23-14 grams of water, which before the experiment contained 23'i4 x 0-00739 = 0-1710 grams of silver nitrate, hence the increase of concentration at the anode is 0-065 1 grams = a - b. The contents of the silver volta- meter required 36-16 c.c. of thiocyanate = 0-1229 grams of silver nitrate = a ; the same amount is dissolved at the anode in the transport apparatus. As the actual increase of con- centration was only 0-0651 grams, 0-1229 - 0-0651 = 0-0578 grams of silver must have left the anode compartment by migra- tion. Hence the transport number for silver is u 0-0578 \ — n = = ^— = 0-470, « -f W 0-1229 and for the NO3' ion 0-0651 ■ - = 0-530. u ■\- V 0-1229 Hence, of the total current 47 per cent, is carried by the silver ions, and 53 per cent, by the NO3' ions. It was shown by Hittorf that the transport numbers are practically independent of the E.M.F. between the electrodes, but depend to some extent on the concentration and on the temperature. It is remarkable that at higher temperatures they tend to become equal. Some of the numbers are given in the next section. Specific, Molecular and Eqaivalent Conductivity — Just as in the case of metallic conduction, the resistance of an electro- lyte is proportional to the length, and inversely proportional to the cross-section of the co lumn between the electrodes. Hence we may define the specific resistance of an electrolyte as the resistance in ohms of a cm. cube, and its specific conductivity as i/specific resistance, expressed in reciprocal ohms. Since, however, the conductivity does not depend on the solvent but on the solute, it is much more convenient to deal with solutions containing quantities of solute proportional to the respective molecular weights. The so-called molecular conductivity, ft., is 2SO OUTLINES OF PHYSICAL CHEMISTRY most largely used in this connection ; it is the conductivity, in reciprocal ohms, of a solution containing i mol of the solute when placed between electrodes exactly i cm. apart. It may also be defined as the specific conductivity, «, of a solution, multiplied by v, the volume in c.c. which contain a mol of the solute. Hence we have /A = KV. As an example, the following values for the specific and mole- cular conductivities of solutions of sodium chloride at i8°, as given by Kohlrausch, may be quoted. Concentration of Solution. I'o molar (w= i,ooo) o"i molar (?;= 10,000) o'oi molar (w= 100,000) o'ooi molar (w = 1,000,000) o'oooi molar (w= 10,000,000) It will be noticed that the molecular conductivity as defined above increases at first with dilution, but beyond a certain point remains practically constant on further dilution. These numbers enable us to illustrate more fully the physical meaning of the molecular conductivity. Imagine a cell of i cm. cross-section and of unlimited height, two opposite walls through- out the whole height acting as electrodes. If a litre of a molar solution of sodium chloride is placed in the cell, it will stand at a height of 1000 cms. We may regard the solution as made up of cm. cubes, 1000 in number, and if the con- ductivity of one of these cubes — the specific conductivity — is Kj, the total conductivity (in other words the molecular con- ductivity) is loooKi. If now another litre of water is added, the height of the solution will be 2000 cms. and its molecular con- ductivity is now 2000K2, where Kj is the specific conductivity ol the half-molar solution. In exagtly the same way, the mole- cular condu. tivity may be determined at still greater dilutions. From the above it is clear that ^ measure of the conducting Sp. Con- ductivity, Molecular Conductivity, K. KV. 0-0744 74'4 0'00925 92-5 O'00I028 102-8 0-0001078 107-8 0-00001097 109-7 ELECTRICAL CONDUCTIVITY 251 power of a mol of the electrolyte in different dilutions is ob- tained by multiplying the volume in c.cs. in which the electrolyte is dissolved by its specific conductivity at that dilution, or in symbols as given above. A glance at the last two lines in the table helps us to under- stand the approximately constant value of ft. in very dilute solutions. When the solution is diluted from i/iooo to 1/10,000 molar, the specific conductivity is reduced to about i/io, but as the volume is ten times as great, the molecular conductivity is only slightly altered. Besides the molecular conductivity, the term equivalent con- ductivity is sometimes used. As the name implies, it is the specific conductivity of a solution multiplied by the volume in c.c. which contains a gram-equivalent of the solute. Kohlrausch's Law. Ionic Velocities — The numbers in the third column of the above table show that the molecular conductivity of sodium chloride increases, at first rapidly and then very slowly, with dilution. This subject was investigated for a number of solutions by Kohlrausch, who found that for solutions of electrolytes of high conductivity (salts, so-called " strong " acids and bases) the molecular conductivity increases with dilution up to about i/ioooo molar solution, and beyond that point remains practically constant on further dilution. Kohlrausch showed further that this limiting value of the mole- cular conductivity, which may be represented by )x.^, is different for different salts, and may be regarded as the sum of two inde- pendent factors — one pertaining to the cation or positive part of the molecule, the other to the anion, or negative part of the molecule. This experimental result is termed Kohlrausch's law, and is readily intelligible on the basis of the theory of electrical conductivity developed above. The limiting value of the mole- cular conductivity is reached when the molecule is completely split up into its ions ; under these circumstances the whole of the salt takes part in conveying the current. For simplicity we will consider solutions of binary electrolytes. In very dilute 252 OUTLINES OF PHYSICAL CHEMISTRY equimolar solutions of different electrolytes, the number of the ions and their charges are the same, and the observed differences of /ioc '^^ only be due to the different speeds of the ions. The limiting molecular conductivities of binary electrolytes are therefore proportional to the sum of the speeds of the ions, and when the units are properly chosen we have liao=u + v, where u is the speed of the cation, v that of the anion. This is the mathematical form of Kohlrausch's law, and expresses the very important result that in sufficiently dilute solution the speed of an ion is independent of the other ion present in solution. From the results of conductivity measurements, only the sum of the speeds of the ions can be deduced, but, as has already been shown, the relative values. lof u and v can be obtained from the results of migration experiments (p. 246). It was found by Kohlrausch that the value of /^oc = u + v for silver nitrate at 18° is irs-5. The accurate value for the transport number of the anion, NO3', is « = v/{u ■+ v) = 0-518. Hence v = o'5i8 x iiS'5 = 6o'8 and u = 0-482 x 115-5 = 55-7. The values of u and v, expressed in these units, are termed the iont'i: velocities, under the conditions of the > experi- ment. The accompanying table gives the ionic velocities, calculated from the results of conductivity and transport measure- ments, for some of the more common ions in infinite dilution 1 at 18°, expressed in the same units as the molecular conductivity of sodium chloride (p. 250): — H- = 318 Li- = 36 OH' = 174 K- = 65 NH^- = 64 CI' = 66 Na- = 45 Ag- =56 r = 67 N03'= 61 It is interesting to observe that the velocity of the H- ion is relatively very high, about five times as great as that of any of the metallic ions. The ion which comes next to it is the OH' ion, ' The more concentrated the solution, the smaller are the ionic velocities owing to the increased resistance to their motion, ELECTRICAL CONDUCTIVITY 253 the speed of which is more than half that of the H- ion, and much greater than that of any of the other ions. Since the conductivity of a solution is, as we have already seen, propor- tional to the speed of the ions, it follows that the solutions of highly ionised acids and bases will have a relatively high con- ductivity. Thus, under conditions otherwise equal as regards concentration, ionisation, temperature, etc., the conductivities of dilute solutions of hydrochloric acid and of sodium chloride will be in the ratio (318 -t- 66) = 384 to (45 -1- 66) = in, or about 3"5 : i. Absolute Yelocity of the Ions. Internal Friction — The absolute velocity of the ions is proportional to the E.M.F. between the electrodes, and inversely proportional to the re- sistance offered to their passage by the solvent. When the fall of potential is one volt per cm. [i.e., when the difference of potential between the electrodes is x volts and the distance between them is x cm.) it can be shown that the absolute velocities, in cm. per second, are obtainable from the values for the ionic velocities given above by dividing by 96,540 or, what is the same thing, by multiplying by i"036 x 10"^ Hence the absolute velocity of the hydrogen ion is, under the conditions described, 318 x i"036 x io~* = o'oo332 cm. per second, and of the potassium ion 0-00067 <^'^- P^^ second at infinite dilution. The speed of the ions is therefore extremely low ; even the hydrogen ions, under a driving force of i volt per cm., only move about twice as fast as the extremity of the minute hand of an ordinary watch. This very slow motion of the moving particles indicates that the resistance to their passage through the solvent is very great. Kohlrausch has calculated that the force required to drive a gram of sodium ions through a solution at the rate of i cm. per second is 153 X 10^ kilograms weight, or about 150,000 tons weight. The absolute velocity of the ions can also be measured directly by a method the principle of which is due to Lodge, and which may be illustrated by an experiment described by 254 OUTLINES OF PHYSICAL CHEMISTRY Danneel. A U-tube is partly filled with dilute nitric acid, and in the lowest part of the tube a solution of potassium permanganate, the specific gravity of which has been increased as much as possible by the addition of urea, is carefully placed, by means of a pipette, in such a way that the boundary between the acid and the permanganate remains sharp. When platinum electrodes are dipped in the nitric acid in the two limbs, and a current passed through the solution, the violet boundary (due to the coloured MnO/ ion) moves towards the anode. From the observed speed of the boundary and the difference of potential between the poles, the speed of the ion for a fall of potential of i volt/cm. is obtained, and has been found to agree exactly with the value obtained by conductivity and transport measurements. This method is not confined to salts with coloured ions, but the moving boundary can also be observed with colourless solutions when, as is usually the case, the refractive index of the two solutions is different. There are, of course, two boundaries, one due to the positive ions moving towards the cathode, and the other due to the negative ions moving towards the anode. When the conditions are such that both can be observed, the relative speeds give the ratio ufv directly. Measurements of ionic velocities on this principle have been made by Masson, Steele and others, and the results are in entire agreement with those obtained indirectly. Experimental Determination of Conductivity of Elec- trolytes — The measurement of the conductivity of conductors of the first class is a very simple operation. Until compara- tively recently, however, no very satisfactory results for the conductivity of electrolytes could be obtained, because when a steady current is passed through a solution between platinum electrodes the products of electrolysis accumulate at the poles and set up a back E.M.F. of uncertain value, a phenomenon known as polarization (p. 373). This difficulty is, however, com- pletely got over by using an alternating instead of a direct ELECTRICAL CONDUCTIVITY 255 current (Kohlrausch, 1880) ; by the rapid reversal of the current the two electrodes are kept in exactly the same condition, and there is no polarization. The arrangement of the apparatus, which in principle amounts to the measurement of resistance by the Wheatstone bridge method, is shown in Fig. 32. R is a resistance box, S a cell with platinum electrodes, between which is the solution the resistance of which is to be measured, ab is a platinum wire of uniform thickness, which may conveniently be a metre long, and is stretched along a board graduated in millimetres, c is a sliding contact. By means of a battery (not shown in the figure) a direct current is sent "■ through a Ruhm- korff coil, K, the latter then gives rise to an alter- nating current, which divides at a into two branches, reach- ing b by the paths adb and acb re- spectively. As a galvanometer is not afifected by an alter- nating current, it is in this case replaced by a telephone T, which is silent when the points c and d are at the same potential. The contact-maker, c, is shifted along the wire till the telephone no longer sounds. Under these circumstances, the following relationship holds — Length of ac Length of cb R = S and since ac, cb and R are known, S, the resistance of the part of the electrolyte between the electrodes, can st once be calculated. As the resistance of electrolytes varies within wide limits, 256 OUTLINES OF PHYSICAL CHEMISTRY different forms of cell are employed according to circum- stances. For solutions of small conductivity, the Arrhenius form represented in Fig. 33. is very suitable. The electrodes, which are stout platinum discs 2-4 cm. in diameter, are fixed (by welding or otherwise) to platinum wires, which are sealed into glass tubes A and B, as shown in the figure. These glass tubes are fixed firmly into the ebonite cover of the cell, so that Fig. 33. Fio. 34. the distance between the electrodes remains constant, and electri- cal connection is made in the usual way by wires passing down the interior of the glass tubes. In order to expose a larger surface, and thus minimise polarization effects, which would interfere with the sharpness of the minimum in the telephone, the elec- trodes are coated with finely-divided platinum by electrolysis of a solution of chlorplatinic acid. For electrolytes of high ELECTRICAL CONDUCTIVITY 257 conductivity, a modified form of conductivity vessel, with smaller electrodes placed further apart, has been found con- venient (Fig. 34). Experimental Determination of Molecular Conduc- tivity — It is clear that the observed resistance of the electro- lyte must depend on what is usually termed the capacity of the cell, that is, on the cross-section of the electrodes and the distance between them. The specific conductivity, and hence the specific resistance, of the electrolyte could be calculated if these two magnitudes were known (p. 235); but it is much simpler to determine the " constant " of the vessel, which is proportional to its capacity, by using an electrolyte of known conductivity. For this purpose, a 1/50 molar solution of potas- sium chloride may conveniently be used for cells of the first type. The method of procedure will be clear from an example. Referring to the figure, we have, for the resistance, S, of the electrolytic cell, R'^^ , , . . _ I ac S = and conductivity KJ = -= — — . ac S R'^f Further, since the specific conductivity, k, must be proportional to the observed conductivity, we have where A is a constant. Since all the other factors, including k, the specific conductivity of potassium chloride, are known. A, the constant of the cell, can be calculated. If, now, with the same distance between the electrodes, a solution of unknown specific conductivity, kj, is put in the cell, and for the resistance R' the new position of the contact is c , the specific conductiv- ity in question is given by the formula ac' "i^^R^" By multiplying kj by the number of c.c. containing i mol of the solute, the molecular conductivity is obtained. 17 258 OUTLINES OF PHYSICAL CHEMISTRY From the results of conductivity measurements in different dilutions, /Xoo can readily be obtained directly for salts, strong acids and bases ; it is the value to which /i approximates on progressive dilution, /too cannot, however, be obtained directly for weak electrolytes, such as acetic acid and ammonia ; before the limiting value of the conductivity is reached with these electrolytes, the solutions would be So dilute as to render accu- rate measurement of the specific conductivity impossible. This difficulty is got over by making use of Kohlrausch's law. The value of fjLao ^oi acetic acid must be the sum of the velocities of the H' and CH3COO' ions. The former is obtained from the results of conductivity and transport measurements with any strong acid, and has the value 318 at 18°. In a similar way the velocity of the CH3COO' ion can be obtained from ob- servations with an acetate for which the value of /too can con- veniently be found, e.g., sodium acetate, fiaa for the latter salt at 18° is 78'i, and as the velocity of the Na' ion is 44^4 at infinite dilution, that of the CH3COO' ion must be 78'i - 44-4 = 337. Hence for acetic acid /xoo ^u + v = 33-7 + 318 = 351-7 at 18°. Results of ConductiYity Measarements — In general, it may be said that the conductivity of pure liquids is small. Thus the specific conductivity of fairly pure distilled water is about io~* reciprocal ohms at 18°, and even this small con- ductivity is largely due to traces of impurities. It is a remark- able fact that the specific conductivity of a number of other liquids, which have been purified very carefully by Walden,^ is of the same order as that given above for water. Mixtures of two liquids have in many cases a very small conductivity, not appreciably greater than that of the pure liquids themselves; this is true of mixtures of glycerine and water, and of alcohol and water. On the other hand, a mixture of two liquids which are practically non-conductors may have a very high conductivity — for example, mixtures of sulphuric acid and water. The results obtained for this mix- ' Zeitsch, Physikal Chem., 1903, 46, 103. ELECTRICAL CONDUCTIVITY 259 ture are represented in Fig. 35, the acid concentration being measured along the horizontal axis, and the -specific conductivity along the vertical axis. The figure shows that, on gradually adding sulphuric acid to water, the specific conductivity of the mixture increases till 30 per cent, of acid is present, reaches a maximum value at that point, and on further addition of acid diminishes. When pure sulphuric acid is present (100 per cent, on curve), the conductivity is practically zero, and is increased /' ■% ^ _> J / > \ 3 ■D C \ V ui 6 « 1 \ "■4 1 (D / 0. 1 \ 0-3 1 \ HjSO , Co icent 'atioi L 'N '>^ 10 20 30 40 50 60 70 80 90 100 per cent. FiQ. 35. both by the addition of water (left-hand part of curve) and of sulphur trioxide (right-hand part of curve). Further, the curve has a minimum between 84 and 85 per cent, of acid, which, it is interesting to note, exactly corresponds with the composition of the monohydrate HjSO^, HjO. According to the electro- lytic dissociation theory, the conductivity depends on the pres- ence of free ions, and the curve for sulphuric acid and water shows in a very striking way that the condition most favourable for ionisation is the presence of two substances. Why ions are formed in a mixture of sulphuric acid and water, and not appreciably, if at all, in a mixture of alcohol and water, is not well understood {cf. p. 317). Analogous phenomena are met with for solutions of solids 2 6o OUTLINES OF PHYSICAL CHEMISTRY and of other liquids in liquids. An aqueous solution of sugar has no appreciable conducting power. The so-called " strong " acids and bases form well-conducting liquids with water. The conductivity of most organic acids and bases is small, and in corresponding dilution ammonium hydroxide is a much poorer conductor than potassium hydroxide. On the other hand, all salts, even the salts of organic acids which are themselves weak, have a very high conductivity. , The conductivity of substances in solvents other than water is usually small, but solutions in methyl and ethyl alcohols and in liquid ammonia are exceptions. The dependence of electrical conductivity on the nature of the solvent will be discussed later. It is interesting to note that many fused salts, such as silver nitrate and lithium chloride, are good conductors, and thus form an exception to the rule that pure substances belonging to the second class of conductors have a very small conductivity. Electrolytic Dissociation — It has already been pointed out (p. 124) that solutions of salts, strong acids and bases, have a much higher osmotic pressure in aqueous solution than would be the case if Avogadrd's hypothesis was valid for these solu- tions. According to the molecular theory, the solutions behave as if there were more particles of solute present than would be anticipated from the simple molecular formula, and van't Hoff expressed this by a factor i, which represented the ratio between the observed and calculated osmotic pressures. This was the position of the theory of solution in 1885. About that time, Arrhenius pointed out that there is a close connection between electrical conductivity and abnormally high osmotic pressures ; only those solutions which, according to van't Hoff's theory, have abnormally high osmotic pressures, conduct the electric current. Kohlrausch had previously shown that the molecular conductivity increases at first with dilution, and for many electrolytes attains a limiting value in a dilution of 10,000 litres (p. 251). Arrhenius accounted for this increase on the assumption that the solute consists of "active" and ELECTRICAL CONDUCTIVITY 261 " inactive " parts, and that only the active parts, the ions, convey the current. The extent to which the solute is split up into ions increases with the dilution until finally (when the molecular conductivity has attained its maximum value) it is completely ionised or completely "active" as far as the conduction of electricity is concerned. The theory of Arrhenius is based upon the views of Clausius on conductivity, as has already been pointed out. Arrhenius, however, went much further, inasmuch as he showed how, from the results of conductivity and of osmotic pressure measure- ments, the degree of dissociation can be calculated, as shown in the following section. Degree of lonisation from Conductiyity and Osmotic Pressure Measurements — According to the theory of electro- lytic dissociation, the conductivity of a solution depends only on the number of the ions per unit volume, on their charges (which are the same for equivalent amounts of different electrolytes) and on their speed. For the same electrolyte we may assume that the velocities remain practically unaltered on dilution (the friction in a dilute solution being practically the same as that in pure water), therefore the increase of molecular conductivity with dilution must depend almost entirely on an increase in the number of the ions. The molecular conductivity at infinite dilution is given by the formula Moo = « + ». where u and v are the speeds of cation an d anion respectively and the molecular conductivity at any dilution, », must therefore be represented by the formula /*„ = a.{u -V V), where u, represents the fraction of the molecules split up into ions. Hence, dividing the second equation by the first, we have 262 OUTLINES OF PHYSICAL CHEMISTRY that is, the degree of dissociation, u, at any dilution, is the ratio of the molecular conductivity at that dilution to the mole- cular conductivity at infinite dilution. For example, \x^ for molar sodium chloride is 74*3 and /^oc = no'S. hence a = /i„/ju,o5 = 74'3/iib"3 = o'673. Hence sodium chloride in molar solution is about two-thirds split up into its ions. We have now to consider the deduction of the degree of dissociation from osmotic measurements. The assumption made in this case is that the osmotic pressure is proportional to the number of particles present, the ions acting as separate entities. If a molecule is partially dissociated into n ions and the degree of dissociation — the ionised fraction — is a, then the number of molecules will be i — u., and the number of ions no.. Hence the ratio of the number of particles actually present to that deduced according to Avogadiro's hypothesis (van't HofTs factor /) will be /=I-a + «a=l+ a(« - l), / - I or a = n - \ As an illustration, de Vries obtained for a CT4 molar solution of potassium chloride i = i"8i, hence, since « = 2, u, = o'8i, or the salt is dissociated to the extent of 8 1 per cent, into its ions, /for a o'i8 molar solution of calcium nitrate is 2-48, therefore, smce « = 3, a = = 074 m this case. The agreement in the values of i obtained from conductivity and osmotic measurements is strikingly shown in the accom- panying table (van't Hoff and Reicher, 1889). The values of /■ (osmotic) are from the results of de Vries, those of i (freezing point) mainly from the observations of Arrhenius, and those of i (conductivity) are calculated by means of the formulae a = ^vll^-ai and «' = i -f a(« - i) as explained above. ELECTRICAL CONDUCTIVITY 263 Substance. Concentration (gram equiv. per litre). i (freezing pt.). i (osmotic). i (conduc- tivity). KCl 0'I4 1-82 l-8i 1-86 LiCl 0-13 1-94 1-92 1-84 Ca{N03), o-i8 2-47 2-48 2-46 MgCla o"i9 2-68 2-79 2-48 CaClg 0-184 2-67 278 2-42 The agreement is satisfactory, and goes far to justify the as- sumptions on which the data have been calculated. It is not certain that the results obtained by the different methods can be expected to agree absolutely ; this point will be referred to at a later stage (p. 281). As regards the mode of ionisation, it is clear that univalent compounds, such as potassium chloride, can ionise only in one way, thus, KCl^K* + CI'. For more complex molecules, how- ever, there are other possibilities, thus calcium chloride may ionise as follows : CaClj ^ CaCl' + CI' as well as in the normal way CaClj^Ca" -1- 2Cr. If ionisation were complete according to the last equation, t would be = 3, as compared with the observed value, 2-67 for o'i84 normal solution, given in the table. Similarly, sulphuric acid may dissociate according to the equation HjSO^^H- -t- HSO4', the latter ion then under- going further ionisation as folfows : HSO^'^H* + SO/'. Effect of Temperature on Conductivity — The conduc- tivity of electrolytes increases considerably with rise of tempera- ture. The temperature coefficient for salts is 0-020 to 0-023, for acids and some acid salts 0-009 ''^ 0-016, for caustic alkalis about 0-020, and does not vary much with dilution. Conduc- tivity data are usually given for 18°, and the specific conductivity, K, at any other temperature, is given by the formula "t = KisLi + ^{' - 18)] where c is the temperature coefficient. As the conductivity of an electrolyte depends both on the number and velocity of the ions, the question arises as to whether the change of conductivity with temperature is due to the alteration of only one or of both these factors. The 2 64 OUTLINES OF PHYSICAL CHEMISTRY matter can be at once decided by calculating the degree of dissociation at the higher temperature from conductivity measurements in the ordinary way, and comparing with that at the lower temperature. For normal sodium chloride at 50°, the value of •* = fi^/fji,^ = 132/203-5 = 0-65, which is only slightly less than the value at 18°, o'678. Hence, as the considerable increase of conductivity with temperature cannot be due to an increase in the number of ions, it must be due to an increase in their speed. This increased velocity is doubt- less connected with the diminution in the internal friction of the medium with rise of temperature, and the consequent diminished resistance to the passage of the ions (p. 253). Grotthus' Hypothesis of Electrolytic Conductivity — Long before the establishment of the electrolytic dissociation theory, Grotthus put forward a hypothesis to account for the conductivity of electrolytes which is of considerable historical interest. He assumed that under the influence of the charged electrodes the molecules of the salt, e.g., potassium chloride, arrange themselves in lines between the electrodes so that the potassium atoms are all turned to the negative electrode, and the chlorine atoms to the positive electrode. Electrolysis takes place in such a way that the external potassium atom is liberated at the cathode and the chlorine atom at the anode. The potassium atom which is left free at the anode unites with the chlorine atom of the molecule next to it, the chlorine atom of the latter with a potassium atom of the molecule next in the chain, and so on. A similar process takes place starting at the anode, in other words, an exchange of partners takes place right along the chain, from one electrode to the other. Under the influence of the charged electrodes, the new molecules twist round till they are in the former relative position, when the end atoms are again discharged, and so electrolysis proceeds. The fatal objection to this ingenious theory is that a con- siderable E.M.F. would have to be employed before any decomposition whatever takes place, hence Ohm's law would not hold {(f. p. 241). Practical Illustrations — The following experiments, which ELECTRICAL CONDUCTIVITY 265 are fully described in the course of the chapter, may readily be performed by the student : — (i) Experiment on the migration velocity of the ions (p. 246). (2) Rough determination of the absolute velocity of the MnO^' ion (p. 254). (3) Determination of the constant of conductivity vessel with «/So potassium chloride. (The specific conductivity, k, of this solution at different temperatures is as follows : o'ooi522 at 0°, o'ooi996 at 10°, o'oo2399 at 18°, and o'oo2768 at 25°.) (4) Determination ofjihe specific and molecular conductivities of solutions of sodium chloride and of succinic acid. As the conductivity of solutions varies greatly with the tem- perature, the conductivity vessel must be partially immersed in a thermostat while measurements are being made. In the case of sodium chloride, measurements may be made with «/i, «/io and n/ioo solutions, and the values obtained for the molecular conductivity compared with those given in Kohlrausch's tables.^ The results in very dilute solutions are not trustworthy unless great attention is paid to the purification of the water used in making up the solutions. In the case of succinic acid, it is usual to start with a x/i6 nwlar solution; 20 c.c. of this solution is placed in the con- ductivity cell in the thermostat, and when the temperature is constant the resistance is determined. 10 c.c. of the solution is then removed with a pipette, 10 c.c. of water at the same temperature added, the resistance again determined after thoroughly mixing the solution, and so on. Measurements are thus made in dilutions of 16, 32, 64, 128, 256, 512 and 1024 litres. From the values of /a, thus obtained, the degree of dissociation can be calculated by the usual formula a = /u..//too • /Aoo in this case can only be determined indirectly ; its value at 25° is about 381. From the values of a in different dilutions, K, the dissociation constant of the acid may then be calculated ; according to Ostwald, K = o-oooo66 at 25°. ' Full details of electrical conductivity measurements and a large amount of conductivity data are given in Kohlrausch and Holborn, Leitvermogen der EUktrolyte, Leipzig, 1898. CHAPTER XI EQUILIBRIUM IN ELECTROLYTES. STRENGTH OF ACIDS AND BASES. HYDROLYSIS The Dilution Law — In a previous chapter it has been shown that chemical equilibria, both in gaseous and liquid systems, can be represented satisfactorily by means of the law of mass action. We have now to apply this law to binary electrolytes, on the assumption that the ions are to be re- garded as independent entities. According to the electrolytic dissociation theory, an aqueous solution of acetic acid contains molecules of non-ionised acid in equilibrium with its ions, represented by the equation CH3COO' + H^^CHjCOOH. Suppose in the volume v of solution the total concentration of the acid is i, and that a fraction of it, represented by a, is split up into ions. The concentration of the undissociated acid is , that of each of the ions (since they are neces- sarily present in equivalent amount) -. Hence, from the law of mass action, \V/ \ V / (l - a)v ^ ' where K, as before, is the equilibrium constant. For conduc- tivity measurements, the above formula may be put in a rather different form by substituting fii,//Xoo for a. It then becomes 266 EQUILIBRIUM IN ELECTROLYTES 267 />./ = K. It is preferable, however, to remember the dilution formula in the iirst form. This relationship, which is known as Ostwald's dilution law, may be tested by substituting a value for a (from conductivity or osmotic observations) at any dilution v, and calculating K, the equilibrium constant ; the value of a at any other dilution may then be obtained from the formula and compared with that determined directly. This was done (from conductivity measurements) by van't Hoff and Reicher, and the results are given in the accompanying table : — Acetic acid: K = o'ooooi78 at i4'i°; /tog = 316. V (in litres) . . 0-994 2-02 I5'9 i8'i 1500 3010 7480 15000 M. . . ■ i'27 i'94 5'26 5-63 46-6 64-8 95-1 129 looo (observed) . 0*40 o"6i4 i'66 1-78 I4"7 20-5 3o'i 40-8 looo (calculated) . 0-42 o'6 rdj 1-78 is'o 20-2 30-5 4o'i The agreement between observed and calculated values is excellent ; it is, in fact, much closer than for any case of ordinary dissociation so far investigated. The table also shows how small is the dissociation of acetic acid solutions under ordinary conditions ; a molar solution is ionised only to the extent of 0*4 per cent., and even a 1/1500 molar solution rather less than 1 5 per cent. The dilution law holds for nearly all organic acids and bases, but does not hold for salts, or for certain mineral acids and bases. The latter point is discussed in a later section. When the deg ree of dissociation is small, as in the case of acetic acid for fairly concentrated solution, a can be neglected in comparison with i, and the dilution law then becomes a2 , — = K or a = VKw . . . (2) that is, /or weak electrolytes the degree of dissociation is approxi- mately proportional to the square root of the dilution. When 268 OUTLINES OF PHYSICAL CHEMISTRY y K» + _— . . (3) a cannot be neglected in comparison with i , a is given by the equation + a/ JS.W + - obtained by solving equation (i) for a. In order to familiarise himself with the use of the dilution formula, the student should calculate a for acetic acid in different dilutions from the value of K given above both by the approximate and accurate formula. The physical meaning of the constant K will be clear if a in the dilution formula (i) is put = ^. Then 2K = j/v, that is, 2K is the reciprocal of the volume at which the electrolyte is dissociated to the extent of 50 per cent. Acetic acid, for instance, will be half dissociated at a dilution of n = 27,777 litres Uf. table). 2x0-000018 ' "' '■■' ' As the method of deriving it indicates, the dilution law applies only to binary electrolytes, i.e., electrolytes which split up into two ions only, and it is not therefore a priori probable that it will hold for dibasic acids, such as succinic acid, which presumably dissociate according to the equation C2H^(COOH)2 2C2H4(COO)2"+ 2H-. It is, however, an experimental fact that when the concentration of succinic acid is expressed in mols (not in equivalents) per litre, the values of K obtained by substitution in the dilution formula remain constant through a wide range of dilution. This indicates that the acid at first splits up into two ions only, doubtless according to the equation P „ /COOH_^P „ /COO' , „. ^2"*\COOH^^2«4\cOOH "^ " and that the second possible stage, represented by the equation P„/COO' _^p„/COO'' „. '^2"*\COOH^^2"*\COO "^ EQUILIBRIUM IN ELECTROLYTES 269 is not appreciable under the conditions of the experiment. In other cases, however, e.g., fumaric acid, the value of K increases with dilution before the dilution has progressed very far, which indicates that the second stage of the dissociation early becomes of importance. Strength of Acids — We are accustomed to estimate the strength of acids in a roughly qualitative way by their relative displacing power. Sulphuric acid, for example, is usually re- garded as a strong acid, because it can displace such acids as acetic and hydrocyanic from combination. This principle can be developed to a quantitative method for estimating the rela- tive strengths of acids (and bases) if care is taken to make the comparison under proper conditions. This is sufficiently secured by making the experiments in a homogeneous system under such conditions that all the reacting substances and prodiuts of reaction remain in the system. We learn in studying inorganic chemistry that many reactions proceed wholly or partially in a particular direction for two main reasons : (a) because an insoluble (or practically insoluble) product is formed which is thus removed from the reacting system, e.g., NajSOi -t- BaClj -» 2NaCl + BaSO^ (insoluble) ; (3) because a volatile product is formed which under the con- ditions of experiment leaves the reacting system, e.g., 2NaCl -1- HgSO^-s-NajSO^ -1-2HC1 (volatile). Such reactions are obviously unsuitable for determining the relative strengths of the acids concerned. Bearing these considerations in mind, we now proceed to investigate the relative strengths of, say, nitric and dichloracetic acids by bringing them in contact with an amount of base insuffi- cient to saturate both of them, and find how the base distri- butes itself between the two acids. If, for example, the acids are taken in equivalent amount, and sufficient base is taken to saturate one of them, we have to determine the position of equilibrium represented by the equation 2 70 OUTLINES OF PHYSICAL CHEMISTRY CHClgCOOK + HNOa^CHClaCOOH + KNO3. It is evident that no chemical method would answer the purpose, because it would disturb the equilibrium. When, however, a physical property of one of the components, which alters with the concentration, can be measured, the position of equilibrium can be determined. A method used for this purpose by Ostwald, depending on the changes of volume on neutralization, will be readily understood from an example. When a mol of potassium hydroxide is neutralized by nitric acid in dilute solution, there is an increase of volume of about 20 c.c. When, on the other hand, the same quantity of alkali is neutralized by dichloracetic acid, the increase of volume is about 13 c.c. It is therefore clear that the complete displace- ment of dichloracetic acid by nitric acid, according to the equation CHCljCOOK + HNO3 -^ CHCI^COOH + KNO3,' would give an increase of volume of (20 - 13) = 7 c.c. ; if no displacement took place, there would, of course, be no change of volume. The change actually observed was 5-67 c.c, which means that the reaction represented by the equation has gone S'67 from left to right to the extent of = 80 per cent, approxi- mately ; in other words, the nitric acid has taken 80 per cent, of the base, and 20 per cent, has remained combined with the dichloracetic acid. The relative strength, or relative activity, of the acids under these conditions is therefore 80 : 20 or 4 ; i. Any other physical property, which is capable of quantitative measurement and differs from the two systems, can be equally well employed for the determination of equilibrium. The heat of neutralization has been used for this purpose by Thomsen, and the measurement of the refractive index by Ostwald ; the principle of the methods is exactly the same as in the example just given. Thomsen's thermochemical measurements were the first to EQUILIBRIUM IN ELECTROLYTES 271 be made on this subject, and he arranged the different acids in the order of their " avidities " or activities. Ostwald then showed that the same order of the avidities was obtained by the volume and refractivity methods, and, further, that the results were independent of the nature of the base competed for, so that the avidities are specific properties of the acids. The relative strength of acids can also be determined on an entirely different principle, depending on kinetic measurements. It has already been pointed out that acids accelerate, in a catalytic manner, the hydrolysis of cane sugar, of methyl acetate, acetamide, etc. Ostwald made many experiments on this sub- ject and reached the very important conclusion that the order of the activity of acids is the same, whether measured by the distribution method (which is, of course, a static method), or by a kinetic method. This affords further evidence in favour of the conclusion just mentioned, that the activity or affinity is a specific property of the particular acid, independent of the method by which it is measured. Thus far had our knowledge of the subject progressed when in 1884 the first paper of Arrhenius appeared. He showed that the order of the " strengths " of the acids as determined by the methods just described is also that of their electrical conductivities in equivalent solution. This fundamentally im- portant fact is illustrated in the accompanying table, in which the conductivities of the acids in normal solution are quoted, that of hydrochloric acid being taken as unity. Relative Activity. Acid. Thermocheraical. Cane Sugar. Conductivity. Hydrochloric 100 100 100 Nitric 100 100 99-6 Sulphuric 49 53-6 6s'i Monochloracetic 9 4'8 4-9 Acetic — o'4 1-4 We have seen that, according to the electric dissociation theory, the electrical conductivity jf an acid is mainly deter- 2 72 OUTLINES OF PHYSICAL CHEMISTRY mined by its degree of dissociation; for example, the con- ductivity of a normal solution of acetic acid is small because it is ionised only to a very small extent. Further, owing to the predominant share taken by the hydrogen ions in conveying the current (p. 252), the relative conductivities of acids will be approximately proportional to their H' ion concentrations. It is therefore natural to suppose that the activity of acids, as illustrated by distribution and catalytic effects, is also due to that which all acids have in common, namely, hydrogen ions. This assumption is in complete accord with the experimental results, as the following illustration shows. The velocity con- stant for the hydrolysis of cane sugar in the presence of 1/80 normal hydrochloric acid is 0*00469 at S4'3° (time in minutes) ; as the acid may be regarded as completely dissociated Ch- = 0-0125. Ch- for 1/4 normal acetic acid (z'=4, cf. p. 267) may be calculated from the dilution formula or directly from the equilibrium equation as follows : — [H-][CH3C00'] _ [HT ^ _M1L_= 0-OOOOI6IS [CH3COOH] ~ [CH3COOH] [0-25 - H-] ^' whence Ch- = 0*002. On the assumption that the catalytic effect of acids is propor- tional to the H- ion concentration, the value of the velocity constant, x, for the hydrolysis of cane sugar by 0-25 normal acetic acid at S4"3° should be o'oi25 : o"oo469 : : o"oo2 : x, whence x = 0-00075. This is identical with the result obtained experimentally by Arrhenius, and we have here a very striking confirmation of the electrolytic dissociation theory. From the above considerations, we conclude that the charac- teristic properties which acids have in common, such as sour taste, action on litmus, catalytic activity, property of neutralizing bases, etc., are due to the presence of H- ions. It must be remembered that direct proportionality between H- ion concen- tration and conductivity is neither observed nor to be expected EQUILIBRIUM IN ELECTROLYTES 273 from the theory ; the approximate proportionality is due to the great velocity of the hydrogen ions, and would be altogether absent if the anions were the more rapid. As there is a simple relationship between the H- ion con- centration of weak acids and their dissociation constants (p. 267), it is clear that the behaviour of an acid can be to a great extent foretold when its dissociation constant has been measured. Such determinations have been made for a great number of weak acids by Ostwald and others, and some of the results are given in the accompanying table, which shows very clearly how greatly the value of K differs for different acids, and the influence of substitution : — Acid. Acetic H-CHaCOO Monochloracetic H ■ CHjClCOO Trichloracetic H ■ CI5COO Cyanacetic H • CHaCNCOO Formic H • HCOO Carbonic H ■ HCO, Hydrogen sulphide H ■ SH Hydrocyanic H • CN Phenol H • OCjHb For a weak acid, a= VKw, where a is the degree of dis- sociation at the volume v. Hence, for two acids at the same dilution a/a' = >Jy^IY^, or the ratio of the degrees of dissocia- tion is equal to the square root of the ratio of the dissociation constants. From the data given in the table it can readily be calculated that in solutions of monochloracetic and acetic acid of the same concentration the ratio of the H- ion concentrations is approximately 9 '3 : i. The eifect of replacing one of the hydrogens in acetic acid by chlorine is thus to form a much stronger acid and the CN group has a still greater effect, as the table shows. A further important point is the effect of dilution on the "strength" of an acid. As the degree of dissociation in- creases regularly with dilution, it is evident that the activity of a weak acid will approach nearer and nearer to that of a strong 18 Value of K at 25° (» in litres). O'OOOOlS = 180,000 X lO"'" o"ooi55 — I-2I — 00037 — 0'0002I4 — — 3040 X lo-i" — 570 X lo-i" — 13 X 10-^° — i"3 X lo-i' 2 74 6UTLiNES OF PHYSICAL CHEMISTRY acid (which is completely active in moderate dilution) until finally, when the weak acid is completely ionised, it will have the same strength as the strong acid in equivalent dilution. It follows that the strength of acids is the more nearly equal the more dilute the solution, and that at " infinite dilution " all acids are equally strong. It can readily be calculated from the conductivity tables that the relative strengths of hydrochloric and acetic acids in different dilutions are as follows : — Concentration »/i »/io njioo «/iooo »/io,ooo a for HCl o-8i 0-91 0-97 0-99 fO a for HC2H3O2 0-004 0-013 0-04 0-13 0-4 Ratio HCl/HCaHjiOa 200 70 24 rs 2-S Strength of Bases — Just as the strength of acids depends on their concentration in hydrogen ions, so the strength of bases depends on the concentration in hydroxyl ions. On this view, potassium hydroxide is a strong base, because in moderate dilution it is almost completely ionised according to the equa- tion KOH Ij K- + OH' ; ammonium hydroxide, on the other hand, is a weak base, because its aqueous solution contains only a relatively small concentration of OH' ions. Since certain organic compounds, including amines and alkaloids, have basic properties, their aqueous solutions must also contain OH' ions. Thus, solutions of pyridine, C5H5N, contain not only the free base, buta certain concentration of C5H5N- and OH' ions, in equilibrium with the undissociated hydrate, as represented by the equation CsHeNOH^CgHgN- + OH'. The strength of bases may be determined by distribution or catalytic methods, corresponding with those already described for determining the strength of acids, as well as by conductivity methods. A fairly satisfactory catalytic method is the effect on the rate of condensation of acetone to diacetonyl alcohol,^ represented by the equation 2CH3COCH3 -s>CH3COCH2C{CH3)20H. •Koelichen, Zeitich. Physikal.Chem., igoo, 33, 129. EQUILIBRIUM IN ELECTROLYTES 275 The order of the strength of bases as 'determined by this method agrees with the results of conductivity measurements. Another method, which is not purely catalytic, since the base is used up in the process, is the effect on the hydrolysis or saponification of esters (p. 207). This process is usually represented by the typical equation CH3COOC2H5 + KOH = CH3COOK + C2H5OH. Experience shows, however, that for the so-called strong bases, which are almost completely ionized in moderate dilution, the rate of hydrolysis is practically independent of the nature of the cation (whether K, Na, Li, etc.), a fact which is readily accounted for on the view that the ions exist free in solution, as the ionic theory postulates, and that the OH' ions are alone active in saponification. The general equation for the hy- drolysis of ethyl acetate by bases may, therefore, be written as follows — CH3COOC2H5 f OH' = CH3COO' + C2H5OH. The relative strength of bases, as obtained from their efficiency in saponifying esters, is in excellent agreement with their strength as deduced from conductivity measurements. The ionization view of the saponification of esters is further sup- ported by the fact that the reaction between ethyl acetate and barium hydroxide is bimolecular and not trimolecular, as would be anticipated if it proceeded according to the equation 2CH3COOC2H5 + Ba(OH)j = (CH3COO)2Ba + 2C2H6OH. The alkali and alkaline earth hydroxides are very strong bases, being ionized to about the same extent as hydrochloric acid in equivalent dilution. Bases differ as greatly in strength as do acids ; . the dissociation constants for a few of the more important are given in the table. Base. Ammonia NHj-OH Methylamine CHjNHj-OH 0-00050 Trimethylamine (CHj)3NH*0H 0-000074 Pyridine CsHjN-OH — Aniline CsHjNHj-OH — 4'6 x 10- Value of K (25°) (» in iiires) 276 OUTLINES OF PHYSICAL CHEMISTRY Interesting results have been obtained as to the effect of sub- stitution on the strength of bases. Thus the table shows that the basic character is increased by replacing one of the. hydrogen atoms in ammonia by the CH3 group, but is greatly diminished by the CgHj group. Mixture of two Electrolytes with a Common Ion — The dissociation of weak acids and bases is greatly diminished by the addition of a salt with an ion common to the acid or base. For example, the equilibrium in a solution of acetic acid is re- presented by the equation [H-] [CH3COO'] = K [CH3COOH], and if by adding sodium acetate the CH3COO' ion con- centration is greatly increased, the H- ion concentration must correspondingly diminish, since the concentration of the undis- sociated acid cannot be greatly altered (nearly the whole of the acid being present in that form in the original solution) and therefore the right-hand side of the equation is practically constant. The exact equations representing the mutual influence of electrolytes with a common ion are somewhat complicated, but an approximate formula which is often useful can be obtained as follows : If the total concentration of a binary electrolyte is c and its degree of dissociation is o, we have, from the law of mass action, (i-a).-^- • • • U If now an electrolyte with a common ion is added, and the concentration of the latter is Co, the above equation becomes {ac){ac + Co) ^^ ^ . (2) (l - a)c This equation is quite accurate. As K, c and Co are known, a, where d is the new degree of dissociation, can be calculated, perhaps most readily by successive approximations. If the degree of dissociation of the first electrolyte is small, . I - a' can be taken as unity without appreciable error ; further. EQUILIBRIUM IN ELECTROLYTES 277 if the second electrolyte is highly ionised and is added in con- siderable proportion, aV can be neglected in comparison with Co, and equation (2) simplifies to (aV) Co^Kc . . . . (3) Otherwise expressed, i/ie concentration of one of the ions of a weak electrolyte is inversely proportional to the ionic concentra- tion of a highly-dissociated salt having an ion in common with the other ion of the weak electrolyte. As an illustration of the application of the last equation, we will consider the effect of the addition of an equivalent amount of sodium acetate on the strength of 0-25 molar acetic acid. In this dilution a for the acid is o'oo85 and a/: — o"oo85 x 0^25 = o'oo2i = CyC- In o'25 molar solution, sodium acetate is dissociated to the extent of 69-2 per cent., hence Co = o"25 X o'692 = o'i73. We have, therefore, a' X o'i73 = o'ooooiS, whence a' = o'oooi. aV is therefore 0*25 x o'oooi =o"oooo25= C-^. in presence of o'25 molar sodium acetate, so that the strength of the acid is diminished in the ratio 85 : i. In an exactly similar way, the strength of ammonia as a base is greatly reduced by the addi- tion of ammonium salts. This action of neutral salts on weak bases and acids is largely taken advantage of in analytical chemistry. For example, the concentration of OH' ions in ammonia solution is sufficient to precipitate magnesium hydroxide from solutions of magnesium salts, but in the presence of ammonium chloride the OH' ion concentration is so greatly reduced that precipitation no longer occurs. Similarly, the addition of hydrochloric acid diminishes the concentration of S" ions in hydrogen sulphide to such an extent that zinc salts are no longer precipitated {cf p. 300). Isohydric Solutions — It is of particular interest to inquire what must be the relation between two solutions with a common ion — two acids, for example — in order that, when mixed, they may exert no mutual influence. This problem was investigated 2 78 OUTLINES OF PHYSICAL CHEMISTRY both theoretically and practically by Arrhenius, who showed that no alteration in the degree of dissociation of either of the salts (acids or bases) takes place when the concentration of the common ion in the two solutions before mixing is the same. Such solu- tions are termed isohydric. The relative dilutions in which two acids or other electrolytes with a common ion are isohydric can readily be calculated from their dissociation constants. The value of K for acetic acid is o'ooooiS, and for cyanacetic acid o'oo37, both at 25°. Since IX = sJYjo approximately, it is clear that the degree of dissocia- tion, a, will be the same for the two acids when the dilutions are inversely as the dissociation constants. The dilution of the cyanacetic acid must therefore be 3700 : 18, or 205 times that of acetic acid for isohydric solutions. Arrhenius has shown that by the principle of isohydric solu- tions the mutual influence of electrolytes with a common ion even of strong acids and their neutral salts, can be calculated with a considerable degree of accuracy, but the methods are somewhat complicated and cannot be given here. Not only is the degree of dissociation of a weak acid greatly influenced by the addition of a strong acid, or other electrolyte with a common ion, but the latter is affected, though to a much smaller extent, by the presence of the former. It can, for instance, be calcu- lated that when a mol of acetic acid and a mol of cyanacetic acid are present in a litre of water, the dissociation of the former is only about 1/14 of its value in aqueous solution, whilst the presence of the acetic acid only diminishes the dissociation of the cyanacetic acid by 0-25 per cent. Mixture of Electrolytes with no Common Ion— The equilibrium in a mixture of two electrolytes without a common ion can be calculated when the concentrations and dissociation constants are known, but the calculation is somewhat compli- cated. If solutions of two highly-dissociated salts, such as potassium chloride and sodium bromide, are mixed, small amounts of undissociated sodium chloride and potassium EQUILIBRIUM IN ELECTROLYTES 279 bromide will be formed ; but as the salts are all highly dis- sociated, the mutual effect is very small. If dissociation is complete, the process will be represented by the equation K- + Cr + Na- + Br' = K- + CI' + Na- + Br', otherwise expressed, the salts will exert no mutual influence. These considerations account for the observation of Hess (p. 148) that the thermal effect of mixing dilute solutions of two binary salts is very slight. At the time Hess made his observation, it was extremely puzzling, because it was known that the heats of formation of different salts were very different, and therefore heat should either be absorbed or given out as an accompaniment of the double decomposition. On the basis of the electrolytic dissociation theory, however, Hess's results at once become intelligible, since both before and after admixture the solution contains mainly the same free ions. To the question which is very often asked as to what com- pounds are present in a mixed salt solution, it must therefore be answered that all the undissociated salts and ions are present which can be formed by interaction of the components, and that the proportions in which the various molecules and ions are present depend on the concentrations and dissociation constants of the various salts. Dissociation of Strong Electrolytes ' — It has been pointed out (p. 267) that the law of mass action holds for weak {i.e., slightly ionised) electrolytes, the ions being regarded as inde- pendent units. The proof of the applicability of the law has been brought more particularly by Ostwald from the results of measurements with organic acids. It is a remarkable fact, however, that the dilution formula, a^l(ji — a)v = K, which is a direct consequence of the law of mass action, does not appear to be valid for the so-called " strong " or highly dissociated electrolytes ; when the values of u, obtained from osmotic or conductivity measurements, are substituted in the above formula, >C/. Drucker, "Die Anomalie der starken Elektrolyte," Ahrens' Sammlung, Stuttgart, 1905. 28o OUTLINES OF PHYSICAL CHEMISTRY K diminishes greatly with dilution. This is well shown in the following table for silver nitrate. The first column contains V, the volume in litres in which i mol of the salt is dissolved, in the second column is given the value of a calculated from con- ductivity measurements at 25°, and in the third column are given the values of K calculated by means of the dilution formula. 16 0-8283 °"253 I'll 32 o'8748 o'igi i-i6 64 o'8993 o'i27 i'o6 128 0*9262 0"I22 I'oy 256 0-9467 o'i24 i*o8 512 o'96i9 o"i25 i"o9 The deviations from the simple law appear to be fairly regular in character, and van't Hoff has proposed an empirical formula which represents with a fair degree of accuracy the behaviour of the great majority of strong electrolytes. The formula in question is of the form (l - a)2p - "^1- in which the symbols have the usual significance. The applica- tion of this formula to solutions of silver nitrate is illustrated in the table, and it will be observed that the values of Kj in the fourth column are fairly constant. Van't HofT was led to propose the above formula by a communication from Rudolphi, who suggested the slightly different formula = K, (l - a) Jv for the variation of degree of dissociation with dilution, but Rudolphi's formula is scarcely as satisfactory as that of van't Hoff. Some observers have suggested a generalised form of van't Hoff's formula,' as follows: — a" (l - a) Jv = ^3. ' C/. Bancroft, Zeihch. Physikal Chent-, 1899, 31, 188, EQUILIBRIUM IN ELECTROLYTES 281 and experiment shows that in many cases n does not differ much from 1-5. When « is I'S the general formula reduces to that of van't Hoff. The reason why the law of mass action does not apply to strong electrolytes, although it holds so accurately for weak electrolytes, has not been satisfactorily elucidated. It was long thought that the values of a obtained from the results of con- ductivity measurements were not the true values of the degree of dissociation, but recent very careful comparison shows that the results obtained by conductivity and freezing-point deter- minations in dilute solution for the best-investigated substances do not, as a rule, differ by more than 2 per cent, on the average, and even these differences may be due largely to experimental error.^ In a few cases only does there appear to be a real difference between the results obtained by the two methods. As neither of the values for a gives a constant value for K when substituted in the ordinary dilution formula, there can be no doubt that strong electrolytes do behave in an anomalous way. Several disturbing causes might be suggested to account for this behaviour, including {a) the formation of complex ions by combination of the ions with non-ionised molecules; {b) mutual influence of the ions ; {c) interaction of the ions and the solvent, including more particularly hydration of the ions, and one or more of these effects may be operative in any one solution. The existence of complex ions in solutions has been definitely proved by Hittorf and others. In solutions of cadmium iodide, for instance, there is evidence that I' ions unite with Cdl2 molecules to form complex ions of the formula Cdl^". The formation of complex ions would diminish the number of non-ionised molecules but not the total number of ions ; it would thus affect the osmotic pressure, but not to any extent the con- ductivity. This disturbing effect will be greatest in fairly concen- trated solutions. In dilute solutions of salts of the alkalis and ' Drucker, loc, cit, ; Noyes, Technology Quarterly, 1904, 17, 393. 282 OUTLINES QF PHYSICAL CHEMISTRY alkaline earths, the values of a obtained by conductivity and os- motic pressure methods are very nearly equal, and this result appears to show that there is little or no complex ion formation in these solutions. As to the possible effect of the ions on each other, practically nothing can be said with certainty. The fact that weak electro- lytes follow the law of mass action through a very wide range of dilution may be connected with the fact that under all circumstances the ionic concentration is small, a condition which no longer holds in solutions of strong electrolytes. As to how and to what extent the mutual influence is exerted, little or nothing is known. The possibility of the interaction of the ions with the solvent has been much discussed, but as no general agreement has been reached on the matter, a short reference to the subject here will sufifice. One way in which this effect might influence the results would be if the ions became associated with a large proportion . of water which no longer acted as solvent. The effective con- centrations of an ion would then be the ratio of the amount present to that of the " free " solvent, instead of to the total solvent, as usually calculated. As, however, no satisfactory method of estimating the relative proportions of free and com- bined solvent in the solution of an electrolyte has yet been suggested the question is at present mainly of theoretical interest (P- 325)- The most logical method so far suggested for dealmg with the pro blem of strong electrolytes is due to Nernst. He con^ders that, owing to their mutual influence, the activity of the various substances (ions and non-ionised substances) present is not pro- portional to their respective concentrations, but certain correct- ing factors have to be applied depending on the extent of the mutual influence. Among these effects, that of the ions on each other and on the non-ionised part of the molecules, as well as the mutual influence between ions and solvent, seem to be of special importance, but so far comparatively little progress has been EQUILIBRIUM IN ELECTROLYTES 283 made with the determination of the relative magnitudes of the correcting factors. Electrolytic Dissociation of Water. Heat of Neutral- ization — So far we have regarded the usual solvent water simply as a medium for dissociation, but there is evidence to show that it is itself split up to a very small extent into ions, according to the equation H20^H- + 0H'. Applying to this equation the law of mass action, we have, as usual, [H-][OH'] = K[H,0], where K is the dissociation constant for water. As the ionic concentrations are extremely small the concentration of the water is practically constant, and therefore the product of the concentration of the ions [H-] [OH'] = K„, a constant. It has been found by different methods, which will be re- ferred to later (p. 293), that the value of the above constant at 2 5° is about 1-2 X 10 ^*. In pure water the concentrations of the ions are necessarily equal, hence Ch=Coh'= vi'2 x io"1* = I'l X 10 "' at 25°. Otherwise expressed, this means that pure water contains rather more than i mol of H- and OH' ions, that is, I gram of H" ions and 17 grams of OH' ions, in 10^ or 10,000,000 litres. The ionic product is independent of whether the solution is acid or alkaline, and therefore in a normal solur tion of a (completely dissociated) acid, since Ch- = i, Cqh' is only 10 " 1*, and in a solution of a normal alkali Ch- is corre- spondingly small. These considerations are of great importance in connection with the process of neutralization. Assuming that the solutes are completely ionised, the neutralization of i mol of sodium hydroxide by hydrochloric acid in dilute solution may be repre- sented as follows : — Na -f OH' + H- -f Cr = Na- + CI' + Hp. 284 OUTLINES OF PHYSICAL CHEMISTRY Since Na- and CI' ions occur in equivalent amount on each side, they may be neglected, and the equation reduces to 0H' + H- = H20, or, otherwise expressed, the combination of hydrogen and hydroxyl ions to form water. The same equation applies to the neutralization of any other strong base by a strong acid ; provided that the solutions are so dilute that dissociation is prac- tically complete, the process in all cases consists in the combination of H- and OH' ions to non-ionised water. It may, therefore, be anticipated that for equivalent amounts of different strong bases and acids the heat of neutralization will be the same, and that this is actually the case is shown in the first part of the table. The magnitudes of the heats of neutralization apply for molar quantities. Heats of Neutralization. Acid and Base. Heat of Neutralization. HCl and NaOH 13,700 cal. HBr and NaOH 13,7°° cal. HNO3 and NaOH i3>7°o cal- HCl and JBa(0H)2 13.800 cal. NaOH and CH3COOH 13,400 cal. NaOH and HF 16,300 cal. HCl and ammonia 12,200 cal. HCl and dimethylamine 11,800 cal. The fact that the heat of neutralization of strong acids and bases is independent of the nature of the acid and base was long a puzzle to chemists, and the simple explanation given above is one of the conspicuous triumphs of the electrolytic dissociation theory. Below the dotted line in the above table are given the heats of neutralization of two weak acids by a strong base and of two weak bases by a strong acid. As the table shows, the heat development in these cases may be more or less than 13,700 cal. for molar quantities, and a little consideration affords a plausible explanation. The neutralization of acetic acid, which EQUILIBRIUM IN ELECTROLYTES 285 is very slightly ionised, by sodium hydroxide, may be repre- sented by the equation CH3COOH + Na- + OH' = CH3COO + Na- + H^O, which may be regarded as taking place in two stages — (i) CH3COOH=CH3COO'-i-H-; (2) H--i-0H' = H20. The heat of neutralization is, therefore, the sum of two effects (i) the heat of dissociation of the acid ; (2) the reaction H- + OH' = HjO, which gives out 13,700 cal. Hence, since the observed thermal effect is 13,400 cal. the dissociation of the acid must absorb 300 calories. For hydrofluoric acid, on the other hand, the reaction H- + F' = HF is attended by a heat development of 16,300 — 13,700 = 2,600 cal. We have thus, an approximate method of determining the heat of ionisation of electrolytes, which may be positive or negative. In the above paragraphs the total heat change has been regarded as the algebraic sum of the heats of neutralization and of ionisation, but it is probable that other phenomena, for example, changes of hydration, also play a part. Hydrolysis — It is a well-known fact that salts formed by a weak acid and a strong base, such as potassium cyanide, show an alkaline reaction in aqueous solution, whilst salts formed by the combination of a weak base and a strong acid, for example, ferric chloride, have an acid reaction. In the previous section it has been mentioned that water is slightly ionised, according to the equation H^O = H- -(- OH', and may therefore be re- garded as at the same time a weak acid (since H- ions are present) and a weak base (owing to the presence of OH' ions). It will now be shown that the behaviour of aqueous solutions of such salts as potassium cyanide and ferric chloride are quanti- tatively accounted for on the assumption that water is electro- lytically dissociated. In a previous section (p. 271) it has been pointed out that when two acids are allowed to compete for the same base, the latter distributes itself between the acids in proportion to their 286 OUTLINES OF PHYSICAL CHEMISTRY avidities, and it has also been shown that the ratio of the avidities of two acids is the ratio of the extent to which they are electrolytically dissociated. The same applies to a salt in aqueous solution, water, in virtue of its hydrogen ion concen- tration, being regarded as one of the competing acids. In the case of a salt of a strong acid, such as sodium chloride, it would not be anticipated that such a weak acid as water would take an appreciable amount of the base, and the available experimental evidence quite bears out this expectation. In other words, an aqueous solution of sodium chloride contains only Na- and CI' ions and undissociated sodium chloride in appreciable amount, and is therefore neutral. The case is quite different for a salt formed by a strong base and a weak acid, such as potassium cyanide. Here water as an acid is comparable in strength to hydrocyanic acid, and therefore there is a distribution of the base between the acid and the water according to the equation KCN + Hp^KOH + HCN, the proportions of potassium cyanide and potassium hydroxide depending "upon the relative strengths of water and hydrocyanic acid. From the equation it is evident that potassium hydroxide and hydrocyanic acid must be present in equivalent amount ; and since the hydroxide is much more highly ionised than hydro- cyanic acid, the solution contains an excess of OH' ions, and must therefore be alkaline, as is actually the case. This process is termed hydrolysis, i.e., decomposition by means of water. Similar considerations apply to the salts formed by combination of weak bases and strong acids, such as aniline hydrochloride. As water is comparable in strength to aniline as a base, an equilibrium is established according to the equation CgHgNHjCl + HOH 2 CeHjNHjOH + HCl. In this case there' is an excess pf H* ions, as hydrochloric acid EQUILIBRIUM IN ELECTROLYTES 287 is much more highly ionised than anilinium hydroxide, and therefore the solution has an acid reaction. A salt formed by the combination of a weak acid and a weak base, e.g., aniline acetate, is naturally hydrolysed to a still greater extent. These three types of hydrolytic action will now be considered quantitatively. {a) Hydrolysis of the Salt of a Strong Base and a Weak Acid — A typical salt of this type is potassium cyanide, the hydrolytic decomposition of which is represented by the equation KCN + HOH ^ KOH + HCN, or, according to the electrolytic dissociation theory, K- + CN' + HOH^tK- + OH' + HCN, on the assumption, which is only approximately true, that potassium cyanide is completely ionised and hydrocyanic acid non-ionised. The equilibrium can now be investigated, and the extent of the hydrolysis determined, if a means can be found of deter- mining the equilibrium concentration of one of the reacting substances, for example, the OH' ions. This could not, of course, be done by titrating the free alkali, as the equilibrium would thus be disturbed, but one of the methods given on p.271 may conveniently be used. The method which has been most largely used is to determine the effect of the mixture on the rate of saponification of methyl acetate, which, as has already been pointed out, is proportional to the OH' ion con- centration. The amount of hydrolysis per cent., looa;, for different concentrations, c, of potassium cyanide (mols per litre) at 25", determined by the above method, is as follows : — c 0-947 0-235 0-095 0-024 1 00a; . 0-31 0-72 I-I2 2-34 K„ . 09 1-2 1-2 1-3 X 10—5 The table shows that, as is to be expected, the degree of hydrolysis increases with dilution. 288 OUTLINES OF PHYSICAL CHEMISTRY A general equation, by means of which the equilibrium con- dition can be calculated when the acid and base are not neces- sarily present in equivalent proportions, can readily be obtained by applying the law of mass action to the general equation B- -f A' -h Hp^B- -1- OH' -1- HA, where B- and A' represent the positive and negative ions respec- tively. As B' occurs on both sides of the above equation, the latter can be simplified to A' -t- H^O ^ OH' + HA. As the salt and the base are practically completely ionised, and the acid is not appreciably ionised. A' and OH' are proportional to the concentrations of salt and base respectively, and HA to that of the acid. Hence, from the law of mass action, [OH'] [HA] _ [base][acid] ^ A' " [unhydrol. salt] * " " ^ ' a constant, as the concentration of the water may be regarded as constant. K& is termed the hydrolysis constant, and, like the ordinary equilibrium constant, is independent of the relative concentrations of the substances present at equilibrium, but de- pends on the temperature. In order to illustrate the use of the above formula, the values of K;, may be calculated from the data for potassium cyanide already quoted. In o'ogs molar solution, potassium cyanide is hydrolysed to the extent of I'lz per cent., hence ^ o-OQS X I-I2 , Cacid = — = 0-001064, ■^base — ^acid 100 and Csait = o"o9S - o'ooio64 = 0-094. „ (o-ooio64)(o-ooio64) _, Hence Ka = ^ ^^V; = I'a x ro ^. o 094 The values of the hydrolysis constant, calculated from the other observations, are given in the table, and are approxi- mately constant, thus confirming the above formula. Con- versely, when from one set of observations the value of EQUILIBRIUM IN ELECTROLYTES 289 Kfc has been obtained, the degree of hydrolysis at any other dilution can be obtained by substitution in the general formula. For convenience of calculation, the simple formula in which the acid and base are present in equivalent proportions, may be written in the form = Kft . . . . (la) (i - x)v in which x represents the proportion of acid and base formed by hydrolysis from i mol of the salt and v is the dilution. This form of the equation shows at a glance that the degree of hydrolysis, that is, the value of*, increases with dilution. More- over, from the great similarity of the formula (la) to the dilution formula, it is evident that when the hydrolysis is small it is greatly diminished by the addition of a strong base, just as the degree of dissociation of acetic acid is greatly diminished by the addition of an acetate. The quantitative relation between the hydrolysis constant, Ki, and the dissociation constants for the weak acid and water respectively may be obtained as follows : The electrolytic dis- sociation of the acid, HA, is represented by the equation [H-][A'] = K, [HA] . . . . (2) where Ka is the dissociation constant of the acid. In the solution there is the other equilibrium [H'] [OH'] = K„ (3) where Ka, is the ionic product for water. Dividing equation (3) by equation (2) we obtain [OH'] [HA] K, A' ~ K« (4) The left-hand side of the above equation is simply equation (i) for the hydrolytic equilibrium (p. 288), hence [base] [acid] _ ^ _ K^ . [unhydrol. salt] ~ '" ~ K^ " " ' ^3} that is, t^ hydrolysis constant Kh is the ratio of the ionic product Kw for water to the dissociation constant of the acid, 19 2 90 OUTLINES OF PHYSICAL CHEMISTRY It has already been deduced from general principles (p. 286) that the hydrolysis is the greater the more nearly the strength of water as an acid approaches that of the competing acid, and the above important result is the mathematical formulation of that statement. In order to illustrate this point more fully, the degree of hydrolysis of a few salts in i/io molar solution at 25° is given in the accompanying table. Salt. Degree of hydrolysis. Sodium carbonate . . . 3- 17 per cent. Sodium phenolate . . . 3 05 „ Potassium cyanide . . . 1-12 „ Borax ..... 0-05 „ Sodium acetate .... o-oo8 „ The numbers illustrate in a very striking way the fact that only the salts of very weak acids are appreciably hydrolysed. Thus although acetic acid is a fairly weak acid (K=i'8x 10"^), sodium acetate is only hydrolysed to the extent of o'ooS per cent, at 25°, and even potassium cyanide is only hydrolysed to the amount of about i per cent, in i/io normal solution, although the dissociation constant of the acid is only i'3 x lo"^. A com- parison of the above table with the dissociation constants of the acids (p. 273) is very instructive. From the known values of K^ and Ka, for hydrocyanic acid and water respectively at 25°, we have Ku, f2 X lo-i* . ^ — -= ^g-= 0-9 X 10-6 = Kh, Ka 1-3 X 10 ' m very satisfactory agreement with the observed value of I'l x 10"* (p. 288). As a matter of fact, however, it is easier to deter- mine the hydrolysis constant than the dissociation constant for a very weak acid, and therefore the latter is often calculated from the observed value of the hydrolysis constant by means of the above formula. K, . (I) EQUILIBRIUM IN ELECTROLYTES 291 {b) Hydrolysis of the Salt of a Weak Base and a Strong Acid — The same considerations apply in this case as for the salt of a strong base and a weak acid. The general equation for the equilibrium is of the form B- + A' + HjO ^ BOH + H- + A' which simplifies to B+H20^B0H + H-. Applying the law of mass action, we obtain [BOH][H-] [base] [acid] B" [unhydrol. salt] exactly the same equation as is applicable to the hydrolysis of he salt of a strong base and a weak acid. Further, it may be shown, by a method exactly analogous to that employed in the previous section, that in this case Kfe =^ .... (2) that is, tke hydrolysis constant ^ufof the salt of a weak base and a strong acid is the ratio of the ionic product for water. Km, and the dissociation constant of the base, Kj. A typical case is the hydrolysis of urea hydrochloride, ^ which may be represented thus — CON2H5 + CI' + Hp^CON^HjOH + H- + Ci: It is clear that the degree of hydrolysis can at once be obtained when the H* ion concentration in the solution has been deter- mined, and for this purpose any of the methods previously described can be employed (p. 275), such as the effect on the rate of hydrolytic decomposition of cane sugar or of methyl acetate or by electrical conductivity measurements. In the experiments quoted in the table, gradually increasing amounts of urea were added to normal hydrochloric acid, and the H- ion concentration deduced from a comparison of the velocity constant for the hydrolysis of cane sugar in the presence of the free acid {k^, and with the addition of urea (li). 1 Walker, Proc. Roy. Soc. (Edin.), 1894, 18, 255. 292 OUTLINES OF PHYSICAL CHEMISTRY Normal hydrochloric acid + c normal urea. c. A. kjko = free HCl. I - k/ko = salt formed. C-l + kjko = free urea. Kh. o 0-00315 = ~ ko I — — — 0-S 0-00237 0753 0-247 °'2S3 0-77 i"o o'ooi84 ^ 0-585 o'4i5 °'S85 0-82 2'0 o"ooii4 0-36 0-64 1-36 0-77 4-0 o'ooo6 o'lg 0-81 3-19 075 On the assumption that the rate of hydrolytic decomposition is proportional to the H- ion concentration, k/ko represents the concentration of the "free" hydrochloric acid, and (i - k/ka) that of the bound acid, which is, of course, that of the unhydro- lysed salt. The concentration of the free urea, that is, of the hydrolysed salt, is therefore c - (i + klk^). Substituting in the general formula — [base] [acid] [f - ( i + /6/^o)] [>^/>^ J [unhydrol. salt] i - k/ko ~ '" The values of the hydrolysis constant are given in the sixth column of the table, and are approximately constant, as the theory requires. The degree of hydrolysis of a few salts of weak bases and strong acids in i/io molar solution at 25° is given in the table, and the results should be compared with the values for the dissociation constants of weak bases (p. 275) in order to illustrate equation (2). Salt. Degree of hydrolysis. Ammonium chloride . . . 0-005 P^f cent. Aniline hydrochloride . . . i -5 „ „ Thiazol hydrochloride . . -19 „ „ Glycocoll hydrochloride . . 20 „ „ Hydrolysis of the Salt of a Weak Base and a Weak Acid — The hydrolysis of aniline acetate, a typical salt of this class, is represented by the equation CgHgNHj - CH3COO + HOH^iCgHsNHgOH + CH3COOH, EQUILIBRIUM IN ELECTROLYTES .293 which, on the assumption that the salt is completely, the base and acid not at all, ionised, may be written as follows — CgHgNHg- + CH3COO' + HOH^tCgHjNHs- OH + CH3COOH. Applying the law of mass action, and using the former symbols, [BOH] [HA] [base][acid] ^ [B-][A-] ~ [unhydrol. sak]^ ~ *' If we express the amounts (in mols) of the base, acid and salt respectively in volume v of the solution by b, a and s respectively, the above equation becomes b\ \v/\vj ab „ = ^ = K,, ©" that is, the degree of hydrolysis of the salt of a weak base and a weak acid is independent of the dilution. Experiment shows that in dilutions of 12 '5 and 800 litres, aniline acetate is hydrolysed to the extent of 45-4 and 43 -i per cent, respectively ; the slight deviation from the requirements of the theory is doubtless due to the fact that the assumptions made in deducing the above formula are only approximately true. Determination of the Dissociation Constant for Water — -It has been shown above that the process of hydrolysis in the case of a salt of a strong base and a weak acid may be looked upon as a distribution of the base between the weak acid and water acting as an acid, and the degree of hydrolysis therefore depends on the relative strengths of the weak acid and water. The relationship between these three factors is expressed by the equation [acid] [base] _ -^ _ ^w [unhydrol. salt] ~ * ~ KT where K^ is the hydrolysis constant, K^ the dissociation con- stant for the acid, and Ka, the ionic product for water. It is clear that if the degree of hydrolysis of a salt and the dissocia- tion constant of the acid are known, K,„ can be calculated, and 2 94 OUTLINES OF PHYSICAL CHEMISTRY this is one of the most accurate methods for determining the degree of dissociation of water. As an illustration, we may calculate Ka, from Shields's value for the hydrolysis of sodium acetate — o-oo8 per cent, in o"i molar solution at 25° (Arrhenius, Feb., 1893). We have Cacid = Cbase = O'OOOoS X OT, Csait = o'l (the amount hydrolysed being negligible in comparison). (o-oooo8 X o-i)2 -a V Hence = o*64 x 10 " = K^. O'l NowKa, = KAKa=(o-64X io-9)x(i-8x io-s) = i-i6x lo-i*. Since [H-][OH'] is thus found to be approximately i"2 x io~i*, the concentration of H- or OH' ions (mols per litre) in water at 25° is i"i x 10"^. Km can also be calculated from measurements of the hydro- lysis of salts of strong acids and weak bases, and, perhaps with still greater accuracy, . from measurements with salts of weak acids and weak bases.^ The degree of dissociation of water has been determined by three other methods at 25° with the following results : — E.M.F. of hydrogen-oxygen cell (Ostwald, January, 1893) (corrected value), i"o x 10 " '^ at 25°. Velocity of hydrolysis of methyl acetate (Van't Hoff- Wijs, March, 1893), 1-2 x 10 " ' at 25°. Conductivity of purest water (Kohlrausch, 1894), i'o5 X 10 " ' at 25°. When it is borne in mind how small the dissociation is, the close agreement in the values obtained by these four inde- pendent methods is very striking, and forms a strong justifica- tion for the original assumption that water is split up to an extremely small extent into ions. The question can be still further tested by applying van't 1 Lunden, jf. Chim. Phys., 1907, 5, 574 ; Kanolt, J. Amer. Chem. Soc, 1907, 29 1402. For salts of weak bases and weak acids the formula Ka= [Ka Ki>]/Ka, applies. EQUILIBRIUM IN ELECTROLYTES 295 Hoff s equation connecting heat development and displacement of equilibrium to the equilibrium between water and its ions. For the degree of dissociation at different temperatures, the following values were obtained by Kohlrausch from conduc- tivity measurements : — Temperature . . 0° 2° 10° 15° 26° 34° 42° 50° Degree of dissociation o"35 0-39 0-56 0-8 i-og f47 i'93 2-48 x 10-' From any two of these measurements the heat development, Q, of the reaction, H- + OH'^^HjO, can be calculated by sub- stitution in the general formula (p. 167). log.oK. - log,oK, = -^ (I^) From the values ^ of K at 0° and 50°, Q = 13,740 cal., and from that at 2° and 42°, Q = 13,780 cal. In a previous section (p. 284) it has been pointed out that, according to the electrolyte dissociation theory, the neutraliza- tion of a strong base by a strong acid consists essentially in the combination of H' and OH' ions to form water. The heat given out in the reaction is about 13,700 cal. for molar quanti- ties, in excellent agreement with the above value. This sup- ports the assumption that the variation of the conductivity of pure water with dilution is due to the displacement of the equilibrium H -t- OH' ^HjO, in the direction indicated by the lower arrow. The value of Q, obtained directly as above, may be termed the Aeat of ionisation of water ; it is the heat given out when i mol of H- and OH' ions combine to form water. The heat of ionisation of any electrolyte can naturally be calculated in the same way from the displacement of the equili- brium with temperature. The effect of increased temperature on the degree of ionisation is almost always slight, and in the majority of cases the ionisation is slightly diminished. As an illustration, the degree of electrolytic dissociation for i/io molar sodium chloride over a wide range of temperature, as deter- 1 K, = (2-48 X io-')2 at 50°; Ki = (0-35 X io-')2 at 0° (p. 283). 296 OUTLINES OF PHYSICAL CHEMISTRY mined by Noyes and Coolidge,i may be quoted. The values obtained were 84 per cent, at 18°, 79 per cent, at 140°, 74 per cent, at 218°, 67 per cent, at 281°, and 60 per cent, at 306°. Corresponding with the small variation in the degree of ionisa- tion with temperature, the heat of ionisation is small, and may be positive (as in the present case) or negative. Theory of Indicators — The indicators used in acidimetry and alkalimetry have the property of giving different colours depending on whether the solution is acid or alkaline. Ac- cording to Ostwald's theory, which has met with fairly general acceptance, such indicators, including methyl-orange, phenol- phthalein and /-nilrophenol, are weak electrolytes, and their use depends on the fact that the ions and the non-ionised com- pounds have different colours. Since salts are almost always highly ionised, it is clear that only weak acids and bases can be employed as indicators. Phenolphthalein is a very weak acid, the non-ionised acid is colourless, and the negative ion red. In aqueous solution it is ionised according to the equation HP ^ H- -I- P' (red) (where P' is the negative ion), but so slightly that the solution is practically colourless. If now sodium hydroxide is added, the highly-dissociated sodium salt is formed, and the solution is deeply coloured owing to the presence of the red anion, P'. If, on the other hand, the solution contains a slight excess of acid, the increased H- ion concentration drives back the ioni- sation of the phenolphthalein in the direction indicated by the lower arrow, and the solution becomes colourless {cf. p. 277). Finally, if a weak base, such as ammonium hydroxide, is added, the ammonium salt will be partly hydrolysed, according to the equation NH^P -)- HOH^NH^OH + HP, and excess of the base will be required in order to drive back 1 Zeitsch. Physikal Chem., 1904, 46, 323. EQUILIBRIUM IN ELECTROLYTES 29'/ the hydrolysis (p. 289) ; in other words, there will not be a sharp change of colour when ammonium hydroxide is added. Methyl-orange is an acid of medium strength, the non-ionised acid is red, the negative ion yellow. As the acid is ionised in aqueous solution to some extent, according to the equation HM (red) :^ H' + M' (yellow), the solution shows a mixed colour. The effect of the addition of acids and alkalis is similar to that on phenolphthalein, and only differs in degree. Since the aqueous solution already con- tains a considerable proportion of H- ions, it is evident, from the considerations advanced on p. 276, that a considerable excess will be required to drive back the dissociation in the direction indicated by the lower arrow, so as to turn the solu- tion red. The proportion of H" ions in such a weak acid as acetic acid is not sufficient for this purpose, and therefore methyl-orange should not be employed as an indicator for weak acids. It is, on the other hand, a suitable indicator for weak bases, such as ammonia, as the salt formed is much less hydrolysed than the corresponding phenolphthalein salt, and therefore the change of colour is sharper. Basic indicators are not in use. The considerations to be borne in mind in selecting an indicator, or in choosing a suitable alkali for titrating an acid, or vice versd, may be put concisely as follows (Abegg) : — Solutions used. Indicator. Examples. Acid. Base. Strong Strong Weak Weak Strong Weak Strong Weak Any Strong acid Weak acid None satisfactory Any Methyl-orange, /-nitrophenol Phenolphthalein, litmus Should be avoided Some investigators maintain that the ionisation theory does not give a satisfactory representation of the behaviour of indi- 298 OUTLINES OF PHYSICAL CHEMISTRY cators, but that the changes of colour are due to changes of constitution, usually from the benzenoid to the quinonoid t)rpe and vice versa} In an aqueous solution of phenolphthalein, for instance, there are only traces of the quinonoid (coloured) modifi- cation, and the solution is colourless, but on the addition of alkali the phenolphthalein salt is formed, the negative ions of which, being of the quinonoid type, are strongly coloured. The Solnbility Prodnct — We have now to consider an equilibrium of rather a different type — in which the solution is saturated with regard to the electrolyte. In such a case there is equilibrium between the solid salt and the non-ionised salt in the solution, so that the concentration of the non-ionised salt remains constant at constant temperature. Further, there is equilibrium in the solution between the non-ionised salt and its ions, which may be represented, in the case of silver chloride, for example, by the equation Ag' -1- Cl'^AgCl. Applying the law of mass action, we have, for the latter equilibrium, [Ag-][C1'] = K[AgCl] = S, where S is the product of the concentrations of the two ions — the so-called solubility product — and is constant, since the right-hand side of the above equation is constant. The equi- libria in the heterogeneous system may be represented as follows : — Ag- + CI' 2 AgCl (in solution) \ \ AgCl (solid). As will be shown later, the solubility product for silver chloride at 25° is I '56 X 10-1°, when the ionic concentrations are ex- pressed in mols per litre. If the solution has been prepared by dissolving the salt in water, the ions are necessarily present in equivalent proportions, so that a solution of silver chloride, saturated at 25°, contains \/i'S6 x lo"!" = i'25 x lo"' mols of Ag- and of CI' ions. The ions need not, however, be present in equivalent propor- ' C/. Hewitt, Analyst, 1908, 33, 85. EQUILIBRIUM IN ELECTROLYTES 299 tions ; if by any means the solubility product is exceeded, for example, by adding a salt with an ion in common with the electrolyte, the ions unite to form undissociated salt, which falls out of solution, and this goes on till the normal value of the solubility product is reached. Perhaps the best-known illustra- tion of this is the precipitation of sodium chloride from its saturated solution by passing in gaseous hydrogen chloride. In this case the origmal equilibrium between equivalent amounts of Na- and CI' ions is disturbed by the addition of a large excess of CI' ions, and sodium chloride is precipitated till the original solubility product is regained, when the solution con- tains an excess of CI' ions and relatively few Na- ions. As already mentioned, the difference between the present form of equilibrium and those previously considered is that the concentration of the non-ionised salt in the solution is constant at constant temperature. If it is diminished in any way, salt is dissolved till the original value is reached ; if it is exceeded, as in the case just mentioned, salt falls out of solution till the original value is reached. Since the equilibrium equation for a binary salt is symmetrical with regard to the two ions, it follows that the solubility of such a salt should be depressed to the same extent by the addition of equivalent amounts of its common ions, whether positive or negative. This consequence of the theory was tested by Noyes, who determined the influence of the addition of equivalent amounts of hydrochloric acid and of thallous nitrate on the solubility of thallous chloride, with the following results : — Solubility of thallous chloride at 25° : — Concentration of Substance added (mols per litre). TINO, added. HCl added. 0-0283 0-147 0-0161 0-0084 0-0032 o-oi6i 0*0083 0-0033 300 OUTLINES OF PHYSICAL CHEMISTRY The figures in the first column show the amounts of thallous nitrate and of hydrochloric acid added, those in the second and third columns represent the solubility of thallous chloride in mols per litre. The results show that the requirements of the theory are satisfactorily fulfilled. The above results hold independently of the relative amounts of ions and non-ionised salt in the solution. Since in dilute solution all salts are highly ionised, it may, however, be as- sumed that difficultly soluble salts, such as silver chloride, are almost completely ionised in solution ; in other words, the con- centration of non-ionised salt in solution may be regarded as negligible in comparison with that of the ions. This deduction is of great importance in estimating the solubility of difficultly soluble salts (see next page). Applications to Analytical Chemistry — The above con- siderations with regard to the solubility product are of the greatest importance for analytical chemistry. A precipitate can only be formed when the product of the ionic concentrations attains the value of the solubility product, which for every salt has a definite value depending only on the temperature. For example, magnesium hydroxide is precipitated from solutions of magnesium salts by ammonia because the solubility product [Mg"] [OH'] 2 is exceeded. When, however, ammonium chloride is previously added in excess to the hydroxide, the OH' ion concentration is diminished to such an extent (p. 277) that the solubility product is not reached, and precipitation no longer occurs. Similarly, zinc sulphide is precipitated when the product [Zn"][S"] exceeds a certain value. _ In alkaline solu- tion, an extremely small concentration of hydrogen sulphide suffices for this purpose, as the sulphide is considerably ionised, but in acid solution the depression of the ionisation of the hydrogen sulphide, in other words, the diminution in the con- centration of S" ions, is so great that the solubility product is not reached. On the other hand, the solubility product for certain heavy metals, such as lead, copper, and bismuth, is so EQUILIBRIUM IN ELECTROLYTES 301 small that it is reached even in acid solution. It is, however, possible to increase the acid concentration (and therefore to diminish the S" ion concentration) to such an extent that the ionic product is not reached even for some of the above metals, for example, lead sulphide in concentrated hydrochloric acid is not precipitated by a current of hydrogen sulphide. On the same basis, a fact which has long been familiar in quantitative analysis, that precipitation is more complete when excess of the precipitant is added, can readily be accounted for. A saturated aqueous solution of silver chloride contains about i"25 X 10"* gram equivalents of the salt per litre, and the ad- dition of ten times that concentration of CI' ions (added in the form of sodium chloride) will diminish the amount of silver in solution to about i/io of its original value (on the assumption that the concentration of the non-ionised salt is negligible in comparison with that of the ions) {cf. p. 277). It is thus evident that in the gravimetric estimation of combined chlorine as silver chloride there might be considerable error owing to the solubility of silver chloride in water, but if a fair excess of the precipitant is used, the error is quite negligible. The concentration in saturated solution at 25°, and the solubility product of a few difficultly soluble salts are given in the accompanying table. Salt. Saturation Concentration Solubility Product (mols per litre). (mols per litre). Silver chloride Ag- = 1-25 X 10"^ 1-56 X lo-io „ bromide „ = 6'6 X 10"' 4-35 X 10-13 „ iodide „ = fo X 10"^ i-o X io~i^ Thallous chloride Tl- = i-6 x lo-^ 2*6 X 10- * Cuprous chloride Cu' = i"i x 10"' 1-2 X IQ- * Lead sulphide Pb" = 5-1 X IO"8 26 X 10- 15 Copper sulphide Cu" = i-i X 10-21 I'2 X I0-*2 Experimental Determination of the Solubility of Diffi- cultly Soluble Salts — When a saturated solution of a rela- 302 OUTLINES OF PHYSICAL CHEMISTRY lively insoluble salt is so dilute that complete ionisation may be assumed (/*„ = /j.^ ), the solubility of the salt may readily be obtained from electrical conductivity measurements. The molecular conductivity at infinite dilution, /x^ , can be obtained indirectly (p. 258), the specific conductivity of the saturated solution is determined in the usual way, and, by substitution in the formula figr^ = kv, we obtain the value of v, that is, the volume in c.c, in which a mol of the substance is dissolved. If the solubility is required in mols per litre, then V = 1000 V, and /i, ijg = 1000 kV, where V is the volume in litres in which a mol of the sub- stance is dissolved. As the specific conductivity of such a solution is small, the conductivity of the water becomes of importance, and it is necessary to subtract from the observed specific conductivity of the solution the conductivity of the water, determined directly. For such measurements, " con- ductivity " water, of a specific resistance not much less than 10^ ohms, should be used. As an example of the determination of solubilities by this method, Bottger found that a solution of silver chloride saturated at 20° had k = i'33 x 10 ~® after subtracting the specific con- ductivity of the water. Hence, as fx,ao for silver chloride at 20°, determined indirectly (p. 258), is 125-5, we obtain, by substitu- tion in the above formula, i25'5=iooo X i"33 X io~'V, and V = 5-J = 94,400, 1-33 X 10-5 that is, 94,400 litres of a solution of silver chloride, saturated at 20°, contain i mol of the salt. In one litre of solution there is, therefore, 1/94,400 = i'o6 x 10 " ^ mol, or 0-00152 grams of silver chloride. The values for the solubility of a number of difficultly soluble salts obtained by this method are given in the previous section (p. 301). EQUILIBRIUM IN ELECTROLYTES 303 Complex Ions — Complex ions have already been defined as being formed by association of ions with non-ionised molecules It is well known that though silver halogen salts are only slightly soluble in water they are readily soluble in the presence of ammonia. This phenomenon is due to the formation of complex ions (p. 281), in which the Ag- ions are associated with ammonia molecules, forming univalent ions of the type Ag(NH3)i.. As nearly all the silver is present in this form and very little in the form of Ag- ions, it is evident that a solution may contain a very considerable amount of a silver salt before the solubility product [Ag*] [X'] is reached. The determination of the exact composition of the complex ions in a solution is sometimes a matter of difficulty, but the law of mass action is often of great assistance in this respect. If, for example, the solution of a silver salt in ammonia contains mainly complex ions of the formula Ag(NH3)-, there must be an equilibrium represented by the equation Ag(NH3)j^ Ag- + 2NHg, and by the law of mass action the expression ^ . IL^ ^^ must be constant. To test this point AgCNHg)- the concentrations of the ammonia and of the silver ions were systematically varied, and it was found that the above expres- sion remained constant, thus showing that the assumption as to the composition of the complex ions is correct. The azure blue solutions obtained by adding ammonia in excess to solu- tions of cupric salts appear from the results of distribution (p. 1 78) and optical measurements to contain the copper exclusively as Cu(NH3)^" ions. The solutions obtained by the action of ammonia on cobalt and chromium salts have been thoroughly investigated by Werner : ' they contain complex ions of the formulae CofNHg)^- and Cr(NH3)„-. Other compounds besides ammonia can become associated with positive ions to form complex cations. For example, Werner has shown that the ammonia groups in the com- plex cobalt ions mentioned above can be successively dis- 1 Summary, Anorganische Chemie, 2nd edition, Brunswick, igog. 304 OUTLINES OF PHYSICAL CHEMISTRY placed by water molecules, forming compounds of the type [Co(NH3)5Hp]-, [Co(NH3),(H,0),]- . . . and finally [Co(H,0)6]- It is probable that in the aqueous solutions of many salts com- plex ions containing water are present. Complex anions, formed by the association of negative ions with neutral molecules, are also known. Solutions of cadmium iodide contain Cdl^" ions (p. 281), and the solution obtained by the addition of excess of potassium cyanide to solutions of silver salts contains potassium silver cyanide, KAg(CN)2, which is largely ionised according to the equation KAg(CN),:^K' + Ag(CNV. Influence of Substitution on Degree of lonisation — Reference has already been made to the influence of substitu- tion on the strength of acids. As the effect of substitution on the degree of ionisation has been most extensively investigated for this class of compound, a few further examples may be given. In the accompanying table, the affinity or dissociation constants for some mono-substituted acetic acids are given, the value of K holding for 25" (concentrations in mols per litre). Acetic acid CHgCOOjH .... o -000018 Propionic acid CHgCHjCOO'H . . o'ooooi3 Chloroacetic acid CHjClCOO'H . . o-ooiss Bromoacetic acid CHjBrCOO'H . . o'ooi38 Cyanacetic acid CHjCNCOO'H , . 0-00370 Glycollic acid CHjOHCOO-H . . 0000152 Phenylacetic acid CgHgCHjCOO-H . 0000056 Amidoacetic acid CHjN H5COO -H . 3 -4 x i o - 1» As the carboxyl group only is concerned directly in ionisation, the above table affords an excellent illustration of the influence of a group on a neighbouring one. The table shows that when one of the alkyl hydrogens in acetic acid is displaced by CI, Br, CN or OH ox QH^ an increase in the activity of the Equilibrium in electrolytes 305 acid is brought about ; the effect is least for the phenyl group and greatest for the cyanogen group. On the other hand, the methyl group (in propionic acid) diminishes the activity slightly, and the amido group diminishes it enormously. These observations can readily be accounted for^ on the assumption that the atoms or groups take their ion-forming character into combination. Thus the CI, Br, CN and OH groups, which tend to form negative ions, increase the tendency of the groups into which they enter to form negative ions. The " negative favouring " character of the phenyl group is slight but distinct. On the other hand, the so-called basic groups, such as NHg, lessen the tendency of the group into which they enter to form negative ions, as is very strikingly shown in the case of amidoacetic acid. The methyl group has also a slight diminishing effect on the tendency of a group to form negative ions. The magnitude of the influence of a substituent on a particu- lar group depends on its distance from that group. This is very well shown by the influence of the hydroxyl group on the affinity constant of propionic acid. Propionic acid CHgCHgCOO'H . . . o'ooooi34 Lactic acid CH3CHOHCOOH . 0000138 ^-oxypropionic acid CHjOHCHgCOO'H . 0-0000311 When the OH group is in the a (neighbouring) position its effect on the dissociation constant is more than four times as great as when it is in the j8 position. It seems plausible to suppose that a comparison of the influence of groups in the ortho, meta and fara positions on the carboxyl group of benzoic acid might throw some light on the question of the relative distances between the groups in the benzene nucleus. The dissociation constants of benzoic acid and the three chlor-substituted acids are as follows: — ' A complete theory of the phenomena in question has recently been worked out by Fliirscheim (Trans. Chem. Soc, igog, 95, 718 ; Proc, igog, 193). 20 3o6 OUTLINES OF PHYSICAL CHEMISTRY Benzoic acid CgH^COOH . . . o'oooo6o o- Chlorobenzoic acid CgH^ClCOOH . . 0-00132 ^- » ,1 „ . . o'oooi55 /- >i >> ,, . . 0*000093 It will be observed that the presence of the halogen in the ortho position greatly increases the strength of the acid, and it is a general rule that the influence of substituents is always greatest in this position. The effect of substituting groups in the meta and para positions is much smaller, and the order of the two is not always the same. As the table shows, w-chlorobenzoic acid is rather stronger than the para acid, but on the other hand /-nitrobenzoic acid is somewhat stronger than the meia acid. Similar considerations apply to the influence of substituents on the strength of bases, but, as is to be expected, the effect of the various groups is exerted in the opposite direction to that on acids. Thus the displacement of a hydrogen atom in ammonium hydroxide by the methyl group gives a stronger base (methyl amine) but the entrance of a phenyl group gives a much weaker base (aniline) {c/. p. 275). Reactivity of the Ions— It is a well-known fact in qualita- tive analysis that in the great majority of cases the positive component of a salt {e.g., the metal) answers certain tests, quite independently of the nature of the acid with which it is combined, and in the same way acids have certain characteristic reactions, independent of the nature of the base present. These facts are plausibly accounted for on the electrolytic dissociation theory by assuming that the positive and negative parts of the salts (the ions) exist to a great extent independently in solution, and that the well-known tests for acids and bases are really tests for the free ions. Thus silver nitrate is not a general test for chlorine in combination, but only for chlorine ions. It is well known that potassium chlorate gives no precipitate with silver nitrate, although it contains chlorine ; this is readily accounted for on the electrolytic dissociation theory because the solution of the salt contains no CI' ions, but only CIO3' ions, which give EQUILIBRIUM IN ELECTROLYTE!:. 3°? their own characteristic reactions. These views appear still more plausible when cases are considered in which the usual tests fail, for example, mercuric cyanide does not give all the ordinary reactions for mercury. This could be accounted foi by supposing that the compound is not appreciably ionised in solution, so that practically no Hg" ions are present, and as a matter of fact the aqueous solution of mercuric cyanide is practically a non-conductor. The chief characteristic of ionic reactions is their great rapidity ; they are for all practical purposes instantaneous, and it is doubt- ful if the speed of a purely ionic reaction has so far been measured. It is well known that silver nitrate reacts with the chlorine in organic compounds such as ethyl chloride and chlor- acetic acid, but very slowly as compared with its action on sodium chloride. There is good reason for supposmg that the reactions last mentioned are not ionic actions, but that the changes take place between the silver salt and combined chlorine. The great reactivity of the ions in cases where it is known that they are actually present has led Euler and others to postulate that all reactions are ionic, and that in very slow reactions we are dealing with excessively small ionic concen- trations. ^ This question cannot be adequately considered here, but it may be mentioned that the available experimental evi- dence does not seem to lend any support to Euler's theory. There is good reason to suppose that chemical reactions may take place between non-ionised molecules as well as between ions. Practical Illustrations. Dilution Law. Conductivity of Acids and Salts — Many of the results discussed in this chapter can be conveniently illustrated by means of the apparatus ^ shown in Fig. 36. The glass vessels each contain two circular electrodes of platinized platinum, the lower one is connected with a wire which passes through the bottom of the vessel and is connected through a lamp to the wire E. The upper electrode, which is movable, is connected to a wire which ' Compare Arrhenius, Electrochemistry (English Edition), p. 180. ^Noyes and Blanchard, J. Amer. Chem. Soc, 1900, 22, 726. 3o8 OUTLINES OF PHYSICAL CHEMISTRY passes through the cork loosely closing the vessel, and is connected to the upper wire F. The electrodes in each vessel should be of approximately the same cross-section, and the four lamps of equal resistance. The wires E and F are connected to the terminals of a source of alternating current, and as they are at constant potential throughout, the fall of potential through each of the vessels from E to F must be the same when a current is passing. ^ C vy vy ^^ Fio. 36. The use of the arrangement may be illustrated by employing it to prove the dilution law in the form u. = ,Jkv. Solutions of monochloracetic acid containing i mol of the salt in i, 4 and 16 litres respectively are prepared, and the vessels A, B and C nearly filled with them. When connection is made with the alternating current, it will be found that the brightness of the lamps is very different, but the positions of the upper electrodes can be so adjusted that the lamps are equally bright. Under EQUILIBRIUM IN ELECTROLYTES 309 these circumstances it is evident that the resistance of each solution is the same. On measuring the distances between the electrodes, it will be found that for the solutions w = i, » = 4, V = 16, the distances are in the ratio 4:2:1. Hence, as the conductivities are inversely proportional to the distances between the electrodes, aoc V». Further, it may be shown that, although acids differ very greatly in conductivity, neutral salts, even of weak acids, have a conductivity nearly as great as that of strong acids. The vessels are filled with 1/4 normal solutions of hydrochloric acid, sulphuric acid, monochloracetic acid and acetic acid respectively, and when the distances are altered till the lamps are equally bright, it will be found that ths electrodes are very near in the acetic acid solution, far apart in the hydrochloric acid solution, and at intermediate distances for the other two acids. Sufficient sodium hydroxide to neutralize the acid is now added to each vessel, and after stirring and again adjusting to equal brightness of the lamps, it will be found that the distances for all four solutions are approximately equal. Equilibrium Relations as shown by Indicators — The equi- librium relations in the case of weak acids and bases may be shown very well by means of indicators. Each of two beakers contains 100 c.c. of water, i c.c. of «/i sodium hydroxide, and a few drops of methyl-orange. To the con- tents of one beaker n hydrochloric acid is added drop by drop by means of a pipette, and to the other n acetic acid is added in the same way till both solutions just become red. It will be observed that whereas about i c.c. of hydrochloric acid brings about the change of colour (owing to its relatively high concentration in H' ions), several c.c. of acetic acid are required to produce the same effect, owing to the much smaller H- ion concentration of the latter solution. If now a strong solution of sodium acetate is added to the last solution, the yellow colour of the methyl-orange will be restored ; the acetate reduces the strength of the acid to such an extent 3IO OUTLINES OF PHYSICAL CHEMISTRY (p. 277) that the H- ion concentration is no longer sufficient to drive back the ionisation of the methyl-orange. The effect of hydrolysis may be illustrated with indicators as follows: Each of two beakers contains 50 c.c. of 1/2 n hydro- chloric acid and a few drops of methyl-orange and phenol- phthalein respectively. If n ammonium hydroxide is slowly added to the solution containing methyl-orange, the colour will change when about 25 c.c. of ammonia has been added, but a much greater quantity of the same solution will be re- quired to redden the phenolphthalein solution. The explanation of this behaviour has already been given. Owing to the fact that the ammonium salt of phenolphthalein is considerably hydrolysed, it is necessary to add a fair excess of the base before the coloured phenolphthalein ions are produced in considerable amount. The Solubility Product — ^The conception of the solubility product may be illustrated by the method employed by Nernst in proving the formula experimentally. A saturated solution of silver acetate is prepared by shaking the finely-powdered salt with water for some time. To a few c.c. of the solution in a test-tube a few c.c. of a fairly concentrated solution of silver nitrate are added, and to another portion of the acetate solution a solution of sodium acetate equivalent in strength to the silver nitrate solution, and the mixtures are well shaken. In each tube a precipitate of silver acetate will be formed. Complex Ions — -The evidence in favour of the view that in solutions of silver salts in potassium cyanide the silver is mainly present as a constituent of a complex anion, Ag(CN)'5, is that the silver migrates towards the anode during electrolysis. The copper in Fehling's solution is also mainly present as a component of a complex anion, as may readily be shown qualitatively by a simple experiment described by Kiister. A U-tube is about half-filled with a dilute solution of copper sulphate, and the two limbs are then nearly filled up with a dilute solution of sodium sulphate in such a way that the EQUILIBRIUM IN ELECTROLYTES 31 1 boundaries remain sharp. A second U-tube is filled in an exactly similar way with Fehling's solution in the lower part and an alkaline solution of sodium tartrate in the upper part, the arrangement being such that the Fehling's solution in the one tube stands at the same level as the copper sulphate solu- tion in the other tube. The U-tubes are then connected by a bent glass tube, filled with sodium sulphate solution, and with the ends dipping in the sulphate and tartrate solutions respectively. A small current is then sent through the U-tubes in series, by means of poles dipping in the outer limbs of the tubes, and after a time it will be observed that the copper sulphate boundary has moved with the positive current, whilst the coloured boundary in the other tube has moved against the positive current towards the anode. It is therefore evident that in the latter case the copper is present in the anion, as stated above. Chemical Activity and lonisation — ^The great difference in chemical and electrical activity produced by ionisation is well shown by comparing the properties of solutions of hydrochloric acid gas in water and in an organic solvent such as toluene. Whilst the former solution conducts the electric current and dissolves calcium carbonate rapidly, the latter solution is a non-conductor, and has little or no effect on calcium carbon- ate. The same fact is illustrated by the interaction of silver nitrate with potassium bromide, ethyl bromide and phenyl bromide respectively in alcoholic solution. Approximately 5 per cent, solutions of the bromides in ethyl alcohol are prepared, and to each solution is added a few c.c. of a saturated solution of silver nitrate in alcohol. With the potassium bromide there is an immediate precipitate, the action being ionic. With ethyl bromide the reaction is very slow, and there is no apparent reaction with phenyl bromide. The reaction between silver nitrate and ethyl bromide is a good example of a chemical change 312 OUTLINES OF PHYSICAL CHEMISTRY which is not ionic, as far as one of the reacting substances (the ethyl bromide) is concerned. Non-ionic chemical changes may, however, be very rapid. A solution of copper oleate in perfectly dry benzene reacts immediately with a solution of hydrochloric acid gas in dry benzene, with precipitation of cupric chloride (Kahlenberg). CHAPTER XII THEORIES OF SOLUTION General — The nature of solutions,^ more particularly as regards the connection between their properties and those of the components, has long been one of the most important problems of chemistry. It was early recognized that the pr operties of a solution are v ery seldom inde ed the mean of the properties of the co mponent s, as must necessarily be the case if solvent and solute exert no mutual influence. Thus we know that when two liquids are mixed either expansion or contraction may occur, the boiling-point of a mixture may be higher or lower than those of either of its components (p. 88), and a mixture of two liquids may have a high conductivity, although the components in the pure condition are practically non-conductors (p. 259). The most obvious way of accounting for observations of this nature is to assume that they are connected with the formation of chemical compounds between the two components of the solution. As a matter of fact, explanations of the observed phenomena on these lines were formerly in great favour. As water was the substance most largely used as a component of solutions (as solvent), the explanation of the properties of aqueous solutions on the basis of fornlation of chemical com- pounds between water and the solute was termed the hydrate theor y of solution. This theory appeared the moreplauiible ^ Por simplicity, only mixtures of two components will be considered in this chapter. 314 OUTLINES OF PHYSICAL CHEMISTRY as a very large number of hydrates — compounds of substances, more particularly salts, with water — are known in the solid state, thus showing that there is undoubtedly considerable chemical affinity between certain solutes and water. In spite of the plausible nature of the hydrate theory, how- ever, it did not prove very successful in representing the properties of aqueous solutions, and some facts were soon discovered in apparent contradiction with it. Thus, as already mentioned, Roscoe showed that the composition of the mixture of hydrochloric acid and water with minimum vapour pressure, alters with the pressure, and therefore could not be connected with the formation of a definite chemical compound of acid and water, as had previously been assumed (p. 90). The development of the electro lyjic_d issociation theor y, which has~^Been discussed in the previous chapters, led to a considerable change of view with regard to the influence of the solvent on the properties of aqueous solutions. The pro- perties of the solvent were to some extent relegated to the background,! and it was looked upon simply as the medium in which the molecules anci the ions of the solvent — the really active things — moved about freely. The fact that such great advances in knowledge have been made by working along those lines naturally goes far to justify the method of procedure. Within the last few years, however, mainly as a result of the investigation of solutions in solvents other than water, it has ■come to be recognized that the s olvent ma^ play a m ore direc t part in determining the properties of dilute solutions thari^some ch emistFw ere formerly inclined to suppose. Although the main properties of aqueous solutions can be accounted for without express consideration of affinity between solvent and solute, it appears probable that the latter effect must be taken into con- ' The properties of the solvent are, of course, all-important in deter- mining whether a substance becomes ionised or not. But it was not found necessary to take the question of affinity into account directly, and the equations representing ionic equilibria did not contain any term referring directly to the solvent. THEORIES OF SOLUTION 315 sideration in order to account for certain secondary phenomena (and possibly also in connection with ionisation) (p. 324). In the previous chapters the evidence in favour of the electrolytic dissociation theory could not be dealt with as a whole, owing to the fact that it belongs to different branches of the subject. In the present chapter a short summary of the more important lines of evidence bearing on the theory will be given, and then a brief account of the investigation of solutions in solvents other than water. Finally, after dealing with the older hydrate theory of solution, the possible mechanism of electrolytic dissociation will be considered. Evidence in Favour of the Electrolytic Dissociation Theory — Th e evidence in favour of the jelectrol ytic dissociatio n theory is partly electrical a nd partly non-elecjrical. The non- electrical evidence goes to show that there are more particles in dUute solutions of salts, strong acids and bases, than can be accounted for on the basis of their ordinary chemical formulae, and that in dilute solution the positive and negative parts of the molecule behave more or less independently. The electrical evidence goes to show that the particles which result from the splitting up of simple salt molecules are associated with electric charges, either positive or negative. The main points are as follows : — (a) If Avogadro's hypothesis applies to dilute solutions, gram-molecular (molar) quantities of different substances, dis- solved in equal volumes of the same solvent, must exert the same osmotic pressure. As a matter of experiment, salts, strong acids and bases exert an osmotic pressure greater than that due to equivalent quantities of organic substances (p. 124). The electrolytic dissociation theory accounts for this on the same lines as the accepted explanation for the abnormally high pressure exerted by ammonium chloride ; it postulates that there are actually more particles present than that calculated according to the ordinary molecular formula. [ff) Many of the properties of dilute salt solutions are additive, 3i6 OUTLINES OF PHYSICAL CHEMISTRY that is, they can be represented as the sum of two independent factors, one due to the positive, the other to the negative part of the molecule. This is true of the density, the heat of formation of salts (p. 148), the velocity of the ions (p. 251), the viscosity, and more particularly of the ordinary chemical reactions for the "base" and "acid" as used in analysis (p. 306). A very striking illustration of the independence of the pro- perties of one of the ions in dilute solution on the nature of the other is the colour of certain salt solutions, investigated by Ostwald. He examined the solutions of a large number of metallic permanganates, and found that all had exactly the same absorption spectra. This is exactly what is to be expected according to the electrolytic dissociation theory, the effect being exerted by the permanganate ion. Similarly, salts of rosaniline with a large number of acids in very dilute solution gave identical absorption spectra (due to the rosaniline cation) but rosaniline itself, which is very slightly ionised, gave a quite different spectrum. Too much stress should not be laid on this criterion, how- ever, as certain properties, e.g., molecular volumes of organic compounds (p. 61) and the heat of combustion of hydro- carbons (p. 148), are more or less additive, although nothing in the nature of ionisation is here assumed. (c) The magnitudes of the degree of dissociation, calculated on two entirely independent assumptions — (i) that the con- ductivity of solutions is due to the ions alone, and not to the non-ionised molecules or to the solvent ; (2) that the abnormal osmotic pressures shown by aqueous solutions of electrolytes are due to the presence of more than the calculated number of particles owing to ionisation — show excellent agreement (p. 263). (i) The heat of neutralization of molar solutions of all strong monoacidic bases by strong monobasic acids is 13,700 calories, in excellent agreement with the value for the reaction H- -I- OH' = HjO, calculated by van't HofPs formula from THEORIES OF SOLUTION 317 Kohlrausch's measurements of the change of conductivity of pure water with the temperature (p. 295). («) The results obtained by four entirely independent methods for the degree of ionisation of water are in striking agreement, in spite of the fact that the assumed ionisation is very minute (p. 294). (/) The formula for the variation of electrical conductivity with dilution, obtained by application of the law of mass action to the assumed equilibrium between ions and non-ionised mole- cules in solution, represents the experimental results in the case of weak electrolytes with the highest accuracy (p. 267). (g) As shown in the next chapter, our present views as to the origin of differences of potential at the junction of two solutions, or at the junction of a metal and a solution of one of its salts, are based on the osmotic and electrolytic dissocia- tion theories, and the good agreement between observed and calculated values goes far to justify the assumptions on which the formulae are based. Many other illustrations of the utility of the electrolytic dissociation theory are mentioned throughout the book. Ionisation in Solvents other than Water ^ — In ac- cordance with the mode in which the subject has developed, we have up to the present been mainly concerned with aqueous solutions, and the justification for this order of treatment is that the relationships in aqueous solution are often very simple in character, as shown in detail in the last chapter. The importance of a theory would, however, be much less if it only applied to aqueous solutions, and it is therefore satisfactory that in recent years a very large number of liquids, both organic and inorganic, have been employed as solvents. Although the progress so far made in this branch of know- ledge is not great, the available data appear to show that ^ Carrara, Ahrens' Sammlung, igo8, 12, 404. 3i8 OUTLINES OF PHYSICAL CHEMISTRY the rules which have been found to hold for aqueous solutions also apply to non-aqueous solutions} Some solvents, such as ethyl and methyl alcohol, acetic acid, formic acid, hydrocyanic acid and liquefied ammonia, form solu- tions of fairly high conductivity with salts and other substances ; these are termed dissociating solvents (p. 123). Solutions in certain other solvents, such as benzene, chloroform and ether, are practically non-conductors, and the solutes are often present in such solutions in the form of complex molecules. These solvents are therefore often termed associating solvents, but it is not certain whether they actually favour association or polymerization of the solute, or have only a slight effect in simplifying the naturally polymerized solute. It is natural to inquire whether there is any connection between the ionising power of a solvent and any of its other properties. It has been found that as a general rule those solvents with the greatest dissociating power have high dielectric constants (p. 225) (J. J. Thomson, Nernst, 1893). This observation is easily understood when it is remembered that the attraction between contrary electric charges is inversely proportional to the dielectric constant of the medium ; it is evident that the existence of the ions in a free condition must be favoured by diminishing the attraction between the contrary charges. The dielectric constants of a few important solvents (liquids and liquefied gases) at room temperature are given in the table. Solvent. D.C. Solvent. D.C. Hydrocyanic acid 95 Acetone 21 Water . 81 Pyridine 20 Formic acid 57 Ammonia l6'2 Nitro benzene 36-5 Sulphur dioxide 137 Methyl alcohol . 32-5 Chloroform . 5"2 Ethyl alcohol . 21-5 Benzene 2 "3 ' C/. Walden, Zeitsch. phyakal. Chem., 1907, 58, 479. THEORIES OF SOLUTION 319 The data are not usually available for an accurate comparison of the dissociating power of a solvent with its dielectric constant, as the values of /ioo for electrolytes in solvents other than water have been determined in only a few cases. It is important to remember that a comparison of the conductivities of solutions of the same concentration in different solvents is in no sense a measure of the respective ionising powers of the solvents, as the conductivity also depends on the ionic velocity (p. 252). The available data are, however, sufficient to show that although there is parallelism, there is not direct proportionality between dielectric constant and ionising power. There appears also to be some connection between the degree of association of the solvent itself and its ionising power. The examples already given show that water, the alcohols and fatty acids, which are themselves complex, are the best ionising solvents. There are, however, exceptions to this as to all other rules in this section ; liquefied ammonia, though apparently not polymerized, is a good ionising solvent. Briihl has suggested that the ionising power of a solvent depends on what he calls subsidiary valencies (the "free affinity " of Armstrong) ; in other words, the best ionising solvents are those which are unsaturated. It is by no means improbable that the dielectric constant, the degree of poly- merization, and the degree of unsaturation of a solvent are in some way connected. The ionising power of a solvent may be partly of a physical and partly of a chemical nature. The effect of a high dielectric constant would appear to be mainly physical, on the other hand, if the effect of a solvent depends on its unsaturated character, it would most likely be chemical in character. The Old Hydrate Theory of Solution ^ — As already men- tioned, attempts have been made to account for the properties of aqueous solutions of electrolytes on the basis of chemical combination between solvent and solute. Among those who 1 Pickering, Watts's Dictionary of Chemistry, Article " Solution " ; Arrhenius, Theories of Chemistry (Longmans, 1907), chap. iii. 320 OUTLINES OF PHYSICAL CHEMISTRY have supported this view of solution, the names of MendelSeff, Pickering, Kahlenberg ^ and Armstrong ^ may be mentioned. Mendeleeff made a number of measurements of the densities of mixtures of sulphuric acid and water, and drew the con- clusion that the curve representing the relation between density and composition is made up of a number of straight lines meeting each other at sharp angles, the points of discontinuity corresponding with definite hydrates, for example, HjSO^, HjO ; HjSO^, 2H2O ; HjSO^, 6H2O and H^SO^, iSoHp. Pickering repeated Mendelfeeff' s experiments, and found no sudden breaks in the density curve, but only changes in direction at certain points. He also drew the conclusion that these points cor- respond with the composition of definite compounds of the acid and water. In this connection it may be recalled that the curve obtained by plotting the electrical conductivity of mixtures of sulphuric acid and water against the composition (p. 259) shows two dis- tinct minima, at 100 per cent, and 84 per cent, of sulphuric acid respectively, corresponding with the compounds H2S0^ (SO5, HjO) and H2SO4, HjO respectively. As it is a general rule that the electrical conductivity of pure substances is small, there is little reason to doubt that the 84 per cent, solution consists mainly of the monohydrate H2SO4, HgO. The con- tention of Mendeleeff and Pickering, that aqueous solutions of sulphuric acid contain compounds of the components, is thus partially confirmed by the electrical evidence. There is not much reason to doubt the truth of the first postulate of the hydrate theory, that in many cases hydrates are present in aqueous solution. The hydrates are, however, in all probability more or less dissociated in solution, and it will not usually be possible to determine the presence of definite hydrates from the measurement of physical properties. ' For a summary of Kahlenberg's views on Solution, see Trans. Faraday Soc, 1905, I, 42. " Proc. Roy. Soc, 1908, 81 A, 80-95. THEORIES OF SOLUTION 321 It is probable that in general the equilibria are somewhat com- plicated, and are displaced gradually by dilution in accordance with the law of mass action, which accounts for the experimental fact that in general the properties of aqueous solutions alter continuously with composition. Having proved the existence of hydrates in salt solutions in certain cases, Pickering ^ attempted to account for the properties of aqueous solutions (osmotic pressure, electrical conductivity, etc.) on the basis of association alone, but as his views have not met with much acceptance, a reference to them will be sufficient for our present purpose. Kahlenberg,^ who has carried out many interesting experiments in solvents other than water, re- gards the electrolytic dissociation theory as unsatisfactory, and considers that the process of solution is one of chemical com- bination between solvent and solute. Armstrong has also attempted to account for the properties of aqueous solutions on the basis of association between solvent and solute.^ Although, as we have seen, cases are known in which a maximum or minimum or a change in the direction of a curve may correspond more or less completely with the formation of a compound between the two components of a homogeneous solution, this does not by any means always hold. It has already been pointed out that the curve representing the varia- tion of the electrical conductivity of mixtures of sulphuric acid and water with the composition has a maximum at 30 per cent, of acid (p. 259). As the pure liquids are practically non- conductors, whilst the mixtures conduct, there must necessarily b&a concentration, between o and 100 per cent, acid, at which the conductivity attains a maximum value. This maximum will clearly have no reference to the formation of a chemical compound between sulphuric acid and water, since this would tend to diminish the conductivity. Similar considerations appear to apply for other physical ^Loc. cit. ^Loc. cit. ^Loc. cit., also Encyc. Britannica, loth Edition, vol. xxvi., p. 741. 21 322 OUTLINES OF PHYSICAL CHEMISTRY properties which attain a maximum value for binary mixtures. The curve representing the variation of the viscosity (internal friction) of mixtures of alcohol and water with composition shows a maximum at o° for a mixture containing 36 per cent, of alcohol, corresponding with the composition (C2H50H)2, gHjO, and it has therefore been suggested that the solution consists mainly of this hydrate. At 1 7°, however, the mixture of maximum viscosity contains 42 per cent., and at 55° rather more than 50 per cent, of alcohol. The last-mentioned mixture corresponds with the composition (CgHsOH)^, sHgO. If we accept the association view of this phenomenon, it must be assumed that at 0° the solution contains a hydrate (C2H50H)2, 9H2O, and at 55° a hydrate (C2H50H)2, sHgO, and that at intermediate temperatures the hydrates with 6, 7 and 8 HjO exist — which does not appear very probable. Now, Arrhenius has shown that as a general rule the addition of a non-electrolyte raises the viscosity of water. Therefore, if the viscosity of the non-electrolyte is less than, or only slightly exceeds that of water, the curve obtained by plotting viscosity against the composition of the mixture must necessarily attain a maximum at some intermediate point. Why mixtures of two liquids have often a higher viscosity than either of the pure liquids is not known, no general agreement having yet been reached on this and allied questions.^ Mechanism of Electrolytic Dissociation. Function of the Sol¥ent — The fundamental difference between associa- tion theories of solution, as discussed in the last section, and the electrolytic dissociation theory is that the advocates of association entirely reject the postulate of the independent existence of the ions. As, however, the different theories of association unaccompanied by ionisation have so far proved quite inadequate to account quantitatively for the behaviour of aqueous solutions, whilst the electrolytic dissociation theory not only affords a satisfactory quantitative interpretation of the 1 Compare Senter, Proc. Chem. Soc, igog, 292. For evidence in favour of the association view of this phenomenon, compare Dunstan, Traus, Chem. Society, 1907, 91, 83; Dunstan and Thole, ibid., 1909, 95, 1556. THEORIES OF SOLUTION 323 more important phenomena observed in solutions of electrolytes (chap. X.), but has led to discoveries of the most fundamental importance for chemistry, it is not surprising that the electro- lytic dissociation theory has now met with practically universal acceptance. It is very likely that as a result of further investi- gation the theory may require modification in some subsidiary respects, but its general validity appears no longer doubtful. We are now in a position to discuss the possible mechanism of electrolytic dissociation, i.e., the factors concerned in the conversion of a non-ionised salt into ions when dissolved in water or other ionising solvent. In this connection two points of importance must be kept in mind: (i) There is a more or less complete parallelism between the ionising power of a solvent and certain of its properties, such as the magnitude of the dielectric constant and its degree of polymerization ; (2) the sum of the energy associated with the ions is usually not very different from that associated with the non-ionised molecules in solution. The first point has already been fully dealt with. The energy relations in the process of ionisation will now be briefly considered. As such elements as potassium and chlorine give out a large amount of heat when they combine to form potassium chloride, it seems at first sight as if the splitting up of potassium chloride into K' and CI' ions must absorb a large amount of heat. Although it has to be borne in mind that the salt is not split up into its component elements (a process which certainly absorbs a large amount of heat) but into K- and CI' ions, of the energy content of which little is known, it is nevertheless probable that the process of ionisation does involve a taking up of energy, as the following considerations show. It has already been pointed out that the heat of ionisation (the heat given out when a mol of a non-ionised salt in solution is completely ionised) may be calculated by the van't Hoff formula connecting heat given out with displacement of equilibrium, when the equilibrium at ~two near temperatures is 324 OUTLINES OF PHYSICAL CHEMISTRY known (p. 285). The available data indicate that the heat of ionisation is small, and may be positive or negative. According to Arrhenius, the energy equation for the ionisation of dissolved potassium chloride is as follows — KCl = K- + CI' + 362 cal, the heat of ionisation being thus exceedingly small. On the other hand, when potassium chloride is formed from its elements, 105,600 cal. are given out for gram-equivalent quantities, hence the energy equation for the decomposition of potassium chloride into metallic potassium and free chlorine is KCl = — "^ + ^ - 105,600 cal. The further separation of metallic potassium and free chlorine into uncharged atoms would probably absorb still more heat, so that the reaction KCl = K + CI must absorb a very large amount of heat. On the other hand, we have just seen that in the splitting up of the salt into charged atoms — the ions — a little heat is actually given out. It seems, therefore, that the process of ionisation must be attended by some exothermic reaction, which more than compensates for the heat presumably absorbed in splitting up the molecules. Up to the present no definite conclusion has been arrived at as to the source of the energy in question. Some of the possi- bilities are as follows : — (a) As the molecule splits up into particles charged with electricity, the energy in question may come from some inter- action between electricity and matter. On this point nothing can be said with certainty in the present state of our knowledge.^ (3) The energy may result mainly from combination between the ions and water. Van der Waals^ (1891) has suggested that ionisation in aqueous solution is essentially a hydration ' Cf. Ostwald, Fitzgerald, British Association Reports, 1890. ' Zeitsch. physikal Chem., i8gi, 8, 215. Cf. Bousfield and Lowry, Trans. Faraday Society, 1907, 3, i. THEORIES OF SOLUTION 325 process ; he considers that it is the affinity of the ions for the solute which effects the break-up of the molecule, and that the energy required for ionisation comes from the heat of hydration of the ions. (c) Dutoit, arguing from the parallelism between the poly- merization of the solute and its ionising power, and assuming that the process of solution is attended with partial simplification of the solute molecules, has suggested that the energy is ob- tained from the depolymerization in question. The suggestion of van der Waals finds a certain amount of support from recent investigations on solvents other than water. Carrara ^ considers that the ions are produced as a consequence of the chemical affinity between the two parts of the molecule and the solute, and that in consequence of the high dielectric constant in ionising media, they, along with their associated solvent molecules, are kept in the ionic condition once they are formed. It should, however, be remembered that this suggestion as to the mechanism of ionisation, although interesting and suggestive, is little more than a plausible speculation, and that there are many points about this process which are very im- perfectly understood. Hydration in Solution^ — In recent years the view that the ions are hydrated to a greater or less extent in aqueous solutions of electrolytes has gained ground very considerably, but it cannot be said that the evidence is very conclusive. Perhaps the most definite positive result is the observation of Kohlrausch, that the influence of temperature on the electro- lytic resistance of dilute solutions of salts approximates to the ^ Loc. cit., p. 417. ^ For a general discussion on hydration in solution, see Trans. Faraday Soc, 1907, 3, 1. For summaries of the methods which have been suggested for determining the degree of hydration in solution, see Baur, Ahrens' Sammlung, 1903, 8, 466 ; Senter, Science Progress, 1907, 1, 386 ; Trans. Faraday Soc, 1907, 3, 24. Cf. also Philip, Trans. Chem. Soc, 1907, 91. 7"- 326 OUTLINES OF PHYSICAL CHEMISTRY temperature coefficient of the mechanical friction of water. This observation at once becomes intelligible if it is assumed that the ions are surrounded by water molecules, as the resist- ance to movement of the water-coated ions would then be the frictional resistance of water against water. Many attempts have been made to determine the degree of hydration both in solutions of electrolytes and of non- electrolytes, but the results are very uncertain. If each ion becomes associated with a number of water-molecules, the total number of solute particles will not be altered, and the osmotic pressure, lowering of freezing-point, etc., will not be directly affected. If, however, it is assumed that only the un- bound part of the solvent can really act as solvent, the effect of association will be to diminish the "free " solvent, and there- fore the effective concentration of the solution — the ratio of solute to free solvent — will be increased, and the lowering of freezing-point will be greater than the calculated value. Unless, however, the average hydration of the solute is very great, the effect in question will only be considerable in con- centrated solutions, under which circumstances freezing-point and other determinations often give unsatisfactory results (p. 122). For our present purpose, it will be sufficient to refer to the method for determining the degree of hydration of electrolytes suggested by H. C. Jones, as this author and his co-workers have collected much valuable experimental material which will be serviceable in attacking some of the yet unsolved problems of solution. The method depends on the observation that in many cases the experimental freezing-point depression is greater than the value to be expected from the degree of dissociation of the solute, and Jones assumes that this is due to the associa- tion of part of the solvent with the solute, so that the depression actually observed is that corresponding with a more concen- trated solution, as described in the previous paragraph. If the true depression in the absence of association (when the whole THEORIES OF SOLUTION 327 of the solute is " free ") can be calculated, the mode of esti- mating the hydration will be evident, but this is just where the weakness of the method lies. Jones calculates the theoretical depression for a particular dilution from conductivity measure- ments at 0°, the values of /*„ and ft.^ being determined directly. To do this it has to be assumed that the exact degree of dissociation can be obtained from conductivity measurements, which is not the case for concentrated solutions,^ although very nearly so for dilute solutions (p. 261), and further, that the van't Hoff-Raoult's law holds strictly for concentrated solu- tions, which is highly improbable (p. 122). Jones himself, while admitting that several of his assumptions are not strictly valid, considers that a nearer approximation to the true values for the degree of hydration is obtained by his method than by any other method so far suggested. While this may be the case, we have no means of knowing the magnitude of the error thus introduced, and the true values for the degree of hydration may be very different from those given by Jones and his co- workers. Moreover, the observed irregularities in freezing- point depression may be due, in part at least, to some cause other than hydration. The present position of the subject may be summed up in the statement that while there is a good deal of evidence in favour of hydration in solution, very little is known on the subject with certainty from a quantitative point of view. ^ The uncertainty in the case of concentrated solutions arises from the difficulty of distinguishing between the effects of alteration of viscosity and of alteration of the degree of dissociation on the electrical conductivity (p. 261). CHAPTER XIII ELECTROMOTIVE FORCE The Daniell Cell. Eleotrical Energy— The Daniell cell consists essentially of a large beaker or other vessel, con- taining a small porous cell. In the outer vessel, surrounding the porous cell, is a solution of zinc sulphate in which dips a rod of zinc, and the porous pot contains a solution of copper sulphate, in which dips a plate of copper. When the copper plate is connected to the zinc by a wire, an electric current flows through the wire. As positive electricity passes in the wire from copper to zinc, the copper is termed the positive, the zinc the negative pole. An examination of the cell will show that when the current is flowing, zinc is being dissolved at the negative pole, and copper is being deposited on the positive pole. If, instead of copper sulphate, the porous pot contains dilute sulphuric acid, hydrogen is given off at the surface of the copper when the zinc and copper are connected. It is, therefore, clear that the chemical change which gives rise to the current is the dissolving of zinc in sulphuric acid, repre- sented by the equation Zn H- HjSO^ = ZnSO^ H- Hg, and that in the Daniell cell the hydrogen is got rid of by reducing copper sulphate in the porous pot, the change being repre- sented by the equation CuSO^ Hg = HjSO^ -l- Cu. Com- bining the two equations, the chemical changes taking place while a Daniell cell is working are represented by the equation Zn -f CUSO4 = ZnSO^ + Cu, which may be written Zn + Cu- -f- SO4" = Zn- -f SO^' -H Cu, 328 ELECTROMOTIVE FORCE 329 or more concisely, Zn + Cu" = Zn- + Cu, that is, zinc changes from the metallic to the ionic form, and at the same time copper changes from the ionic to the metallic form. The Daniell cell may be looked upon as a machine for the conversion of chemical to electrical energy, and it is of great interest to inquire whether chemical energy is transformed into the equivalent amount of electrical energy, or whether other kinds of energy, such as heat, are also produced in the cell. This question can at once be settled by determining the heat equivalent, in calories, of the chemical energy transformed when I mol of copper in solution is displaced by zinc, and comparing it with the electrical energy (measured in calories) obtained during the process. From Thomsen's measurements (p. 144) the displacement of I mol of copper in dilute solution by zinc is associated with a heat development of 50,130 calories. The electrical energy in volt-coulombs is, as has already been pointed out, the product of the electromotive force E in volts and the quantity of elec- tricity in coulombs. E for the Daniell cell is about I'og volts at room temperature. From Faraday's law we know further that the liberation of a gram-equivalent of positive or negative ions is associated with the passage of 96,540 coulombs, hence, as zinc and copper are bivalent, the reaction Zn -I- Cu" = Zn" -H Cu is associated with the passage of 2 x 96,540 coulombs. The electrical energy, in calories (i volt-coulomb = o'23gi calories), is therefore given by*' ECt = i'09 X 2 X 96,540 X o"239i = 50,380 cal. as compared with 50,130 calories, the heat equivalent of the chemical change which has taken place in the cell. The excel- lent agreement between observed and calculated values shows that in this case the assumption that the chemical energy is ' C is the current, t the time and Ct therefore the quantity of elec- tricity. 330 OUTLINES OF PHYSICAL CHEMISTRY transformed completely to electrical energy is approximately fulfilled. It should be remembered that in an actual cell other chemical changes may accompany the primary ones ; for example, those giving rise to the so-called E.M.F. of polarization (p. 373). In comparing the heat equivalent of the main chemical action taking place in the cell with the electrical energy obtained, such changes must, of course, be allowed for. In the Daniell cell, however, there is no polarization, and the only reaction which takes place to any appreciable extent is the displacement of copper by zinc, as has already been assumed. In this chapter we are mainly concerned with such non-polarizable cells. On account of the excellent agreement between the amount of chemical energy expended and the electrical energy generated in the Daniell cell, it was at first thought that the transformation of chemical to electrical energy in all cells is practically com- plete, but further investigation showed that this is by no means always the case. As indicated above, the question can readily be investigated for a non-polarizable element by comparing the heat equivalent, Q, of the chemical change taking place in the element with the electrical energy generated while known quantities of the reacting substances are being transformed. The electrical energy may conveniently be measured as follows. The poles of the cell are connected by a thin wire of high re- sistance, R. If r is the internal resistance of the cell, the electrical energy generated in unit time is given by EC = CMR + r). Now R may easily be made so large compared with r that the amount of electrical energy converted to heat in the cell is negligible in comparison with that transformed in the outer wire. If then the current is measured and R is known, the quantity of electrical energy produced by the cell in unit time is known, and hence that produced when n x 96,540 coulombs have passed round the circuit. This quantity of electricity energy is obtained during the chemical transformation of « equivalents of the cell ELECTROMOTIVE FORCE 331 .material, and may be compared with Q, the heat given out when the chemical change takes place in a calorimeter. When a Daniell cell is examined in this way, it is found, as has already been pointed out, that the electrical energy is practically equal to Q, the heat equivalent of the chemical energy. There are, however, elements in which the electrical energy thus ex- pended in the outer wire is less than the heat of the reaction ; in this case part of the chemical energy is expended as heat in the cell. In other elements, however, the electrical energy, ECt, is actually greater than the heat of reaction, Q, so that the element, while working, takes heat from its surroundings and transforms it into electrical energy. Relation between Chemical and Electrical Energy — The exact relationship between the chemical energy transformed and the maximum energy obtainable electrically in a reversible galvanic element can be obtained on thermodynamical principles by means of a cyclic process. The formula expressing the relationship (Willard Gibbs, 1878; Helmholtz, 1882), usually known as the Helmholtz equation, is as follows : — ;zFE - Q = «FT^ . . . (i) where E is the E.M.F. of the cell, Q is the heat equivalent of the chemical change for molar quantities, expressed in electrical units, F is 96,540 coulombs, T is the absolute temperature at which the cell is working, and n is the valency, or the number of charges carried by a mol of the substances undergoing change. By dE/dT is meant the rate of charige of the E.M.F. of the cell with temperature — in other words, the tetnperature coefficient of the E.M.F. The Helmholtz formula is simply a direct application of the free energy equation A-U = T^ . . . (3) 332 OUTLINES OF PHYSICAL CHEMISTRY to a chemical change taking place in a galvanic cell. In the latter formula, U represents the total diminution of energy in a reacting system, and A is the available or free energy, that is, the maximum proportion of the total change of energy, U, which can be transformed into work (p. 151)- In order to obtain formula (i), Q, the heat of reaction measured calorimetrically, is substituted for U in the free energy equation, as the heat of reaction is equivalent to the total diminution of energy, U, when no external work is done. For A, the free energy, we substitute «FE, which is, as shown above, an expression for the maximum energy obtainable electrically for molar quantities. dAjdT in the free energy equation then becomes nFTdE/cTr (n and F being constants), equation (i) being thus obtained. The equation should be remembered in the second form. From the first form of the Helmholtz equation, some very important conclusions can be drawn as to the behaviour of reversible elements : — {a) If (fE/(fr is positive, that is, if the E.M.F. of the element increases with temperature, the electrical energy, «FE is greater than the heat of reaction, Q, and the cell takes heat from its surroundings while working. {b) If dEldn is negative, that is, if the E.M.F. of the element diminishes as the temperature rises, the heat of re- action, Q, is greater than the electrical energy, «FE, and the cell warms while working. [c) If the E.M.F. does not alter with change of temperature (as is approximately the case in a Daniell cell), the heat of reaction, Q, is equal to the electrical energy, and the cell does not alter in temperature while working. {d) At absolute zero, that is, T = o, the right-hand side, and therefore also the left-hand side, of equation (i) becomes zero, hence at the absolute zero the heat of reaction (diminution of chemical energy) is always equal to the maximum electrical energy obtainable (or in general to the free energy, rf. p. 152). The appUcability of the Helmholtz formula to chemical ELECTROMOTIVE FORCE 333 changes which can be brought about reversibly in a galvanic element has been proved experimentally by Jahn and others. As an example, we will consider a cell made up of zinc and silver in contact with solutions of the respective chlorides. The observed E.M.F. of such a cell at 0° is r'oi5 volts, and the electrical energy in calories for the transformation of i mol of the reacting substances is given by «FE = i'oi5 x 96,540 x 2 X 0*239 = 46,840 calories. The heat of reaction (due to the displacement of the equivalent amount of silver from solu- tion by 1 mol of zinc) is 52,046 cal. Hence, as the heat of reaction is greater than the electrical energy, the temperature co- efficient of the E.M.F. is negative, and is given by the formula (/E «FE - Q (46,840-52,046)4-184 , , Tf, = TT-rp = — 7— —r = - 0-00041 (volts flti ni V 2 X 96,540 X 273 *■ per degree) in excellent agreement with the experimental value, - 0-00040. As the value of dEjdT is required in volts, the energy in the above equation is necessarily represented in volt- coulombs (calories x 4-184). In order further to illustrate the above statements, which are of fundamental importance for our work, they will now be repeated in a somewhat different form. The quantities of energy given in the following paragraphs refer to molar quantities throughout. When a chemical change takes place without the performance of external work, the total change of energy, U, is equal to the heat of reaction, Q, measured in a calorimeter. When the same reaction takes place in a battery the poles of which are connected by a thin wire, the whole apparatus, including the connecting wire, being enclosed in a calorimeter, the heat developed in the latter is again Q for molar quantities transformed, the electrical energy in the connecting wire being degraded to heat. When the cell is in the calorimeter, and the thin connecting wire outside, there are three possible cases : — (a) If the heat of reaction, Q, is equal to the maximum 334 OUTLINES OF PHYSICAL CHEMISTRY electrical energy obtainable, nFE, and if further the resistance of the cell is zero (in practice, very low) no heat will be de- veloped in the calorimeter, and the equivalent of Q calories of electrical energy will pass round the external wire. (i) If the heat of reaction is greater than the maximum electrical energy obtainable, heat will be developed in the calorimeter as well as in the external circuit. {/:) If the heat of reaction is less than the maximum electrical energy heat will be absorbed in the calorimeter, and the heat equivalent of the electrical energy in the outer circuit will be greater than Q (provided that the resistance of the cell is negligible). It has already been pointed out that the maximum work can only be obtained by carrying out a process reversibly, and therefore the Helmholtz formula only applies to elements in which the process can be effected reversibly. This means that if an element such as the Daniell is giving out electrical energy at an E.M.F. represented by E, it can be restored to its initial condition by passing through it, at an E.M.F. only just exceeding E, a quantity of electrical energy equal to that given out. In order that an electrochemical process should be completely reversible, the energy should be given out and taken in at the same potential, which in practice is impossible. A completely reversible process is therefore only an ideal case, which can be more or less completely attained to in actual practice. Many electrochemical processes are irreversible, more par- ticularly those in which gases are evolved. For example, a Daniell cell in which the copper sulphate solution is replaced by sulphuric acid is irreversible, as, owing to the escape of hydrogen, it cannot be restored to its former condition by passing a currenrin the contrary direction. Measurement of Electromotive Force — The difference of potential between the two poles of a cell may have very dififerent values according to the conditions of measurement. If the poles are connected by a wire of very high resistance, ELECTROMOTIVE FORCE 335 R, and the resistance of the cell is r, the fall of potential in the wire is CR and in the cell Cr. Since E = C(R + r), it is clear that the fall of potential CR in the outer circuit is only equal to E when the resistance R is infinitely large compared with r. It is therefore easy to understand why the resistance of volt-meters (instruments on which the difference of potential between two points can be read off directly in volts) is always very high. A further complication in measuring the E.M.F. of a cell while working is that in many cases the products of electrolysis accumulate on the electrodes, and set up an electro- motive force in the opposite direction to the E.M.F. of the cell itself — a phenomenon which is termed polarization. These difficulties are avoided by measuring the difference of potential between the poles of a cell when the circuit is open, that is, when the cell is not sending a current. In the present chapter, the symbol E stands for the E.M.F. of the cell on open circuit. The effect of completing the circuit will be dealt with more fully at a later stage. The E.M.F. of a cell on open circuit is most conveniently measured by the Poggendorff compensation method. The principle of the method is that the E.M.F. of the cell is just compensated by an equal and opposite E.M.F. so that no current passes, and the measurement consists in altering an adjustable E.M.F. till the above condition is fulfilled. The arrangement of the apparatus for this purpose is shown in Fig. 37. A is a lead accumulator, or other source of constant E.M.F., which is connected to the two ends of a uniform wire BC, which may conveniently be a metre in length. The cell E, the E.M.F. of which is to be measured, is connected through a sensitive gal- vanometer G and a tapping key to one end of the bridge wire at B, and on the other to a sliding contact. The slider is moved along the wire until a position D is found at which, when con- tact is made, no current passes through the galvanometer. It is then clear that the following relation holds (4/ p- 255) : E.M.F. of accumulator : E.M.F. of cell : : length BC : length BD, so that 336 OUTLINES OF PHYSICAL CHEMISTRY the E.M.F. of the cell can readily be calculated. As the E.M.F. of the lead accumulator is not quite constant, it is preferable in accurate determinations to standardize the apparatus by finding the position on the bridge wire conesponding with the E.M.F. of a constant cell, such as the Clark or Cadmium cell (p. 337), when the latter is substituted for the cell E in the diagram. As null instrument, for showing that the point of balance has been reached, by the fact that a current no longer passes when contact is made, a high resistance galvanometer or a capillary electrometer (p. 358) may be used ; the former may be made the more sensitive, but the latter is in many respects very convenient. FiQ. 37. The measurement of the E.M.F. of a cell on open circuit may also be made by means of the quadrant electrometer, the deflection of the needle being proportional to E, but this method is in some respects less advantageous than the compensation method. In general, the observed E.M.F. of a cell on closed circuit is less than that on open, circuit ; this is due, as already indicated, to polarization effects and to the effect of the internal resistance of the cell. Standard of Electromotive Force. The Cadminm Element — The importance of obtaining a cell, the E.M.F. of which is accurately known, has already been pointed out. ELECTROMOTIVE FORCE 337 The cadmium element, sometimes called the Weston eleraent,i which is most largely in use for this purpose, will now be described. The cell itself consists of an H-shaped glass vessel, the side tubes are closed at their lower ends, and platinum wires, sealed in the glass, pass through near the lowest points of the side tubes. In the bottom of one of the tubes is a layer of mercury about I cm. deep, above which is a paste (5 mm.) of mercurous sulphate, which has been carefully freed from traces of mercuric salt. In the bottom of the other side tube is a layer of cadmium amalgam (about 13 per cent, of cadmium quite free from zinc) above which is a paste (5 mm.) of cadmium sulphate, prepared by rubbing together in a mortar water and crystallized cadmium sulphate, and pouring off the clear saturated solution. The remainder of the cell on both sides, as well as the connecting tube, contains a saturated solution of cadmium sulphate, in which are moderately large crystals of the solid salt, and both side tubes are hermetically closed at the top, a small air space being left to allow of expansion. When required as a standard of E.M.F., connection is made by means of the platinum wires, which are in contact with the mercury and amalgam respectively. The great advantage of the cadmium element is that its E.M.F. is practically independent of temperature. The E.M.F. at temperatures from 0° to 30° is as follows : — 00 o ^o o ^a o o 5 10 IS 20 25 30 I'oiSg i'oi89 1-0189 I'oiSS i"oi86 i'oi84 i-oi8i volts, the mercury being positive. When in use the element should only be allowed to send a very small current for a very short time; if this condition is not observed the E.M.F. soon alters owing to polarization. The mode of action of the element will be understood when the section on the calomel electrode has been read. ^ The true Weston element differs slightly from that here described. 22 338 OUTLINES OF PHYSICAL CHEMISTRY The corresponding cell with zinc amalgam and zinc sulphate instead of cadmium amalgam and cadmium Sulphate, was formerly in general use as a standard element under the name of the Clark cell. Its chief drawback is that the E.M.F. alters considerably with temperature. The E.M.F. of the Clark cell is given by the equation E = 1*4328 - o'ooiig (/ — 15°) — o'ooooo7 (f - 15)^. Solution Pressure — In a former section it has been shown that the relation between chemical and electrical energy in a voltaic cell is given by the Helmholtz formula This formula has been deduced from considerations which are quite independent of any assumption as to the mechanism of the establishment of differences of potential in a cell, and therefore holds quite independently of any theory as to the origin of differences of potential. A much deeper insight into this problem is gained on the basis of a theory due to Nernst, based on the theory of electrolytic dissociation, and this theory will now be considered. Every substance has a tendency to change from the form in which it actually exists to another form. Water, for example, has a tendency to pass into vapour, and if the vapour be con- tinually removed from its surface, a definite quantity of water will change completely to vapour. The tendency in question is measured by the vapour pressure of the water, and is con- stant at constant temperature. Further, a solid, such as sugar, when brought in contact with water, tends to pass into solution, and from the analogy with water and water vapour we may say that sugar has a definite solution pressure, which is constant at constant temperature, since the active mass of a solid, such as sugar, is constant (p. 173). On the other hand, the dissolved sugar has a tendency to separate in the solid form, which is the greater the higher the concentration, and when the solution is ELECTROMOTIVE FORCE 339 supersaturated the tendency to the separation of solid sugar is greater than the tendency of the latter to pass into solution. From the considerations advanced on p. 98, it is clear that the pressure of the sugar in solution is its osmotic pressure, and under definite conditions sugar will enter into or separate from solution according as its solution pressure is greater or less than its osmotic pressure. These considerations, in conjunction with the ionic theory, enable us to express the E.M.F. at a junction metal/solution in terms of solution pressure and osmotic pressure. If a metal is dipped into water it tends to dissolve, in consequence of its solution pressure, P, and as it can only do so in the ionic form, it sends a certain number of positive ions into solution. The solution thus becomes positively charged, and the metal, which was previously neutral, becomes negatively charged in conse- quence of the loss of positive ions. This process will proceed until, by the accumulation of positive electricity in the solution, the latter becomes so strongly positive that it prevents the pas- sage of more positive ions into solution. As the charge on the ions is so great, this process comes to a standstill when the amount of ions gone into solution is still excessively small, too small to be detected by analytical means. The state of affairs is rather different when a metal is dipped into a solution of one of its salts, e.g., zinc in a solution of zinc sulphate. In this case there are already positive metallic ions in the solution, which tend to resist the entrance of further positive ions, and what actually occurs will clearly depend upon the relative values of tM solution pressure, P, of the metal and the osmotic pressure, p, of the ions in solution. There are, in fact, three possible cases, which are represented diagrammatically in the accompanying figure : — (a) If P > p, the metal sends ions into the solution until the accumulated electrostatic charges prevent further action ; the metal is then negatively and the solution positively charged. (^) If P < /, the positive ions from the solution deposit on 340 OUTLINES OF PHYSICAL CHEMISTRY the metal until the electrostatic charges prevent fiyrther action ; the metal is then positively and the solution negatively charged. (f) If P = /, no change occurs, and there is no difference of potential between metal and solution. As will be shown later, the solution pressures of the different metals are very different. Those of the alkali metals, zinc, iron, etc., are so great that they always exceed the osmotic pressures of their respective solutions (which cannot be increased beyond a certain point owing to the limited solubility of the salts), and these metals are, therefore, always negatively charged with _ Metal Metal + Metal - f ^ f -^ + _ + + + - + - + + — ' + + - + Solu + tion. Soli tion. _ 9olution._ p»p. p=p. P^PI Fig 38. reference to their solutions. On the other hand, the solution pressure of mercury, silver, copper, etc., is so small that they become positively charged, even in very dilute solutions of their respective salts., Calculation of Electromotiye FoFces at a Junction Metal/Salt Solution — Provided that the changes at the junction of an electrode with a solution are reversible, the E.M.F. at the junction can readily be calculated in terms of the solution pressure, P, of the metal and the osmotic pressure, /, of the solution. This can perhaps be done most simply by calculating the maximum work obtainable when a mol of ELECTROMOTIVE FORCE 341 the electrode metal is brought from the pressure P to the lower pressure /, (i) osmotically, (2) electrically. If a mol of a dissolved substance is brought reversibly from the pressure P to p the work gained (in this case the osmotic work) is {ff. p. 13s) A = RTlogZ Further, the dissolving of i equivalent of a metal is associated with 96,-540 coulombs, and that of a mol of a metal of valency n with 96,540 n coulombs. The work done is the product of the E.M.F. E in volts and the quantity of electricity, 96,540 n coulombs. Equating the osmotic and electrical work, we have « 96,540 E = RTlog,P// RT P or E = —^ logj- . . (i) 96,540^ ^'p ^ ' In order to obtain E in volts, R must be expressed in electrical units (volt-coulombs). If, at the same time, the change is made to ordinary logarithms (by multiplying by 2*3026) the above equation becomes 2-302 6 X 1-99 X 4-183 T P 6-0001983 T ,_ P ^= ^^^:^n '°Sio;^= n '°SioJ The numerical values of 2-3026 RT/Fat 0°, 18°, 25° and 30° are as follows : — Absolute temperature 273° 273 + 18° 273 + 25° 273 + 30 Value of 2-3026 RT/F 0-0541 0-0577 0-0591 0-0601 At room temperature (15-20°) the value of the expression in question is about 0-058, and the general formula becomes which should be remembered. It is clear from the form of the above equation that a tenfold increase or decrease in the osmotic pressure of the ions of the metal will produce a change of E.M.F. of 0-058 volts for a univalent metal, and o'o^8/n volts for a «-valent metal, at room temperature. 342 OUTLINES OF PHYSICAL CHEMISTRY Differences of Potential in a Yoltaic Cell — Two such electrodes as have just been described may be combined together to form a voltaic cell. This may be done in many ways, but a convenient arrangement is that for the Daniell cell represen ted in Fig. 39. in which the solutions are separated by a porous partition, A, which prevents convection, but allows the current to pass. When the poles are placed in the respec- tive solutions, the zinc becomes negatively charged, since Pj> /j ; on the other hand, the copper becomes positively charged as/2>P2- ■^s already explained, the solution and precipita- tion soon come to a standstill because of the accumulation of electrostatic charges. If, however, the elec- trodes are connected by a wire, the contrary charges neutralize each other through the wire, and in the solution more metal can then be dissolved and de- posited respectively (as there are no longer any opposing forces), the corresponding charges are again neutralized, and so on. The neutralization of charges through a conductor corresponds with the passage of a current. The general question as to the seat of the E.M.F. in such a cell as the Daniell has now to be considered. If the poles of the cell are connected by a wire of metal M, there are no less than five junctions at which there may be contact differences of potential ; two metallic junctions, Zn/M and M/Cu, two metal/ solution junctions, Cu/CuSO^ and Zn/ZnS04, and one liquid junction, ZnS04/CuS0^. The question as to whether there are contact differences of potential at the junction of two metals gave rise to great difference of opinion, and the controversy z i Cu + + + usq, ^^ — -~ — -c Fig. 39. ELECTROMOTIVE FORCE 343 lasted the greater part of last century. It is now generally agreed, however, that if there are such differences they are exceedingly small in comparison with those of the junctions metal/salt solution. The difference of potential at the liquid junction is of much more importance and can be calculated by Nernst's theory (p. 364). It also is small in comparison with those at the liquid/metal junctions, and may, therefore, be left out of account for the present. The distribution of differences of potential in the Daniell cell with open circuit is represented in Fig. 40 (a), the ordinates Fig. 40. representing the potentials of the different parts of the circuit' The horizontal lines, AB, CD, DE and FG, illustrate the very important fact that the copper, the zinc and the solutions are each of a definite constant potential, and the ordinates, BC and EF, that there are sudden alterations of potential at the junc- tions metal/solution. For simplicity the solutions of zinc sulphate and copper sulphate are represented as being at the same potential, which is only approximately true. It is as- sumed for the present that the difference of potential be- tween copper and N copper sulphate solution is o'sSs volts, the copper being positive, and that the potential difference, Zn/«ZnSO^, is o"S2 volts, the metal being negative. The 344 OUTLINES OF PHYSICAL CHEMISTRY total difference of potential between zinc and copper on open circuit is thus 0*585 + 0-52 = i'io5 volts. When the circuit is closed by connecting the copper and zinc by a wire of fairly high resistance, R, the distribution of poten- tial in the cell is as shown in Fig. 40 (3). The sudden changes of potential at the junctions ZnSO^/Zn and CuSO^/Cu are of the same magnitude as before, but the difference of potential between the zinc and copper, measured by the vertical height, AG, is much less than on open circuit. This is owing to the fall of potential in the cell owing to the resistance of the elec- trolyte, so that the solution in contact with the zinc is at a higher potential than that in contact with the copper, as repre- sented by EDC. If C is the current passing through the cell, and r is the resistance of the electrolyte, the E.M.F. of the cell on closed circuit is given by E = CR 4- Q,r, and CR, the fall of potential in the external wire (represented in the figure by the vertical distance AG), approaches the more nearly to the E.M.F. of the same cell on open circuit the greater R is compared with r (compare p. 335). The E.M.F. of such a combination as the Daniell cell is the algebraic sum of the E.M.F.s at the two junctions, and is represented by the formula E-E,-E, = »-fl(.og..?|-.og..J). Where Pj and Pj are the solution pressures of zinc and copper respectively, /j represents the osmotic pressure of the zinc ions in the solution, and /j that of the copper ions. The values of /j and /2 are therefore known, but the absolute values of the solution pressures Pj and Pg are unknown. The - sign of En is due to the fact that at that junction ions are leaving the solution. In obtaining E as the algebraic sum of the differences of potential Ej and E2 at the two junctions, it is naturally of the utmost importance to take the values of Ej and Eg with their proper sign. Perhaps the best method of avoiding errors in this ELECTROMOTIVE FORCE 345 connection is to consider the tendency of one kind of electricity, say positive electricity, to pass round the circuit. In going round the circuit in the Daniell cell, starting with the zinc, the different junctions are met with in the order Zn I ZnS04 | CuSO^ | Cu 0-52 0-585 1-105 and this is a very convenient method of representing the Daniell or any other cell. Now at the junction Zn/ZnSO^ positive electricity tends to pass from zinc to solution at a potential (pressure) of 0-52 volts, as indicated by the arrow. Further, as the osmotic pres- sure of Cu" ions in copper sulphate solution is greater than the solution pressure of copper, positive electricity tends to pass across the junction CuSO^/Cu, in the direction of the arrow at an E.M.F. of 0-585 volts. It is clear that the forces at the two poles are in the same direction, and therefore positive electricity tends to pass through the solution in the direction indicated by the lower arrow at a total E.M.F. of 0-520 + 0-585 = 1-105 volts. Further illustrations are given at a later stage. Influence of Change of Concentration of Salt Solution on the E.M.F. of a Cell — The general equation just given may be written in a slightly different form by substituting for the pressures the corresponding concentrations. Considering first the solution pressure, Pj, of the zinc, it is theoretically possible to choose a Zn-- ion concentration, Cj, such that its osmotic pressure will just balance the solution pressure of the metal ; this may be substituted for Pj in the general equation. Similarly, for p-^, the osmotic pressure of the zinc ions in the solution, we may substitute the corresponding concentration, fj. Dealing in the same way with the copper side of the cell, the equation for the Daniell cell (or any other cell of similar type) becomes 346 OUTLINES OF PHYSICAL CHEMISTRY E = E,-E,=°-:^«(log,„|-log,„|^). In this form the general equation may be employed to in- vestigate the question as to how the E.M.F. of the cell is affected by varying the concentration of the salt solutions. For the zinc side, since Cj is greater than ci, it is clear that the quotient CJc^, and therefore Ej, is increased by diminish- ing fj, the concentration of the Zn" ions. For the copper side, however, as Cj is less than c^ (p. 342), the quotient Cjcjy therefore Eg, will evidently be diminished by diminishing the copper sulphate concentration. The general rule with re- gard to the influence of change of ionic concentration on the E.M.F. of a cell may be expressed as follows: Diminishing the concentration of a solution from which ions are separating lowers, and diminishing the concentration of a solution into which new ions are going increases, the E.M.F. of a cell. It is evident from general principles that the effect must be as described ; in the first case, the tendency to the separation of ions is lessened, and the E.M.F. falls; in the second case, the entrance of new ions is facilitated, and the E.M.F. increases. If the concentration of the Cu" ions in the solution is pro- gressively diminished, a point must be reached at which the solution pressure of the metal is just balanced by the osmotic pressure of the Cu" ions. If the concentration is still further diminished, the tendency for copper to pass into solution will steadily increase, and ultimately may become greater than the tendency of zinc to pass into solution. It should therefore be theoretically possible to reverse the direction of the current in the Daniell cell by sufificiently diminishing the Cu" ion con- centration, and this state of affairs can be realised experimentally by adding potassium cyanide to the copper sulphate solution. A further important deduction can also be drawn from the general equation. As c-^ and c,^ stand for the concentration of the positive ions in the solution, the E.M.F. of the cell should be independent of the nature of the negative ion, pro- ELECTROMOTIVE FORCE 347 vided that the salts are equally ionised. This consequence of the theory is completely borne out by experiment. For twenty- one different thallium salts, in N/so solution, the difference of potential between metal and solution varied only from 0-7040 to 0-7055 volts, the slight variations being readily accounted for by differences in the degree of ionisation. Concentration Cells — We have now to consider what are termed "concentration cells," cells in which the E.M.F. de- pends essentially on differences of concentration. In some respects, concentration cells are simpler than those of the Daniell type, which have so far been considered. Concentration cells may be divided into two main classes — (a) Those in which the solutions are of different concen- trations. {J}) Those in which the substances yielding the ions are of different concentrations. (a) Concentration Cells with Solutions of Different Concen- trations — As a type of the elements in question, we will con- sider a cell in which silver electrodes dip in solutions of silver nitrate of different concentrations, c-^ and c^. The arrange- ment for the practical determination of the total E.M.F. of such a combination is shown in Fig. 41, where A and B repre- sent the cells containing the silver nitrate solutions and the vessel C contains an indifferent electrolyte. As this form of cell is largely employed in measurements of E.M.F., it may be well to describe it fully. It consists of a glass tube 3-4 cm. wide, with a straight side- tube D on one side and a bent side- tube E on the other, the latter being employed for making con- nection with the indifferent electrolyte in C as shown. Into the lower end of a glass tube, F, is cemented a thick rod of silver covered with the finely-divided metal by electrolysis, and the glass tube is held by a cork, closing the cell. The cell is filled with a solution of silver nitrate of definite strength through the bent tube by suction through the straight side-tube, D, which is then closed by a clip. The other " half-cell," B, is prepared 348 OUTLINES OF PHYSICAL CHEMISTRY in exactly the same way, but contains a solution of silver nitrate of different concentration. The ends of the bent tubes are then dipped into an indifferent electrolyte in the vessel, C, as shown, and the total E.M.F. of the combination determined by the potentiometer method in the usual way, connection with the silver electrodes being made by wires passing down the interior of the glass tubes. In this case, the general equation for an electrolytic cell, E=^(log,„^-log,^) simplifies to E = 0-058 (•°S"f) (I) r — '-^ f^ ^ — =A ^ 1 v % v= C f--A Fig. 41. since C, the solution pressure of the metal, is the same on both sides, and is therefore eliminated. A cell of the type Ag AgNOgdil AgNOgConc Ag works in such a way that silver is deposited from the more concentrated solution, in which the osmotic pressure is higher, and is dissolved at the pole in contact with the weaker solution, which offers less resistance to the entrance of Ag- ions. The ELECTROMOTIVE FORCE 349 change, therefore, proceeds in such a way that the differences of concentration tend to equalize, and when the solutions have reached the same concentration, the current stops. Positive electricity therefore passes in the element from the weak to the strong solution, as indicated by the arrow, and in the connecting wire from the strong to the weak solution ; the electrode in contact with the strong solution becomes positively charged, the other electrode negatively charged. The equation shows that the E.M.F. of such a concentra- tion cell depends only on the respective concentrations of the positive ions in the two solutions and their valency, and not on the nature of the electrodes or on the nature of the anions, and the experimental results are in full accord with this deduction. Otherwise expressed, the E.M.F. of any element made up of a univalent metal M dipping in solutions of one of its salts of different concentration is of the same absolute value as that of the silver concentration cell, provided that the solutions are of corresponding concentration, and ionised to the same extent. Further, if the solutions are dilute, and electrolytic dissociation therefore fairly complete, the ratio of the ionic concentrations in different dilutions will be approximately the same as the ratio of the concentrations themselves. Thus, in the example under consideration, the ratio cjc-^ for r/ioo molar, and i/iooo molar solutions, will be approximately xo : i ; logiofjM is therefore i, and the value of E for the cell Ag I AgNOg j mj 1000 AgNOa mjioo Ag is 0-05 8/« = o'o58 volts, since n, the valency of the ions con- cerned, is unity. If, however, the solutions are more concentrated, the fact that ionisation is incomplete must be taken into account in calculating the E.M.F. of a cell. Suppose, for instance, it is required to calculate the E.M.F. of the cell Ag I AgNOa mj 100 \ AgNOg mj 10 \ Ag. 3SO OUTLINES OF PHYSICAL CHEMISTRY N/io silver nitrate solution is ionised to the extent of 82 per cent, at 18°, whence c^ = o'o82, and N/ioo silver nitrate to the extent of 94 per cent., whence c-^ = 0-0094. We have therefore cjc-^ = o-o82/o-oo94 = 8'72, and E = 0-054 volts, in excellent agreement with the experimental value. Strictly speaking, it is not justifiable in cells of this type to neglect the contact difference of potential between the two solutions, which may amount to a considerable fraction of the total E.M.F. The accurate formula for the calculation of the E.M.F. of cells of this type is given in a succeeding section (p. 364). If, however, both solutions contain an indifferent electro- lyte in equivalent concentration great in comparison with those of the active salt, the difference of potential at the liquid junction becomes negligible, and the above formula (i) holds accurately {cf. p. 363). It is evident from the formula that the E.M.F. of a con- centration cell cannot be greatly increased by increasing the concentration on one side, owing to the limited solubility of the salts used as electrolytes. On the other hand, the E.M.F. may be greatly increased by diminishing the ionic concentra- tion on one side. Conversely, when a cell is made up with a solution of silver nitrate of known Ag" ion concentration, c-^, and one of unknown concentration, Co, and the E.M.F. of the cell is measured, Co can readily be calculated. This principle has been applied more particularly for the determination of very small ion concentrations, and may be illustrated by the determination of the Ag- ion concentration in a saturated solution of silver iodide. When the concentration on one side is very small, it is usual to add some salt, with or without a common ion, to eliminate the potential difference at the liquid junction, and also to increase the conductivity in the cell, so as to render the measurements more accurate. In this case potassium nitrate may conveniently be used. The observed E.M.F. of the cell Ag I KNO3 + Agl I AgNOg o-ooim + KNO3 | Ag ELECTROMOTIVE FORCE 351 is o"22 volts. Since c-^ — o'ooi, we have E = o'22 = 0-058 logio(o'ooi/co), whence <:<, = i"6 x io"8. In other words, a litre of a saturated solution of silver iodide contains i'6 x 10"* mol of silver iodide, in excellent agreement with the value, I'S x io~^ mol, obtained from conductivity measurements (p. 301). ip) Cells with Different Concentrations of the Elec- trode Materials (Substances Producing Ions) — Not only can concentration cells be obtained by employing different con- centrations of an electrolyte, but also by using metals, or other substances yielding ions in different concentrations. The con- centration of metals can for our present purpose be most satis- factorily varied by employing their solutions in mercury, the so-called amalgams. For example, a concentration cell can readily be built up as follows : — Zinc amalgam conc./zinc sulphate solution/zinc amalgam dilute which differs from the cells of the first type in that the osmotic pressure of the zinc ions in contact with the two poles is the same, but the concentration, and therefore the solution pressure of the metal on the two sides, is different. The E.M.F. of a cell of this type is represented by the general formula (p. 341) „ O-O00I983T/, P, , P„\ Since the same solution (in this case zinc sulphate) is in contact with both electrodes, /j ^p^, and the formula becomes o'oooioS^T, P, E = ^ log,„p-;- On the assumption that Pj and Pj, the solution pressure of the zinc in the concentrated and dilute amalgams respectively, are proportional to the respective concentrations, we obtain 352 OUTLINES OF PHYSICAL CHEMISTRY which is exactly the same form of equation as that for cells with different electrolyte concentrations. As the solution pressure of the zinc is higher in the con- centrated amalgam, it passes into solution from the latter and is deposited in the less concentrated amalgam, so that the con- centrations tend to become equal. It follows that positive electricity passes in the cell from the concentrated to the dilute amalgam, as shown by the arrow. As an illustration, the E.M.F. of a cell for which Cj = 0-14 mol and Cg = o'oo2i4 mol of zinc per litre of amalgam at 23° may be calculated. If it be assumed that zinc is unimolecular when dissolved in mercury, « = 2, and 17 o'oooiqSa X 2q6 , o'i4 ■c- = — ^—- logio ^— = 0-053 volts, 2 *^" 0-00214 in excellent agreement with the observed value, 0-052 volts. So far, the possible effect of mercury on the potential has been disregarded, and this is justified by the excellent agreement between observed and calculated values for the E.M.F. on the assumption that mercury simply acts as an indifferent solvent. The explanation is that for a mixture of two metals it is the metal with the higher solution pressure that goes into solution, and mercury can consequently be used as solvent in potential measurements for any metal which is "less noble," i.e., which has a higher solution pressure than mercury itself. As indicated above, the E.M.F. of a metal dissolved in mer- cury depends on the concentration. The difference of potential between a saturated solution of a metal in mercury and an aqueous solution of one of its salts is the same as that between the salt solution and the pure metal, and even for dilute amal- gams the E.M.F. is not very different from that of the pure metal, as the example shows. On the other hand, the potential of a metal in chemical combination with a more noble metal may be quite different from that of the pure metal. The energy relations in concentration cells in which very dilute solutions are employed are remarkable. In the silver ELECTROMOTIVE FORCE 353 nitrate concentration cell described above, the change con- sisted simply in bringing Ag ions from the pressure /j to the lower pressure /j- When a perfect gas expands from the pressure p^ to p^, no internal work is done, and this is the more nearly the case for ordinary gases the lower the pressures. In an exactly corresponding way no internal work will be done when a salt is further diluted in sufficiently dilute solution ; in other words, the heat of dilution will be zero. This means that the change of chemical energy (Q in the Helmholtz formula), also termed the heat of reaction, is zero, so that the electrical energy obtained from a concentration cell with suffi- ciently dilute solutions does not come from a chemical change at all, but entirely from the surroundings. Under these circum- stances, as Q is zero, the Helmholtz formula simplifies to Electrodes of the First and Second Kind. Tlie Calomel Electrode — So far only electrodes which are reversible with regard to the positive ion have been considered; these are termed electrodes of the first kind. In an exactly similar way it is possible to construct electrodes which are reversible with regard to the negative ion — these are termed electrodes of the second kind. The most important electrode of the latter type is the calomel electrode, which consists of mercury in contact with solid mercurous chloride and a saturated solution of the latter salt in potassium chloride solution as electrolyte. The calomel electrode is reversible with regard to CI' ions, just as the CU/CUSO4 electrode is reversible with regard to Cu" ions. If positive electricity passes from metal to solution, the mercury combines with CI' ions and calomel is formed ; if passed in the reverse direction chlorine goes into solution and solid calomel disappears. The electrode, therefore, acts like a plate of solid chlorine, which gives up or absorbs the element de- pending on the direction of the current. 3S 354 OUTLINES OF PHYSICAL CHEMISTRY In order more fully to illustrate the above statements with regard to the calomel electrode, we will consider the working of the "double concentration cell" — Zn I ZnCljdil | HgCl | Hg | HgCl | ZnCl^conc | Zn obtained by interposing a calomel electrode between the half- elements Zn/ZnCladil and ZnCljConc/Zn. Positive electricity passes in the cell in the direction of the arrow, zinc dissolving in the dilute solution and being deposited from the concentrated solution, so that the net result of the pro- cess is the transference of zinc chloride from the concentrated to the dilute solution. The calomel electrode, however, plays an essential part in the process. When i mol of zinc dissolves in the dilute solution, two equivalents of mercury are liberated from the calomel and two equivalents of CI' ions remain in solution. At the other side of the compound cell, a mol of zinc is deposited, and simultaneously two equivalents of mercury combine with the equivalent amount of chlorine to form calomel. The calomel electrode has therefore been instrumental in effect- ing the transference of the CI' ions, and has acted in such a way that when positive electricity passes in the direction Hg/HgCl calomel is formed and CI' ions disappear. When the current passes in the opposite direction, HgCl/Hg, calomel disappears and an equivalent of CI' ions are formed. In other words, the calomel electrode acts like an electrode of solid chlorine, as already mentioned. As the mercury is liberated at one side and produced at the other in equivalent quantity, it plays no essential part in the process. Theoretically, only calomel (solid and in solution) and mercury are required to form the electrode, but potassium chloride is always added to increase the conductivity of the solution. As the tendency of CI' ions to enter or leave the solution depends on the concentration of CI' ions already present, the difference of potential between mercury and the ELECTROMOTIVE FORCE 355 solution must depend on the concentration of the potassium chloride solution used. A normal solution is mostly largely employed. The calomel electrode is largely used as a normal electrode by means of which the E.M.F.s of other electrodes may be com- pared ; its chief advantage for this purpose is that it can readily be reproduced with an accuracy of about i millivolt. A conven- ient form of the elec- trode is shown in Fig. 42. A vessel of the type already described in connection with concentration cells (p. 347) may con- veniently be used. A layer of dry mercury is first placed in the bottom of the vessel, then a paste made by rubbing in a mortar mercury and calomel with some of the po- tassium chloride solu- tion, and the vessel is then filled up with ^-potassium chloride solution which has previously been saturated with calomel by shaking with excess of the latter. Connection with the mercury may conveniently be made by means of a platinum wire sealed at the bottom into a glass tube A, the latter passing up through the rubber stopper closing the vessel. In making measurements, the bent side- tube, C, must also be filled with the potassium chloride solu- tion. This is done by suction at the straight side-tube, B, which is then closed by a clip. ^Hg,CJ,^Hg Fig. 42. 3S6 OUTLINES OF PHYSICAL CHEMISTRY For measuring the potential of another electrode by means of the calomel electrode, the arrangement already shown in Fig. 41 is used. Neglecting for the present the differences of potential at the liquid junctions, the E.M.F. of the combination in question is the algebraic sum of the differences of potential at the two metal/solution junctions. It follows that if the single potential difference between mercury and solution is known, the single potential difference at the other electrode can readily be cal- culated. Unfortunately no single potential difference is known with certainty (see next section), and it is, therefore, necessary to refer them to an Arbitrary standard. Two such standards are in general use, (a) the so-called " absolute " standard ; {b) the hydrogen standard. As regards the first standard, Ostwald as- sumes that the potential difference between mercury and the solution in the normal calomel electrode is o's6o volts at 18°, the mercury being positive, and differences of potential referred to this standard are termed " absolute potentials " (see next sec- tion). On the other hand, Nernst refers E.M.F.s to the hydrogen standard, on the assumption that there is no difference of poten- tial between a platinum electrode saturated with hydrogen and a normal solution of an acid. The " absolute " potentials, referred to the calomel electrode, have a theoretical basis, and there is reason to suppose that the real, but at present unknown, single potential differences are not very different from the " absolute " potentials. Independently of this, however, the use of the calomel electrode in actual measurements is justified by the fact that it can be reproduced with a high degree of accuracy. The use of the hydrogen electrode as standard is purely arbi- trary, as it is not pretended that the difference of potential between electrode and solution is actually zero, but the refer- ence of potential differences to this standard has certain advan- tages. It is, in fact, usual to make the actual measurements with the calomel electrode, and then to refer them to the hydrogen standard, on the basis that when the hydrogen ELECTROMOTIVE FORCE 3S7 electrode is taken as zero the E.M.F. of the normal calomel electrode is - 0-283 volts. In order to illustrate the use of the calomel electrode for potential measurements, the separate determination of the dif- ferences of potential metal/solution for the two parts of the Daniell cell will be considered. When the zinc electrode is combined with the calomel electrode, as shown in Fig. 41, to form the cell Zn «-ZnS04 KCl (in vessel C) HgjCla i nKCl Hg 0-520 0-560 1-080 the E.M.F. of the combination, as shown by potentiometer measurements, is i-o8o volts, the zinc being negative with regard to mercury, so that positive electricity flows in the cell from zinc to mercury, as indicated by the lower airow. In order to obtain the potential difference Zn/ZnSO^, we proceed as follows (p. 345 ). It is known that mercury in contact with a solution of calomel becomes positively charged, and that for the calomel electrode the tendency for positive electricity to pass across the junction towards the mercury is 0-560 volts. The tendency for positive electricity to pass round the circuit is equivalent to i-o8o volts, hence the E.M.F. at the Zn/ZnSO^ junction must act in the direction shown by the upper left-hand arrow, and is 1-080 — 0-560 = 0-520 volts. In other words, the E.M.F. at the junction Zn/ZnSO^ is 0-520 volts, the zinc being negatively charged. Similarly, the observed E.M.F. of the cell Cu I «-CuSO^ I KCl I HgjCl^ in n-KCl | Hg 0-585 < — 0-560 0-025 3S8 OUTLINES OF PHYSICAL CHEMISTRY is o'o25 volts, the copper being positive with regard to mercury, hence positive electricity flows from mercury to copper in the cell, as indicated by the lower arrow. As far as the calomel junction is concerned, the tendency for positive electricity to flow round the circuit is equivalent to o"56o volts towards the right, as indicated by the arrow. Hence in order that for the whole cell the tendency of positive electricity may be to flow towards the left at a potential of 0*025 '^ol's the E.M.F. at the Cu/CuSO^ junction must act in the opposite direction to that at the calomel junction and exceed it by 0*025 volts. The E.M.F. at the junction Cu/CuSO^ is therefore 0-585 volts and positive electricity flows from solution to copper, as indicated by the arrow. The total E.M.F. of the cell Zn/ZnSO^CuSOi/Cu is, there- fore,-o'52o + ( — o*585)= — i*io5 volts, which agrees with the value obtained by direct measurement (p. 34^1). It is evident from the above that although the single potential differences at the junctions depend upon the value of the potential assumed for the standard, the E.M.F. of the complete cell does not depend upon the E.M.F. of the standard, which is eliminated. If referred to the hydrogen electrode as standard, the poten- tial diff'erence Zn/w-ZnSO^ is - 0-520 + ( - 0-283) = - o"8o3 volts, and that for Cu/«-CuSO^ is + 0-585 + ( - 0-283) = + 0-302 volts, the E.M.F. of the Daniell cell being as before = (-0-803) + ( - 0-302) = - 1-105 volts. Single Potential Differences. The Capillary Eleotro- jQeter — When mercury and sulphuric acid are in contact in a capillary tube, and the arrangement is connected with a source of E.M.F. in such a way that the mercury is in contact with the negative pole and the acid with the positive pole, the area of the surface of separation between acid and mercury tends to diminish. The following out of this observation of Lippman's has led to an approximate estimate of the absolute differences of potential at metal/solution junctions. When mercury and sulphuric acid have been in contact for ELECTROMOTIVE FORCE 359 some time, it is probable that there is a constant difference of potential between them, brought about in a rather complicated way. We have already learnt that well-defined differences of potential are established when a metal is in contact with a solution of one of its salts of definite concentration, and that is probably the state of affairs in the present case. We may suppose that some of the mercury dissolves in the sulphuric acid to form mercurous sulphate, and that the solution im- mediately in contact with the mercury is saturated with regard to the salt. As, however, thjs osmotic pressure of solutions of mercury salts is in general greater than the solution pressure of mercury, Hgj" ions deposit on the mercury and the latter becomes positively charged with regard to the solution. The two kinds of electricity attract each other, and we will assume with Helmholtz that the effect of this attraction is that there is a layer of positive electricity near the surface of the mercury holding a corresponding layer of negative electricity near the surface of the acid (" Helmholtz double layer ") {cj. Fig. 38). Now there will be a certain surface-tension at the junction mercury/solution in the capillary tube, and, as is well known, the effect of surface tension is to make the areas of the surfaces in contact as small as possible. This tendency will, however, be counteracted by the electric layers; the positive charges will repel each other and tend to enlarge the surface, and the same is true of the negative charges. The effect of the diiference of potential is, therefore, to diminish the surface tension. The fact that a contrary E.M.F. applied to the junction tends to diminish the surface of separation between acid and mercury will now be readily understood. The con- trary E.M.F. diminishes the difference of potential between acid and mercury, part of the force diminishing the surface tension is removed, and the latter attains more nearly its true value when undisturbed by electrical forces. When the con- trary E.M.F. is gradually increased, the surface tension increases at first, attains a maximum value, beyond which it gradually 36o OUTLINES OF PHYSICAL CHEMISTRY diminishes. It is plausible to suppose that the surface tension increases as the difference of potential between mercury and acid gets smaller and smaller, that it attains its maximum value when the contact E.M.F. at the junction is just neutralized by the contrary E.M.F. , and that it again diminishes as the latter is further increased and the surfaces become charged with electricity of opposite sign to the original charges. This at once gives us a method of determining single differences of potential. It is only necessary to note when the surface tension attains its maximum value ; under these circumstances the applied E.M.F. is clearly equal to the single difference of potential at the junction mercury/solution and the problem as to the value of a single potential difference is solved. In this way Ostwald estimated the E.M.F. of the normal calomel electrode at o'56o volts. Unfortunately the matter is not quite so simple as the above considerations would lead us to suppose, and it is fairly certain that the absolute potentials arrived at in this way may differ considerably from the true values. It has already been pointed out that two standards are in use, and that the use of the calomel electrode for measuring differences of potential has certain practical advantages. Before considering another method which has been suggested for measuring single differences of potential, it should be men- tioned that the phenomena just described have been applied to the construction of an electrometer — the so-called capillary electrometer. The electrometer consists essentially of two quantities of mercury between which is placed dilute sulphuric acid. One quantity of mercury is in contact with the acid at a large surface, the other at a very narrow surface in a capillary tube, as above described. When the apparatus is so arranged that the mercury and acid are in equilibrium at a position in the capillary tube, and the two quantities of mercury are then connected with a source of E.M.F., the potential at the surface will alter owing to the alteiation in the concentration of the ELECTROMOTIVE FORCE 361 mercurous salt produced by the current, and as, owing to the alteration of the surface tension, there is no longer equilibrium, the position of the surface of contact will alter. The use of the apparatus as an electrometer will now be evident. It is best so to arrange matters that the mercury at the narrow surface is connected with the negative pole of the external source of E.M.F. through a tapping key, and the junction is observed through a small microscope. If an external E.M.F. is applied, the surface will move when the key is momentarily depressed, and for small differences of potential (up to o'oi volt) the movement of the meniscus is proportional to the applied E.M.F., so that the name electrometer is justified. When the applied E.M.F. is zero, no movement of the meniscus occurs on making contact, and the electrometer may therefore be used as a null instrument. When not in use, the electrometer should be connected up with a cell of E.M.F. not exceeding i volt. An alternative very instructive method of determining single potential differences, the theory of which is due mainly to Nernst and the practical realization to Palmaer, will now be de- scribed. When mercury in a fine stream is allowed to flow into an electrolyte containing a definite concentration of mercurous salt {e.g., mercurous chloride), Hg.^" ions from the solution deposit on the drops as they enter (the osmotic pressure of Hg^" ions in the solution being greater than the solution pres- sure of the mercury), the drops thus become positively charged, and further become surrounded with a layer of the liberated Cr ions. When the drops reach the bottom of the vessel containing the electrolyte, the positive ions are given up and reunite with the CI' ions to form more calomel. The net result of this process is that the solution gets poorer in calomel where the drops enter, and richer where they unite with the mercury. A concentration cell is thus formed, and it is evident that positive electricity must flow from the weak to the strong solution, that is, from top to bottom of the vessel, a deduction which is borne out by experiment. 362 OUTLINES OF PHYSICAL CHEMISTRY Now it must be possible to reduce the concentration of Hgjj" ions to such a point that the osmotic pressure of the Hgj- ions is just equal to the solution pressure of the mercury ; there is then no deposition of Hgj" ions on the entering drops, and no current flows. Conversely, when no current results when mercury is dropped into an electrolyte containing Hg^- ions, the difference of potential between mercury and the solution must be zero. If the Hgg" ion concentration is still further reduced, the solution pressure of the mercury is greater than its osmotic pressure in the solution, and the current flows in the opposite direction. The Hgjj"' ion concentration was reduced by adding potassium cyanide till the point of no current and therefore zero difference of potential was reached. The solution in equilibrium with mercury under these conditions may be termed the null solu- tion. If then a cell is built up of the type Hg I null solution | solution of salt of metal M | M O «! 1?2 i?2, the difference of potential between metal and solution, can be determined directly if the E.M.F. «i at the junction of the solution is known or can be made negligible. In this way Palmaer has found that the E.M.F. at the junction Hg/yz/ioKCl saturated with HgjClj is 0-573 volts at 18°, cor- responding with about -0-520 volts for «/iKCl, as compared with Ostwald's value of 0-560 volts. Some writers consider that the problem of the determination of single potential differences is thus finally settled, but Palmaer himself does not consider that all the difficulties of the measure- ments have been overcome, so that the above results should only be taken as provisional.^ Potential Differences at Junction of Two Liquids— Up to the present, we have left out of account the possible dif- ferences of potential at the junction of two solutions. When the E.M.F. of a cell is considerable, the error thus arising is only slight, but if the E.M.F. is small, as for many concentra- 1 Cf. Palmaer, Zeitsch. physikal Chem., 1907, 59, 129. ELECTROMOTIVE FORCE 363 tion cells, the potential difference at the liquid contact be- comes of importance. It has been shown by Nernst that in many cases these dif- ferences of potential can be calculated according to his theory of electromotive force, and the results obtained in this way have been fully confirmed by experiment. The calculation is effected most readily for solutions of the same electrolyte in different concentrations, for example, solutions of hydro- chloric acid. When the solutions are brought in contact the acid will tend to diffuse from the more concentrated to the more dilute solution. As, however, the acid is highly ionized, the H- and CI' ions will diffuse independently, and, as the former move the more rapidly, the dilute solution will soon contain an excess of H- ions and the strong solution an excess of CI' ions. Owing to the electric charges conveyed by the moving ions, the dilute solution will become positively charged, and the strong solution negatively charged. However, the excess of positive electricity in the dilute solution will retard the entrance of H' ions and accelerate the CI' ions, so that in a short time the ions will be moving at the same rate. The difference of potential thus produced will persist until both solutions attain the same concentration. The above considerations show that the contact difference of potential between two solutions is due to the different migration velocities of the two ions, and the dilute solution takes the potential corresponding with that of the more rapid ion. The contact difference of potential between dif- ferent solutions of the same salt will be the smaller the more nearly the speed of the two ions agrees, and this explains why solutions of potassium chloride and of ammonium nitrate are used as connecting solutions in potential measurements (com- pare p. 350). It can easily be shown that the potential difference E be- tween two solutions of a binary electrolyte with univalent ions (for example, hydrochloric acid) is represented by the formula 364 OUTLINES OF PHYSICAL CHEMISTRY r, U — V 2''1026RT , C, ^ = ;7T^ — F — >°g«.7 where Cj and c^ represent the ionic concentrations of the two solutions, and u and v the migration velocities of the anion and cation respectively. From the above equation it can be calculated that the contact E.M.F. between N/io and N/ioo hydrochloric acid is 0-036 volt, a result which is fully con- firmed by experiment. From the above result, the value of E may be calculated for the cell Ag I AgNOgw/io I AgNOjw/ioo | Ag when the contact difference of potential between the two solutions is not practically eliminated by the use of potassium nitrate. Taking the junctions in order, we have E = i:^\ RT logio ^' + ^" RT logio i! - RT logi„ &] 2''?o26r u ~ V , Ci u + V „_, , t:{l = . 2 X 0-058 logio- U + V ^2 for room temperature. For silver nitrate = 0-522 (p. 233), c^ = 0-082, q = u + V 0-0094. Hence E = 0-522 X 2 X 0-058 X 0-945 = 0-057 volts, in excellent agreement with the Value found experimentally, 0-055 volts. Gas Cells — So far we have dealt only with solid substances and amalgams as electrode materials, but it is interesting to note that gases may be used in the same way. This is made possible by using metallic electrodes, usually of platinum coated with the finely-divided metal, as absorbents for the gases. The ELECTROMOTIVE FORCE 365 prepared platinum electrode is partially immersed in the solution of an electrolyte, and the gas is bubbled through till the potential difference between electrode and solution becomes constant. As an example of a gas electrode, the hydrogen electrode, already referred to, will be described. The form of cell repre- sented in Fig. 41 may be used ; it is half filled with normal acid, the platinum pole, held by a weU-fitting cork, is partially immersed in the acid, and hydrogen gas is passed in by the bent side-tube and allowed to bubble through the acid for ten or fifteen minutes till the electrode is saturated. The straight side-tube, which has been open, is now closed by a clip, and the electrode is ready for use. The platinum pole itself usually consists of a piece of platinum foil joined by hammering to a platinum wire, the latter being sealed into the bottom of the glass tube carried by the cork closing the cell. Electrical con- nection may be made by a copper wire passing down through the glass tube and dipping into a little mercury at the bottom, the mercury being also in contact with the upper part of the platinum wire which projects into the interior of the glass tube. The electrode is completely reversible and behaves like a plate of metallic hydrogen. When positive electricity passes from solution to metal, hydrogen ions are discharged accord- ing to the equation 2H- -> Hj ; when it goes in the contrary direction gaseous hydrogen becomes ionised according to the converse equation, Hj -> zH-. A hydrogen concentration cell is obtained when two hy- drogen electrodes, containing the gas at different pressures, are combined in the usual way. Such cells correspond exactly with those made up with amalgams of different concentrations, and the E.M.F.s can be calculated by the same formula (p. 351). The direction of the current is such that the pressures on the two sides tend to become equal, so that hydrogen becomes ionised at the high pressure side and is discharged as gas at the low pressure side. 366 OUTLINES OF PHYSICAL CHEMISTRY Concentration cells with oxygen, sulphuretted hydrogen and other gases have also been investigated. Cells in which the electrodes are in contact with different gases, for example, the hydrogen-oxygen cell, are referred to below. Potential Series of the Elements — During the considera- tion of the Daniell cell (p. 340), it was pointed out that metals differ greatly with regard to their solution pressures. Zinc, for example, has a very high solution pressure, whilst that of copper is very small. The difference of potential between a metal and a solution of one of its salts at room temperature is represented by the formula P 0-058 , P n p and if p, the osmotic pressure of the positive ions of the salt, is the same for all the electrodes, say that represented by a normal solution of a salt, it is evident that the value of E is propor- tional to the solution pressure of the metal. As regards the standard to which the E.M.F.s are to be referred, the hydrogen standard has in this case certain advantages. The potential of metals with regard to normal solutions of their salts is therefore obtained by measuring the E.M.F. of cells of the type H2(Pt) I «H' I normal solution of the metallic salt | metal, the difference of potential H2(Pt) | «H- being taken as zero. The E.M.F. of the combination H2(Pt) I «H- I M-ZnSO^ I Zn 0770 measured with the potentiometer in the usual way, is 0770 volts, the hydrogen being positive with regard to the zinc. The value of E^nsOi-Zn is therefore -t- 0-770 volts, the poten- tial difference at the other junction being zero by definition. ELECTRO MOtlVE FORCE 367 and positive electricity goes in the cell in the direction indicated by the arrow, that is, the solution tension of zinc is greater than that of hydrogen, so that the former displaces the latter (indirectly) from solution. On the other hand, the E.M.F. of the cell H^CPt) I «H- I wCuSO^ I Cu > 0-329 is 0-329 volts, copper being positive ; positive electricity goes in the solution in the direction represented by the arrow. Hydro- gen therefore goes into solution and copper is deposited, so that the solution pressure of hydrogen is greater than that of copper. In an exactly corresponding way, the potential of any other metal may be determined. The following table contains what is termed the potential series of some important elements. The numbers represent the potential difference, in volts, between a metal and a normal solution of one of its salts, referred to the hydrogen electrode as standard. For those elements with a higher solution pressure than hydrogen the numbers have the positive sign, for a reason which will be considered later. Na Mg Al Mn Zn Cd Fe Co Ni + 2-58 1-482 1-276 1-075 0-770 0-420 0-334 0-232 0-228 Pb H^ Cu Hg Ag I Br CI + 0-151 ±0 -0-329 -0-753 -0771 -0-520 -0-993 - i'3S3 The numbers for chlorine, bromine and iodine, are comparable with the others, and are obtained in a somewhat similar way. The value for chlorine, for example, may be obtained by measuring the E.M.F. of a cell of the type. Hj(Pt) I « - H- I « - CI I Cl2(Pt), the right-hand electrode being reversible for chlorine just as the left-hand one is reversible for hydrogen (see below). By means of this table, the E.M.F, of a cell made up of two 368 OUTLINES OF PHYSICAL CHEMISTRY metals in contact with normal solutions of their salts can at once be calculated. As the following schemes show, a zinc- nickel element has the E.M.F. 0770 - o"228 = 0*542 volts, and a zinc-silver element the E.M.F. 0770 - (-cyyi) = I "541 volts. Zn I «Zn" I «Ni" | Ni *■ < 0770 0-228 > 0-542 V. Zn I «Zn" I «Ag- | Ag 0770 0771 ^ 1-541 V. positive electricity flowing in the respective cells, in the direc- tions indicated by the lower arrows. The student should have no difiSculty in understanding these schemes in the light of the considerations advanced on p. 345. Both in the case of zinc and of nickel the solution pressure of the metal is greater than the osmotic pressure of the metallic ions in normal solution, and, therefore, when arranged to form a cell, the tendency for posi- tive electricity to pass round the circuit is in the opposite direc- tion at the two junctions. Positive electricity, therefore, flows in the direction in which the acting force is the greater, and the total E.M.F. is the difference of the forces at the two junctions. In the zinc-silver cell, on the other hand, the forces act in the same direction, and the total E.M.F. is therefore the su7n of the forces at the junctions. It is evident from the above that metals which stand higher than hydrogen in the tension series can liberate hydrogen from acids, and the numbers in the table are a measure of the energy of the reaction. On the other hand, hydrogen at atmospheric pressure should displace the metals which stand below it in the tension series, and it has been proved by experiments with platinized platinum electrodes saturated with hydrogen that such is the case. ^ Further, each metal is able to displace from combination any metal below it in the tension series under equivalent conditions, and the difference of potential between the metals is a measure of the free energy of the change. ' That the changes do not take place readily under ordinary con- ditions ig doubtless dug to the reaction velocity being small. ELECTROMOTIVE FORCE 369 Cells with Different Gases — The simplest example of these cells is the hydrogen-chlorine cell, already referred to. One-half of the cell consists of a hydrogen electrode in acid, the other of a similar electrode saturated with chlorine, and the two electrodes are combined as represented in Fig. 41, the intermediate vessel containing acid of the same strength as that in the cell. The chemical change which takes place in the cell is the combination of hydrogen and chlorine to form hydro- chloric acid. Representing the cell as usual — H^CPt) \nH-\ nCY \ Cl2(Pt), I-3S it is clear that positive electricity flows in the cell from hydrogen to chlorine in the direction represented by the arrow, the chlorine becoming the positive and the hydrogen the negative pole. The E.M.F. of the cell in normal acid at the ordinary temperature is about i"35 volts. The most important cell of this type is the hydrogen-oxygen or Grove's cell, the two poles being saturated with hydrogen and oxygen respectively. When connection is made the gases gradually disappear, hydrogen becoming ionized at one pole and oxygen uniting with water to form hydroxyl ions at the other pole. The cell may therefore be represented by the following scheme — water ^2^^') (acid, alkali or salt) 02(Pt) 1-23 and positive electricity flows through the cell from hydrogen to oxygen as represented by the arrow, so that hydrogen is the negative pole and oxygen the positive pole. The hydrogen electrode is reversible with regard to hydrogen, as follows : Hj^^aH-, the reaction taking place at the oxygen electrode is as follows : HgO -I- JOjJ^aOH'. When employed as indicated 24 370 OUTLINES OF PHYSICAL CHEMISTRV above, the change is that represented by the two upper arrows and 2F passes through the wire ; when, on the other hand, 2F is sent through the cell in the opposite direction, the changes at the two poles are represented by the two lower arrows. There is reason to suppose that if absolutely indifferent electrodes were used for absorbing the gases, and the changes at the electrodes were fully reversible, the E.M.F. of the cell would be I "23 volts. ^ The values actually observed are smaller, probably owing to the formation of an oxide of platinum, which has an oxygen potential different from that of free oxygen. Theoretically, only pure water is necessary as electrolyte, but,in order to increase the conductivity, dilute acid or alkali or a dilute salt solution is employed as electrolyte. The E.M.F. of the cell is independent of the nature of the electrolyte, but this is not the case for the single potential differences at the electrodes. Oxidation-Reduction Cells — The gas cell just described is a typical oxidation-reduction cell, as when working hydrogen is being oxidized at the negative pole and oxygen reduced at the positive pole. As may be anticipated, corresponding cells can be con- structed in which instead of hydrogen another reducing agent is used, and instead of gaseous oxygen another oxidizing agent. Indifferent metals, such as platinum or iridium, are used as electrodes in all cases. We will first consider a cell built up of a hydrogen electrode on one side and a platinized platinum electrode dipping in a solution of a ferrous and a ferric salt on the other. When the two electrodes are connected up, a current flows in the cell from the hydrogen to the other electrode. Hence at the hydrogen electrode gaseous hydrogen is going into solution as hydrogen ions according to the equation H2 + 2F = 2H-, and at the other electrode Fe"- ions are being reduced to Fe- ions according to the equation 2Fe— - 2F = 2Fe", the charges neutralizing each other through the wire and thus producing 1 Corresponding with tlie free energy of formation of water from its elements. ''aF or 2 X 96,540 coulombs converts a mol of hydrogen to H' ions. ELECTROMOTIVE FORCE 371 a current. When the same quantity of electricity is passed through the cell in the opposite direction, Fe- ions are con- verted to Fe"' ions, and hydrogen gas is liberated at the other pole ; the cell therefore works reversibly, and the measurement of the E.M.F. gives a measure of the free energy or affinity of the reaction. The total change is, of course, expressed by the equation 2Fe"" + Hj = 2Fe" + zH'. Other oxidizing agents can be measured in the same way against the hydrogen electrode, and from the results a table of various solutions, arranged in the order of their oxidizing potentials, can be obtained. Some of the values obtained in this way may be given. SnClg in HCl — o'23 volts FeCls in HCl — 0*98 volts NHjOH in HCl - 0-38 volts KMnO^ in H2SO4 - i -50 volts The above are only meant to indicate the order of the results, as the accurate values depend greatly on the concentration and composition of the solutions. The four solutions mentioned, even stannous chloride, in acid solution exert an oxidizing action on gaseous hydrogen, and therefore the direction of the current is the same as in the ferric chloride cell. As might be anticipated, potassium per- manganate has the highest oxidation potential. When, on the other hand, a platinum electrode dipping into a solution of stannous chloride in potassium hydroxide is con- nected with a hydrogen electrode so as to form a cell H,(Pt) «H- < — Sn" in «OH' (Pt) 0-560 hydrogen ions are discharged and the stannous salt becomes oxidized, positive electricity, therefore, flowing in the cell in the direction of the arrow. The change which takes place in the cell may be represented by the equation 2H- + Sn" =Sn"" + Hj, the hydrogen acting as the oxidizing agent. In this case we 372 OUTLINES OF PHYSICAL CHEMISTRY may say that the stannous chloride solution has a certain reduc- tion potential. The above considerations- are sufificient to show that the terms " oxidizing agent " and " reducing agent " are relative and not absolute ; whether a substance acts as an oxidizing or a reducing agent depends on the substance with which it is brought in contact. The hydrogen electrode may be replaced by a platinum electrode dipping in a solution of a reducing agent, an oxida- tion-reduction cell containing only liquids being obtained. One well-known cell of this type consists of platinum electrodes dipping in solutions of ferric chloride and stannous chloride respectively. The changes at the electrodes may be represented by the equations (i) 2Fe- - 2F = 2Fe" (2) Sn- -f 2F = Sn— and the total change as follows — 2Fe- -1- Sn- = 2Fe" -1- Sn-- It is now easy to understand what at first sight appears very puzzling, that a ferric salt can oxidize a stannous salt at a dis- tance, the solutions being in separate cells and possibly con- nected by an indifferent solution. The above equations show that the essential feature of the phenomenon is the transference of two positive charges from the iron to the tin ions through the wire. As a definite potential may be ascribed to every substance acting as an oxidizing or reducing agent, it is clear that the E.M.F. of an oxidation-reduction cell may be represented as the algebraic sum of the differences of potential at the two junc- tions. When a strong oxidizing solution is combined with a still stronger oxidizing solution to form a cell, the former will be oxidized at the expense of the latter, but the E.M.F. of the cell will be small, as the solutions are acting against each other. The further apart two solutions are in the oxidation-reduction potential series, the greater will be the E.M.F. of the cell formed by their coipbination. ELECTROMOTIVE FORCE 373 We are now in a position to give a clear definition of oxida- tion and reduction in dilute salt solutions. A substance is oxidized when it takes up positive charges or loses negative charges, a substance is reduced when it takes up negative charges or loses positive charges. The usual definition of oxidation as consisting in an addition of oxygen to a compound or the abstraction of hydrogen from it, is clearly inapplicable to salt solutions, and the above definition affords a satisfactory representation of the observed phenomena. On the other hand, the older definition retains its value for changes in which organic compounds are concerned, and for solid compounds ; these have so far been very little investigated from an electro- chemical standpoint. Electrolysis and Polarization — If an external E.M.F. of I volt is applied to two platinum electrodes dipping in a con- centrated solution of hydrochloric acid, it will be found that the large current which at first passes when connection is made rapidly diminishes and finally falls practically to zero. The ex- planation of this behaviour is that while the current is passing hydrogen accumulates on the cathode and chlorine on the anode, thus setting up an E.M.F. which acts against the E.M.F. applied to the poles of the cell. This phenomenon is termed polarization. In the above case the gases go on accumulat- ing in the electrodes till the back E.M.F., which we will term e, is equal to the applied E.M.F., when the current ceases. If, however, an E.M.F. of i*5 volts is applied at the electrodes, a continuous current passes through the solution and it is evident that in this case the back E.M.F. e has not attained the value of I '5 volts. The explanation is evident when it is remem- bered that the E.M.F. of a cell in which platinum electrodes are charged with hydrogen and chlorine respectively at atmo- spheric pressure is i*35 volts (p. 369). When an E.M.F. of I "5 volts is applied, the electrodes become charged up to atmospheric pressure, but no higher, the excess of the gases escaping into the atmosphere. It follows that e cannot under 374 OUTLINES OF PHYSICAL CHEMISTRY ordinary circumstances attain a higher value than i'35 volts, so that electrolysis proceeds at an E.M.F. of E - « = 0T5 volts. The E.M.F. which must just be exceeded in order that a continuous current may pass through an electrolyte is termed the " decomposition potential" of the electrolyte, and it is clear from the above example that the decomposition potential is equal to the E.M.F. of a cell in which the products of electrolysis are the combining substances. As the E.M.F. of such a cell is the algebraic sum of the differences of potential at the electrodes, it is clear that the decomposition potential is also the sum of two factors, namely, the sum of the potentials required to discharge the anion and cation respectively. The decomposition potential of an electrolyte may be deter- mined in two ways. According to the first method, the external E.M.F. applied to the electrodes is gradually raised and the point noted at which there is a sudden increase in the current. The value of the current, C, is determined by the equation E - « = CR, where R is the resistance of the circuit, and will obviously increase rapidly as soon as E is greater than e. The second method is to charge the electrodes up to atmospheric pressure by using an E.M.F. greater than e, then the external circuit is broken and the E.M.F. of polarization measured at once. This method depends upon the fact already indicated, that the de- composition potential is that E.M.F. which is just sufficient to overcome the E.M.F. of polaiization. As has just been pointed out, the potential required to dis- charge an ion such as Zn" must just exceed the difference of potential at the junction Zn/Zn", and is, therefore, the same as the potential of the metal in volts in the tension series (p. 367). Further, the E.M.F. required to decompose an electrolyte is clearly the sum of the separate differences of potential required to discharge the anion and cation respectively, and is, there- fore, obtained by adding the values for the two ions in the ELECTROMOTIVE FORCE 375 tension series. The matter becomes clearer when we consider that the potential difference between an element and its ions may conveniently be regarded as a measure of the affinity of the element for electricity. Thus the affinity of zinc for positive electricity is equivalent to 0770 volts, and that of chlorine for negative electricity to i'3S3 volts. To convert zinc ions to metallic zinc we must, therefore, apply a contrary E.M.F. which just exceeds the affinity of zinc for positive electricity, in other words, the decomposition potential of zinc ions is 0770 volts. On this basis, the decomposition potential of zinc chloride should be 0770 + i'3S3 = 2 •123 volts, of hydrochloric acid 1-353 volts, and of copper chloride (-0-329 ^ i'3S3) = 1-024 volts respectively. This is fully confirmed by the experimental determinations of Le Blanc, who obtained the following values : ZnClj =2-15 volts, HCl = i"3i volts, CuClj = 1-05 volts, an agreement within the limits of experimental error. Separation of Ions (particularly Metals) by Electro- lysis — The results just mentioned are well illustrated by the phenomena observed when a mixture of electrolytes is electro- lysed at different values of the applied E.M.F. The foregoing considerations show that on gradually raising the E.M.F. that chemical change takes place most readily for which the least difference of potential is required, and this may be taken advantage of for the electrolytic separation of metals which are discharged at different potentials. Suppose, for example, a mixture of hydrochloric acid, zinc and copper chlorides is subjected to electrolysis. Below i volt practically no change will occur, but at it volts, a little above the decomposition potential for copper chloride, copper will be deposited on the cathode. When it has been almost completely removed, and the potential is raised to 1-4 volts, hydrogen will be liberated at the cathode. Finally, the attempt may be made to remove zinc by raising the external E.M.F. above 2-2 volts, but this cannot be effected in acid solution, as there is a large excess of hydrogen ions, which are more easily discharged than zinc. 376 OUTLINES OF PHYSICAL CHEMISTRY In an exactly corresponding way, almost all the bromine may be electrolytically separated from a solution containing zinc chloride and zinc bromide before the chlorine appears. It is, therefore, clear that it is the value of the E.M.F., and not the strength of the current, which is of primary importance for the separation of metals, and in recent years methods based on this principle have become of great commercial importance. Besides the value of the applied E.M.F., the concentration of the ions in contact with the cathode is of great importance, as the decomposition potential necessarily depends on the ionic concentration, and hence great attention is now paid to the eflficient stirring of the electrolyte. ^ The Electrolysis of Water — It is an experimental fact that when aqueous solutions of many strong acids and alkalis are electrolysed, only hydrogen and oxygen are liberated as products of electrolysis, and the decomposition potential, the E.M.F. which must be applied in order to liberate these gases in appreciable amount, is about i'66 volts. It has usually been considered that one or both of these gases are formed by the action of the primary products of electrolysis on the solvent, but this does not account for the fact that the decomposition potential is in general the same for different acids and bases. Le Blanc and Nemst, on the other hand, consider that the gases are a product of the primary decomposition of water. As already mentioned, water is ionised according to the equation HjOl^H" + OH' and also, though to a much smaller extent, according to the equation OH'^H" + O". By special methods it can be shown that water can be split up at i • i volts (which corresponds approximately with the potential of the hydrogen- oxygen cell) (p. 370), and Nemst considers that the chemical change then taking place is the discharge of H" and divalent O" ions ; the electrolysis is very slow because of the exceedingly 1 The electrolytic separation of metals on this principle is described in recent papers by Sand (Journal of the Chemical Society, 1907, 91, 373, igo8, 93, 1572), and others. ELECTROMOTIVE FORCE 377 mfnute concentration of the O" ions. The more rapid decom- position at I '66 volts is due to the discharge of H- and OH' ions the latter combining to form water and oxygen according to the equation 2OH' = HjO + O. At a still higher potential, when sulphuric acid is used as electrolyte, SO^" ions are discharged, and the evolution of oxygen becomes still more vigorous. Al- though there is some evidence in favour of the views just indicated, the electrolytic decomposition of water does not seem yet to be thoroughly understood.^ Accumulators — As is well known, accumulators are em- ployed for the storage of electrical energy. An accumulator is a reversible element ; when a current is passed through it in one direction the electrodes become polarized, and when the polar- izing E.M.F. is removed and the poles of the accumulator are connected by a wire, the products of electrolysis recombine with production of a current and the cell slowly returns to its original condition. It will be clear from the above that the Grove's gas cell is a typical accumulator or secondary element ; when a current is passed through it in one direction the electrodes become charged with hydrogen and oxygen, and these gases can be made to recombine with production of a current. From a technical point of view, however, a satisfactory accumulator must retain its strength unaltered for a long time when the poles are not connected, and must be easily transported. A gas accumulator would be in many respects unsuited for commercial purposes. The apparatus most largely used for the storage of electricity is the lead accumulator, the electrodes of which in the un- charged condition contain a large amount of lead sulphate (obtained by the action of sulphuric acid on the porous lead of which the electrodes largely consist at first) and dip in dilute sulphuric acid. The accumulator is charge by sending an electric current through it. At the cathode, the lead sulphate is reduced by the hydrogen ions (or rather by the discharged hydrogen) to metallic lead according to the equation ' Compare Foerster, Zeitsch. fhysikal. Chem., 1909, 69, 236, 378 OUTLINES OF PHYSICAL CHEMISTRY PbSOl + 2H- - zF = Pb + 2H- + SO/' or more simply, PbS04 - 2F = Pb + SO/' On the other hand, the SO4" ions wander towards the anode and react with it according to the equation PbSO^ + SO4" + 2H2O + 2F = PbOjj + 4H- + 2SO/' so that the anode and cathode consist mainly of lead peroxide and metallic lead respectively. On connecting up to obtain a current (discharging), SO/' ions are discharged at the new anode (the lead pole), and reconvert it to lead sulphate, according to the equation Pb + SO/' + zF = PbSO^, and simultaneously H- ions are discharged at the new cathode (the peroxide pole), the peroxide being reduced to the oxide, and acted on by sulphuric acid to reform the sulphate, according to the equation PbOa + 2H- + H2SO4 - 2F = PbSO^ + 2H2O. The chemical changes taking place on charging and discharging are summarized in the equation Pb + PbOa + zHjSO^^ 2PbS0i + ^H^O ; the upper arrow represents discharging, and the lower arrow charging. The E.M.F. of the lead accumulator is about 2 volts. It is not strictly reversible, but under ordinary conditions of working about 90 per cent, of the energy supplied and stored up in it can again be obtained in the form of work. The Electron Theory 1 — In the previous chapters we have learnt that certain atoms (or groups of atoms) can become associated with definite quantities of electricity, and that certain other atoms can take up twice as much, three times as much, and so on. No atom is associated with less positive electricity 'Nernst, Theoretical Chemistry, chap. ix. ; Rutherford, Radio-Activity ; Ramsay, Presidential Address, Trans. Chem, Soc, 1908, 93, 774. ELECTROMOTIVE FORCE 379 than a hydrogen atom, and we may therefore state that a hydrogen atom unites with unit quantity of electricity to form an ion. A barium ion has twice as much positive electricity, and a ferric ion three times as much positive electricity as a hydrogen ion. Further, since quantities of hydrogen and chlorine ions in the proportion of their atomic weights are electrically equivalent, it follows that CI' (and other univalent negative ions) contain unit quantity of negative electricity. This increase by steps in the amount of electricity associated with atoms at once recalls the law of multiple proportions, and it appears plausible to ascribe an atomistic structure to electricity ; in other words, to postulate the existence of positive and negative electrical particles, which under ordinary cir- cumstances are associated with matter. On this view, the number of dots or dashes ascribed to positive and negative ions respectively indicates the number of electrical particles (positive or negative) with which the atoms become associated to form icwis These views ^ (Helmholtz, i88z) have received powerful supprort during the last few years from the results of experi- ments on the passage of electricity through vacuum tubes, the so-called Hittorf's or Crookes' tubes. When a current at very high potential is sent through a highly evacuated tube, rays from the cathode — the so-called cathode rays — stream across the tube with great velocity, and it has been shown that these rays consist of negative electricity. The speed of the particles depends on the E.M.F. between the poles of the tube, but at a difference of potential of 10,000 volts is about one-fifth of the velocity, of light. The mass of these particles is about i/iooo of that of the hydrogen atom. They are usually termed negative electrons. More recently, it has been dis- covered that the yS rays given off from disintegrating radium at a speed approaching that of light also consist of negative electrons. 1 Helmholtz, Faraday Lecture, Trans. Chem. Soc, 1882. 38o OUTLINES OF PHYSICAL CHEMISTRY As negative electrons have thus been found to exist separate from matter, it is natural to expect that free positive electrons may also be isolated. So far, however, this has not been found possible, and opinions differ somewhat as to the reason. Nernst, following Helmholtz, considers that there is no ground for doubting the existence of positive electrons ; the reason why it has not yet been found possible to isolate them is due to their great affinity for matter. Further, Nernst and others assume that positive and negative electrons unite to form neutral atoms or neutrons, and that these neutrons constitute the ether which is assumed to pervade all space. Other investigators regard a positive ion as an atom minus one or more negative electrons ; the loss of a negative electron would leave the previously neutral atom positively charged.^ From observations on the effect of a magnetic field on the cathode discharge, it has been calculated that the actual charge carried by a univalent ion (positive or negative) is about 4 x 10 ~ i" electrostatic units. The application of the electron theory to ordinary chemical changes yields interesting results. For simplicity we will assume the existence of positive electrons, and designate them by the symbol ©, negative electrons by the symbol 0. When hydro- gen and chlorine unite to form hydrochloric acid, we assume that under ordinary conditions the valency of the hydrogen is satisfied by that of the chlorine. We may, however, dis- place a chlorine atom by a positive electron, and thus obtain the saturated chemical compound H ® or H ■ ; in an exactly similar way, the hydrogen may be displaced by a negative electron, forming the saturated compound C10. In the same way, a dilute solution of copper sulphate contains the /© /© saturated compounds Cuc^ or Cu " and 80.^ or SO/'. \© \0 The electrons, therefore, behave exactly as univalent atoms, ' Ramsay, loc, cit. ELECTROMOTIVE FORCE 381 the positive electrons enter into combination with positive elements such as H, K, Na, Ba, etc., the negative electrons enter into combination with negative elements or groups, such as CI, Br, I, NOg, SO4. Nothing is known as to the constitution of a non-ionised salt molecule in solution. The formula for non-ionised sodium chloride may perhaps be Na ®0C1, the molecule being held together at least partly by electrical forces. Just as there are great differences in the affinity of the elements for each other, so the elements have very different affinity for electrons. Zinc and the other metals have a great affinity for positive electrons, the so-called non-metallic ele- ments have in many cases considerable affinity for negative electrons. The order of the elements in the tension series may be regarded as the order of their affinity for electricity. On this view the potential required to discharge the ions is simply the equal and opposite E.M.F. required to overcome the attraction of the element and the electron (p. 375). Practical Illustrations. Dependence of Direction of Current in Cell on Concentration of Electrolyte — It has already been pointed out (p. 346) that the current in a Daniell cell may be reversed in direction by enormously reducing the Cu" ion con- centration by the addition of potassium cyanide. The two chief methods for diminishing ionic concentration are (i) the forma- tion of complex ions (as in the above instance) ; (2) the forma- tion of insoluble salts. When a cell of the type Cd CdSO^ dilute KNO3 I CUSO4 dilute Cu is set up, and the poles are connected through an electroscope, it will be found that positive electricity passes in the cell in the direction of the arrow. If some ammonium sulphide solution is then added to the copper sulphate solution, "insoluble" copper sulphide is formed, and the concentration of the Cu- 382 OUTLINES OF PHYSICAL CHEMISTRY ions is reduced to such an extent that the current flows in the reverse direction. If the Daniell cell Zn ZnSO^ I KNOj dilute CuSO^ dilute Cu is built up in the same way, it will not be found possible to re- verse the current by the addition of ammonium sulphide, owing to the greater solution pressure of the zinc as compared with cadmium ; but if potassium cyanide is added, the current changes in direction, owing to the fact that the Cu" ion con- centration in a strong solution of potassium cyanide (in which the copper is mainly present in the complex anion Cu(CN)4") is considerably less than in a solution of copper sulphide. The following experiments, which are described in consider- able detail in the course of the chapter, should if possible be performed by the student. For further details text-books on practical physical chemistry should be consulted. (a) Preparation of a standard cadmium cell (p. 337). {d) Measurement of the E.M.F. of a cell by the compensation method (p. 335). (c) Preparation and use of a calomel " half-cell " (p. 35S). (d) Preparation and use of a capillary electrometer (p. 360). (e) Measurement of the E.M.F. of a concentration cell (P- 348). (/) Measurement of the E.M.F. of the hydrogen-oxygen cell (p. 369). (/) Determination of the solubility of a difficultly soluble salt, e.g., silver chloride, by E.M.F. measurements (p. 350). INDEX Abnormal molecular weights in solu- tion, 123. — vapour densities, 40-42. "Absolute" potentials, 356, 360,362. Absorption of light, 69-73. — spectra and chemical constitution, 73- Accumulators, 377. Acetic acid, atomic volume of, 61. density of vapour, 41. dissociation of, 267. Acids, catalytic action of, 205, 219, 272. — effect of substitution on strength of, 304. — strength of, 269-274. Active mass, 156. of solids, 173. Additive properties, 62, 251, 315. Affinity, chemical, 148, 154, 271. — - constant, 157, 273, 275. Amalgams, cells with, 351 Ammonium chloride, dissociation of, 42, 219. — hydrosulphide, dissociation of, 176. Argon, position in periodic table, 23. Associated solvents, ionising power of, 319- Associating solvents, 123. Association in gases, 41. — in solution, 124, 318-322. Atomic heat, 12. — hypothesis, 5. — refractions, values of, 65. — volumes, 60. — weights, determination of, 8-15. standard for, 17. table of, 19. Attraction, inolecular, 34, 58. Available energy, 104, 150, 332. Avidity of acids, 269-274. Avogadro's hypothesis, 10, 36. deduction of, from kinetic theory of gases, 32. valid for solutions, 103, 109. Bases, catalytic action of, 220. — strength of, 274-276, 292. Beckmann's methods, it6, 12a Benzoic acid, distribution between solvents, 178, 198. Beryllium (glucinum), atomic weight of, 10, II. Bimolecular reactions, 207, 230. Binary mixtures of liquids, 84-91. distillation of, 87. vapour pres ure of, 87. Blood, catalysis by, 202, 229. Boiling-point, elevation of, 114-11S. Boron, atomic heat of, 12. Brownian movement, 129. CADMitfM St ndard cell, 336. Calomel electrode, 353. Calorimeter, 146, 147, 153 Capillary electrometer, 360. Cane sugar, hydrolysis of, 205. Carbon, atomic heat of, 12. — dioxide, critical phenomena of, 49. Catalysis, 217-224. — mechanism of, 222. — technical importance of, 219. Cathode rays, 379. Chemical affinity, 148, 154, 271. Chemical equilibrium and pressure, 169. and temperature, 166, 169. Clark cell, 338. CoUigative properties, 6b. Colloidal platinum, 220, 232. — solutions, 127-129, Colloids, diffusion of, 128. — electrically charged, 129. 383 384 OUTLINES OF PHYSICAL CHEMISTRY Combining proportions, law of, 4. — volumes of gases , law of, 9. Combustion, heat of, 145. Complex ions, 281, 303, 310. Components, definition of, 181. Concentration cells, 347-353. Conductivity, electrical, effect of tem- perature on, 263. — — equivalent, 251. — — of pure substances, 258. measurement of, 254-258. — molecular, 249, 257, 265. — specific, 23s, 249. Conservation of energy, law of, 140. — of mass, law of, 3. Constant boiling mixtures, 89. Constitutive properties, 62. Continuity of gaseous and liquid states, S3; SS- Copper sulphate, hydrates of, 174. Corresponding states, law of, 56. — temperatures, 57. Critical constants, 51, 56. — phenomena, 49-58, 69. — solution temperature, 86. — temperature, determination of, 77. Cryohydrates, 188. Crystallisation interval, 192. Crystalloids, 127. " Cyclic" processes, 133, 136. Daniell cell, 328, 342, 346. ■ — — reversal of current in, 346, 381. Decomposition potential of electrolytes, 374- Deliquescence, 175. Density of gases and vapoiu'S, 36, 43. ■ determination of, 37, 41, 48. Dielectric constant, 225, 318, — — and ionisation, 318. Diffusion of gases, 33. — in solution, 108. — — and osmotic pressure, gS, 108. Dissociating solvents, 123. Dissociation constant, 266, 273, 275. — ele(^ol3rtic, 260-263, 3iS"3^7' degree of, 261 evidence for, 315-317. mechanism of, 322. of water, 283, 293. — of salt hydrates, 174. — • in gases, 42, 125, 163. solution, 125, 260-263. — thermal, 163. Distillation of binary mixtures, .87, 91. — steam, 90. Distribution coefficient, 95, 178, 197. Dulong and Petit's law, 11. Effloeesence, 175. Electrode, calomel, 353. — hydrogen, 356, 365. Electrodes, normal, 355, 356. Electrolysis, 236-238, 373. — of water, 376. — separation of metals, etc., by, 375. Electrolytes, strong, 279-282. Electrolytic dissociation. See Dis- sociation, electrolytic. Electrometer, capillary, 360. Electromotive force and concentration of solutions, 345. measurement of, 334. standards of, 336. Electrons, 378. — and light absorption, 72. valency, 380. Elements, i. — disintegration of, 2. — periodic classification of, 20. — potential series of, 366. — table of, 21. Enantiotropic substances, 197. Endothermic and exothermic com- pounds, 144. Energy, available, 104, 150, 332. — chemical, 140, 331-334. — conservation of, 140. — free, 104, 150, 332. — internal, of gases, 46. — intrinsic, 143. — kinds of, 139. Enzyme reactions, 221. reversibility of, 222. Equilibrium, effect of pressure on, 169. of temperature on, 166-170. — false, 218. — in gaseous systems, 161-164. — kinetic nature of, 158, 160, 241. — in electrolytes, 266-312. — in non-electrolytes, 164-166, Equivalents, chemical, 8, 15, 237. — electrochemical, 237. Ester equilibrium, 156, 164. Esters, hydrolysis of, 206. — saponification of, 207, 275. Eutectic point, 187, 191. Exothermic and endothermic com- pounds, 144. Expansion of gases, work done in, 27. Faraday's laws; -037. INDEX 38s Ferric chloride, hydrates of, 194. Fluidity, 74. Formation of compounds, heat of, 143. Freedom, degrees of, 179, 182, Freezing-point, lowering of, 119-121, 194. Friction, internal. See Viscosity. Gas cells, 364. — constant, R, 26, 102. — laws, 25-26. deduction of, 31-33. • deviations from, 28, 33-35. Gases, 25-48. — behaviour of, on compression, 51. — kinetic theory of, 29-35, 4^' — liquefaction of, 58. — solubility of, in liquids, 82. — specific heat of, 43-48. Gay-Lussac's law of gaseous volumes, 9- of expansion of gases, 25. Gladstone-Dale formula, 64. Grotthus' hypothesis, 264. Heat of combustion, 145. additive character of, 148. — of ionisation, 28 ;, 295, 324. — of solution, 146, 153. Helium, liquefaction of, 59. — critical constants of, 51. Helmholtz formula, 331-334, 353- — views on valency, 379. Henry's law, 82, 95, 178. Hess's law, 125. Heterogeneous equilibrium, 172-199. Hydrate theory, 313, 319. Hydrated ions, 326. Hydration in solution, 325-327. Hydrates, dissociation of, 174. in solution, 320. Hydrogel, 129. Hydrogen electrode, 356, 365. Hydrogen iodide, decomposition of, 159, 161. Hydrogen-oxygen cell, 369. — peroxide, decomposition of, 202, 229. Hydrogen sulphide, dissociation of, 167. Indicators, theory of, 296, 309. Intermediate compounds in catalysis, 223. Ionic and non-ionic reactions, 307. Ionisation and chemical activity, 311. 25 Ionisation degree of, 261, 281. — energy relations in, 323. — heat of, 285, 29s, 324. — mechanism of, 322-325. — r61e of solvent in, 314, 318, 322- 325- lonismg power of solvents, 318, 319. — and free affinity, 319. Ions. 236. — complex, 281, 303, 310. — migration of, 236, 243-249. — reactivity of, 306, 311. — velocity or mobility of, 252-254. Irreversible electro-chemical processes, 334' Isohydric solutions, 277. Isomorphism, 13-14. Isosmotic solutions, 105. Isotonic coefficients, 106. — solutions, 105. JOULE-Thomson effect, 58. Kinetic energy, 32, 46, 140. of gas molecules, 46. — theory of gases, 29-35, 46- Kohlrausch's law, 251. Lead accumulator, 377. Le Chatelier's theorem, 169. Light, absorption of, 69-73. Liquefaction of gases, 58. Liquids, molecular weight of, 125. — miscibiUty of, 84, 95. — properties of, 49-79. Lorenz-Lorentz formula, 64. Mass action, law of, 155-160, 173. and strong electrolytes, 279- 283. in heterogeneous systems, 172. proof of, 160. Maxima and minima on curves, 76, 88, 319-322. "Maximum work" and chemical af- finity, 150. Medium, influence of, on reaction velocity, 224. Metastable phases, 184. Migration of the ions, 236, 243-249. MiscibiUty of liquids, 84. Mixed crystals, 13, 95, 190, 192. Molecular attraction, 34, 58. — surface energy, 125. — volume, 60, 78. 386 OUTLINES OF PHYSICAL CHEMISTRY Molecular volume in solution, 62. — weight of colloids, 128. of dissolved substances, 109- I2S- — — of gases, 36-43. — — of liquids, 125-127. • abnormal, 40, 123. Molecules, velocity of gaseous, 33. Monotropic substances, 197. Morse and Frazer's measurements of osmotic pressure, 104. Multiple proportions, lav^ of, 4. Natural law, definition of term, 6, 7. , , Neumann s law, 13. " Neutal salt action," 84. Neutralization as ionic reaction, 284. — heat of, 148, 283-285, 316. Neutrons, 380. Normal electrodes, 355, 356. Octaves, law of, 20. Optical activity, 66-69, 229. van't Hoff-Le Bel theory of, 67. Order of a reaction, 213. Osmotic pressure, 97-109. — — and diffusion, 98, 108. and elevation of boiling-point, 109, 138. and gas pressure, 102, 103. — — and lowering of freezing-point, 109, 136. and lowering of vapour pres- sure, 109, 131. ' measurement of, 99, 105. ■ mechanism of, 106. Ostwald's dilution law, 266, 307. Oxidation, definition of, 373. Oxidation-reduction cells, 370. Ozone-oxygen equilibrium, 168. Partial pressures, law of, 81, Periodic system, 20-24. — law, 23. — table, 21. Phase, definition of terra, 172. — rule, 179. Phosphorus pentachloride, dissociation of, 163, Plasmolysis, 105. Polarization, electrolytic, 330, 335, 373. — of light, 66. Potential differences at liquid junctions, 362. Potential differences, origin of, 342. single, 356, 358-362. — series of the elements, 366. Potentials, "absolute," 356, 360, 362. Prout's hypothesis, 17. Quadruple point, 196. R, value of, for gases, 27. for solutes, 102. Radium, 2, 379. Raoult's formula, 112. Reaction, order of, 213. Reactions, consecutive, 216. — counter, 216. — side, 215. Reduction, definition of, 373. Refraction formulae, 64. Refractivity, 63-66. Reversibility in cells, 334. Reversible reactions, 151, 156, 222, Rotatory power, 66, 229. magnetic, 69. Salt solutions, solubility of gases in, 84. Semi-permeable membranes, 81, 97, 105, 107, 130. Sodium sulphate, solubility of, 93. Solubilities, determination of small, 300-302, 350. Solubility, coefficient of, 83. — curves, 86, 93, 196, — effect of temperature on, 93, 96. — of gases in liquids, 82. — of liquids in liquids, 84. — of solids in liquids, 91-94. — product, 298. Solution, heat of, 146, 153. Solutions, boiling-point of, 114. — colloidal, 127-129. — freezing-point of, 119. — isotonic, 105. — solid, 94, 192. — supersaturated, 92. Solvent, influence of, on ionisation, 318, 322-325. Solvents, associating, 123, 318. — dissociating, 123, 318. Specific heat of gases, 43-47. solids, 11-13. Spectrum, absorption, 70. effect of dilution on, 71. Strong electrolytes, ionisation of, 279. Substitution, effect of, on ionisation, 273; 276, 304- INDEX 387 Sulphur, equilibrium between phases, 183. — vapour density of, 41. Supersaturated solutions, 92. Surface tension and molecular weight of liquids, 125-127. Tellurium, atomic weight of, 24. — position in periodic table, 23. Temperature coefficient of chemical reactions, 225-229. of conductivity, 263. Theory, definition of term, 7. Thermoneuirality, law of, 148, 279. Transition curves, 184. — points, 183, 197. determination of, 198, 199. Transport numbers, 246-249. Trimolecular reactions, 209. Triple point, 181. Unimolecular reactions, 202, 229. Valency, 15. Van der Waals' equation, 33-35, 53-57. Van't Hoff-Raoult formula, 112. — Hoft's factor, i, 125, 262. Van't Hofif's theory of solutions, loi. 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Cooper. Illus. i2mo. cloth. 213 pp. $2.00 WINCHELL, N. H. and A. N. Elements of Optical Min- eralogy. An introduction to microscopic petrography. 350 ill. 4 plates. 8vo. cloth. 510 pp. $3.50 WINKLER, C, and LUNGE, G. Handbook of Technical Gas Analysis. Second English Edition. Illustrated. 8vo. cloth. 190 pp. $4.00 WORDEN, C. E. The Nitrocellulose Industry. A com- pendium of the history, chemistry, manufacture, com- mercial application, and analysis of nitrates, acetates, and xanthates of cellulose as applied to the peaceful arts. With a chapter on gun cotton, smokeless pow- der and explosive cellulose nitrates. Illustrated. 8vo. cloth. Two volumes. 1239 pp. net, $10.00 D. VAN NOSTRAND COMPANY Publishers and Booksellers 23 nURRAY AND 37 WARREN STREETS, NEW YORK. SECOND ISSUE, 1909 12mo. cloth 575 Pages Net. $2.50 VAN NOSTRAND'S Chemical Annual A HANDBOOK OF USEFUL DATA for analytical, manufacturing and investi- gating chemists and chemical students. BASED ON BIEDERM ANN'S "CHCMIKER KALENDER" EDITED BY Prof. J. C. OLSEN, A,M., Ph.D. Polytechnic Institute of Brooklyn ; formerly Fellow Johns Hopkins University ; author of " Quantitative Chemical Analysis" WITH THE CO-OPERATION OF EMINENT CHEMISTS CONTENTS New Tables— Physical and Chemical ConEtact ot the Essential Oils and Alkaloids. Melting Points and Composition of the Fusible Alloys. Density of Carbon Dioxide Polenslce Values of Oils, etc. Tables for the Calculation of GraTimetrio, Volumetric, and Gas Analyses. ■ Tables ot the Solubility, Boiling and Freezing Points, Speciflc Gravity, and Molecular Weight of the commonly used Inorganic and Organic Com- pounds. Speciflc Gravity Tables of Inorganic and Organic Compounds. Other Physical and Chemical Constants of Chemical and Technical Pro- ducts. Conversion Tables of Weights and Measures. New Books and Current Literature of the Year. ALL TABLES WILL BE REVISED ANNUALLY TO GIVE THE MOST RECENT AND ACCURATE DATA D. Van Nostrand Company 23 Murray and 27 Warren Sts., New YorK