'ni\s: (Allege of JKgncultuw KlVfotnell MtiimvBity \ Ktlyata, Jf. g. ^ibtaty Cornell University Library QD 565.T7 The conductivity of "q"S,K^{JS,«m[,|'r The original of tiiis book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002984403 _The=^ Conductivity of Liquids Methods, Results, Chemi- cal Applications and^^ Theoretical Considerations By Olin Freeman Tower, Ph.D., Assistant Professor of Chem- istry, Western Reserve University. Easton, Penna : Chemical Publishing Compan 1905. Copyright, 1905, by Edward Hart. preiface:. This little treatise is designed to present in English a summary of the recent work on the electrical conductivity of liquids, and to aid, if possible, in the more complete adoption of the Kohlrausch system of units in this country. It was in 1897 that Kohlrausch and his associates first proposed the new unit of conductivity based on the ohm. Kohlrausch and Holborn recalculated all the old important conductivity results in terms of this new unit and published them in their "Leitver- mogen der Elektrolyte." Thereafter, consequently, no advantage was to be derived from the continued use of the old and less rational system of units. The new system was soon in general use throughout Germany, but its adoption in other countries has been much slower, and up to the present time there are some writers, especially in this country and in France, who continue to use the old system based on the Siemens unit. Most of the con- ductivity results of the last eight years will be found in the appen- dix, recalculated, when necessary, to reciprocal ohms. The confusion in this field has, unfortunately, not been confined to the units alone, but is found also in the use of the symbols em- ployed to indicate specific conductivity, equivalent conductivity, and many of the other related magnitudes. For . instance, A. is employed by some to indicate specific conductivity, by others to in- dicate equivalent conductivity, and is sometimes expressed in Siemens units and sometimes in reciprocal ohms. The transport number of the anion has long been indicated by n, but occasion- ally a writer employs p for this purpose. The word "normal" is used by many physical chemists in the sense of molecular normal, but the avoidance of ambiguity demands that it be used in physi- cal chemistry, as in analytical cheipistry, to indicate equivalent normal only. The nomenclature and symbols employed in this book are es- sentially the same as those used by Kohlrausch and Holborn. In a few instances, however, I have ventured to introduce a change IV PREFACE for the sake of simplicity. For example, Kohlrausch and Hol- born express the temperature coefficient of conductivity by C, a letter difficult to w^rite and sometimes not easy to print, c has been substituted for this. The Ostwald dissociation constant, I a' . ... ■ have retained in its original form,' viz., k =7 r— , instead of ^ ,' (i — a)v thereby avoiding some additional ciphers. A few similar unimportant changes will be noticed. I have attempted to avoid ■. paralleling Kohlrausch and Hol- born's "L,eitverm6gen der Elektrolyte," except in the case of cer- tain standard methods, which must appear in any, book of this character. Considerable space has, therefore, been given . to transport numbers and to the theory of, electrolytic dissociation. On account of the increasing interest in, non-aqueous solution.s and in non-aqueous solvents,, a relatively large amount of space has been devoted to these subjects. The greater portion of this text was written in 1903, and it should therefore have appeared "some tinie ago, except for my own absence from this country during part of the time since, and for delay due in nowise to negligence on the part of the present publishers. The references and the conductivity tables have been brought down to 1905, wherever possible. For any failure to do this, I hope the preceding apology ^y ill, suffice. I am under obligations to Professor Edward W. Morley for many suggestions, and to Dr. W. D. Briggs for aid in proof-read- ing. Cleveland, October, 1905. CON-TEN-rS. PAGK Chapter I. — Units. Method for Determining Conductivity i Chapter II. — Apparatus Used in Determining Conductivity 12 Chapter III. — Sources of Error with Alternating Currents. Calibration of Bridge Wire 25 Chapter IV. — Determination of Resistance Capacity 32 Chapter V. — Water. Preparation of Solutions 40 Chapter VI. — Dissociation of Electrolytes ; Dissociation Constants 49 Chapter VII. — The Migration of the Ions 64 Chapter VIII.— Determination of /2 oo- Absolute Velocity of the Ions. Graphic Representation of Conductivity 83 Chapter IX. — Influence of Temperature and Pressure 94 Chapter X. — Solutions Containing Two Electrolytes 104 Chapter XI. — Applications of Conductivity Measurements 118 Chapter XII. — Conductivity of Single Substances 128 Chapter XIII. — Non-Aqueous Solutions 135 Chapter XIV — Conductivity of Electrolytes in Mixed Solvents 152 Appendix, Conductivity Tables, etc 159 THE CONDUCTIVITY OF LIQUIDS. CHAPTER I. Units. Methods for Determining Conductivity. THE KOHLRAUSCH SYSTEM OF UNITS..— Conductivity is al- ways determined by measuring its reciprocal resistance. Con- ductivity is, therefore, always defined in terms of units of re- sistance. Until recently the Siemens mercury unit has been the basis of the unit of conductivity of solutions, and, in fact, of all liquid conductors. This, in turn, has been very generally repro- duced from the conductivities of various standard solutions, which values, as given by dififerent authorities, have not always been identical. Within a few years, however, Kohlrausch and asso^ ciates^ have proposed a standard unit of conductivity based on the ohm and have determined with great care the conductivities of many standard solutions in terms of this unit. It is, conse- quently, very easy to reproduce and has now been very generally adopted by both physicists and chemists. This unit of conductivity is defined as the conductivity of a column of liquid i cm. in length and i sq. cm. in cross section, which has a resistance of i ohm. Conductivity expressed in terms of this unit is called the specific conductivity and is designated by K, The conductivity of a solution, which depends almost entirely on the dissolved substance, is, however, best expressed by means of the equivalent conductivity, which takes into account the con- centration. The equivalent concentration 7 is the fraction of a gram-equiva- lent of the solute in i cc. solution. The dilution cp is the reciprocal of this, that is «? = — and is the number of cubic centimeters V in which a gram-equivalent of the solute is dissolved. Since in most cases 77 and cp are rather cumbersome numbers, it is customary in referring to the concentration of a solution to give » Kohlrausch, Holborn, and Diesselhorst ; Wied. Ann., 64, 417 (1898). 2 THE CONDUCTIVITY 0^ LIQUIDS in their stead m and v, respectively. These quantities are based CD on I liter of solution, so that m =^ 10007, and v = . m and v ' 1000 sometimes refer to gram-molecules per liter instead of gram- equivalents. When they are used thus in this book, it will be so stated. The equivalent conductivity A equals the specific conductivity divided by the equivalent concentration or multiplied by the dilu- tion, that is, ^ = — , or = a?/f. V The molecular conductivity M is sometimes given. This is equal to the specific conductivity divided by the molecular concentra- tion. For monobasic substances the equivalent conductivity and the molecular conductivity are, of course, equal. UNITS FORMERLY EMPLOYED.— Until recentlythe specific con- ducivity k was the conductivity of a column of liquid i m. long and I sq. mm. cross section, referred to the conductivity of a column of mercury of the same dimensions (Siemens unit) as unit. The ohm equals 1.0630 Siemens unit. This unit of conductivity is, therefore, 100 X 100 X 1.0630 times the new one, so that K = 10630^. Occasionally specific conductivities are met with expressed in units in which the conductivity of a column of liquid I cm. long and i sq. cm. cross-section is referred to the Siemens unit. Conductivity, expressed in this way, will be designated by l,^ consequently K ^= 1.0630/. The equivalent conductivity, when based on the Siemens unit, has been commonly designated by A. and the molecular conduc- tivity by /*. Since concentrations were formerly almost invariably expressed in liters instead of cubic centimeters, it was convenient to multiply the small numbers obtained by lo^, sO' that A. = 10 — : m and, therefore, • The symbols which have been used by different authorities to indicate conductivities referred to the Siemens unit have been very much at variance. See preface. METHODS FOR DETERMINING CONDUCTIVITY 3 A = 1.0630^, and M= i.o630><. k In Kohlrauscli's earlier work A. = lo" — , and consequently here m A = 0.1063^.. Although 1.0630 is theoretically the factor for converting con- ductivities expressed in units based on the Siemens unit into those expressed in the ne\v units, the factor actually required is, in most cases, a little greater than this. It is 1.0690 for most of the work which has originated with Kohlrausch and his asso*- ciates. The last equation in the preceding paragraph should, therefore, really be k A = o. 1069A., or = 0.1069 — • m The factor is 1.066 for most of the work from Ostwald's labor- atory. More exact information concerning this factor can be found in the paper by Kohlrausch, Holborn and Diesselhorst, re- ferred to above. The conductivities of the more important solu- tions have been recalculated by Kohlrausch and Holborn and are given, expressed in the new units, in their Leitvermogen der Blek- trolyte. Most of the recent conductivity results will be found in the appendix to this book. ABSOLUTE UNITS.— Absolute electromagnetic units (C. G. S.) are sometimes employed, espt^cially in formulating certain theo- retical relations. In this system^ the unit of current strength =10 amperes, the unit O'f potential ^ lO""** volts and the unit of re- sistance = ia—9 ohms. If K represents the electrical conductivity of a liquid when the unit is the conductivity ,of a cubic centimeter whose resistance is io~~9 ohms, then K = IQ-'/f. RESISTANCE CAPACITY.— Since the vessel in which the con- ductivity of a liquid is measured is never of standard dimensions, it is always necessary to introduce a factor to reduce the resist- ance actually measured to conductivity expressed in the proper units. The factor is called the resistance capacity, or sometimes simply the capacity, of the vessel and is designated by C. The 4 ■ THE CONDUCTIVITY OF LIQUIDS resistance i? of a column of liquid i cm. in length and i sq. cm. in cross section is, according to definition, equal to — ohm. If the column is / crn. long and s sq. cm. cross-section and the electrodes entirely fill the cross-section, obviously J? ^= ohm, K s or / I The resistance capacity Cis, therefore, equal to —, that is, / cm. „ = L cm. s cm. Consequently the dimensions of the resistance capacity are re- ciprocal centimeters. In general for any vessel C Since C is expressed in reciprocal centimeters, and R in ohms, the dimensions of the specific conductivity are — — -. — . cm. X ohm TEMPERATURE. — The conductivity of most solutions changes about 2 per cent, for each degree of temperature, and the tem- perature coefficient of many pure liquids is even greater than this. It is, therefore, essential when determining conductivity that the temperature remain constant and that it be expressed in terms of some fixed standard. The hydrogen scale is the standard com- monly employed, and all temperatures given in this book are based on that scale. At i8° an accurate mercury thermometer of Jena normal glass registers about o.i" too high (see Chapter IX). METHODS EOR DETERMINING CONDUCTIVITY. CLASSIFICATION. — Methods for determining the conductivity of solutions are simply methods for measuring resistance applied to liquid media. They are of three classes : ( i ) Methods in which a direct current traverses the solution; (2) methods in which an METHODS FOE DETERMINING CONDUCTIVITY 5 alternating current traverses the solution; (3) indirect method in which no electrodes are used, the solution being simply exposed to the influence of a strong electromiagnetic field^. This last method has only become of theoretical interest, so it will not be further considered. When a direct current is passed through a solution, polarization takes place upon the electrodes, and unless this can be eliminated it seriously interferes with the accurate determination of the conductivity. Various means have been employed to try to com- pensate this polarization, but very few of the methods so devised for determining conductivity compare in accuracy and rapidity with those in which alternating currents are employed. Recently, however, a method of this class has been described by Stroud and Henderson,^ for which certain advantages are claimed over methods of the second class. Fig. 1. STROUD AND HENDERSON'S METHOD.— The method depends on the elimination of polarization on the electrodes by the em- ployment of two electrolytic cells of similar form, but of different resistance capacity in two adjacent branches of a Wheatstone bridge and balancing the difference of resistance between them by means of suitable known resistances. This principle was not new at this time, but the value of Stroud and Henderson's applica- tion of it lies in the simplicity of their apparatus and in the ac- curacy with which measurements can be made. 1 Guthrie and Boys : Phil. Mag. (5), 10, 328 (1880). 2 Phil. Mag. (5), 43. 19 {1897)- 6 THi; CONDUCTIVITY OF LIQUIDS The apparatus is arranged as in Fig. i. C and c are two elec- trolytic cells of different capacity; r and / are equal resistances of I ODD ohms each ; J? is a rheostat containing resistances up to 20,000 or 30,000 ohms ; G is a D'Arsonval galvanometer. Resistance is introduced at R until the resistance of c + i? is, as nearly as possible, equal to that of C. Then, since r and / are equal, equal currents are traversing C and c, and, therefore, the polarization in each cell should be equal. These polarizations are opposed and in theory eliminated. It was found, as a matter of fact, that more than 99 per cent, of the polarization could be eliminated in this way. The rest could be drowned or at least reduced to insignificance by using high resistances and high volt- ages. With cells having a difference of resistance of about 20,000 ohms and with a resistance in the galvanometer of 300 ohms, good results were obtained with an electromotive force of 30 volts. a=o ^v_^ \y Fig. 2. Cells giving the best results are of the form shown in Fig. 2. They consist of three parts, of which the two upright portions are small thick-walled test tubes with necks on the side. Into these necks fit the well-ground ends of a tube of, as nearly as pos- sible, uniform bore. The diameter of the upright portions in Stroud and Henderson's apparatus was 1.2 cm. and the height 6 cm. The external diameter of the horizontal tube was 0.6 cm. The internal diameter was suited to the resistance of the elec- trolyte. In cell C this tube was about 30 cm. long, and in c, 5 cm. The relative resistance capacity of the two cells can be deter- mined from the following data : Length of horizontal tube in C 29.70 cm. Weight of mercury to fill same, plus watch glass. 29.836 grams. Length of tube in c 4,89 cm. Weight of mercury plus watch glass 11. 481 grams. Density of mercury at temperature of experiment 13.558 METHODS FOR DETERMINING CONDUCTIVITY 7 The difference between the resistance in C and in c is the re- sistance of the electrolyte in a tube, whose length is 29. 70 — 4. 89 = 24.8rcm. The volume of this length of tube = — ^^5^ = i.-?S4 cc. 13-558 ^^^ The resistance capacity C therefore (page 4) equals — = — '—. — — = 454.6. This is the constant by which the re- 1-354 ciprocal of the resistance is to be multiplied to give the specific conductivity of the electrolyte in reciprocal ohms. The electrodes are of platinum foil in cylindrical form to fit the vertical tubes. To these are welded platinum wires, which are connected with the wires from the bridge by means of mercury cups. One set of measurements, as made by Stroud and Henderson, with fifth-normal KCI is given below. The temperature of the cells was controlled by means of an oil-bath. The readings were all reduced to 18° by using the temperature coefficient 0.021 (see Chapter IX). The current was passed alternately in each direc- tion. Direction of current. + Temperature. 18.26° Resistance. 21,035 Resistance re- duced to 18". 21,149 . — 18.19 21,045 21,129 + 18.17 2I,OJ5 21,119 — 18. 1 1 21,065 21,113 + 18.08 21,085 21,120 — i8.o6 21,095 21,121 Mean, 21,125 c The specific conductivity of the solution therefore ^ k = ~^= 454-6 0.02152. Since for a fifth-normal solution v =^ 0.0002, 21,125 A = 107.60. Another solution of fifth-normal KCI, prepared independently from the above, gave A z= 107.18. The agreement is good, and the authors conclude, from many considerations, that the errors in the method itself are small, much less than in the careful preparation of two solutions of the same concentration. OTHER METHODS OF THE FIRST CLASS.— When the resist- 8 THE CONDUCTIVITY OF LIQUIDS ance of the liquid is very great, around 100,000 ohms, its conduc- tivity can be measured in a single cell by employing correspond- ingly great electromotive forces, as 100 volts. In such cases polarization can be neglected and measurements made similarly to above, c is, of course, dropped out, and the ratio of r to / is more conveniently made that of i to 10 or of i to 100. Cells of a form used by Stroud and Henderson are suitable. The elec- trodes should have a large surface and be covered with platinum black. The conductivity of good electrolytes can be measured in this way by using capillary tubes in the cell to increase the re- sistance. When making the readings the current should be on only for an instant.^ Fuchs (1875) originated a method with direct currents, whereby polarization on the electrodes can be avoided by making use of electrostatic measurement. A constant cvirrent is sent through a column of the electrolyte and through a known resistance. The potential difference is determined alternately with an electrometer at two cross-sections of the solution by means of secondary elec- trodes and at the ends of the known resistance. The circuit through the secondary electrodes acquires, under these conditions, only the slight current necessary to charge the electrometer. If in the former case the potential difference is found to be V and in the latter case V, letting / be the current strength, we have the following relations : V = IR and V = IR', from which we obtain The method is rather cumbersome, but yields good results.^ METHOD OF KOHLRAUSCH.— This belongs to the methods of the second class in which an alternating current traverses the electrolyte. Measurements are made by means of a Wheatstone bridge and the disappearance of the current in the cross branch is detected with a telephone. On account of the simplicity of the 1 For further details concerning this method see the following : Kohlrausch and Heydweiller : Wied. Ann., 53, 218 (1894) ; Ibid., 54, 385 (1895) ; Warburg : Ibid., 54, 396 ; Wildermann : Zlschr. phys. Chem., 14, 247 (1894) ; Kohlrausch : Ibid., 15, 126(1894) ; Malmstrom : Ibid., 22, 331 (1897), 2 See in this connection Bouty and Foussereau : /. de Phys. (2), 4, 419 (1885) ; also Shel don ; Wied. Ann., 34, 122 (1S88). METHODS FOR DETERMINING CONDUCTIVITY 9 apparatus required and the accuracy of the results obtained, this method is used more extensively than any other. As commonly employed, the apparatus is arranged essentially as in Fig. 3. A current from the battery B operates the induc- tion apparatus I, whence an alternating current passes to the ends Figs- of the bridge M M'. The resistance to be measured is placed in the branch A M, the known resistance R in A M'. M M' is a wire of as nearly uniform resistance as possible, along which slides the contact C. The telephone T is in the cross-branch A C. A measurement is made by moving C along M M' until the tele- phone is either silent or gives a minimum tone, then the resistances are in the following proportion : S:R = MC:CM'. To insure the greatest accuracy R should be made approximately equal to Sj so that C will be near the middle of MM'. From MC this proportion we have S ^= J? -Tyri, denoting the length MC by a and CM' by 6, then S = Ji ~. If the wire MM' is i meter (1000 mm.) in length, as is frequently the case, this equation becomes S = R , and much of the labor of computation 1000 — a can be saved by making use of Obach's tables (see appendix), which give for any value of a the corresponding value of 1000 — lO THE CONDUCTIVITY OF LIQUIDS Since the resistance of an electrolyte is given by the equation S = Ji —r, the specific conductivity is given by K R~ and for a wire i meter long this becomes C K = R looo — a in both of which C is the resistance capacity of the electrolytic vessel. In order to illustrate the method of calculation, the re- sults obtained with a tenth-normal solution of potassium chlo- ride are given in the accomipanying table. To insure greater ac- curacy, more than one reading (three in the table) are usually made at each concentration. Since the bridge wire is seldom of Conductivity of Tenth-Normai, KCl at i8°. C= 0.1289. R. a. mm. a corrected " Ohms. mm. 1000—0' K. 8 592.0 590.2 1.4402 O.OIII88 10 535.8 5350 1. 1505 0.01X204 12 489.6 A 489.8 0.9600 Mean, O.OIII89 O.OIII94 uniform resistance, as in this case, it is necessary to correct the readings a, as is seen in column 3, (see Chapter III). It is to be ob- served that the resistance R was chosen so as to bring the readings near the middle of the bridge, that is, near 500. Under favorable conditions the quantity a can be read accurately with a telephone to within from o.i to 0.3 mm. The method is seen, therefore, to be simple and quite accurate. Its rapidity is limited only by the time necessary for the solution in the electrolytic vessel to assume the temperature of the bath. Variations of the method and different forms of apparatus which are sometimes employed, will be discussed in the next chapter. METHODS FOR DETERMINING CONDUCTIVITY II OTHER METHODS.— Another method, which combines some features both of the first and of the second class, has been de- scribed by Mcllhiney.^ It consists in determining with a gal- vanometer the potential difference between the ends of a known resistance placed in series with the solution of unknown resist- ance. The current is supplied by a gravity battery, and before passing through the electrolyte it is transformed into an alter- nating current by means of a rotary pole changer, but the current passing through the known resistance and the galvanometer is direct. The method is fairly rapid, but is capable of only an approximate degree of accuracy. A method in many respects similar to Mcllhiney's has been used recently by Morgan and Hildburgh.^ In this an alternating current traverses the electrolyte, but is transformed into a direct current by means of a hydrogen rectifying cell before passing through the galvanometer. A small alternator was used by these investigators as the source of the current with excellent results. 1 /. Am. Chem. Soc, 20, 206 (1898). sy. Am. Chem. Soc, 23, 304 (igoo). CHAPTER II. Apparatus Used in Determining Conductivity. ELECTROLYTIC VESSELS.— These should be selected according to the resistance of the liquid under investigation. If the liquid is a good electrolyte, as fairly concentrated solutions of strong acids or bases or of most salts, vessels of the Kohlrausch type, Fig- 4- as shown in Fig. 4, are the most suitable. Whatever the form of vessel employed, care should be exercised to keep the electrodes in as nearly the same position as possible, otherwise the resist- ance capacity may vary. In form a shown above, the electrodes are fused through the sides, so that their position is fixed. They should pass through the glass high enough so that they will not come in contact with the liquid of the temperature bath. The wires which come through should be fastened to binding posts on the support to prevent their being broken off. The cavers of most electrolytic vessels are of ebonite, which is an excellent material for this purpose because it is a good insulator. In vessel Fig. 4&, the electrodes are usually adjusted so as just to rest in the narrow portion of the tubes, which tends to keep them in an in- variable position. A small hole near the upper part of the con- cavity allows the escape of air or of electrolytic gas. The dimen- sions of a vessel should be suited to the resistance capacity de- sired. For capacities of from i to 5 cm.— ^, suitable dimensions for AITARATUS USED IN DETERMINING CONDUCTIVITY 13 form b are: diameter af vertical tubes, 15 mm.; diameter of con- necting tube, 9 mm. ; capacity up to the water mark, 15 to 30 cc. In form a the resistance capacity varies somewhat for different fillings of liquid. The height at which the liquid stands when the capacity is determined should, therefore, be marked on the glass, and whenever the vessel is used it should be filled to the same height. For determining the conductivity of the so-called weak elec- trolytes, that is, solutions of comparatively low conductivity, as solutions of most organic acids or bases or dilute solutions of n ^x Kl yy pf n U L^ l—JUZTT' Fig- 5- salts, vessels of the type shown in Fig. 5 should be used. Form a, due to Arrhenius, is one of the best, as it permits the electrodes to be set at any distance apart and the capacity thus changed at will. Care must, however, be exercised to keep them from slipping in the cover during use. A suitable size is about 8 cm. in height by 3 cm. in diameter. The electrodes fill the cross-section of the 14 THE CONDUCTIVITY OF LIQUIDS vessel and the platinum wires connected with them are inclosed in glass capillary tubes. Connection is made with copper wires by means of mercury in the capillary tubes, or better, by soldering directly to the platinum wires of the electrodes. Forms b and c are due to Kohlrausch. The first is a small bottle from lo to loo cc. capacity, with semi-circular electrodes fused through the sides. It may be closed with a ground glass stopper, or better, with a small thermometer ground to fit the opening. Vessel c permits three different positions of the electrodes, so that the same vessel can be used for solutions of very different conductivities. The electrodes are nearest together in the position indicated in the figure, by turning one of them through i8o° they are in the second position and somewhat farther apart, then by turning the other electrode through i8o° a third position can be obtained in which the distance apart of the electrodes is the greatest.^ For either one of these last two forms the resistance capacity must be deter- mined for a definite filling, as with forms a and b, Fig. 4. Dl >A/ ID Fig. 6. For very bad conductors, as distilled water and most organic liquids, it is advantageous to use other forms of vessels with still lower resistance capacities. Two such forms are shown in Fig. 1 Loomis has devised a modification of this form of vessel, which permits accurate ad- justment of the electrodes at any angle. See Phys. Rev., 8, 258 (1899). APPARATUS USED IN DETERMINING CONDUCTIVITY 1 5 6, a and b. The first, due essentially to Pfeiffer, is made by fusing together two tubes so that they form a cylindrical vessel. The electrodes consist of concentric cylinders of platinum foil, one being against the inner glass wall and the other against the outer. The conducting wires are fused through the glass walls of the vessel. Form b, due to Schall, is somewhat similar to the Ar- rhenius vessel. The electrodes, however, are very close together and are held firmly apart by fusing short pieces of glass rod be- tween them. The vessel can be closed with a ground glass stopper, or with a thermometer as in Fig. 5, &. All glass used for making electrolytic vessels should be of good quality, very resistant to the action of water or to that of any other substance with which they may come in contact. Further- more, such vessels should be steamed out or soaked out with warm water for a long period prior to use, especially if they are to be used for solutions whose conductivity is slight. Vessels of variable resistance capacity of the form shown in Fig. 14, Chapter IV, are sometimes very advantageously em- ployed. They are best adapted to the determination oif the con- ductivity of concentrated solutions, where comparatively large resistance capacities are desired. ELECTRODES. — Platinum is by far the most serviceable metal for electrodes. For measuring conductivity the electrodes are usually covered with platinum black, which tends toi decrease polarization and to produce a sharper tone-minimum in the tele- phone when this instrument is employed. To insure a suitable kind of spongy coating on the electrodes the platinizing solution, suggested by Lummer and Kurlbaum, is commonly employed. This is a 3 per cent, solution of commercial platinum chloride (HaPtClg) to which is added 0.025 P^''' cent, of lead acetate. The process is best carried out directly in the electrolytic vessel, which is filled well over the electrodes^ with this solution. The platinum deposits on the cathode. A suitable current can be obtained from two accumulators by introducing resistance from' a rheostat until the evolution of gas is only moderate. In order to prevent ex- cessive absorption of chlorine by the anode it is advisable to change 1 The electrodes must be thoroughly cleaned beforehand with a strong solution of so- dium hydroxide, then rinsed with distilled water several times, and not touched again- with the hands before platinizing. i6 THE CONDUCTIVITY OF LIQUIDS the direction of the current every few minutes. In this way a suitable deposit is formed on both electrodes in from ten to twenty minutes. Under any circumstances, however, some chlorine is held tenaciously by the electrodes. This can be removed by elec- trolyzing a dilute solution of sulphuric acid or of sodium acetate, the direction of the current being frequently changed. Finally, the electrodes should be washed off repeatedly with distilled water and left standing in water until used. M III '" I' '" I II /^ \ Fig- 7. In certain cases blank electrodes are to be preferred. For ex- ample, they are better with concentrated solutions of strong acids and bases on account of the absorbent power of the platinum black of covered electrodes; with liquids which possess extra- ordinarily great resistance, as water of a high degree of purity; and with organic liquids, when it is found they are being oxidized on account of the presence of the platinum black. Blank elec- APPARATUS USED IN DETERMINING CONDUCTIVITY I7 trodes should always be thoroughly cleaned and finally rinsed with alcohol and dried before using. Dip electrodes are sometimes very useful, especially when it is desired to measure the conductivity of a liquid in the bottle or other vessel in which it is preserved. According to Kohlrausch. the most useful form, Fig. 7, consists of two small platinum elec- trodes welded to platinum wires and these in turn inclosed in a capillary tube. Since such electrodes must have the same resist- ance capacity, regardless of the form of vessel in which they are used, they must be protected by a small glass bell fastened to the capillary in order to intercept the lines oif force. A small hole near the top of the bell allows the escape of air or any gases formed. RESISTANCES.— Every laboratory should possess a good re- sistance box having a sufficient variety of separate resistances. The wire of which the resistances are made should be non-in- ductively wound and have only a very small temperature coeffi- cient. All resistances of standard make are now so constructed. The range of resistances in a box should be suited to the purpose for which it is to be employed. Resistances from o.i to 100 ohms are well adapted to use with concentrated solutions ; for solutions of higher resistance they may range from i to 10,000 or even 50,000 ohms, while for general use in an electrochemical labor- atory a box containing resistances from i to 10,000 ohms is very satisfactory. As to the number of separate resistances, i, 10, 100, etc., ohms will answer. It is very convenient, however, to have a set so arranged that any resistance from i to 10,000 ohms can be obtained. Kohlrausch recommends sets of i, 2, 7, 20, 70, 200, 700, 2000 and 7000 ohms as ample for most purposes. A set of resistances should be calibrated before use by com- paring the separate resistances with one another, and finally by comparing one of them with a standard resistance. Graphite lines on ground glass are sometimes used as resist- ances. Such resistances are not designed to replace a resistance box. For high resistances, however, they are often more satis- factory, since they are free from capacity, which sometimes causes trouble with wire resistances. Every time such a graphite re- sistance is used it should be compared with some known resistance. i8 THE CONDUCTIVITY OF LIQUIDS A preliminary calibration is not worth while on account oi the irregular changes which graphite resistances seem to undergo.^ Wildermann,^ who gives excellent directions for the preparation of such resistances, found them to be sufficiently constant for his purpose. MEASURING BRIDGES FOR USE WITH ALTERNATING CUR- RENTS. — The form most commonly employed, consisting of a wire I meter long, has already been described in connection with the Kohlrausch method for determining conductivity (Chapter I).' W^hen great accuracy is not required, for laboratory instruction for example, a smaller coinbination bridge, represented in outline Fig. 8. in Fig. 8, is very serviceable. The wire is only 25 cm. long, but is graduated so as to give directly the reading -7-. An induction coil and a resistance box are usually mounted on the same base, as is seen in the cut. The primary current is connected with the binding posts, A, B, the resistance to be measured with C, D, and the telephone with E, F. Frequently greater accuracy is desired than can be obtained with a meter wire. In this case various means may be employed o o I ^ II O O -a I <[a I rr I #!• I t\f -7^ Fig. 9. to lengthen the wire. The apparatus represented in Fig, 9 has, l- See VoUmer : IVied. Ann., 52, 334 (1894). 2 Ztschr. phys. Ckem., 14, 235 (1894). s Such a bridge wire can be easily constructed. Kor directions see Ostwald and Luther : Physico-chemische Messungen, p. 346. APPARATUS USED IN DETERMINING CONDUCTIVITY 19 besides the primary meter wire, two secondary wires, each ■ of which has the same resistance as the primary. One of the sec- ondary wires can be connected with the left end of the primary wire, and the other with the right end. The wire can then be considered to be 3 meters long, and the ratio -7- is obtained from the reading a' on the primary wire, according to the following relation : a 1000 + a' b 2000 — a' If desired, a wire 2 meters long can also be obtained with this apparatus. A second arrangement, whereby a wire of considerable length Fig, 10. can be used, is represented in Fig. 10. In this case the wire is wound on a roller of hard rubber or other insulating material, and the sliding contact is effected by means of a small roller which travels along the wire. All these different forms of apparatus can be obtained from most of the firms which manufacture stand- ard physical apparatus. Thirdly, additional arbitrary resistances can be introduced at either end or at both ends of the bridge wire. As has already been stated, results are most accurate when the readings are made near the middle of the bridge wire. For this reason it is customary, when additional resistance is introduced, to place equal resist- ances at each end of the bridge wire. On the supposition, how- ever, that they are unequal, let them be designated by R-^ and i?.„ 20 THE CONDUCTIVITY OF LIQUIDS and the resistance of the bridge wire by R. Then, if the bridge reading is A, the ratio a:b is equal to \ ^ lOOO / V lOOO / or f looo -^ + Aj : f looo -^ + looo— ^j. The total resistance can be made ten times that of the bridge wire by making the two resistances, i?i and R2, equal, and making each one equal to 4.5*i?. Then the ratio a : b equals (4500 + A) : (4500 + 1000—^), or (45°+!^) = (iooo-(45o + 4))- The value of -7- can then be found directly from Obach's tables by p . A . using 450 + — for a. Sometimes it is desirable to measure resistances very much greater than any that can be obtained from the resistance box at hand. In this case, proceeding in the usual way, it is impossible to bring the reading near the middle of the bridge wire. Deter- minations can, however, be readily made by introducing the extra resistance, referred to above, only at one end of the wire and opposite the resistance to be measured. If R^ is the resistance introduced and it is made eqital to 9 R, Obach's tables can again be employed, '■/^^ A being used for a, provided that the additional resistance was introduced at the right hand of the bridge. INDUCTION APPARATUS.— Alternating currents for conduc- tivity measurements are produced almost exclusively by means of induction coils with a Neeff s interrupter. Ostwald recommends a small coil, such as is frequently used with some medical appli- ances. The tone minimum in the telephone depends to a con- siderable degree on the nature of the induction apparatus, so if continued difficulty is experienced in obtaining a sharp minimum. APPARATUS USED IN DETERMINING CONDUCTIVITY 21 Other induction coils should be tried. Sometimes the sharpness is increased by removing the brass tube which sometimes sur- rounds the core. Filing down the little iron point on the spring frequently increases the rapidity of the vibrations. Kohlrausch recommends a somewhat larger apparatus having a core of soft iron about i cm. in iliameter and 8 cm. in length. This is wound with two coils of copper wire, the inner consisting of 200 windings of wire 0.5 mm. in diameter, and the outer of 1000 windings of wire whose diameter is 0.25 mm. A current from one or two Daniell elements or from one accumulator is suffi- cient to operate it. If the interrupter vibrates against a mercury pole, its point should be of platinum. To prevent its becoming warm, the mercury, in this case, should be in a cup arranged so that water can be kept circulating over it. Fig. II. The so-called string interrupter (Saitenunterhrecher), Fig. 11, is sometimes employed. The vibrations of a horizontal steel string, ah, under tension, open and close both the primary and secondary circuits. The vibrations are induced by a small elec- tromagnet m in the primary circuit. The contacts, as shown in the figure, are commonly between platinum^ points and mercury. This form of interrupter is especially well adapted for use with the optical telephone or vibrations galvanometer, because the vibra- tions can be so easily controlled by simply adjusting the tension of the string. INSTRUMENTS FOR DETERMINING CURRENT ABSENCE WITH ALTERNATING CURRENTS.— The telephone is the cheap- est and most commonly used of any of the instruments for detect- ing the absence of current in conductivity determinations with al- ternating currents. One should be selected which gives a good tone with relatively weak currents. This can only be determined 22 THE CONDUCTIVITY OF LIQUIDS satisfactorily by trial. A slight buzzing sound of the inter- rupter, like the singing of a mosquito, is best adapted to produce a clear tone in the telephone. Under the most favorable conditions one should be able to make the setting correctly to V.oo.ooo, and under ordinary conditions to Veooo of the length of the bridge wire. A beginner frequently finds it helpful to close one ear with cotton or with a suitable wooden plug. With a little experience, however, one finds no difficulty in distinguishing the sound in the telephone from that of the interrupter. It is usually impossible to obtain absolute silence in the tele- phone. The setting is then made by moving the contact slightly backwards and forwards until two points are found, one at the right and the other at the left of the minimum, where the tone is the same. The correct setting is midway between these two points. Since the source of the current and the current measuring in- strument can be interchanged, it is usually advantageous to change the arrangement shown in Fig. 3. The induction ap- paratus is then in A C and connected with the sliding contact, and when the key of the contact is open no current flows through the bridge. When difficulty is experienced in obtaining a clear tone in the telephone, it can be frequently much improved by introducing resistance, if necessary up to several thousand ohms, in the secondary circuit between a pole of the induction apparatus and the sliding contact on the wire. Under such conditions, to avoid statical charging of the telephone or other parts of the apparatus, the other pole of the induction coil should be grounded. Another instrument which may be used to measure alternating currents is the so-called optical telephone. It is more complicated and much more difficult to adjust than a common telephone, but when once adjusted very accurate measurements can be made with it. An outline of the essential features of the apparatus is shown in Fig. 12. A corrugated strip of German silver or of brass foil swings between the poles of two horseshoe magnets, each of which is formed, as in the Bell telephone, by attaching small electromagnets to larger permanent magnets. The poles are arranged, as in the figure, so that one positive and one negative pole are on each side, unlike poles being opposite each other. The current passes through the electromagnets in such a way APPARATUS USED IN DETERMINING CONDUCTIVITY 23 that by altering its intensity the magnetism of one of the per- manent magnets is increased while that of the other is dimin- ished. On the corrugated metallic filament between the magnets are fastened two circular discs of soft iron. To these discs is attached a brass pin b, which transfers the motion of the filament to a mirror m, from which a beam of reflected light is thrown on a scale in the observing telescope. A current of 5 X io~* am- peres, under favorable conditions, gives a sensible deflection. c, I n. N L Fig. 12. A disadvantage of the optical telephone is that it will react only with a current whose period of alternation corresponds to that of the tone of the metallic filament. The string interrupter, page 21, with vibrating metallic string is best adapted for use with this instrument, since it permits an adjustment of the period of alternation of the current within certain limits. The filament of the optical telephone can also be adjusted, so that its tone may be varied within a limited range. When the difference between the period of vibration of the filament and the period of the cur- rent is too great to be brought into harmony by either oif these means, the filament of the instrument must be replaced by one whose tone corresponds to the alternation period of the current. Four filaments, whose periods of vibration are 64, 128, 256 and 512, will be found sufficient for the adjustment in nearly every 24 THE CONDUCTIVITY OI^ LIQUIDS case. Reference is made to the articles of Wien^ for further par- ticulars as to the apparatus itself and as to the means employed to overcome the effects of overtones. Other instruments which have been used to measure alter- nating currents are the electrodynamometer and the vibrations galvanometer. The former is now but little employed, and the latter is somewhat similar in its construction and use to the optical telephone.^ I Wied. Ann., 42, 593, and 44, 681 (1891). * See Rubens : IVied. Ann., 56, 27 (1895). CHAPTER III. Sources of Error with Ai■ The figures in the above table are all taketi from Kohlrausch, Holborn, and Diessel- horst : Wied. Ann.. 64, 440 and 451 (1898), except those for gypsum, which are the values given by Hulett : Ztschr. phys. Chem.^ 42, 577 (1903). DETERMINATION OF RESISTANCE CAPACITY 37 Whatever the method used for determining the resistance ca- pacity of a vessel, attention should be given to the following point. When the electrodes of a vessel stand vertically (Fig. 4, a. Fig. 5, b and c), the resistance capacity must be determined for a defin- ite filling, that is, either for a certain volume or up to a mark on the glass. Then, whenever the vessel is used the liquid should stand at the same height, otherwise the capacity will be different from that determined. Vessels of the Arrhenius form with the electrodes horizontal (Fig. 5, a) possess a constant resistance ca- pacity, no matter how much solution is used, provided the elec- trodes are covered in every instance.^ CALIBRATION OF A VESSEL TOR VARIABLE RESISTANCE CAPACITY. — It is frequently desirable to possess a vessel whose "1 \ ' f - « » - « y'-i i- 1 J - J - I'-l I'-f 1-0 I- I ~ t \ ' s ,"Xi ,-.» . -* - -J Fig. 14. resistance capacity can be readily varied. Such vessels are- com- monly of the U-tube form, as shown in Fig. 14. The electrodes, 1 J. Phys. Chem., 6, 557 (1902). 38 THE CONDUCTIVITY 01^ LIQUIDS one of which is in each limb, are capable ol being raised or low- ered. The calibration is accomplished by filling the tube with one of the standard solutions best adapted to the range of capacities which it is wished to determine, for instance, tenth-normal potas- sium chloride. First a position of the electrodes is sought, where, being at the same height, they yield some simple value for the capacity, as i. /f 1=0.01119 for tenth-normal KCl at 18°. The C resistance, therefore, under the above conditions is ' -= 0.01119 = 89.4 ohms. Consequently a resistance of 89.4 ohms 0.01119 is introduced, and both electrodes are raised or lowered together until the resistance of the solution exactly equals this. If it is difficult with the apparatus at hand to introduce fractions of an ohm, the necessity for it can be overcome by properly changing the temperature. For example, in this case the temperature of the bath can be set at 23.44°, at which temperature k = 0.01250 for tenth-normal KCl. The required resistance is then 80 ohms. The position of the electrodes thus determined is marked 0.5 on each limb of the tube. One only of the electrodes is then raised until the resistance is one and a half times 89.4 ohms at 18°, or one and a half times 80 at 23.44°. This new position is marked i. The second elec- trode is then raised until the resistance is twice its first value and the position on this limb marked i. This procedure is continued until the desired number of calibrations have been made. For any setting of the electrodes the resistance capacity is given by simply adding together the numbers on each limb against which the electrodes are set. For instance, if one electrode stands at , the mark 1.5 in one limb and the second electrode at the mark 2.5 in the other limb the resistance capacity is then 4. Of course, conductivities depending on resistance capacities obtained in this way are by no means as accurate as those depending on the re- sistance capacity O'f a vessel in which the electrodes have an in- variable position. If the bore of the tube is uniform the calibration can be made DETERMINATION OF RESISTANCE CAPACITY 39 by the direct method in each of the vertical limbs, after the ca- pacity has been determined for the bent portion by means of a solution of known conductivity, as above. That is, after the first positions of the electrodes in each limb, marked 0.5 on the above tube, have been determined, the remainder of the calibra- tion can be made, when the diameter of the tube is known, by ■laying off the proper lengths from the line marked 0.5, according to the formula, l^ Cs (page 4). CHAPTER V. Water. Preparation op Solutions. CONDUCTIVITY OF WATER.— The conductivity of ordinary water is (Juite considerable owing to the impurities which it con- tains. After a single distillation the conductivity is usually re- duced to from 3 to 6 X io~"*. By distilling with special care the conductivity can be brought as low as 0.7, or 0.8 X io~^- The purest water whose conductivity has ever been measured, is prob- ably that prepared by Kohlrausch and Heydweiller^ by redistilling in vacuo water which was already as pure as could be obtained in contact with air. The glass apparatus used by them for this purpose had been in contact with water for ten years, and, there- fore, was very resistant to the further action of this liquid. The specific conductivity of this pure water at 18° is given by Kohlrausch and Heydwelller in reciprocal Siemens units as 0.0404 X io~^°. From their results the conductivity has been calculated at o", 18°, 25", 35" and 50° in reciprocal ohms, and the values so obtained are given in the table below in the column Obs. These investigators also estimated the temperature co- efficient of the conductivity of pure water according to the prin- ciples of the dissociation theory. Combining this with their most probable value for the conductivity of water at 18° and estimat- ing the effect of the impurities still present, they derive a theo- retical expression for the conductivity of pure water at any tem- perature t, which, recalculated to reciprocal ohms, is as follows : 22250 loV = 0.03586 X io~ (273 + ')" X (319 -|- 7.50- From this the values in the column Theoret. are calculated. Specific conductivity. Temperature. Obs.2 Theoret. 0° 0.016 X IO~* 0.012 X IO~^ 18 0.043 X io-« 0.038 X io-« 25 0.063 X io-« 0.058 X io-« 35 o.ioo X io-« 0.094 X io-« 50 0.190 X io~' 0.183 X 10- « 1 U^ied. Ann., 53, 209 (1894). 2 These numbers are based on the value 0.0404 X lo-ioat 18° and on re-sults obtained by Kohlraunch and HeydweiUer on January 28 and February 14 ; he. cit., p. 227 WATER. PREPARATION OE SOLUTIONS 4I The conductivity of water is seen to vary greatly with the temperature, which is in accord with the principles of thermo- dynamies. In round numbers the conductivity of pure water at 18° may be taken as 0.04 X lO""^, about ten times less than that of any water in contact with the air. PUlilFICATION OF WATER.— By a single distillation the con- ductivity of water, as has been said, is usually reduced to from 3 to 6 X io~^. In preparing solutions for conductivity deter- minations water of this degree of purity should be used only when the conductivity of the solution has a considerable value, that is, exceeds o.ooi. For the preparation of solutions whose conduc- tivity is less than this, distilled water must be still further purified Hulett'^ recommends distilling water twice, once from an acid solution and the second time from an alkaline solution. Before the first distillation 5 cc. each of sulphuric acid and of a concen- trated solution of potassium dichromate (or permanganate) are added to each liter of water. This distillate is then made alkaline with baryta water, 25 cc. to a liter, and distilled again. Hulett used a condenser of platinum, which was thrust well up into the neck of the retort, so that only the water condensing in the plat- inum tube would run into the receiver. A condenser of silver, "block tin or even a good quality of glass may replace the platinum without materially affecting the result. Jones and Mackay^ have also described a method for purifying water very similar to the above'. The two distillations are, how- ever, continuous, the distillate from the first being collected in a retort from which it is at once distilled into a permanent receiv- ing flask. The second retort contains, instead of baryta water, an alkaline solution of potassium permanganate. Water can be obtained by these methods which has a conductivity as low as 0.8 X io-«. In a recent article Kohlrausch^ suggests several means by which the conductivity of water may be greatly reduced. He found that the conductivity of distilled water diminished by simply standing an contact with platinized electrodes, presumably on account of 1 Ztschr. phys. Chem., 21, 297 (1896), and J. Phys. Chem., i, 91 (1896J. i Am. Chem. J., 19. 9° (1897). s Ztschr. phys. Chem., 43, 193 (1902). 42 THE CONDUCTIVITY 01? LIQUIDS the oxidation of traces of ammonia. By allowing a rapid current of COj-free air to pass through water in the conductivity vessel, where it was also in contact with the electrodes, the conductivity was reduced to 0.28 X 10—^, the lowest value yet obtained for the conductivity of water in contact with the atmosphere. The removal of CO, from water by aeration in order to im- prove its conductivity has been frequently practised. The con- ductivity of water which has been only once distilled, may be greatly reduced by this method. COa-free air is commonly ob- tained by passing out-door air through a long tube filled with moist soda-lime or through a concentrated solution of caustic potash. In either case the air should afterwards be passed through a washing bottle, containing distilled water, before it reaches the water to be purified. Walker and Cormack^ describe a very efficient method for puri- fying water. They first distil from an alkaline solution, then this distillate is acidified with phosphoric acid and redistilled, and finally it is distilled a third time without the addition of any chemical. Water treated in this way was found to possess a con- ductivity of 0.7 X io~^. From the partial pressure of COj in the atmosphere they have calculated that the conductivity of water, distilled in contact with air, should be about 0.65 X io~^ on account of this impurity alone. This affords an explanation of the improvement in the conductivity of water when COj is re- removed. Water can also be quite efficiently purified by freezing. A clean flask, containing the water to be purified, is placed in a freezing mixture (salt and ice) whose temperature is about — 10°. When about one-half of the water has frozen around the inner surface of the flask, the remainder, which contains most of the impurities, is poured off. By treating v/ater which had been once distilled in this way, Nernst was able to reduce the conduc- tivity to 2 X io~°. Kohlrausch and Heydweiller found the same value for the conductivity of a sample of water which was oib- tained from a piece of natural ice. The conductivity of this water, before freezing, was probably fully 150 times greater than 2 X 10—^. » J. Chem. Soc. 77, 8 (1901). WATUR. PREPARATION OF SOLUTIONS 43 INFLUENCE OF THE SOLUBILITY OF GLASS ON THE CON- DUCTIVITY OF WATER.— Electrolytic vessels and all flasks and bottles used in handling pure water or very dilute solutions should be of a good quality of glass, quite resistant to the solvent action oif water.^ Glass vessels should be boiled out with water or steamed out^ prior to use. The longer a vessel has been in contact with water, provided it is of good glass, the more resistant is it to the action of water and consequently better adapted to employ- ment for conductivity work. The higher the temperature of water the greater is its effect upon glass.^ Some glass, no matter how long it is treated with water or steam, is never fit for uses of this kind. The solubility of the glass of any vessel can be tested by determining, from day to day, the conductivity of water allowed to stand in it. This may be done either directly in the vessel itself by means of dip electrodes, or in an electrolytic cell by carefully transferring some of the water with a pipette. If the glass is of good quality the conductivity per loo cc. water should not increase more than i X io~^ in a week. PREPARATION OF SOLUTIONS. BY WEIGHING. — The preparation of solutions for conductivity determinations reqtiires great care in order that the error, in- troduced by inaccuracies of concentration, may not exceed the errors involved in the measurement of the conductivity. This has been frequently overlooked. A solution of known strength is, if the substance is of a nature to permit it, always best prepared by weighing. All weighing should be reduced to weight in vacuo in order to be on a uniform basis. This is readily accomplished by means of the following equation : ( ■ ^ ^ \^ ^ s sJ' s s in which the letters have the following significance : ' Kohlrausch : If^ied. Ann., 44, 577 (1891); Kohlrausch and Heydweiller: tVied. A nn. S3, 210 (1894). 2 Ostwald and I k. 1-25 0.429 0.27 4 0.764 0.62 1.695 0.504 0.31 8 0.815 0.44 2.625 0.619 0.39 16 0.875 0.38 5-19 0-731 0.39 32 O.90S 0.28 8.65 0.792 0.35 64 0.927 0.18 25-5 0.941 0.47 128 0.947 0.13 Caesium Nitrate. 2.33 0-578 0.34 • • .... ... 3-365 0.641 0.34 4 0.761 0.61 4.81 0.704 0.35 8 0.822 0.47 7.09 0.750 0.32 16 0.872 0.37 10.2 o.Sro 0.34 32 0.913 0.30 5r.6 0.95 0-35 64 0.941 0.23 130-7 0.98 0.33 128 0.948 0.14 The constancy of k for rubidium nitrate when derived from the cryoscopic measurements is only fair, while for caesium nitrate it is excellent, so we have here the first example of a strong elec- trolyte which follows Ostwald's dilution law.^ LIMITATION OF THE EQUATION, a = -^-. The dissociation of the above salts, when calculated from the conductivity, does not, however, give a constant value for k. It has already been mentioned that the freezing-point method and the conductivity method yield different values for the degree of dissociation in the case of most strong electrolytes ; consequently, the accuracy of the equation, a = -—r-, for strong electrolytes has frequently been questioned, notably by Jahn,^ who has estimated that in the case 1 Picric acid, a strong electrolyte, whose dissociation as calculated by the freezing- point or conductivity method does not follow the law of mass action, has just been found by Rothmund and Drucker to do so when the dissociation is derived from its partition be- tween the solvents benzene and water. Zlsckr. phys. Ckem.^ 46, 827 (1903). 2 Zlschr. phys. Ckem.^ 33, 545 {1900). DISSOCIATION CONSTANTS 57 of electrolytes like NaCl it gives results about lo per cent, too high.^ From the results of Biltz, just given, the only inference is that the Arrhenius equation is, indeed, unreliable when applied to strong electrolytes, and that the deviation from the true value is not constant, but is a function of the electrolyte itself. The true value of the degree of dissociation is also not given by cryoscopic measurements, except in the case of certain electrolytes which approximate the limiting conditions pointed out by Biltz. This latter method is, however, undoubtedly less influenced by the secondary reactions, which take place in the solution of strong electrolytes, than the conductivity method. Steele^ has recently derived a relation to express the degree of dissociation of electrolytes having complex anions," which shows that in some cases the equation, a = —r~, cannot be expected to -/J-oo yield the true value of the dissociation as long as the dilution is such that the complex ion is present. Defining the degree of dissociation as the ratio of the concen- tration of the ions of one kind — in this case cations — to the total concentration of the electrolyte, we have x = — , in which x is the degree of dissociation thus defined, c the concentration of the cation and tf the total concentration of the electrolyte. The specific conductivity of this solution then is K = £[<4 + 4)_f'(/ —4,)]. In this c has the same signification as above, c' is the concen- tration of the complex anion, 4, 4, and 4' are migration num- bers* of the cation, the simple anion and the complex anion re- spectively, and £ is the quantity of electricity carried by i gram- equivalent. Now letting ^ = — , we have 1 See in this connection Noyes : Science, ■20, 579 (1904)- 8 Zhchr. phys. Chem., 40, 730 (1902). a Such as Na2S04, which undoubtedly dissociates partly into Na and NaS04, and partly into 2Na and SO4. * For an explanation of the migration numbers see the next chapter. 58 THE CONDUCTIVITY OP LIQUIDS For any other concentration Now since A = — , V J ^[(4+4)-/?(4-40] ^^ ^[(4 + 4)-A(4-40] Vl At infinite dilution c ^ ij and /? ^ o, and therefore vi ^ a:[(4 + 4)-yg(4-4-)] A. 4 + 4 from which •^ j_ /? 4—4 " = ^ + ^"4^r4- Therefore only when 4 ^ 4 or yS ^ o, does — j — represent the true degree of dissociation. Even in the case of strong binary electrolytes — i— may not always represent the true degree of dis- sociation ; for, as we have already seen, complex ions of some sort doubtless exist in such solutions. DILUTION FORMULAS FOR STRONG ELECTROLYTES. -Ost- wald's dilution law does not hold for solutions of strong electro- lytes, as the strong acids and bases and most neutral salts. Such substances are much too completely dissociated in concentrated solutions to be able to follow the law on dilution. The reason that such electrolytes do not obey the law has not as yet been satis- factorily explained. One possible explanation is that the ions of strong electrolytes may increase the dissociating power of water. The addition of a non-electrolyte to water, we know, de- creases the dissociating power of water, hence it is argued the presence of strong electrolytes may increase it. Arrhenius^ ap- pears to have found grounds for this view in investigating the dissociation of weak acids in the presence of salts. The disso- 1 ZUchr. phys. Chem., 31, 211 (1899). DISSOCIATION CONSTANTS 59 ciation coostants of salts, calculated according to the Ostwald formula, increase as the concentration O'f the solution increases. The dissociation constants of the weak acids in Arrhenius' ex- periment increased also as the concentration increased, although not so much as the constants of strong electrolytes. Others have sought to explain this apparent inapplicability of the law of mass action in this case on the ground that Arrhenius' equation for the degree of dissociation, a = ■ " , does not hold for solutions of strong electrolytes. It is true that the degree of dissociation, as found by the freezing-point method, does, in some cases vary considerably from that found by the above equation. However, the agreement is, in many cases, so perfect that the burden of proof must be thrown on the opponents of the Arrhenius equation.^ Several formulas of an empirical nature connecting the degree of dissociation of strong electrolytes with the dilution have been proposed. Of these Rudolphi's^ differs from Ostwald's in sub- stituting for the dilution v its square root, so that it has the form, : = constant. (i — a)i/v The value of this constant for potassium and sodium chlorides is shown in the fourth column of the table below. The conductivity determinations were made by Kohlrausch and ■Maltby^ at i8°, and are the most recent figures for these elec- trolytes. The values of the expression , ._ are seen to be fairly constant, but show a gradual falling off with increasing dilution. Another empirical dilution formula is that of van't Hoff.* We have seen that the Ostwald dilution formula is derived from the expression, 1 See besides the discussion on pp. 55-58 the following : Euler : Ztschr. phys. Chem., 29, 603 (1899) ; Biltz : Ibid., 40, 185 (1902) ; Goebel : Ibid., 42, 59 (1902) ; Jahn : several arti- cles, see especially Ibid., 41, 257 (1902) ; Sackur: Ztschr. Elektrochem., 7, 784 (1901); Ilx = '' + ''', OTiiy, = u + v. » Pogg. Ann., 89, 177 (1853), and many other articles in later volumes of this journal. THE MIGRATION OF THE IONS 65 of concentration, and from these he calculated the relative veloci- ties of the ions. N P N P ++++++++ :-!-+ + -)-"++ + + + + + + + + + + + + t +;+ + + + D D a b Fig- IS- It can readily be shown by means of diagrams, Fig. 15, how a difference in the velocities of the ions is able to cause a change of concentration about the electrodes. Let the cations be repre- sented by + a'^d the anions by — and suppose the ions to be ar- ranged in the solution in rows, as in Fig. 150!^ there being an equal number of each kind of ions on each side of the porous dia- phragm D. Since 8 molecules are present in each compartment the original concentration about each electrode may be represented by 8. Now let us suppose a current to be passed and the cations to move twice as fast as the anions. After a certain interval the conditions may be represented by Fig. 15&. Each ion, which has no partner, is supposed to be set free and discharged at the elec- trodes. Six positive and six negative ions have, therefore, been liberated. The concentration in the cathodic compartment has de- creased from 8 to 6, while in the anodic compartment it has de- creased from 8 to 4, a loss of 2 and 4 respectively. This means that the loss in concentration around the cathode is to the loss in concentration around the anode as the velocity of the anion is to the velocity of the cation; that is, the losses in concentration about the electrodes are inversely proportional to the speeds of the correspondingly named ions. If. therefore, the change in concentration aroimd the electrodes is accurately determined after a certain interval of electrolytic action, the relative velocities of the ions, or as they are termed transport numbers, can be at once ascertained. HITTORF'S METHOD FOR DETERMINING TRANSPORT NUM- BERS. — As has already been stated, the method just outlined was first employed by Hittorf, and it is, therefore, usually known by 66 THE CONDUCTIVITY OF LIQUIDS his name. It is sometimes known as the indirect method, for the reason that the velocities of the ions are not directly measured, but are deduced from the change in concentration of the solution during electrolysis. The determination of the transport numbers of the ions of silver nitrate, by Loeb and Nernst/ affords an ex- cellent example of this method on account of the simplicity of the apparatus employed. 'c^ Fig. l6. The kind of electrolytic vessel used by them is shown in Fig. i6. Convection currents must, of course, be avoided, and to in- sure this, diaphrams are used in many forms of apparatus. Here, however, no diaphragm is required, because the form of the vessel is designed to prevent diffusion, the heavier portion of the solu- tion, at the end of the experiment, being in the lower portion of the apparatus. The cathode C is a piece of silver foil cylindrically rolled, and the anode A consists of a flat spiral of silver wire. This wire, where it passes throiugh the solution, is covered with a glass capillary tube to prevent contact with the liquid. The open- ing at B is so arranged that the apparatus can be filled or emptied while in a constant temperature bath. The vessel is filled with a 1 Ztschr.phys. Chem„ 2, 948 (i838). THE MIGRATION OF THE IONS 67 known quantity of silver nitrate solutioin of known strength, and a feeble current is passed for some hours, the quantity of elec- tricity being measured by a voltameter. At the termination of the experiment approximately one-third of the solution is re- moved at B (anode portion) and the amount oi silver determined in it analytically; a second third of the solution (middle portion) is then removed and analyzed; finally, the last third remaining in the vessel (cathode portion) is analyzed. If the experiment was successful the concentration of the middle portion should remain unchanged, showing that there were no disturbing con vection currents. In an experiment of this kind the total amount of silver nitrate in the solution has not changed, because for every Ag ion which separated out at the cathode one went into solution at the anode. There was no separation of NO- ions from the solution, as they simply dissolved silver from the anode. The concentration was continually increasing about this pole, due to the migration O'f NO3 ions in this direction. In an actual experiment 32.2 mg. silver were deposited in the voltameter, while the concentration of silver aroimd the anode in- creased 16.8 mg. and aroimd the cathode decreased by this amount. If no Ag ions had migrated from the anode the concentration would have increased around this pole by 32.2 mg. silver, so the fall in concentration, due to the migration of Ag ions, was actu- ally 32.2 — 16.8 = 15.4 mg. silver. Therefore, since the relative speeds of the ions are proportional to the fall of concentration around the oppositely named electrode we have Speedof anion (NO,) Fall around cathode 16.8 — i ^ — = := = 1, 09 1 ^ f. Speed of cation (Ag) Fall around anode 15.4 This quantity r is the ratio of the rate of migration of the anion to that of the cation. The transport number of the anion n is the ratioi of its share in the transport of electricity to the total transport of electricity. This is equal to the ratio of the speed of the anion to the sum of the speeds of both ions, that is, since the migration numbers are proportional to the speeds of the ions, 4 Correspondingly the transport number of the cation is 68 THE CONDUCTIVITY 01? LIQUIDS 4 + 4 = I - From the relation we also have i + r If we substitute for r in this equation its value as found above for silver nitrate, we obtain i.oqi n = ; ^ O.S22. I + 1. 091 0.522 is, therefore, the share in the transport of electricity taken by the NO3 ion in a solution of silver nitrate. The share taken by the Ag ion is i — 0.522^0.478. We can also obtain n directly from the losses in concentration around the electrodes, since these are proportional to the speeds of the ions and to the migration numbers. Accordingly, we have from' the above ex- periment 4 16.8 "^4+T.= i6.8 + i5.4=^°-'"- Hittorf's method of determining transport numbers has been used by a great number of investigators^ and has yielded very satisfactory results. It is the most trustworthy method in use, because its sources of error and the conditions necessary to secure a high degree of accuracy seem to be quite clearly understood. THE DIEECT METHOD OF DETERMINING THE VELOCITY OF THE IONS.— The method of Hittorf, as has already been shown, is an indirect method for the reason that the velocities of the ions are derived from changes of concentration around the electrodes. The first successful attempt to measure directly the velocity of 1 For the most recent work with this method see the following: Hopfgartner: Ztschr, phys. Chem , 25, 113 (1898) ; Bein : Ibid., 27, I (1898) ; Starck : Ibid., 29, 385 (1899) ; Jahn and Students : Ibid„ 37, 673 {1901); Mather: Am. Chem. J., 26, 473 (1901) ; Noyes -.J. Am. Chem. Soc, 23, 37 (1901) ; Noyes and Sammet : Ibid., 24, 944 (1902) ; Steele and Denison : J. Chem. Soc, 81, 456 (1902). For certain sources of error, with semipermeable membranes, and for corrections to former results, see Hittorf: Ztschr. phys. Chem., 39, 613 (1902) ; and 43i 2.^9 (I903). THE MIGRATION OF TH^ IONS 69 the ions was that of Lodge.^ Methods, depending on the same principle, have since been employed by Whetham,^ Masson,' and Steele,* each one of whom added substantial improvements to the method as practiced by his predecessor. This method is of less wide application than that of Hittorf, both on account of the limitations in the choice of indicator solutions (see below) and because of the fact that it cannot be applied with accuracy to very dilute solutions. Fig. 17. The method, as used by Steele, consists essentially in noting the movement of the boundary between a pair of solutions sub- jected to electrolysis. The solution into which the boundaiy moves contains the electrolyte, the speed of whose ions is to be determined, while the other, which is gelatinized, contains an electrolyte, the so-called indicator. The electrolyte ttnder inves- tigation is bounded at each end by such an indicator solution. For instance, when determining the speeds of the ions of potassium chloride, the indicator used at the anode was sodium acetate and at the cathode lithium chloride. 1 Brit. Ass, Reports, 1886, p. 389. 2 Phil.^Trans., 1893, p. 337 ; 1895, p. 507 ; also Zlschr. phys. Chem., 11, 2jo (1893). 8 Ztschr.phys. Chem., 29, 501 (1899). * Substantially the same article in the following journals : Phil. Trans., 1901, p. 105 ; J. Chem. Soc, 79. 414 (1901) ; Ztschr.phys. Chem., 40, 689 (1902). 70 THE CONDUCTIVITY OF LIQUIDS The form of apparatus best adapted to the investigation of the simplest type of salts is shown in Fig. 17. The tubes A and B contain the electrolyte under investigation. To B is attached the tube B so that the solution will be under atmospheric pressure throughout the experiment. Each tube can be connected with the larger tubes C C at the top, or Z? Z? at the bottom, which contain the gelatinized indicator solutions. When both indicator solu- tions are lighter than the solution in A B, they are placed in the upper vessels, C C ; when they are both heavier in the lower ones, D D ; when one is lighter and one is heavier, the lighter is placed in C and the heavier in D. When a current is passed, the boundaries move into the tubes A B with a speed, which, under certain conditions, depends only on the nature O'f the ion ahead and on the electromotive force. The motion of the boundary can be easily followed by the difier- ence in refraction of the two layers, a small gas flame being placed behind the apparatus toi illuminate the tube. It is necessary for the success of an experiment that the speed of the indicator ion be less than that of the ion whose speed is being measured, that the resistance of the indicator solution be only a trifle greater than that of the solution it follows, and that the electromotive force be kept within certain limits determined by trial. The selection of a suitable indicator is, in the case of many solutions, a matter of considerable difficulty. No indicators that split up hydrolytically can be used on account of the great speed of H and OH ions. The distances traveled by the two boundaries and hence by the two ions are read off at certain intervals by means of a cathetometer. From these readings and the current measurements made at the same times the ratio ~ or r is easily obtained, from which n, the transport number of the anion, can be readily cal- culated. The transport numbers obtained by Masson and by Steele differ in a good many instances from those determined according to the method of Hittorf. Abegg and Gaus^ have, consequently, sub- jected Steele's method to a critical investigation in order to dis- cover possible sources of error. 1 Zischr. phys. Chem.^ 40, 737 (1902). THE MIGRATION OF THE IONS "Jl They point out certain additional conditions, which must be fulfilled in order to avoid inaccuracy, and they furthermore have shown experimentally that the deviation from Hittorf's results is not due to variable current strength, but to the fact that the electrolyzed solution is cataphoretically transported even through the relatively dense gelatinous layers. Correcting for this cata- phoresis which they measured in the case of half-normal potas- sium chloride, Steele's value of 0.490 for the transport number of the anion becomes 0.508, in good agreement with the values ob- tained by Hittorf's method with potassium chloride solutions of the same concentration. Denison^ has continued the investigation oif Steele's method, and the results of his work may be summed up as follows : After making the proper correction for cataphoresis the trans- port numbers of all the alkali metals, except lithium, agree with those obtained by the method of Hittorf. In cases where complex ions are formed or hydrolysis takes place the numbers do not agree with those of Hittorf. It is probable that gelatine is able to combine with some salts, giving rise to complex ions. The gelatine solutions should be kept in the liquid condition; for in solid gelatine solutions the speed of the cation, relative to that of the anion, seems to be lessened, as is apparently alsO' the case in concentrated aqueous solutions. VALUES OF TEANSPORT NUMBERS OF SOME UNIVALENT ELECTROLYTES. — Transport numbers vary somewhat with the temperature and also with the concentration of the solution.. Un- fortunately no standard temperatures or concentrations have been employed in determining these numbers, as has been the case in measuring conductivity. The transport numbers of most unival- lent — or, as they are frequently called because they dissociate into only two ions, binary — electrolytes vary but little with the tem- perature. The values found by Bein for the transport number of the anion of potassium, sodium and lithium chlorides, at different temperatures, are shown below. 10°. 20°. 51°. Potassium chloride 0-503 • • • • • ■ • • Sodium chloride 0.615 0,583 Lithium chloride 0.624 .... ' Ztschr. phys. Chem., 44, 575 (1903). 76°. 97°. 0.513 — ;::; 0.547 0.621 ^2 THE CONDUCTIVITY OF LIQUIDS For concentrations less than fifth-normal Bein could detect no variation of the transport numbers of potassium and sodium chlo- rides with the concentration. For lithium chloride, however, at 20° the transport number varies from 0.672 at a concentration of fifth-normal to 0.624 at hundredth-normal.^ In general, the trans- port numbers of most binary electrolytes vary but little with the concentration, provided that the concentration does not exceed tenth-normal. Jahn and Bogdan's results with dilute solutions of sodium and potassium chlorides are shown in the accompanying table. V. NaCl. KCl. 30 0.605 0.505 60 0.603 0.502 90 0.604 0.502 120 0.605 0-503 For electrolytes whose transport numbers show no variation below a certain concentration, the correct values of the transport numbers at infinite dilution are considered to be equal to this con- stant number. Such constant values of the transport numbers of some univalent electrolytes are given in the table below. They are taken from the sources already mentioned and are given, as nearly as possible, in the order of their trustworthiness. Transport Numbers of the Anion at Mean Temperature (about 20°) IN DlI,UTE SOIS0, and Cu< Cu/ ^SO, Since the nature of the ions is thus changing- on dilution, we should expect to find the transport numbers varying at different concentrations. This is in fact the case, and is due probably both to the change in the ratio of the number of anions to the number of cations and to the fact that these different ionic aggregations undoubtedly possess different speeds. If, however, the transport number of a bivalent electrolyte becomes constant on diluting, we may infer that at this dilution the only ions present in measurable quantity are the simple ones and that this constant value is also the correct transix>rt number at infinite dilution. It is difficult in solutions whose concentration is less than o.oi normal to determine accurately transport numbers by the Hittorf method and absolutely impossible by the direct method. By means of the Hittorf method it has been found, however, that some bivalent electrolytes yield transport numbers apparently constant near this concentration, or at least are approaching a constant value which can be extrapolated without great error. Some trans- port numbers, determinations of which have been carried out for dilute solutions, are given below. The values are all based on half molecules, and v is, therefore, the number of liters in which a gram-equivalent is dissolved, and m is the corresponding equiv- alent concentration. The numbers represent transport numbers of the anion at temperatures in the vicinity of 20". Starck's transport numbers of sulphuric acid show a continuous decrease with the concentration to sixteenth-normal, while Hit- torf's results show an apparent increase as the concentration de- creases from normal. For concentrations greater than normal (not given above) Starck is in accord with others in finding that the value of the transport number increases with the concentra- tion. Bein's value at the concentration twentieth-normal is nearly the mean of the values found by Hittorf and by Starck at low concentrations, and for other reasons, which will be considered ' See Bredig : Ztschr. phys. Chem., 13, 202 (1894). THE MIGRATION OF THE IONS 75 8§ So 0\ 3 C to m >n in S S SL 666 : : : : : -g| .Sap lO lO lO •« -^ 5 .2 „-i •'^ ^ g I-, d o o o ^"c r? Hi (U d o o VO lO »o »o d d d d B M, ^_^ . o • •»! o gf-S. : . ^— ' '■ o ct • o ■ vo ° d ■ d w d a W , , "1? •• : • * • - l-l o .--N ,— > WW 5B- d "■ ^ : o c/} " d 'l- o , r^ a H- w lO ■ d « d d d n S y V ^-^ ^ — * WW &^ US'! O « M W d d lO lO d<5, d "?vff ° d tn !zi w ^ o < W ti • ^ — y : vo i-i ^; "? n «3 '. M ■ ^. "^ d vo t^ • d d d d Tl ■*-• O .tl t, o Si .2 o " -^ ■ ■ ■ .^ « W g « 6 6 6 6 6 p?^ ;;- i 'O S '^ " a : : : : : g ° « | 8 • • • • • |1"S5 2 S S o ^ O 00 _ m o\ \o ov vo lO ^ vo d d d d o lO V? Tf " 00 « vo vo lO '^. dodo . .. o •H W 4) in o .5 " VO d a o vo O Cog W W „• „• >o r^ : ;;;;*,; 00 M 1- t-i O M o o . ^-.^ • ^ : o : : : : : : • • a : «^ : : : : : : 5. ;-:2;^S^i w I ^ ^ ;: o (U S 00 «i „ ^j o oo i^ +j o Iz; " O w to c? w 76 THE CONDUCTIVITY OF LIQUIDS later, this value seems to be the most trustworthy for the transport number of the anion of sulphuric acid in dilute solutions. Recent results of my own, which have not yet been published,^ confirm this value of Bein. Jahn and Buschnewski have recently found that the transport number of BaCl^ has a value practical! v constant (0.550) between the concentrations 0.03 and 0.005. Noyes obtained the value 0.558 at w = 25, and Bein 0.559 at z^ = 100. The results in the table beyond z^ = 20 are estimates from these values. Hopfgartner, working at concentrations between normal and tenth-normal, found values somewhat higher than those found by Noyes or by Bein. For CaCl, at the concentration o.oi Bein obtained the transport number 0.553, ^^'^ ^^ the concentration 0.005 Steele and Denison found 0.562. The transport numbers of fev/ compounds have been so com- pletely investigated as those of cadmium, particularly the chlo- ride and iodide. Unfortunately, however, the value of A„ cannot be very accurately estimated for these substances, so that the migration number of cadmium is by no means so well fixed as might be expected. The presence of complex ions in the more concentrated solutions is illustrated in a marked manner by the conduct of cadmium iodide. Its transport number is considerably greater than i at concentrations greater than normal.^ As the concentration, however, decreases from normal it is seen that the transport number rapidly decreases in value, showing that the complex ions are being decomposed. At the concentration o.oi the transport number has become practically constant, indicating that no complex ions are present in solutions more dilute than this. The transport number of cadmium chloride behaves similarly,, although in not so marked a manner. The transport numbers of other bivalent electrolytes exhibit this conduct commonly only in a slight degree. In discussing binary electrolytes mention was made of the fact that the transport numbers of these electrolytes also undergo a change in concentrated solutions. This change is very likely 1 Since wiiting this they have been published,/. Am. Chem. Soc, 26, 1039 (1904). The value found in dilute solution is given by the equation, m = 0.1788 + 0.0011 {t — 2o°)_^ " See the values given by Kohlrausch and Holborn : Leilvermbgen der BlectrolyU. For a theoretical discussion of this fact see Steele and Denison : /. Chem. Soc, 81, 457 (1902). THE MIGRATION OF THE IONS TJ partly due to increased viscosity of the solution which affects the speed of the anion and cation differently, but for the most part it must be ascribed to the existence of complex ions here as well as in solutions of bivalent electrolytes (see page 55). MIGRATION NUMBERS OF BIVALENT IONS.— On account of the variation of the transport numbers of bivalent electrolytes with the concentration, Kohlrausch's law of the independent migration of the ions had never been conclusively proved to hold true for such electrolytes until recently. Kohlrausch, in a paper published in 1898/ collected all the transport numbers which had been de- termined up to that time in dilute solutions, and pointed out that it was very probable that the law was of universal application, the errors being no greater than were to be expected from the in- sufficiency of the data in many cases. Very recently, however, the investigations of Noyes and of Steele and Denison have shown that it is possible to determine transport numbers quite accurately in very dilute solutions. Constant values have been_ obtained for the transport numbers of BaCU, Ba(N03)-2 and CaClg, and, in fact, for most of the electrolytes of the above table. These results supply additional evidence to support the law of the independent migration of the ions in its application to bivalent electrolytes and place the migration numbers of bivalent ions on a firmer foun- dation. According to the most probable value of the migration num- ber of the H ion (318 at 18°), the value A«, for ^^H^SO, cannot be far from 388. Assuming this value as a basis for com- putation and using Starck's smallest transport number (0.135 ^t V -- 16), we obtain for the migration number of the H ion 336, which is undoubtedly too high. From Bein's value (0.180 at V = 20) the migration number 318 is obtained, which agrees with the above value. From Bein's value we also find the migration number of yiSO^, to be 70. From Noyes' value (0.504) of the transport num- ber of ^KaSO.j at the concentration 0.04, assuming J« =135.5, the migration number of ^^SO^ is found to be 68.3. Steele and Denison have calculated 68.2 for the migration number of 3^2 SO^ from the transport number obtained by them.' for CaSO^. From 1 IVied. Ann., 66, 785. 78 THE CONDUCTIVITY OF WQUIDS CuSOj, on the assumption that Ay, = ii8, the migration number of ^S04 is found to be 73.2. The approximate average of all these, viz., 70, was formerly adopted by Kohlrausch, as the migra- tion number of this ion. Kohlrausch, however, in his most recent work^ considers 68.1 the most probable value of this quantity. The migration numbers in the table below are taken from the paper of Kohlrausch and Griineisen. Migration Numbers of Bivalent Ions. Anions. Cations. 18°. 25°. 18°. 25°- Si-5 61 51-5 61 55- r 65 45-9 54 46.6 55 47-2 55 47-4 55 61. 1 71 ^SO,.... 68.1 79 )4Ca... yi, CjOi-.- 62.6 69 >«! Sr ... >^ Ba . . . ^Mg.. ■^ Zn . . . ^Pb... EFFECT OF COMPLEX IONS ON TRANSPORT NUMBERS.— We have just seen that in all solutions of bivalent electrolytes much stronger than tenth-normal there very likely exists, besides simple ions, one or more kinds of complex ions. It has also been shown that in the behavior of solutions of strong univalent electrolytes there are certain anomalies, which can only be explained on the assumption of the presence of some sort of complex ions (see pages 55, 77). In cases then where such complex ions are present the transport numbers as determined simply represent changes in concentration around the electrodes caused by the movement of all the ions, and the effect dvte to any one of them cannot, in general, be estimated. KiimmelP has, however, recently attempted such an estimation in one of the more simple cases of this kind by means of the principles of isohydric solutions. Solutions are isohydric when they possess a common ion having the same concentration in each solution (see, for fuller discussion, Chapter X). Whether the simple laws of isohydric solutions hold when one of the electrolytes is binary is doubtful, but Ktimmell's application of the principle is so ingenious that it deserves notice. He employed solutions of MgCU varying in concentration from 1 Kohlrausch and Griineisen : Sitzungsber. Kgl. pr. Akad. IVfss., Berlin, 1904, p. 1215. 5, Ztschr. Elekirochem., 9, 975 (1903). THE MIGRATION OF THE IONS 79 twice-normal to twentieth-normal. He assumes that at these con* centrations no ions more complex than the AfgCl'ioti are present and that the friction of the ions on one another can be neglected. The concentration of the CI ions is then determined by finding the solution of KCl isohydric with each oif the MgClj solutions. The concentration of these ions in the latter solution is then the same as that in the former. The accompanying table exhibits the results thus obtained. Ec|uivalent, dilution, v, of MgCIa solution. 0.5 0.668 I.O 2.0 lO.O 20.0 Ai- MgClj at 25°. 56.0 63.0 69.1 77-5 99-5 104.0 Dilution, •tf, of iso- hydric KCl solution. 0.60 0.806 1. 215 2.434 12.2 22.3 Degree of dissociation of KCl. 0.68 0.703 0.72 0.754 0.88 0.895 Concentration, c, of CI ions. I-I33 0.872 0-593 0.310 0.0722 0.0401 Letting c = the concentration of the CI ions, c^ of the MgCl ions and c^ of the — ^ ions, and also letting 4, l^ and 4^ be the migration numbers of these three ions, respectively, and noting that Cj ^ c — Ci, we then obtain A^ = cvl„ + c^vl^ -f (c—c^vlc^. (i) Substituting 4 = 76 and l^ = 57,^ and assuming /^ = o, the following values for the concaitration of the MgCl ion at the dif- ferent dilutions are obtained: V = 0.5 0.668 I 2 10 20 c-^ = 0.68 0.38 0.17 0.04 o o Assuming that only MgCl and CI ions are present in the moiSt concentrated solution, we have r^ ^ o and Cj = c, from which we find that 4i = 23. That is, the maximum value of the migra- tion number of the MgCl ion is 23, while we may assume o to be its minimum value as above. Substituting then 4i = 23 in equa- tion (i) we have again for the concentrations of the MgCl ions the following values : V £1 0.5 0.668 I 2 10 20 Cj = 1. 133 0.649 0.288 0.073 o o The concentration of the MgCl ions at different dilutions must, 1 These values are those used by Kiimmell and are for 25°. 8o THE CONDUCTIVITY OF LIQUIDS therefore, lie between the values found in these two tables. The two tables' agree in representing the concentration of these ions at dilutions from lo liters up as equal to zero; that is, it is highly probable that there are no MgCl ions at concentrations beyond tenth-normal. To calculate the transport number of the anion Ktimmell pro- ceeds as follows : For a gram-equivalent of chlorine to separate at the anode, it is necessary that there migrate from the anode ' " lb MgCl ions, and-^ — 'j—r- . — - — jMgions, (2) /,. + 4 ■ « + -^ '^ ' 4, + 4 ■ « + -^ in which a and h are partition coefficients indicating how the cur- rent is divided between the MgCl and corresponding CI ions on the one hand and the Mg ions with their corresponding CI ions on the other hand. At the same time there migrates to the anode 4 « , 4 b , . 4' + 4 ■ « + -5 L^- L' a + b and this is the transport number oi the anion. Now let us imagine the solution divided into two layers, one containing all the MgCl ions and the corresponding CI ions and the other the Mg ions and the CI ions corresponding tO' them. If /f, and K.^ represent the conductivities oif these two layers re- spectively, and K the total conductivity of the solution, we have /f J -|- /fj ^ K. Remembering that c := — . then ^». 10" = A = aA^ = cvA^ = c^v{l,^ -\- 4) + c^v{l,^ -f 4), and, therefore, ^ _ ^.(4. + 4) ^ _ ell,, -h 4) From these and from (2) we obtain for the transport number of the CI ion „ _ _4 ^i(4i + 4) ^ 4 -' /^+4 ^i(4, + 4) + ^,(4. + 4) ' 4. + 4 c^h^ + 4 ) ^ 4(^1 + gj) , . c,(Jn + 4) + clh, + 4) ^.(4, + 4) + f,(4. + 4)' ^^' This is the true transport number of the anion. It differs from THE MIGRATION OF THE IONS 8l the transport number actually measured for the reason that some chlorine goes to the cathode with the MgCl ions. Correcting for this the apparent transport number is , =: 4(Ci + c,) /^^__ " c,{l^ + 4) + c,{l^ + 4) In + 4 ■ c,{ln + 4) _ 4(g, + c.^—hA (.-^ c,{ln + 4) + ^.(4, + 4) c,{h, + 4) + clh, + 4)' ^^^ By means of this equation, equation (i) and the transport num- bers of magnesium chloride,^ c■^ and 4i can be calculated. From the vajues so obtained Kitmmell judges that the migration number O'f the MgCl ion is approximately lo, and that the concentration of this ion, at the different dilutions cannot be far from the following : V = 0.5 0.668 I 2 fj ^ 0.8 0.45 0.2 0.05 Noting that c^ = c — f,, and letting /J = -L = the ratio of the complex ions to the total cations, equation (4) becomes ""''- 4 + 4-/8(4-4.) ■ ^^^ When /^ < 42 — 4i> which, from the value just found foi 4i and from the values in the table, page 78, is probable, the numer- ator decreased as /5 increases relatively less rapidly than the de- nominator, that is, the value of the fraction increases. This sig- nifies that the transport number of the anion increases with the formation of complex cations, or increases as the concentration of the solution increases, which is in accord with the observed facts for electrolytes of this type. Equation (4) was derived on the assumption of complex cations being present. Steele, on the other hand, gives an expression for the transport number of an electrolyte possessing complex anions, which he derives as follows:^ Let c be the concentration of the cation and c' of the complex anion, then c — c' will be that of the simple anion ; and let 4, 4 and 4' be the migration numbers of the cation, the simple anion 1 Kummell used Hittorf's corrected values : Zischr.phys. Chem., 39, 629 (1902). ' Ztschr. phys. Chem., 40, 729 (1902). 82 THE CONDUCTIVITY OF LIQUIDS and the complex anion respectively. The total quantity of current passing through the electrolyte is proportional to ^4+ (c — c')i„ + c'lj, and that carried by the anions alone is proportional to (c — ^)4 + c'la: Therefore, the migration number of the anion is ^ (c-c')L + c'L' ^ ch + ^(4.-4) ^ d + (f-^)4 + ^4' <4 + 4) + ^(4— 4)' Let m be the number of single ions into which the complex anion decomposes on complete dissociation, then the change of concen- tration, due to the migration of these ions, is proportional to w4', and the increase in concentration on the anode is proporti&nal to {c — f')4 + c'ml^,. Therefore ^ _ r4 + dimh—Q _ 4 + K^L—L) <4 + 4) + ^'(4—4) 4 + 4 + ^(4.-4)' (6) c' in which /? := — ; = the ratio of the complex anions to the total number of anions. Since 4' is probably less than 4, the denominator tends to be- come smaller as the concentration of the complex ions increases, but unless m is very small mlj>la, and the numerator will in- crease with the concentration of the complex ions; that is, the transport number will increase as the concentration of the solution increases. This is the same as was found above for complex cations, and agrees with the actuai determinations. Equation (6) may be changed to the form 4 + ^(4—4) + 4 ■ In order that n may be greater than i, it is only necessary that ftlaim. — 1)>4. This last will be true if either ^ or m are large, as is undoubtedly the case with many of the cadmium salts. CHAPTER VIII. Determination oe Jc. Absolute Velocity of the Ions Graphic Representation of Conductivity. DIRECT METHOD FOR THE DETERMINATION OF A..— It has already been shown that as the dihition of a solution increases the equivalent conductivity also increases and tends to approach a maxin:^um value. With strong electrolytes, especially most neutral salts, this maximum value may be estimated from actual measure- ments of the conductivity at high dilutions, as in the following examples : Potassium chloride. Silver nitrate. Barium chloride. m. A- m. A- m. A- 0.0005 . 128.09 0.0005 113.88 0.0005 118.3 0.0002 128.76 0.0002 114.55 0.0002 Ilg.8 o.oooi 129.05 o.oooi 115.01 o.oooi 120.5 y/„ = 130.1 yi„ =115-8 . //„ =121.6 This can either be done by mathematical extrapolation, or better, by means of graphic representation as in Fig. 19 (see latter part of this chapter). In this figure it will be seen that by extending curve I (KCl), it would be a simple matter to find where it be- comes parallel to the axis of abscissas. The ordinate at this point is the limiting value of the equivalent conductivity sought. A« oi the stronger acids and bases can be estimated in the same way, but with a less degree of accuracy because their true con- ductivity at such high dilutions is more difficult to determine (see page 47). For the great majority of acids and bases, however, recourse must be taken to the indirect method in order toi estimate the value of the equivalent conductivity at infinite dilution. INDIRECT METHOD FOR THE DETERMINATION OF J™.— In the case of weak electrolytes, whose equivalent conductivity shows no indication of approaching a maximum value at the highest dilu- tions at which it is possible to make accurate measurements, it is impracticable to calculate A«, in any such way as the above. For instance formic acid, the strongest of the three electrolytes whose conductivity is given on page 52, is only about 35 per cent, dis- sociated at a dilution of 1024 liters, and from the equivalent con- ductivity at that dilution, viz., 49, it is clearly impossible to esti- mate the value at infinite dilution, vis., 409. 84 THE CONDUCTIVITY OP LIQUIDS In order to calculate A„ in such cases some electrolyte is se- lected which has a common ion with the weak electrolyte, and for which A^ can be estimated by the direct method; and from this known quantity the value required is calculated by the aid of the proper migration numbers. In the case of weak acids, for ex- ample, the sodium salts are employed because they are very com- pletely dissociated. The chlorides of the weak bases, like am- monia, are usually selected for the same reason. By making use of the migration numbers, given in the preceding chapter, A„ of the acids or bases themselves can then be readily calculated. The difference between A„ of an acid and A„ of its sodium salt is evidently the difference between the migration numbers of H and of Na. This difference at i8° is 274.5 and at 25° is 301. Therefore, to obtain ^4^ of acetic acid at 25° from 94.1, the value of ^co of sodium acetate at the same temperature, we have 94+301^395, which is the desired quantity. Similarly for weak alkalies, like ammonia (NHjOH), we add to the value of A„ of ammonium chloride the difference between the migration numbers of OH and CI, which is ill at 18° and 124 at 25°. Ostwald^ has pointed out that the difference between the equiv- alent conductivity at infinite dilution and the equivalent conduc- tivity at any given dilution not too small is practically constant for strong electrolytes of the same class. That is, A„ — A^ = d for salts of the same type. These constant differences for three different types of salts are given in the table below. The numbers are, of course, average values, and the accuracy of the values de- creases from d-^ up to d^. Differences between A^ and A^ at 18° and 25°- Both ions One ion univalent Both ions univalent. and one bivalent. bivalent. rfi. Ik. di. V. 18°. 25°. 18°. 25°. iS°. 250. m. lOOOO I.o I.I 2.0 2.3 5 6 o.ooor 5000 1.4 1.6 2.8 3-2 7 8 0.0002 2000 2.0 2.3 4.4 5-1 II 13 0.0005 1000 2.7 3-1 6.1 7.0 16 18 o.oor 500 3.6 4.2 8.3 9.6 23 26 0.002 200 5.5 6.3 12.3 14.2 33 38 0.005 100 7.5 8.6 16.5 19.0 42 48 O.OI 50 9-8 11.3 21.5 24.5 SI 58 0.02 1 Lehrhuch d. aUg. Chemie.^ a, i, 693. DETERMINATION OF Aoo. 85 These differences can be used to calculate the value of A, oi salts which are known to be greatly dissociated in dilute solutions, as, for instance, sodium or potassium salts. This is accomplished by determining the equivalent conductivity of such a salt at a few of the dilutions given above, most conveniently at 50, 100, 200, 500 and 1000 liters, and then adding to these values the corre- sponding values in the above table. The average of the values so obtained is the number sought. A^ of weak acids can be derived in a very similar manner from the equivalent conductivity of their sodium salts at any of the above concentrations. The equivalent conductivity is determined at several concentrations and to the values so obtained the corre- sponding numbers in the table are added, increased by the differ- ence between the migration numbers of H and of Na. The proper values to add to the conductivities oi the sodium salts of mono- basic acids have been calculated and are given below for both 18° and 25°. V loooo 5000 2000 1000 500 200 100 50 d„, 18° 275.5 275.9 276.5 277.2 278.1 280.0 282.0 284.3 d^, 25° 302.1 302.6 303.3 304.1 305.2 307.3 309.6 312.3 To illustrate the use of these numbers the value of A„ oi benzoic acid is calculated in the accompanying table from the conductivity of sodium benzoate. The measurements were made at 25", and, according to the figures obtained, the value of A^ of benzoic acid at this temperature is approximately 387. yt- A CO* V. Sodium benzoate. d«. Benzoic acid. 5° 74-3 312.3 386-6 100 77.6 309.6 387.2 200 79.8 307-3 387-1 500 8r.5 305-2 386.7 1000 82.8 304.1 386.9 Kohlrausch, in a recent article, gives some variations of these methods for calculating A„, and reference is made to his paper^ for a more complete discussion of this subject. J„ OF SOME OF THE COMMON ELECTROLYTES. —The values of A„ of a number of electrolytes are given in the table below. They are calculated from the most trustworthy data avail- 1 JVifd. Ann., 66, 785 (1898), 86 THE CONDUCTIVITY OF LIQUIDS able, many of them being the results of recent determinations by Kohlrausch and associates. In most cases the numbers at 25° are calculated from those at 18° by means of the temperature coeffi- cients of Deguisne^ or of those compiled by Kohlrausch.^ 18°. =5°- »KC1 130. 1 150-1 'NaCl 109.0 126.8 'LiCl 98.9 1 15.0 'RbCl I33-0 153-0 =CsCl 133-6 .... 'NH^Cl ... 129.8 150. 1 »KBr 132.3 152-6 'KI 131-1 15I-2 'KF 111.3 129.0 mci 131-5 HCl 383.6 427.7 HNO3 .... 380.0 423.2 HC2H3O2.. 353 395 ^ BaClj . . 120.7 140.7 y^srci,... 117.1 136-7 ^CaCl, .. 1 17. 1 136-7 y^MgCl,.. 111.5 129.7 J^ZnCl^.. 112. 2 130-7 >^H,S04.. 386 431 'A H,C,0,. 381 421 18°. 25°- 'KNO3 126.5 145-6 'NaNOs . . . 105-4 122.3 'NHiNOj . . 126.2 145-6 'AgNOa ... 1 16.0 134-1 'KCIO3 .... 119.7 138.1 'KIO, 98.5 .... 'KSCN .... 121.3 .... KCjHaOj .. 101.5 117-4 NaC^HjO^.. 80.4 94-1 »T1N03 .... 127.9 KOH 241.0 273-9 NaOH 219.9 250.6 NH^OH . . . 240.7 273-9 'AK^SOf. 132.6 153-4 A Na^SOi 111.5 130. 1 ^Ba(N03), 117. 1 136.2 A CaCNOs)^ "3-5. 132.2 >^CaSO,... 119.6 140 AZnSOi-.. 114.7 134 ACaSOi--- II5-3 134 No mention is made in the above table of any of the carbonates or of any of the trivalent electrolytes as phosphoric acid and the phosphates. Any value of A^ that might be assigned for these substances would be very uncertain, in the former case because hydrolytic action renders it impossible tO' measure accurately the conductivity at high dilution, and in the latter case because the dissociation of such compounds is not well understood. On the basis of V3H3PO4, A„ of this substance is given by Foster' as 120.8 at 18°. A^ OF ORGANIC ACILS.— Ostwald^ has measured the conduc- 1 Dissertation, Strassburg, 1895. Given by Kohlrausch and Holborn : Leitvennogen der Eleklrolyie. ^ Sitzungsber. Kgl. pr. Akad., Wiss., Berlin, igoi, 1026. Reproduced in this book, Chapter 9. 8 These numbers are derived from recent determination by Kohlrausch and associates : SiUungsber. Kgl.pr. Akad., Wiss., Berlin, 1899, 665 ; 1900, 1002 ; 1902, 581. « Phys. Rev., 8, 257 {1899). 6 ZUchr.phys. Chem., 3, 170, 241, 369 (1889) ; Summary, p. 418. ABSOLUTE VELOCITY OF THE IONS 87 tivity of a great number of organic acids, and has also estimated their molecular conductivity at infinite dilution. He has found, with few exceptions, that the dibasic acids are so weak that in dissociating they conduct themselves similarly to monobasic acids. It has been shown (page 61 ) that succinic acid yields a constant value for the dissociation constant fe up to a dilution of 1,024 liters, which indicates that such acids are dissociated appreciably within this dilution into only two ions, H and HA, HgA being the formula of the acid. Exceptions to this are oxalic acid beyond a dilution of 25 liters and malonic beyond a dilution of 256 liters. The values of A^ of some of the more common organic acids are given below. They are derived from Ostwald's values of /<« by reducing to reciprocal ohms and correcting for the migration number of the hydrogen ion, which has been adopted in this work. yi„ OF Organic Acids at 25°. Acids. Symbols. Ax- Acids. Symbols. Vx- Formic HCHO2 409 Benzoic HCvH^O^ 387 Acetic HC.HjO^ 395 Salicylic HCHjOs 387 Propionic HC3H5O, 390 Malonic H2C3H2O4 389^ Butyric HCjHtOj 387 Succinic U,C,Ufi, 387* Monochloracetic HC2H2CIO2 393 Malic H^C.H.Os 387^ Dichloracetic HCjHCl^Oj 392 Tartaric H,C,H,Oe 387^ Trichloracetic uc^a^o. 389 Maleic HjC.H^O, 387' Glycollic HC^HjOa 394 Fumaric H2C4H2O4 387^ Lactic HCsHjOs 389 Ostwald has called attention to the fact that A^ of the organic acids decreases with increase of the number oif atoms in the molecule. Since A^ is made up of two constants, one the migra- tion number of the H ion and the other of the organic anion, the migration numbers of the organic anions must decrease with the increase of the number of atoms in the molecule. This decrease finally reaches a constant value (about 20), after which further increase in the number of atoms has no efifect on the speed of the ion. Bredig^ has found the same general principles true with regard to organic cations. ABSOLUTE VELOCITY OF THE IONS.— The migration numbers 1 This value for the dibasic acid is on the assumption of dissociation into only two ions at infinite dilution. 2 Ztschr. phys. Chem., 13, 289 (1894) 88 THB CONDUCTIVITY 0? LIQUIDS la and 4 express the velcx:ity of the ions in terms of conductivity units. The actual velocities in centimeters per second can be ob- tained from these in the following manner. Since k is the con- ductivity of I cc. of a solution when the electromotive force is i volt, the equivalent conductivity, ^ = — or q)K, may be looked upon as the conductivity of i cc. under like conditions, provided that a whole gram-equivalent of the substance were dissolved in I cc. and the substance were dissociated to the same degree as at the actual concentration r). For instance, the equivalent conduc- tivity of a normal solution is looo times its specific conductivity. This is, however, the conductivity which would be obtained by bringing looo more carriers of the electricity into the I cc, pro- vided that each carrier retained unchanged its ability to carry the current. And this again is the same as imagining that the whole gram-equivalent of the substance is dissolved in the i cc, but that the dissociation remains the same as in the original normal solu- tion. By the same reasoning ^m can be considered as the con- ductivity of I cc. containing one whole gram-equivalent entirely dissociated. Now, since 96,580 coulombs of electricity are carried by each gram-equivalent of an electrolyte, if the whole gram-equivalent were decomposed in one second, the ions composing each mole- cule would have together moved i cm. and the conductivity would be 96,580. But the conductivity under these conditions is only ^00, and, therefore, a gram equivalent has traveled only — — 96580 cm. and each ion has traveled separately —~ — cm. and 96580 96580 cm. This gives for the velocity of the anion, o 000010354. 4 cm. per second, and for the velocity of the cation, 0.000010354. ^c cm. per second, when the electromotive force is i volt. These expressions give the velocities of the ions in solutions sufficiently dilute so that their friction on one another can be neglected. This has been shown to be the case when the concen- tration does not exceed tenth-normal. GRAPHIC REPRESENTATION OP CONDUCTIVITY 89 VELOCITIES OF Ions Under the Infi,uence of an Ei.ectromotive Force of One Voi,t. Centimeters Centimeters Anions. per second. Cations. per second. CI 0.000679 K 0.000668 NO3 0.000642 Na 0.000449 CjHsOj 0.000383 Ag 0.000559 OH 0.00183 H 0.00329 The velocities of some of the principal ions at 18° are given in the accompanying table. The extreme smallness of these veloci- ties is due to the great resistance offered by the water, that is, the friction of the ions on the water molecules. Anything which tends to decrease this friction will increase the velocity of the ions, as, for instance, raising the temperature of the solution. Mixing alcohol with water increases the viscosity of the water and con- sequently the friction on ions moving through it. This is the principal reason why the conductivity of solutions to which a little alcohol has been added is diminished. GRAPHIC REPRESENTATION OF CONDUCTIVITY.— The con- ductivity of an electrolyte may be given simply in a table in which opposite either the percentage content or the concentration is placed the corresponding specific conductivity. For most pur- poses, however, a knowledge of the equivalent conductivity is pre- ferred. Tliis latter is, therefore, more commonly given in tables than the specific conductivity. (See tables in appendix). The spe- cific conductivity can be readily obtained' from' siuch a table, when desired, by simply multiplying the equivalent conductivity by the concentration expressed in gram-equivalents per cubic centimeter. In many cases, however, a graphic representation is very desir- able, for one can see at a glance the general trend of the con- ductivity, and it also affords an excellent means for accurate inter- polation. By such a method conductivity is represented in the form of a curve on coordinate paper, employing the concentration or dilution as abscissas and the specific or equivalent conductivity as ordinates. By using the specific conductivity the changes which the conductivity undergoes with change of concentration are best brought out, as, for instance, in the case of sulphuric acid (Fig. 18). Here the curve shows very readily the various maxima and minima of the conductivity. / ?J /> / Nl S \ V^ ?>• ^ N / some warm body or by care- ful addition of small quantities of warm water, either by hand or preferably by means of a slowly flowing continuous current. For temperatures from 5° to 50° above room temperature the foirm oif thermostat described by Ostwald' is very serviceable. It is shown in Fig. 20. The gas flame is automatically regulated by the ap- paratus at B, which is shown in increased size in b. The expan- sion of the liquid in the bulb at the bottom of the bath forces the mercury up against the mouth of the gas tube, thus regulating the flow of gas. A pin hole just above the mouth oif the gas tube allows enough gas to pass, so that the flame is never entirely ex- tingushed. Either alcohol or a 10 per cent, solution of calcium chloride may be used as the expansive liquid in the bulb. The bath is commonly stirred by means of a wind-mill stirrer, which can be operated by hot air from a Bunsen burner. All baths should be stirred, and the greater the difference in temperature between the bath and the room the more active should be the stirring. If this difference exceeds 10° the stirrer shoiild be driven rapidly by means of an electric or a water motor, as one operated by hot air is hardly adequate. A temperature below that of the room can be best secured by running a stream of faucet water — or if this is not cool enough, a stream of water artificially cooled — through the bath, care being taken to regulate the flow so that the temperature will remain constant. A tem- perature of 0° is very easy to maintain by cooling the bath with ice. Covering the outside of a thermostat with felt, decreases radia- tion and hence permits keeping the temperature more n^rly con- stant. Radiation can be somewhat hindered by using a bath which is rather deep in proportion to its diameter, so as to leave exposed comparatively little water surface. Little is accomplished by covering a shallow bath of considerable diameter with felt. If a still higher degree of constancy of temperature is required a thermostat devised by Bradley and Browne^ is recommended. Its efficiency consists in employing an extremely sensitive regu- 1 Zlschr. phys. Chem., a, 565 (1888). 'J- Phys- Chem., 6, 118 (1902). g6 THE CONDUCTIVITY Olf LIQUIDS lator to control the flow of water, the temperature of which is regulated in a reservoir in a manner very similar to that used in the Ostwald thermostat. A constancy of temperature within a few thousandths of a degree can thus be attained. STANDARD THERMOMETER SCALE.— All accurate conductiv- ity measurements should be given for standard temperature re- ferred to the scale of the hydrogen thermometer. The following are the corrections to be applied to an accurate mercury ther- mometer to reduce the readings to the hydrogen scale. The num- bers are to be subtracted. For ther- mometers of 0°. 5°. 10°. 15°. l8°. 20°. 25°. 30°. 35°. 40°. 45°. 50°. Jena glass. No. 16 (normal) o 0.03 0.06 0.08 0.09 0.09 o.io o.il 0.12 0.12 0.12 0.12 No. 59 ■■ o o.oi 0.02 0.03 0.03 C.04 0.04 0.04 0.04 0.03 0.03 0.03 Calibration tables from the Reichsanstalt include these correc- tions. They have also recently been taken into consideration by some makers in dividing the thermometer scale. TEMPERATURE COEITICIENTS.— If it is desired to find the conductivity of a substance at one temperature from measurements made at some other temperature, it is necessary to know the change in conductivity of the substance per degree of temperature. This is called the temperature coefficient of the substance. For nearly all salt solutions the temperature coefficients vary from 0.021 to 0.024, for caustic alkalies from 0.019 to 0.021, and for acids and some acid salts thej^ have still smialler values. The temperature coefficient c is found by determining the con- ductivity of a substance at two temperatures, t^ and tz, not too far apart. Since 18° is considered the standard temperature for conductivity measurements, we have I /^ BaCl2. 250 248 244 225 KI 231 225 221 207 )^ MgClj 254 253 248 243 KNO3... 222 223 220 218 "^ CuSO, 256 226 198 198 NaCl...- 253 254 246 241 HCl 163 158 J53 152 NaC2H„02 268 274 261 271 HNO3... 154 152 147 143 NaOH 213 202 202. X H3PO4 154 140 88 78 Influence of Temperature. — The coefficients vary also with the temperature to a certain extent. The results below are from the work of Schaller,^ and they were obtained with solutions at a dilution of 1024 liters. The coefficients have been multiplied by 10,000. 1 Ztschr. phys. Chem., 4, 96 (1889). i Ztschr. phys. Chf.m., 25, 497 (1898). 98 THB CONDUCTIVITY 0^ LIQUIDS TemperaThrb Cokf:ficient : '^i(25 ^t) — I '^26 t-25 ■ % (25 + 1). KCl. NaCl. KNO3. NaNOs. HCl. 32.5° 207.1 215.8 201.0 208.4 141. 37-5 206.9 217.5 202.7 213.6 139.2 42.5 210.5 220.2 204.7 217.4 135.4 47-5 213.0 223.7 , 207.0 219.I 132.0 52.5 215-2 226.5 209.0 220.3 I2S.3 57-5 216.2 229.7 208.8 221.6 125.0 62.0 216.7 231.9 209.3 225.1 123.2 , Here again the temperature coefficients of the acids seem to show the greatest changes. The coefficients of the salts increase with the temperature, while those of the adds decrease. At higher temperatures, however, the coiefficients of salts also decrease. Quadratic Equations for Temperature Reduction. — Since the co- efficients themselves vary thus with the temperature, in reducing conductivity determinations from one temperature to another, a quadratic equation is better adapted to yield accurate results than a simple linear equation like the above. Such a quadratic equation has the form in which 18° is usually taken as ta- in order to evaluate both c and c' in the above equation the conductivity must be known at three different temperatures, that is, the conductivities k^, k^, and k^ at the temperature tg , t^ and t.^. From these we are able to obtain the two equations: I K—K„ = c + d'{,t-Q, (a) = c^c'{t,-t,.). ib) rom (h), I I ( K—K, '^~K,\ rA By substituting then the value of c' in either (a) or (fc) c can be readily determined. In order to secure the greatest accuracy the temperatures should be chosen so that f^ lies midway between INFLUENCE OF TEMPERATURE AND PRESSURE 99 ^0 and t.^. Deguisne^ has determined the values of c aiad c' for a number of electrolytes. The temperature coefficients of the acids, as has been said, vary considerably with the concentration, De- guisne's results with the principal acids are therefore given below. Values of c and c' in the Foi = '^leEl + <^-l8) + ^(/— 18)^]. m. HCl. HNOs. % H2SO4 HH3P0,. IO*C. 10%. 0.00005 172.4 1.5 159.2 6.2 166.9 12.8 206.6 75.6 O.OOOI 166.0 9.2 164.7 14.7 166.9 12.8 174.2 6.8 0.00 1 164.2 15.5 163.0 14.4 158. 1 36.2 158.8 28.1 O.OI 164.1 17-3 161. 7 19.4 130.8 IOI.5 146.3 61.6 0.05 — 136.3 78.2 Kohlrausch^ has recently tabulated a considerable number of temperature coefficients in the order of their magnitude and has derived therefrom some interesting relations. His table is re- produced below. The coefficients are to be used in the same equa- tion as that given in the preceding table. They hold for solutions of a concentration of about o.ooi. Electrolyte. io*c. loi'c'. Electrolyte. io*c. loV. HNO3 163 16 K2SO4 222 77 HCl 164 15 Pb(N03)2 224 78 H2SO4 165 17 BaClg 225 83 H3PO4 169 I NaCl 226 84 KOH 190 32 SrSOj 228 84 KNO3 210 62 NajSO^ 233 97 KI 212 58 MgSOj 238 95 AgNOa 216 67 NaHQH^Oi 241 109 KCl 217 67 NaF 242 102 NH4CI 219 68 NaC2H302 242 110 NaNOj 220 75 NaCsHgOj 243 in Ba(N03)2 220 75 Na^COs 262 151 KF 222 79 It is seen that as c increases c' also increases, and within the limits of experimental error the following relation holds : c' = 0.0163 (c — 0.0174). Since, therefore, c' can be calculated from c, the change of con- ductivity with the temperature may be expressed by a single ar- 1 Dissertation, Strassburg, 1895. D^guisne's results are given in full by Kohlrausch and Holborn : Leitvermogen der Eleklrolyte. 2 Sitzungsber. Kgl. pr. Akad. Wiss., Berlin, 1901, p. 1026. lOO THE CONDUCTIVITY OF LIQUIDS bitrary constant. If the above equation holds, at about — 39" all aqueous solutions of electrolytes lose their conductivity. Kohl- rausch infers that this may very likely be true, since this is also the temperature at which water loses its fluidity, according to the generally accepted equation for the coefficient of viscosity : 77 = 2.g8g{i + 38. s)"'"" in C. G. S. units. It is unfortunately impossible to verify this conclusion with dilute solutions at svich low temperatures. Kunz^ has, however, attempted a verification with concentrated solutions of sodium hy- droxide, calcium chloride, and sulphuric acid. His results with 60.9 per cent. H^SOi follow : Temperature. o° —10.5°. —20.3°. — 33-4°. — 51. 9°. —69.9°. lOOOK 232 171 124 71.9 19.4 1. 31 In concentrated solutions, therefore, Kohlrausch's conclusion seems not to be upheld. But it is hardly a satisfactory test to attempt to support a relation derived from the conduct of o.ooi normal solutions by facts obtained by working with solutions 10,000 times more concentrated. Kunz concludes that conductivity decreases as the temperature is lowered on account of the increas- ing viscosity of the medium in which the ions move, and that con- ductivity only ceases at the absolute zero. The data on temperature coefficients has been recently added to also by Foster,^ and by Jones and Douglas.^ The former has determined the coefficients of a number of normal solutions. Jones and Douglas have determined the conductivity of many acids, bases, and salts at four temperatures, from o° to 35", and at dilu- tions varying, in general, from i to 2048 liters, but have only par- tially reduced the data thus obtained (see appendix. Table V). TEMPERATURE COEFFICIENTS AT HIGH TEMPERATURES.— In the case of most aqueous solutions the temperature coefficients first increase with rise of temperature, then decrease. Arrhenius* has deduced from theoretical considerations that at high tempera- tures the coefficients continue to decrease with rise of temperature until they become zero, after which they become negative. Or 1 Compi.Send., 13s. 788 (1902) ; also Ztschr. phys, Chem., 42, 593 (1903). 2 Phys. Rev., 8, 257 (1899). > Am. Chem. J., 26, 428 (1901). 1 Ztschr. phys. Chem., 4, 96 (1889). INFLUENCE OF TEMPERATURE AND PRESSURE lOI what amounts to the same, the conductivity increases with the temperature, reaches a maximum and then decreases. He was able to verify this for sokitions of hypophosphorous acid and phosphoric acid, the maximum conductivity of the former being at about 55" and of the latter at 75". Since then maxima of con- ductivity have been found for solutions o^f copper sulphate and of a number of organic acids. The maximum conductivity of most aqueous solutions, however, lies so high that the experiment- al difficulties have prevented the verification of the Arrhenius the- ory for any considerable number of electrolytes. In many cases it has been predicted that this point lies even higher than the crit- ical temperature of water. The change in conductivity of a solution with the temperature may be due primarily to two causes : change in the speed of the ions, and change in the degree of dissociation. At high tempera- tures the degree of dissociation seems to decrease to counteract the heating effect,'^ and at a certain point this influence overcomes the tendency of the ions to move faster on account of the dimin- ished viscosity of the water, so that at temperatures above this the conductivity falls off until at the critical temperature it becomes very small, almost zero in many cases. This last is contrary to predictions which have been ventured on the basis of the Arrhenius theory, but it seems to be supported by some of the most careful measurements with non-aqueous solutions,^ where, on account of the low critical temperature of many solvents, experimental verifi- cation is possible. REDUCTION OF CONDUCTIVITY MEASUREMENTS FOR SMALL TEMPERATURE DIFFERENCES. — When only a few conductivity measurements are to be made, in order to save time required to adjust a temperature bath at 18°, the measurements may be made at room temperature, care being exercised to take the temperature of the solution at the instant when the measurements are made. Subsequently, the results can be reduced to 18° by means of the coefficients given on page 99. If the temperature interval is slight the temperature coefficient c can be employed alone without sensi- ble error. 1 That is, recombination of the ions at these temperatures absorbs heat. 2 See Eversheim : Drud. Ann., 8, 560 (1902) ; Walden and Centnerszwer: Ztschr. hys. Chem., 39, 538 (1902), and also discussion in Chapter 12. I02 THE CONDUCTIVITY OP LIQUIDS For example, a tenth-normal solution of silver nitrate gave K = 0.00793 at 19.32°. The temperature coefficient c of silver nitrate in the table is in round numbers 0.022. Since the differ- ence of temperature here is only 1.32°, the use of this approximate coefficient will cause no appreciable error. Employing the formula we have '' I + c(^i— 18)' 0.00793 0.00793 0.00771. '* I + 0.022 X 1.32 1.029 By means of the same coefficients the equivalent conductivity at one temperature may also be calculated from that at some other temperature not too remote. HiTFIUENCE OF PRESSUEE ON CONDUCTIVITY.— The effect of an increase of pressure on the conductivity of electrolytes has been investigated by Fanjung,^ Tammann,'' and Bogojawlensky and Tammann.^ It might be conjectured a priori that an increase of pressure would increase the friction of the particles in solution and consequently decrease the conductivity. Such, however, is not the case, for the conductivity increases with the pressure. As Tammann points out in his latest investigation where he employed pressures up to more than 3500 atmospheres on both strong and weak electrolytes, this behavior is due to two causes : First, contrary to the conduct of most liquids the viscosity of water and its dilute solutions decreases with increase of pressure. This de- crease of the viscosity causes the ions to move more rapidlj-. Secondly, the dissociation of electrolytes in solution in distinction from the dissociation of gases is accompanied by a contraction of volume. An increase of pressure is, therefore, favorable to this and increases the dissociation of the electrolyte. Tammann's results with tenth-normal solutions of sodium chlo- ride and of acetic acid, one an example of strong electrolytes and the other of weak, are given below. The pressure is given in kilograms per square centimeter, and in the column headed -^ 1 Zischr. phvs. Chem., 14, 673 (1894). 2 Ibid.^ 17, 725 (1895^ and also Wied. Ann.^ 69, 767 (1899). 3 Ztschr. phys. Chem., 27, 457 (1898). INFI^UENCB OJ? TEMPERATURE AND PRESSURE IO3 is given the ratio of the electrical resistance of the electrolyte at the pressure p to the resistance at the pressure unity. The meas- urements were made afo". A7io-NaCl. Af/io-CsHiOa. Ra Rp Pressure. i?. ■ Ri ■ I 1. 000 1. 000 500 0.925 0.855 1000 0.889 0.734 1500 0.869 0.644 2000 0.858 0.582 2500 0.854 0.526 3000 0.855 o.4«7 3500 0.857 0.460 4000 0.858 0.430 Since the conductivity varies inversely as the resistance, the conductivity of the well dissociated electrolyte, sodium chloride, is found to increase much less with the pressure than that of the weak electrolyte, acetic acid. Tammann ascribes this to the fact that the second of the above influences is not operative to an ap- preciable extent in the case oif a dilute solution of sodium chlo- ride, while it is in the case of a dilute solution of acetic acid. That is, the contraction in volume of the acetic acid solution is much greater with increase of pressure than that of the sodium chloride solution. Fanjung found that the conductivity of a solution con- taining an electrolyte in such concentration that it was practically completely dissociated also increased with the pressure. The first of the causes mentioned above is, of course, the only one which can be active in such a case and the increase in conductivity is due to the more rapid movement of the ions. To draw the con- clusion from this, however, that in every case the increase in con- ductivity, due to increased pressure, is caused simply by an in- creased velocity of the ions and not by increased dissociation, is entirely unwarranted. As to the efifect of changing the temperature, Tammann found by investigation at 20° and 40°, as well as at 0°, that the higher the temperature the less the increase in the conductivity with in- crease of pressure in the case of the tenth-normal solution of sodium chloride, but that in the case of the solution of acetic acid change of temperature has but little influence on the effect of the pressure in changing the conductivity. CHAPTER X. Solutions Containing Two Electrolytes. ISOHYDRIC SOLUTIONS. — In considering a solution containing two electrolytes it is usually convenient to assume that it has been formed by mixing two solutions, each one of which contains only one electrolyte. The simplest conditions then prevail between the conductivity of the mixture and the conductivities of the two component solutions when the latter are isohydric', that is, the component solutions possess a common ion in equal concentration. This is true when in which a^ is the dissociation of one of the electrolytes at the dilution v^, and a^ is the dissociation of the other at the dilution z/j. A fifth-normal solution of acetic acid is isoyhdric with a 450th-normal solution of hydrochloric acid, because the concen- tration of the hydrogen ions in the two solutions is equal. Such solutions can be mixed in any proportion without altering their dissociation, and hence the conductivity O'f the mixture is the mean of the conductivities of the separate solutions and can, there- fore, be calculated according to the following formula : _ K^A -f- K^B "- A+W' in which k^ and k^ are the conductivities and A and B the pro- portions of the component solutions. A single case, in which this last formula applies, is not suffi- cient proof that two solutions are isohydric. Solutions are only proved to be isohydric when, mixed in several quite different pro- portions, this formula gives the correct conductivity in each case. This is illustrated by the following examples taken from the work of Ho'fmann." 1 Arrhenius : Wied. Ann., 30, 51 C1887) ; Zlschr. phys. Chem., a, 284 (1888). 2 Zlschr. phys. Chem., 45, 584 (1903)- SOI.UTIONS CONTAINING TWO ELECTROLYTES I05 IsoHYDRic Solutions. K measured. K calculated. 3.22-normal HCl /ci = 0.7441 3.32-normal HBr /C-2 = 0-7504 I vol. HCl + I vol. HBr 0.7465 0.7472 I " HCl + 3 " HBr 0.7489 0.7488 3 " HCl + I " HBr 0.7470 0.7457 NoN-IsoHYDRic Solutions. Deviation. K measured. * z calculated Per cent. 3.22-normal HCl /c-i= 0.7441 .. 2.05-normal HjCrOi /c-2 = 0.2382 .. I vol. HCl + I vol. HjCrOi 0.4909 O.491I 0.0 I " HCl + 3 " HjCrOi 0.3479 0.3647 -4.6 3 " HCl + I " HjCrO^ 0.6395 0.6176 +3-5 If only the conductivity of the first mixture of the HCl and HsCrO^ solutions had been measured, one might easily have been misled into considering them isohydric. The conductivity of the last two mixtures, however, shows this to be far from the case. COMPONENT SOLUTIONS NOT ISOHYDRIC; WAKEMAN'S IN- VESTIGATION. — When the component solutions are not isohydric the conditions are much less simple than above. The simplest case of this kind is where both electrolytes have a common ion and each obeys the law of mass-action in its dissociation, that is, is a weak electrolyte. In a case of this kind, although the solutions actually mixed are not isohydric, the mixture can be imagined to be formed from two solutions of the same electrolytes which are isohydric. The difficulty, however, arises in ascertaining the unknown con- centrations of such isohydric solutions of the components. Vari- ous algebraic expressions have been derived to meet the require- ments of such cases, notably by Arrhenius and by van Laar, but on account of the number of unknown quantities involved they can be solved only by approximation. Wakeman^ has shown that in certain simple cases the concen- trations of the isohydric solutions of the components can be found without much difficulty by trial. He mixed equal volumes of a 0.3117-normal acetic acid solution (z/j^ = 3.208) and of a 0.0041 56-normal cyanacetic acid solution {z/, = 240.6). A gram-molecule of the two together was, there- 1 Zlschr.phys. Ckem., 15, 159 (1894). Io6 THE CONDUCTIVITY O? LIQUIDS fore, contained in 6.331 liters. The value of the constant of the Ostwald formula for these acids is k^^ = 0.000018 and fej = 0.0037. The degree of dissociation at the dilutions v^ and v^ are ffj = 0.00757 and «, =: 0.5984. If the solutions first mixed were isohydric. 3^ =-^ But 0.00757 , , a 0.5984 '^' = 0.002360, and — ^ == ^ ^ — 0.002487. z'j 3.208 • o > ^^ 240.6 Consequently these solutions were not isohydric. We can now imagine for a moment that the solvftion of the mixed electrolytes is separated into two equal parts, one super- imposed upon the other, and each part containing a single elec- trolyte. Then, since the original acetic acid solution contained 75 times as many mols- per liter as the original cyanacetic acid solution, 75/76 mol acetic acid would be in the upper half in 3. 1655 litres, and 1/76 mol cyanacetic acid in the lower half in the same volume. Now the concentration of hydrogen ions is greater in the lower solution, so we can imagine water to pass from the upper acetic acid layer into the lower cyanacetic acid layer, until the concentration of the hydrogen ions has become equal. The change of dilution required cannot, however, be calculated directly from the difference in concentration of the hydrogen ions at the be- ginning, because as the solutions become stronger or weaker the degree of dissociation also changes, thereby complicating the process. However, the required change of concentration can be esti- mated approximately in the following manner. According to Ostwald's dilution formula when V*: + ^-*.=V*: + f The subscript i always refers to acetic acid, while 2 refers to the cyanacetic acid. ' The word mol has come into general use indicating a gram-molecule. SOLUTIONS CONTAINING TWO ELECTROIyYT^S I07 Everything is known here except z\ and z\, and one of these can be expressed in terms of the other, thus : 1/76 v^ = 6.331—75/76 v^. This value can then be substituted for v^ in the preceding equa- tion, and the equation solved for v.^. This would, however, be too complicated and tedious a process for practical use. Wakeman therefore finds by trial values for v-^ and v^, which make When 2^1 = 3.0695, and v^ = 250.93, the solutions are isohydric, for from Ostwald's formula transformed, we obtain, by first substituting the value of Vi and then of v^ with the corresponding constant, a^ = 0.007406 and a^ = 0.6053, ^nd we find —^ = — — = 0.00241 S- In this mixture 75/76 mol acetic acid and 1/76 mol cyanacetic acid are present. The quantity of electricity, therefore, which is carried by the ions of the acetic acid is proportional to 75/76 «! = 75/76 X 0.007406 = 0.007308, and that carried by the ions of the cyanacetic acid is likewise proportional to 1/76 «2 = 1/76 X 0.6053 = 0.007965. Hence the whole quantity of electricity carried by the solution is proportional to the sum of these two, or to 0.015273, and conse- quently this can be considered to be the degree of dissociation of a mol of the mixed acids at the dilution, v = 6.331. Wakeman compared the values of a calculated in this way, at different dilutions with those derived directly from the conduc- tivity of the mixture. The results are given in the accompanying table. The values of the Ostwald dissociation constant, as cal- culated from both values of «, are shown in the last two columns. io8 the conductivity of liquids Conductivity op Mixtures of Acetic Acid and Cyanacetic Acid in THE Ratio of 75 Mols Acetic Acid to i Moi, Cyanacetic Acid. ^1 (acetic acid) = 0.000018. i^ (cyanacetic acid) == 0.0037. A^ = 388. looa. 100.4. V. yl'. Measured. Calculated. Measured. Calculated, 6.33 5.87 1. 51 1.53 0.00367 0.00374 12.65 7.83 2.03 2.02 0.00327 0.00329 25-3 10.46 2.70 2.66 0.00295 0.00292 50.6 13-93 3-59 3.57 0.00264 0.00261 101.2 18.77 4.84 4.78 0.00243 0.00237 202.4 25-47 6.56 6.48 0.00228 0.00222 404.8 34.75 8.96 8.81 0.00218 0.00210 809.6 47.61 12.27 11.94 0.00212 0.00200 The values of a as calculated, agree excellently with those found from the measurement of the conductivity, which afifords good evidence of the correctness of the theory of isohydric solu- tions. The small quantity of cyanacetic acid present is seen to exert considerable influence on the conductivity of the acetic acid, especially at the lower dilutions. This is shown by the fact that the dissociation constant is about twice as great as that of acetic acid alone at the earlier concentrations, but it rapidly decreases as the dilution increases until at the later dilution it does not differ much from that of acetic acid. Wakeman found that the effect of other acids on the conductivity of acetic acid was very similar to that just shown, the effect, of course, being less the weaker the acid and the more dilute its solution. Quite recently Barmwater'' has also treated this same subject from the standpoint of isohydrism. His results for the most part are similar to those obtained by Wakeman, his essential contribu- tion being a new and more scientific method of approximation to determine the degree of dissociation of the electrolytes in a mixture. WOLFS "B" VALUE.— In general, when the component solu- tions of a mixture are not isohydric, the conductivity of the mix- ture is less than the mean of the conductivities of the component solutions. This is also expressed by saying that the conductivity of a mixture of electrolytes is usually less than the sum of the 1 Wakeman expressed these results in mercury units. They have been recalculated to reciprocal ohms. 2 Zischr.phys. Chem., 45, 557 (1903). SOLUTIONS CONTAINING TWO ELECTROLYTES IO9 conductivities of the component electrolytes at the same concen- tration at which each exists in the mixture. WolP has investi- gated the conductivity of mixtures of dilute solutions of strong electrolytes with solutions of weak electrolytes, and he ascribes this decrease in conductivity just mentioned to three causes: viz., to a decrease in the dissociation of the strong electrolyte by a change in the solvent caused by the presence of the weak elec- trolyte, to the retarding of the speed of the ions of the strong electrolyte on account of the increase in viscosity of the solvent due to the same cause, and finally toi an isohydric influence de- pending on the double decomposition of the two electrolytes. The second of these influences seems to be iii general the more marked. It is well known that the addition of a small quantity of alcohol to a solution of an electrolyte increases the viscosity and at the same time decreases the conductivity. Wolf shows that the addition of a weak electrolyte like acetic acid has an efifect very similar to that due to the addition of alcohol.^ The following fig- ures, taken from his results, will serve as an illustration. F0UK.TH-N0RMA1, KCl -|- n Alcohoi,. K. «!• K/ound. d. D. 3-1II 0.03052 0.01923 37-0 II.9 1-556 0.03052 0.02422 27-65 13-3 0.778 0.03052 0.02722 10.8 13-9 0.194 0.03052 0.02968 2.8 14-2 FOURTH-NORMAI, KCl + n Acetic Acid. n. "1. K2. K calculated. K.found. d. D. 3.II 0. 030572 0.001912 0.03248 0.02418 27.2 8-7 1.556 0. 030572 0.001738 0.03231 0.02783 14.6 9-4 0.778 0. 030572 0.001372 0.03194 0.02963 7.6 9-7 0.1945 0. 030572 O.OC073I 0.03130 0.03071 1-9 9-95 n Represents the concentration of the alcohol or acetic acid in norm-al terms, k^ is the conductivity of the potassium chloride solution as found /c^ is the same for the acetic acid solution, k found is the conductivity of the mixture as found, k. cal is the sum of /Cj and k^, and d and D are obtained according to the following relations : 1 Zlschr. phys. Ckem., 40, 222 {1902). 2 Arrhenius called attention to this fact some time ago : Zlschr. phys. Chem., 9, 506 (1892). no THE CONDUCTIVITY OF LIQUIDS , ICO /£■ cal. — K found or in the first table, ioo(/f, — K found) , „ d ^^-5 ^ -, aud D =—. D is therefore the percentage depression of the conductivity of the potassium chloride- solution produced by an addition of i gram- molecule of alcohol or of acetic acid. This is very nearly a con- stant in the two cases, which shows the effect of the addition of acetic acid is similar to that of the addition of alcohol, but less in degree. Wolf, therefore, considers the value of D as an approxi- mate measure of the increase in the viscosity of the solvent caused by the addition of another substance; he shows, however, that it is not directly proportional to this. Rudorf^ has investigated, at greater length, the relation between the D value and the viscosity of the solution, and he has found that, although one can approximate to the eiifect of the viscosity from the value of D in many cases, still no general relation can be established between them. He also finds the D value less constant than Wolf did, the general rule being that it increases as the con- centration of the solution increases until a maximum is reached, after which it decreases. DISSOCIATION OF ELECTEOLYTES IN MIXTUHES.— When two electrolytes are present in the same solution, Schrader^ has cal- culated the degree of dissociation of each in the following manner. Considering only primary separation at the electrodes, then Z{ Z1 and Z% zt in which Mj and n.^ are the transport numbers of the anions of the two electrolytes, Z" and Z° are the amounts of the anions that have migrated to the anode, Zf and Zl are the same for the cations, jv" andj/J are the amounts of the anions separated at the 1 Ztschr.phys. Chem.., 43, 257 (1903). 2 Ztschr. Elektrochem., 3, 498 (1897). SOLUTIONS CONTAINING TWO ELECTROLYTES III electrodes, and yl and jc ', are the same for the cations. Dividing the first equation above by the third, and the second by the fourth, we obtain Now letting i^ be the part of the current carried by electrolyte I, and Jo that carried by electrolyte 2, and letting further Al, Ai, A\, A% be the equivalent weights of the respective ions, then and y^ = i^A,, y" = i^A%. If a: = 4, then y. Al' yt At ^ ' Combining (i) and (2) we have ^ Ztn,At ^ Z{ii—n,)Al Ztn^A", Zl{i—n,)A'=; ^^^ "We will let a\ and al represent the degree of dissociation of the two electrolytes in the mixture, and 4, and 4i, and 4^ and /^a be the migration numbers of the ions. Now since only the dissoci- ated portion of the electrolytes take part, in carrying the current Ai^%^ '«.«x(4, + ln)> and^l = ^ =^^«^(4^ + 4), (4), in which =^7. etc. represent the amount of each ion separated at Ai the electrodes in terms of equivalents, and m^ and m^ are the concentrations of the two electrolytes. From equations (2) and (4) we obtain ^^ »?i«;(4i + In) Since 4i + 4i = ^«i and 4, + 42 = ^«2. For the single electrolytes let a^ and a, be the degree of disso- ciation, /fi and K^ be the specific conductivity and A^ and A^ be 112 THE CONDUCTIVITY OP LIQUIDS the equivalent conductivity of each respectively, tion of Arrhenius (page 51) we have From the equa- 5 «„ ^i^» lOOO/f, w. , we have, combining the "1 i^i Since A^ = ! and A. last equation with (5), There will therefore be no change in the degree of dissociation of But if X ^—^, then — ^^ — -. The accompanying table gives the value of these quan- tities for solutions of KI and KCl. The subscript i indicates the former electrolyte. K the electrolytes when mixed, if ;t = — . Solution No. Concentra- tion of KI (mi). Concentra- tion of KCl (OTj)- fn^jtM^' X. "ill's- !• 0.02595 0.02571 1.009 0.997 1.027 2 0.03442 0.04748 0.725 0.704 0-751 3 0.03074 0.06176 0.498 0.500 0.522 4 0.01992 0.03720 0.535 0.486 0.557 In this case, therefore, x hys. Chem., 27, 345 (1S98). 2 This formula is expressed in terms of mercury units ; in terms of the Kohlrausch units it becomes, » Ztschr. phys. Chem., 25, 115 (1898). ri4 THE CONDUCTIVITY OF LIQUIDS in the unit of time, and Ui and U2 their absolute speeds, we then have «i = ^jC/i, and a^ = c^U^. But U= 1,eE, therefore «! = cJ,,sE, and a^ = cJ.,^bE, in which l,^ and 4j are the migration numbers of the cations, g is the charge on each gram-ion and U is the potential differ- ence between the electrodes. Dividing one of these by the other, ^ '-\^n n- fi, ^/gg Since -p is practically constant, the last equation signifies that the ratio of the concentrations of two cations is proportional to the quantities of these ions carried by the current to the cathode. Hopfgartner tested this by determining the decrease at the anode in the concentrations of the cations of two mixed electro- lytes having a common anion, and thereby finding values for a^ and oij. His results show that the ratio of the concentrations of the cations in a mixture of two well dissociated binary electrolytes is not very different from the ratio of their concentrations when the electrolytes are in solution singly. When, however, one of the electrolytes is bivalent, as BaCl2, the difference is quite con- siderable, possibly because the dissociation of such electrolytes is not so simple as was assumed. The derivation of Schrader's results (page no) was based on the hypothesis that, considering only primary separation at the electrodes, Z' Z' i—n, = -^, and i—n, = -^, that is, that the transport numbers of electrolytes remain un- changed in mixtures. By transformation Z' Z' from which, if n is known for the single electrolytes, the amounts of each cation separated at the electrode can be calculated. Then, if the hypothesis is correct, the sum of the amounts of silver SOLUTIONS CONTAINING TWO ELECTROLYTlJS "5 equivalent to these should be equal to the amount of silver de- posited in the voltameter. Hopfgartner applied the data he had collected to an investigation of this point. Most oi his results are shown in the accompanying table. silver Separated at cathode. Na. Silver calcu- lated from tbese. Difference in per cent, of silver found. H. these. voltameter. I vol. N/i-NaCl + 9 vol. N/i-HCl. 0.02074 2.3042 2.3475 0.01662 1.8576 1-897 I vol. N/i-NaCl + 4 vol. N/i-HCl. 0.01889 2.1562 2.195 0.01326 1. 5417 1.559 0.01609 1.8500 1.820 4 vol. N/i-NaCl + I vol. N/i-HCl. 0.00467 1.0902 1. 121 0.007170 1.8052 1.743 0.007999 1.87.S9 1.845 9 vol. N/i-NaCl + I vol. N/i-HCl. 0.0004321 1.5281 1.545 0.000461 1.5062 1-545 I vol. N/5-NaCl + 1 vol. N/5-HCI. 0.005255 0.6987 0.716 0.009525 1-3478 1.360 0.01089 I-5291 1.561 Silver calcu- Silver in lated from volta- H. these. meter. 1 vol. N/i-BaCl2 + 4 vol. N/i-HCl. 0.02213 2.5093 2.562 0.02209 2.5432 2.562 0.00835 0.9216 0.938 I vol. N/i-BaClj + 1 vol. N/i-HCl. 0.01527 2.0179 2.075 0.01178 1.5235 1-591 0.010455 I-34I2 1.405 I vol. N/s-BaClj + I vol, N/5-HCI. 0.009750 1.3193 1.320 0.009855 1.2993 1.320 0.00372 0.4585 0.470 The agreement in these tables between the amount of silver found and that calculated is good, when it is considered that the 0.0155 0.0149 0.02646 0.0246 0.0254 0.1257 0.2211 0.2167 0.2274 0.2156 0.0285 0.0690 0.0768 Separated at cathode. Ba. 0.0814 0.1056 0.0147 0.238 0.1625 0.1373 O.1716 0.1517 0.0370 —1.8 —2.1 —1.8 — i.i +1-7 —2.8 +3-6 +1.6 —1.2 —2-5 —2.4 —0.9 — 2.0 Difference in per cent, of silver found. — 2.0 -0.7 -1-7 —2.7 -4-2 —4-5 -0.05 -1.6 -2.6 Il6 THE CONDUCTIVITY OF LIQUIDS amount calculated depends on the determination of two sets of transport numbers, one ior the single electrolytes and one for the mixtures. The transport numbers of electrolytes, therefore, seem to be uninfluenced by mixing even at higher concentrations than those at which Schrader worked. DOUBLE SALTS.— Some time ago Bender^ and Klein^ found that the conductivity of solutions of mixtures of two salts possessing a common ion is somewhat less than the sum of the conductivities of the two salts separately, but that when the two salts were capable of forming a double salt the conductivity was found to be very much. less than the sum of the conductivities of the con- stituents. Quite recently Jones and his students^ have made a number of investigations along this line. Their results, which confirm, in general, the conclusions reached by Bender and by Klein, may be summed up as follows : ( i ) Mix- tures of electrolytes not capable of forming double salts possess a conductivity which is always somewhat less than the sum of the conductivities of the electrolytes separately. (2) Experiments with a variety of types of double salts, as, for instcmce, double sulphates, chlorides, bromides, iodides, cyanides and nitrates, showed that the conductivity of such double salts is always less than the conductivities of the constituents separately, that this diff- erence decreases as the concentration decreases, that this differ- ence is greater than when the two substances are not able to form a double salt, and that it persists at greater dilutions. (3) The conductivity of a double salt is somewhat less than the conduc- tivity of a mixture of its own components. This apparently shows that the state of equilibrium is different when a double salt is dissolved in water from that when its constituents are mixed to- gether in water. Rosenheim and Bertheim* have recently investigated the con- ductivity of mixtures of different acids for the purpose of ascer- taining whether they form double compounds. They found that 1 IVied. Ann., 22, 179 (1884). 2 Ibid., 27, 151(1886). 8 Jones and Mackay : Am. Chetn.J., 19, 83 (1897) ; Jones and Ota : Ibid,, 22, 5 (1899) ; Jones and Knight : Ibid., 22, no ; Jones and Caldwell : Ibid., 25, 349 (1901) ; see also I,indsay : Ibid., 25. 62. * Ztschr. anorg. Chem., 34, 427 (1903) ; see also in this connection, Hofmaun: Ztschr. phys. Chem., 45, 584 (1903). SOLUTIONS CONTAINING TWO ELECTROLYTES II7 the conductivity of a mixture of tartaric and malic acids is con- siderably greater than the sum of the conductivities of each singly. They, therefore, inferred that if the conductivity of a mixture of two acids is either much greater or much less than the sum of the conductivities of the single acids, the formation of a double compound is indicated. The}' then employed this method toi in- vestigate mixtures oif phosphoric and molybdic acids, and found evidence for the existence of at least one and perhaps more com- pounds between them. CHAPTER XL Applications oe" Conductivity MeasurEmbnts. DETERMINATION OF THE BASICITY OF ACIDS.— Ostwald^ has devised an empirical method for determining the basicity of an acid from the conductivity of its normal sodium salt. An ex- amination of the table (page 84) shows that the difference in the conductivity of a sodium salt of a dibasic acid, as NajSO^, at successive dilutions is about twice as great as the correspond- ing difference in that of a sodium salt of a monobasic acid, as NaCl. For the sodium salt of a tribasic acid this difference would be about three times as great as that for the sodium salt of a monobasic acid, and so on. The difference between the equivalent conductivity at z/ ^ 32 and that at v =1024 is for the sodium salts of monobasic acids approximately equal to 10 at 25°. Ostwald's rule is, therefore, to find J, the difference between the equivalent conductivities at 25° of the sodium salt of the acid at z/ := 32 and at ?7 = 1024, A thenw, the basicity of the acid, willbeequal to . This has been found to hold fairly well for those acids with which it has been tried and whose basicity runs from i up as high as 5. The solution of the sodium salt may be obtained from the solu- tion of the acid to be investigated by, neutralizing a suitable quan- tity of this solution with a sixteenth-normal solution of pure sodium hydroxide, using a drop of phenolphthalein as indicator. The resulting solution is then diluted so that the concentration of the salt will be thirty-second-normal. If the acid is insoluble in water some of it may be added directly to a given volume of the sodium hydroxide solution until the color of the indicator just disappears. After filtering, the solution is neutralized exactly, if necessary, by means of a drop or two of sodium hydroxide solu- tion. The solution, however, should not react alkaline. The i024th-normal solution can be readily obtained from the thirty- second-normal by dilution. 1 Ztschr. phys. Chem., I, 105 (1887), and £, 901 (1888) ; see also Ostwald and Luther • Physico-chemische Messungen^ p. 423. APPLICATIONS OF CONDUCTIVITY MEASUREMENTS II9 The accompanying results were obtained by Ostwald with sodium pyridinetricarbonate at 25°. Under /^ the conductivity is given in reciprocal mercury units, which were used by Ostwald V- M. A- 32 82.1 87.S 1024 I 13. I 120.6 ^~3i-u 33.1 in these measurements. Under A the same is expressed in re- ciprocal ohms. Applying the formula, n = — , we have « = 3. i from /^ and 3.3 from A. The basicity is thus found to be 3. Since, however, the formula was derived with conductivities ex- pressed in the old units, and furthermore, since tlie units now in use are 1.063 times smaller than the old (in Ostwald's work, 1.066), the rule is better expressed, when conductivities are given in reciprocal ohms, by n = . TITRATION OF ACIDS AND BASES BY MEASURING CONDUC- TIVITY. — On account of. the rapid rate of migration of H and OH ions, solutions of acids and of bases possess a greater specific conductivity than solutions of neutral salts of the same concen- tration. Advantage can be taken of this fact to determine the neutral point when neutralizing a base with an acid, or vice versa. When near the neutral point the conductivity is measured after each successive addition of a small quantity of the acid or of the base. The solution is neutral when the conductivity is a minimum. Plotting the results in a curve (see Chapter VIII) aids greatly in fixing the minimum. This method is, of course, slow and is consequently only of value where indicators cannot safely be employed. It, moreover, cannot be used when the salt formed undergoes hydrolytic decom- position.^ DETERMINATION OF THE PURITY OF UaUIDS.— As was shown in the chapter on the conductivity of water (Chapter V), the specific conductivity of a sample of this liquid supplies a sim- ple and sure means of judging its purity. The purity of other ^ For a more complete exposition of tlie method, see Kohlrausch : Ztschr.phys, Chem.^ 12, 773 (1893); 33. 257 (igoo) ; also DuHberg, Ibid., 45, 137 (1903). I20 THE CONDUCTIVITY OF LIQUIDS liquids can be estimated in precisely the same manner. However, the conductivity of but few liquids has been investigated as thor- oughly as that of water, so that the data for the estimation of the degree of impurity of most of them are very incomplete. Suffi- cient determinations of the conductivity of non-aqueous liquids have been made (see appendix. Table 9) to illustrate the useful- ness of the method. Some of the values of the conductivity of methyl alcohol, which have been found at 25°, are given below. Specific Conductivity of Methyl Alcohoi,. Authority. kXio^. Carrara 0.072 Walden 1.45 Schall I to 2 Jones and Lindsay 2.3 Carrara and Levi 2.5 Kahlenberg and Lincoln 5.7 Zelinsky and Krapiwin 18 to 30 Carrara obtained the low value, given above, by distilling in vacuo a product which had been purified as completely as possible by other means. Without the conductivity method it would ver\' likely be extremely difficult to estimate the difference in purity of the above samples, and no other method, to say the least, could be applied with equal rapidity. Walden has recently made a wide application of this method in determining the purity of a number of organic solvents. His re- sults with acetonitrile^ are given as an exarhple. The sample employed was a preparation of Merck. It was first shaken up with lead oxide and then distilled from phosphorus pentoxide, passing over between 80° and 80.5", from which it was inferred to be practically pure. The conductivity showed this, however, to be far from the case. It Xio«. Fraction from ist distillation from P2O5 4.45 " 2nd " " " 3.0 " 3rd " " " 1.3 " 4th " " " 2.06 Stood 3 years in a brown bottle, and then distilled from Na^SOj: Fraction from ist distillate 1.8 " 2nd " 0.6 1 Ztschr. phys. Chem., 46, 149-151 (1903). APPLICATIONS OF CONDUCTIVITY MEASUREMENTS 121 Stood a month over P^Oj with frequent shaking and then dis- tilled : Fraction from ist distillate 0,41 " 2nd " 0.396 This last value was the lowest obtained and is somewhat less than one-tenth that given by the first distillate from P2O5, which was considered to be a practically pure sample. DETiSRMINATION OF THE POINT OF SOLIDIFICATION OF FUSED SALTS.— As is pointed out in the latter part of the next chapter, fused salts conduct electricity quite well, and solid salts, near their fusing point, also possess some conductivity, although considerably less than when melted. Liebknecht and Nilsen^ have recently developed a method for determining the solidifying point or fusing point of an electrolyte based on these facts. They employed a three-limbed tube of hard glass as conduc- tivity vessel. The outside limbs served for the insertion of the electrodes, while the middle one held a thermometer, or at high temperature a thermocouple. The substance under investigation was melted in the tube; tlien, as it was slowly cooled, the con- ductivity was measured by the Kohlrausch method with telephone and alternating current, the temperature being taken at the time of each measurement. On plotting the conductivities thus ob- tained the point of solidification would be indicated by a sudden change in the direction of the curve. By starting with the solid substance, just below its melting-point, this point could be deter- mined in the same manner by gradually raising the temperature. A sharper minimum was obtainable with the telephone by using carbon electrodes than by using metallic ones. The solidifying point of mixtures was also investigated, and it was found that this point was identical for such pairs of salts as KCl and NaF, and NaCl and KF. ANALYSIS OF SOLUTIONS CONTAINING A SINGLE ELECTRO- LYTE. — Since the conductivity of nearly all electrolytes is a sim- ple function of their concentration, if a solution is known to con- tain a certain substance in the pure state, the concentration can be found by measuring the conductivity. For this purpose tables of the conductivity of electrolytes are indispensable. Many such 1 Berichle, 36, 3718 (1903). 122 THB CONDUCTIVITY OF LIQUIDS tables will be found in the appendix of this book. A more com- plete set is given by Kohlrausch and Holborn, Leitvermogen der Blektrolyte. From tables which give specific conductivities the concentration can be at once found by interpolation from the determined value of the specific conductivity of the solution. If it is necessary to use a table in which the equivalent conductivity alone is given, a small table oi specific conductivities for the range required should be calculated from it. In most cases interpolation will be easier and more accurate when made from a curve constructed from the given specific conductivities (Chapter VIII). In case the tem- perature at which the conductivity measurements are made is not the same as that for which the values in the table are given, the measurements should be reduced by the proper temperature coefficients. When the solution is concentrated difficulties are sometimes encountered in estimating the concentration on account of the con- ductivity being in the vicinity of its maximum value. In such cases the solution should be diluted with from twO' to four volumes of water, according to the nature of the substance, before the con- ductivity is determined. When the solution is very dilute, more difficulty is experienced in accurately determining the concentra- tion from the conductivity on account of the influence of the con- ductivity of the water employed. In case the substance in solution is a neutral salt, a fairly accurate value will be obtained by simply substracting the conductivity of the water from that of the solu- tion. Van't Hofif^ has found a method similar to this useful in de- 'termining when water is completely saturated with a mixture of salts. When employed in connection with the specific gravity he was able to determine, for instance, when a solution was satu- rated with a mixture of sodium chloride, magnesium chloride and carnallite. The agitation of the solution is continued until the conductivity becomes constant. With proper precautions the method is very helpful, particularly in cases where the density of the solution changes but little as the point of saturation is ap- proached. 1 Ztschr. Eleklrochem., 6, 57 (1899). See also Dawson and Williams, Ibid., 6, 141 (1899) APPLICATIONS OF CONDUCTIVITY MEASUREMENTS 123 DETERMINATION OF THE SOLUBILITY OF DimCULTLY SOLUBLE SALTS. — The principle in this case is the same as in the analysis oif a dilute solution containing a single electrolyte, except that for the majority of difficultly soluble salts no con- ductivity tables are at hand from which interpolations can be made. Approximate values of the conductivity of such salts can, how- ever, be calculated from the migration numbers of the different ions (pages 73, 78) and from the differences between Act, and A^ at different concentrations, as given on page 84, as will be illus- trated below. The water used in determinations of this kind should be of a high degree of purity, and its specific conductivity must be known. The substance whose solubility is to be determined is pulverized in an agate mortar, and the powder so obtained is repeatedly shaken up with water, each time the turbid liquid being carefully decanted or siphoned off from the material which has settled. Finally, when the residue has largely subsided after the last treat- ment witb water, a portion of the still slightly turbid liquid is re- moved with a pipette to a conductivity cell of one of the forms shown in Fig. 5, and the conductivity measured. The substance is again shaken up with water, and the conductivity redetermined until it is found to be constant. If a gradual uniform change is observed in the conductivity, it may be due to decomposition of the substance or to a change in the amount of water of crystalliza- tion, both of which affect the degree of solubility. When the greatest accuracy is desired the final saturation should be conducted directly in the conductivity vessel, which must then be of a suitable form. Kohlrausch^ has used a form similar to that shown in Fig. 5, b, into which a thermometer projects. Sat- uration is accomplished by rapidly rotating the vessel, the con- ductivity being measured from time to time until it becomes con- stant. The time required for saturation varies greatly for differ- ent substances. For illustrations of different behavior in this respect consult the paper of Kohlrausch just cited. Having determined the conductivity of the saturated solution in either of the above ways, the conductivity of the water used in preparing the solution is subtracted, and from the difference, k, i Ztschr. phys. Chem., 44, 197 (1903)- 124 THE CONDUCTIVITY OF LIQUIDS the concentration of the solution is estimated. A few examples will best illustrate the method of calculation. (i) Silver Chloride at i8°. Conductivity of water = 1.25 X 10—^. Conductivity of saturated solution = 2.48 X IQ— ^, there- fore /f= 1.23 X io-° for AgCl alone. From 4 +4, (Table, page 73) A„ for AgCl = 119.6. By means of the numbers in column di, page 84, the following values of the conductivity may be calculated from A^i . m = loooij. A . K = TjA . O.OOOI 118.6 11.86 X IO~° o.oooi 118. 8 63.64X1°""° To obtain an approxim.ate value of the concentration when k = 1.23 X io~^, we have 1.23 100077^ — -— X 0.0001 ^O.OOOOIO"??. 11.86 A value more nearly accurate is found from the equivalent con- ductivity, because this varies but little with the concentration. The interpolated value of yJ from the concentration already found, is 1 19.4. From this the concentration is found as fellow's: K 1.23X10-^ ^^ . ?7 ^ —T = — = 0.0103 X 10 . A II9-4 The concentration is, therefore, 0.0103 X io~^ gram-equivalent per ctibic centimeter, or 0.0103 milligram-equivalent per liter. Multiplying this by the equivalent weight, which in this case is also the molecular weight, 143.4, the concentration is found to be 1.48 mg. per liter. (2) Barium oxalate (anhydrous) at 18°. Conductivity of water = 1.3 X 10— ^- Conductivity of saturated solution ^ 71.7 X 10—^. K = 70.4 X 10-"* for i^BaCjOi alone. From table, page 78, Aa, = 119. From this and from the numbers in column d^, page 84, we can construct the following table : m == looOTj. A. K = 7]A. O.OOOI 114 II. 4 X i°~° 0.0002 112 22.4 X IO~° 0.0005 i°8 54-0 X 10— » o.ooi 103 103.0 X 10—" The approximate value of the concentration is, therefore, 16.4 10007=; 0.0005 "I X 0.0C05 ^0.000667. APPWCATIONS OP CONDUCTIVITY MEASURHJMENTS I25 Interpolating to find the equivalent conductivity at this concen- tration, we obtain as its approximate value io6. From this the more accurate value of the concentration is obtained : K 70.4 X 10-^ ----we ?7^— j-^= = 0.66 X 10 gram-equiv. per cc. Multiplying by the equivalent weight, 112.5, the concentraticnn of a saturated solution of barium oxalate at 18° is found to be 74.3 mg. per liter. Kohlrausch^ and also Bottger^ have recently determined, with the greatest care, the conductivity of many difficultly soluble salts (see appendix. Tables 7 and 8). The latter has also calculated the solubilities of the salts investigated. ANALYSIS OF MIXTURES CONTAINmG TWO ELECTROLYTES. — Sufficient data are not yet at hand to determine, in general, by means of conductivity measurements the quantities of two elec- trolytes present in a solution. For such to be possible, another property must also be known besides the conductivity, as, for instance, the specific gravity or the index of refraction. Further- more, tables would be required connecting these different propor- ties with the concentration of the solution and with the relative quantities of the two substances. The conductivity may, hov/ever, be of service in many cases in fixing the relative quantities of two electrolytes in a solid mix- ture. In general, the following method, suggested by Kohlrausch, might be employed in such a case. The mixture is dissolved in water to a definite concentration, for example, 5 per cent., and the conductivity of the resulting solution measured. Then by determining the conductivity of solutions formed by dissolving different relative proportions of the same substances so that the total concentration will be the same, viz., 5 per cent., a table could be constructed from which the unknown ratio in which the sub- stances exist in the mixture could be estimated. Such a m^ethod is, however, so laborious that it will hardly come into general use, except where there is constant need of determining the concen- tration of solutions containing always the same two substances. 1 Zlschr.phys. Chem., 44, 197 (1903). 2 Ibid,, 46, 521 (1903). The methdd of calculating the solubility is considered in detail in this article. 126 THE CONDUCTIVITY OF LIQUIDS There are certain cases, however, where the conductivity of the mixture is the mean of the conductivities of the two components, in which this method may be quite useful. It has been shown at the beginning of this chapter that the above conditions hold only when the solutions of the single substances are isohydric, that is, have a common ion of the same concentration in each. This is practically true also for salts of a similar nature at the same con- centration, as, for example, the chlorides, bromides and iodides of the same metal, or the same salts of allied metals. In such cases it can be assumed that the conductivity of the mixture is the mean of the conductivities of the components, when the solu- tions of the components are of equal concentration. This means that if the conductivities of solutions of KCl and KBr of equal concentration are k^ and k^ and that of any mixture of these two solutions containing A parts of the former substance and B parts of the latter is k, then _ i^.A + '<,B "- A+B ■ If we consider, for the sake of simplicity, that A and B are the quantities of the two substances in a unit quantity of the solid mixture, that is,A-\-B^=i,\t follows that K =Ak^-\-{i—A)k.^. When /fj is greater thap /Cj, A = -? , B = and ^- = -? , which shows that only the ratio of the conductivities are required in order to calculate A or B. If, therefore, the same resistance is retained at R in the Wheatstone bridge arrangement (Chapter I, Figf- 3) while the different conductivities are being measured, the ratio, as taken directly from Obach's table, can be employed in each case instead of the actual conductivity.^ The following example, with a mixture containing KCl and KBr, will illustrate the method : a is the position on the bridge and K the corresponding number from Obach's table for a 5 per cent, solution of the mixture, a-^, a^ and /fj, k^ the similar quan- tities for 5 per cent, solutions of the pure components. 1 For further discussion of this method see Erdmann : Bertchie, 30, 1175 (1897). APPUCATIONS OF CONDUCTIVITY MEASUREMENTS 127 Unknown mixture. KCl. KBr. a = 498.0 aj = 701.3 «! = 475-S /<•= 0.9920 Ki = 2.348 /Ci = 0.9066 „ K — K^ 0.9920 0.9066 ^ — „ „ — „ -.0 e^c 0.0854 ^ = 0.0592. K^ /fl 2.348 — 0.9066 1.4414 Therefore, KCl is found to compose 5.92 per cent, of the mixture. CHAPTER XII. Conductivity of Single Substances. INTRODUCTION. — Heretofore we have discussed almost ex- clusively the conductivity of aqueous solutions, that is, of mix- tures of the so-called electrolytes with water. These are the best conducting liquid media. Incidentally, the conductivity of water has been considered. We shall now pass to a consideration of the conductivity of single substances, which is quite analogous to the conductivity of water itself. First, the conductivity of those substances which are either liquid at ordinary temperatures or can be liquefied by means of pressure at slightly lower temperatures will be taken up. Then we shall discuss the conductivity of substances which are solid at ordinary temperatures, but possess a conductivity after they have been converted into the liquid state by fusion. Thirdly, attention will be called to the conductivity of certain solid com- pounds which retain their conductivity even below the fusing point. This last subject does not strictly belong in a book on the conductivity of liquids, but, since it is closely related to the conductivity of fused solids, mention will be made of it in this connection. METHODS EMPLOYED IN MEASURING THE CONDUCTIVITY OF OF PURE LIQUIDS. — Within recent years the conductivity of a considerable number of non-aqueous liquids has been measured, chiefly in connection with investigations on the conductivity of non-aqueous solutions in which these liquids were used as sol- vents. In nearly every instance the method of Kohlrausch with Wheat- stone bridge and alternating current has been used. Wildermann^ has, however, successfully employed another method. He used a direct current with great external resistance and measured the cvtrrent strength with a galvanometer. The only advantage he claims for it over the Kohlrausch method is that he considers it yields more accurate results when measuring the conductivity of liquids possessing enormous resistances. 1 Ztschr. phys. Chem.. 14, 247 (1894). CONDUCTIVITY OF SINGLE SUBSTANCES I29 Since the resistances of the hquids are, in most cases, very great, special attention should be given to the compensating re- sistances which must occasionally be as high as 400,000 ohms. It is impossible to use the ordinary kind of differentially wound resistance coils for this purpose on account oif their capacity. Graphite lines on glass have been used by some investigators for resistances over looo ohms.^ These resistances, however, exhibit considerable fluctuation from time to time, so that unless fre- quently controlled their value is uncertain. Wildermann suc- ceeded in preparing resistances of this kind which remained con- stant long enough to make a series of measurements (see page 18). Cohen^ used resistance coils made by winding a single wire alternately forwards and backwards, according to the method of Chaperon. By such winding, capacity is largely eliminated, while the resistances are still free from induction. When meas- tiring very high resistances, it is advisable to use a condenser to compensate the capacity of the resistance coils. No difficulty then is commonly experienced in obtaining a sharp minimum with the telephone. Electrolytic vessels employed for non-aqueous liquids are usu- ally similar to those used in determining the conductivity of water and should have a small resistance capacity. Any of the forms of vessel shown in Figs. 5 and 6 (Chapter II) are suitable for this purpose. The one devised by Arrhenius is probably more fre- quently employed than any other. When, however, the conduc- tivity of a liquid possessing enormous resistance is to be measured the forms shown in Fig. 6 are preferable. Special types of vessel are used in many instances, particularly where from the nature of the liquid it is necessary to subject it to unusual temperatures or pressures.^ Nearly all investigators in this field have used electrodes cov- ered with platinum black, for the reason that the readings are less liable to fluctuation than when blank electrodes are used. It is necessary, however, in the case of most organic liquid."! to avoid prolonged contact with platinized electrodes on account of in- > Vollmer : JVeid. Ann, 52, 328 (1894); Wildermann : Ztschr. phys. Chem. 14, 231 (1894). 2 Ztschr. phys. Chem., as, 17 (1898). » See Goodwin and Thompson: Phys. Rev., 8, 38 (1899); Walden and Centnerszwer: Ztschr. phys. Chem., 39, 517 (1902). 130 THE CONDUCTIVITY OF LIQUIDS cipient oxidation. Cohen^ found that at 25", when alcohol is used, this oxidizing action is so great as to preclude accurate measure- ment, but at 18° it is slow enough not appreciably to affect the readings when proper precautions are taken. Some investgators, as, for instance, Euler^ and Walden,^ have used blank electrodes successfully. VAIUES OF THE CONDUCTIVITY OF PURE nftUIDS.— The conductivity of most pure liquids is slight, being of about the same order as the conductivity of pure water. The values of the con- ductivity of such liquids, both organic and inorganic, are given in the appendix, Table 9. An inspection of this table shows that values of the conductivity of the same substance as found by different investigators vary in many instances quite considerably. This is undoubtedly due to different degrees of purity of the liquids employed. A comparison of the values found by Frenzel and by Franklin and Kraus for the conductivity of ammonia, and by Carrara for the conductivity of methyl alcohol, with the values obtained by others, serves to show how much conductivity is re- duced by efficient purification. The same may be said of many of Walden's results. Most of the values, therefore, in the table are to be looked upon simply as upper limits, the true conductivity of the pure substance being very likely somewhat lower. If subjected to rigorous methods of purification, the fatty acids, with the exception of formic acid, would probably be found to be non- conductors. Examples of the effect of such purification are con- sidered more at length in the preceding chapter. Recent work on the temperature coefficient of the conductivity of ammonia has brought out an interesting fact. Goodwin and Thompson found the coefficient to be about o.oii, while Frenzel, with a much purer sample, found it to be considerably higher than this (see Table 9). Consequently, the temperature coefficient of pure ammonia like that of pure water is greater than the coeffi- cient of the slightly impure liquid. The influence of small quantities of water on the conductivity of liquid ammonia has been investigated by Cady and by Frenzel. ' Ztschr. phys. Chem., as, 22-23 and 26-27 (1898). -Ibid. 28, 619 (1899). " Ibid., 46, 131 (1903). CONDUCTIVITY OS SINGLIl SUBSTANCES I3I Cady found this influence to be slight, but the ammonia which he employed, as shown by its conductivity, was undoubtedly not pure. Frenzel's results, with a very pure sample, are given below. They show the effect on the conductivity of 4 cc. ammonia of adding the quantities of water given in the first column. The effect is Water added. Conductivity at — 60°. Mg. irx 106. 0.0 0.3549 1.4 0.6051 1.4 0.9966 2.8 1-996 seen to be quite marked and contradicts aitirely Cady's conclu- sions. When this is, however, compared with the effect of small quantities of CO2 and NH,, on the conductivity of water it cannot be considered to be exceptional. CONDUCTING AND NON-CONDUCTING LiaUIDS.— There seem to be no constitutional characteristics which distinguish inorganic ■liquids that conduct electricity from those that are non-conduc- tors. A list of most of those that conduct has already been given in the table. According to Walden the following are non-con- ductors :^ Antimony pentachloride, boron trichloride, bromine, phosphorus tribromide and trichloride, disulphur dichloride, sul- phur trioxide and tin tetrachloride. Frankland and Farmer^ have found nitrogen peroxide to be a non-conductor, and liquid hy- drogen sulphide does not conduct according to Skilling.* Whether a substance is saturated or unsaturated appears to make no differ- ence in its conducting power. It may be said that all those com- poimds which conduct contain as their principal element a member of the fifth or sixth groups of the periodic system. But, on the other hand, a number of substances are non-conductors which contain such an element. Of the organic liquids the following may be said, speaking gen- erally, to be non-conductors : Hydrocarbons, their halogen sub- stitution products and the ethers. Those that conduct are alco- hols, aldehydes, acids, esters, nitriles, nitro-compounds and am- monia substitution products. General constitutional differences 1 Most of these have been investigated qualitatively much earlier. See Ostvpald Lehrbuch, d. Allg. Chemie. 3, i, 776. !/. Chem. Soc, 79, 1356 (1901). 8 Am. Chem. J., a6, 383 (1901). 132 THE CONDUCTIVITY OF LIQUIDS distinguishing conductors from non-conductors are, therefore, found among organic compounds, which are lacking in the case of inorganic. But even here the line of demarcation is not hard and fast. Furthermore, any class of compounds which may be designated as conductors, gradually loses this property as the number of carbon atoms increases, so that the higher members of the series are non-conductors. CONDUCTIVITY OF FUSED ELECTROLYTES.— Fused electro- lytes conduct electricity well. Bouty and Poincare^ have devised an excellent method for determining the conductivity of fused salts. As used by Poincare,^ to determine the conductivity of a number of such salts under different conditions, it consisted essen- tially in using silver electrodes and to prevent polarization adding to the fused electrolyte a small quantity of that silver salt having the same anion. Only an extremely small quantity of the silver salt is required, not enough to affect appreciably the value of the conductivity of the electrolyte. Some of the regularities observed by Poincare are the following : (i) The conductivity increases with the temperature. (2) The conductivities of similar salts, as, for instance, the halogen salts of any one metal, have nearly equal values at equal distances from their fusing-points. For example, the molecular conductivity of NaCl, NaBr and Nal at 50° above the melting-point of each is 120.6, 124..0 and 123.6, respectively. However, this apparent regularity is not to be unduly emp'hasized without additional evi- dence. (3) The conductivity of mixtures of fused salts is prac- tically additive, that is, is approximately the sum of the conduc- tivities of the components. C0NDUCTT7ITY OF SOLID ELECTROLYTES.— Many salts pos- sess a considerable conductivity below their points of fusion, as has been observed by W. Kohlrausch' and also by Graetz.* Fritsch^ has shown that this conductivity is greatly increased by the presence of small quantities of other solid substances as im- purities, such mixtures acting apparently as solutions of the im- 1 Ann. chim. phys.^ (6) 17, 52 (1889). ^ Ibid., (6)21,289(1890). 8 Wied. Ann., IT, 642 (1882). * Ibid.. 40, 18 (1890). !• Ibid., 60, 300(1897). CONDUCTIVITY OF SINGLE. SUBSTANCES 1 33 purity in the solid salt. The following figures show the effect of the addition of from i to 2 per cent, of KBr to solid AgBr. The conductivity is expressed in arbitrary units. tperiment Conductivity Conductivity number AgBr aft er addition of KBr I 4° 5° 2 32 190 3 52 loS' After standing i day 211 i^ days 270 2 days 550. The increase of the conductivity on standing was probably due to more thorough diffusion of the impurity. The conductivity of both pure substances and of mixtures was also found to in- crease rapidly with the temperature. The conductivity of SiOa, in distinction from that of salts, increased very little on the addition of such impurities as metallic oxides and KP*. No effect could be observed on the conductivity of metallic oxides by the addition to them of other metallic oxides. WHY DO PURE LiaUIDS CONDUCT ELECTRICITY ?— In ac- cordance with the dissociation theory it is assumed that the con- ductivity of pure liquids and also of fused salts is due toi sdf- ionization, that is, that a small portion of the substance is dis- sociated into ions in a manner similar to the dissociation of sub- stances in solution. Many liquids that conduct electricity are associated, however, that is, in the liquid state their molecular weight is greater than the simple formula which expresses the molecular weight in the gaseous condition. This is true of water. Nevertheless there are good grounds for assuming that some few of tliese associated molecules are broken down into the simple ones, and that an exceedingly small number of these dissociate into the ions H and OH. The reason for this assumption, beyond the fact that water is a conductor, are based mostly on results obtained from the investigation of electromotive forces, especially of gas cells and of neutralization cells. From the latter it is estimated that the number of gram-ions of hydrogen in a liter of water is 0.8 X ^^—7, a value which agrees well with that cal- culated by Kohlrausch from the conductivity. Other liquids are supposed to dissociate in a somewhat similar 134 THE CONDUCTIVITY OF LIQUIDS manner. Frenzel,^ in measuring the electromotive force of polar- ization in liquid ammonia, found at the anode three decomposition points, hence he believes that pure NH3 dissociates in three stages: Some molecules are dissociated into H and NH^, then some few of the latter undergo further dissociation into H and NH, and an exceedingly small number of NH ions into H and N. Walden^ assumes dissociation of the organic liquids investigated by him into definite ions without, however, anything to guide him except analogy and conjecture. Quite recently Bottomley^ has shown that the molecular co 25°. V. Nal. A WCl. A. 5^Srl2. i,i^ci. V, A- HCl. 8 7-1 4.1 ■• 0.65 3-42 1.91 16 8.1 5-1 4.0 0.74 5-44 1-77 32 9.2 6.1 4.7 0.86 8.93 1-57 64 10.6 7.3 5.4 1. 10 14.29 I-5I 128 12.0 8.8 6.0 1-43 25.42 1-33 256 13-4 10.2 1.84 512 14.7 "■5 2.37 1024 15-9 12.7 3-o6 2048 17.0 13.5 3-73 32 64 Formic acid. (Z.-T.) 25'. A- KCl. 43-4 46.4 2-93 5.86 A- HCl. 31.6 32.8 144.7 289.4 Acetone (Laszczynski) 18°. A- KI. I16.6 128.3 12.44 24.88 A- WCl. 4.88 7-05 143-9 287.8 A- AgNOj. 14.2 15.7 128 51.9 11.72 32.7 578.8 145.2 49.76 10.02 575.6 17.6 256 58.0 23.45 32.6 II57.6 155.4 99.52 13.8 512 61. 1 46.90 33.2 2315.2 163.3 138 THE CONDUCTIVITY Of LIQUIDS Acetonitrile. Propionitrile. Benzonitrile. (D. . & F.) 25° (D. & F.) 25'.. V. A- AgNOa. (Wi acoln) 25°. / AgNOs. V. AgNOa 8 58.1 32 37-2 8 5-1 i6 76.0 64 49.0 16 6.8 32 i8.7- 93-7 Butyronitrile. 32 9-3 64 128 23.8 30.0 1 10.5 126.1 64 12.7 (D. & F.) 25". 128 16.3 256 37-0 140.2 V. yl' AgNOa. 256 18.9 512 154 64 25.5 512 21.6 1024 167 128 32.4 1024 24-3 Pyridine. Quinc iline. n) ^•. A- Pipei (Lino J. ■idine. (L. & G.) 25°- (I.incolll) 25°. (Lincol oln) 25" V. yl ,. ■u. A- V. A- KI. 'l Ztschr. anorg. Chem., 35, 225 (1900). 140 THE CONDUCTIVITY 0^ LIQUIDS solutions neither conduct themselves nor do their solutions con- duct. It may be said, however, that, in general, those liquids, which are themselves conductors, yield solutions that conduct. The conductivity of alcoholic solutions steadily diminishes with increase in the atomic weight of the alcohol, so that, although solutions in methyl alcohol conduct well, those in amyl alcohol conduct but feebly. The same is true of the members of any homologous series whose solutions conduct, that is, that increase in the number of carbon atoms in the molecules of the solvent is always attended by a decrease of the conductivity of solutions in that solvent. The nitrites serve as a further illustration of this. Furthermore, solutions in pyridine are seen to conduct quite well, while those in piperidine and in quinoline are rather poor conductors. Solutions in acetone seem to be, in general, good conductors, as is seen in the case of KI, which conducts better than when dissolved in the alcohols. The conductivity of LiCl and of AgNOg, however, is much less in acetone' than when dis- solved in either methyl or ethyl alcohol. Similar irregularities in the conductivity of the same electrolyte in different solvents are frequently met with. It cannot, therefore, be inferred that the conductivity of a certain electrolyte in one solvent will be greater than in another, simply because the conductivity of some other electrolyte is greater when dissolved in the first solvent than when dissolved in the second. In nearly every instance the equivalent conductivity increases with the dilution as it does in the case of aqueous .'solutions. There are, however, some exceptions to this, as can be observed above in the cases of mercuric cyanide in ammonia, hydrochloric acid in isoamyl alcohol and silver nitrate in piperidine. A few other examples of the same kind can be found scattered through the literature of this subject. The significance of such conduct is not yet clearly understood. It has been found that the alkali metals dissolve in liquid am- monia and that the solutions so formed conduct electricity well, and, what is more remarkable, without polarization. For a dis- cussion of this interesting subject reference is made to the work NON-AQUEOUS SOLUTIONS I41 of Franklin and Kraus.^ The same investigators^ have also found that sulphur dissolves in ammonia, and that the resulting solution conducts fairly well. Walden^ has recently shown that solutions of bromine in sulphur dioxide and iodine in sulphuryl chloride are conductors. INFLUENCE OF TEMPERATURE ON THE CONDUCTIVITY OF NON- AQUEOUS SOLUTIONS.— We have already seen (Chapter IX) that, theoretically, the conductivity of aqueous solutions in- creases with rise of temperature, reaches a maximum, and then decreases. The effect of change of temperature on the conduc- tivity of non-aqueous solutions appears to be similar. Whether the temperature coefficient of the conductivity of a solution is positive or negative, therefore, depends on the nature of that por- tion oif the temperature curve at which the conductivity is being investigated. The negative temperature coefficients, found by Cattaneo* for ethereal solutions, are to be thus explained. In fact, Eversheim^ has recently shown that the conductivity of HCl in ether is a maximum at — 20°. The conductivity of solutions in the following solvents has been investigated at the critical temperature: In ammonia by Franklin and Kraus f in sulphur dioxide by Hagenbach f and by Walden and Centnerszwer ;* in sulphur dioxide, in ether and in chlorethane by Eversheim;^ in methyl and in ethyl alcohol by Kraus.' In all these cases it was found that the conductivity passes through a maximum and then decreases towards the critical temperature, at which point it becomes very small. Walden and Centnerszwer infer that conductivity ceases altogether at the critical temperature, but this view is not shared by the other in- vestigators. In fact, the recent work of Kraus appears to afford conclusive evidence that it is not so, for solutions in methyl alco- hol possess a considerable conductivity above this temperature, — 1 Am. Ckem.J., as, 306 (1900). ' /6id., 24, 89 (1900). s Ztsckr. phys. Chem., 43, 385 (1903). < IVied. Beibl., 17, 1085 (1893). 6 Drud. Ann., 8, 539 (1902)- ^Am. Chem. J., 24, 83 (1900). ' Drud. Ann , 5, 276 (1901). Ztschr. fihys. Chem., 39, 538 (1902)- » Phys. Rev., iS, 4° and 89 (1904) . 142 THE CONDUCTIVITY OF LIQUIDS more than can possibly be accounted for by any experimental errors. Kraus, however, finds that the temperature coefficient undergoes a sudden change at the critical temperature, which can be readily recognized by plotting the conductivities in a curve. Although the changes which the conductivity of non-aqueous solutions undergoes with the temperature follow, in a general way, Arrhenius' theory (see page loo), his formula, as Eversheim points out, by no means applies to the particular cases which have been investigated. DISSOCIATION OF ELECTROLYTES IN NON-AttUEOUS SOLU- TIONS. — It has already been stated that the theory most generally adopted to account for the conductivity of aqueous solutions is that some of the molecules of the electrolyte, the so- called active portion, are dissociated into particles called ions. The question therefore arises whether the same hypothesis will afford an equally adequate explanation of the conductivity of non- aqueous solutions. From the investigations of this subject, reported for the most part in the articles cited in the course of the presentation of the foregoing results, the following facts may be gathered. (i) In the majority of instances the equivalent conductivity increases with the dilution, but a maximum value can be even ap- proximately estimated in but few instances, which are chiefly found in alcoholic solutions.' (2) The molecular weight of the solute in dilute aqueous solu- tions which conduct well, when determined by the freezing point or boiling point method, is in nearly every case considerably less than the true molecular weight. In non-aqueous solutions this is not so frequently the case. It is true in general of most alcoholic solutions, but more usually not true of non-alcoholic solutions. In fact, in many such solutions which conduct well, the molecular weight of the solute is found to be greater than normal, showing that the electrolyte is polymerized rather than dissociated. As examples of this behavior may be cited potassium iodide in sul- phur dioxide and hydrochloride acid in formic acid, which are seen according to the above table' to be good conducting solutions. 1 Values have been given to yi^ of many electrolytes in other non-aqueous solvents without the data, however, warranting it. NON-AQUEOUS SOIjUTIONS I43 The molecular weights of the electrolytes in both these instances have been found by the freezing point method to be just about twice the normal values. (3) Since it is impossible to estimate the value oi A^ with any degree of accuracy for most non-aqueous solutions, it is of course impossible to calculate the ratio,— r- , or the degree of dissocia- tion. In the cases where it is possible to estimate A^ , the de- gree of dissociation thus calculated has seldom been found to agree with that calculated from determination of the freezing point or boiling point of the solution. However, with electrolytes in methyl alcohol or in ethyl alcohol the agreement can in many instances be considered to be good. (4) Ostwald's dilution law (Chapter 6), which we have seen holds for aqueous solutions of weak electrolytes, does not hold in most cases where it is possible to apply it to non-aqueous solu- tions. In alcoholic solutions, where the degree of dissociation can quite generally be determined and consequently the applicability of the law tested, in the majority of cases it does not hold. Some instances where it has been found to hold are for trichloracetic acid in ethyl alcohol and for potassium chloride in formic acid^. (5) Kohrausch's law of the independent migration of the ions cannot of course be adequately tested where it is impossible to estimate accurately A^ . According to Carrara it holds roughl) for most electrolytes dissolved in methyl or in ethyl alcohol, and he has prepared a table of migration numbers of the ions in these solvents. From this brief summar\' of the facts at present known, it may be said that the conduct of electrolytes in alcoholic solutions bears the greatest resemblance to that in aqueous solutions, and in such solutions dissociation into ions very similar in kind to that in water probably takes place. Tliis similarity in conduct to aqueous solutions decreases with increase in the molecular weight of the alcohol, so that amyl alcohol solutions have practically lost this resemblance. Electrolytes in most other solvents show but little evidence of dissociation of a kind similar to that which takes place in dilute aqueous solutions. It has been stated that elec- trolytes in non-aqueous solutions appear to be very generally 1 other instances have recently been found by Godlewski, Ref. Central-B., 1904, II, "75- 144 THE CONDUCTIVITY OP LIQUIDS polymerized. These polymerized molecules may be made up by the aggregation of two or more molecules of the solute, or may be formed by the union of one or more molecules of the solute with one or more molecules of the solvent. Evidence that a union of this last sort sometimes takes place lies in the fact that heat is evolved when some substances are dissolved in certain solvents, for example silver nitrate in pyridine. Doubtless the former, that is true polymerization of the solute, also actually takes place in some instances. Such behavior is not entirely foreign to aqueous solutions, as for instance solutions of cadmium salts. But in such cases the decomposition of the polymerized mole- cules takes place rapidly on diluting the solution, so that in solu- tions whose concentration is not greater than ^/^oo normal all evi- dence of polymerized molecules and even of complex ions has dis- appeared. (See discussion under transport numbers of bivalent ions. Chapter 7). This is, however, very different from the conduct of most non-aqueous solutions ; . for, although the poly- merized molecules seem to be somewhat broken up on dilu- tion, this procedure is very slow; and it is doubtful, if in many cases any evidence can be found for the existence of particles smaller than normal molectiles, that is, particles of the same kind as the ions of dilute aqueous solutions. Walden^, however, in a recent article is strongly of the belief that all electrolytes undergo dissociation no matter what the sol- vent may be, though the ions may differ in different solvents. The next question then is to determine what ions are present in a given case. Without any direct evidence he assumes in each case dissociation of a kind which appears to him' to be most probable under the given conditions. For example, he ascribes the conduc- tivity of bases like pyridine when dissolved in sulphur dioxide to the formation of complex molecules R = N = S^ , in the case //"^ of pyridine, C5H5N = S/ , which dissociates into the cation R r=: N and into the anion, SO^. 1 Ztschr.phys. Chem., 43, 385 (1903). NON-AQUEOUS SOIvUTIONS 1 45 Before leaving this subject another striking difference between the behavior of aqueous and some non-aqueous solutions should be mentioned. This is the fact that the equivalent conductivity of some electrolytes in certain non-aqueous solvents decreases on dilution, while no example of this kind is known among aqueous solutions. The significance of such conduct is not clearly under- stood. In conclusion it may be stated that electrolytic dissociation of the same kind as that which takes place in water, if it occurs at all in non-aqueous solvents, occurs probably in methyl and ethyl alcohols, and it is interesting to note that these liquids resemble water constitutionally in that each contains an hydroxyl group. Formic acid, whose solutions show some similarity to aqueous solutions, also contains an hydroxyl group. Our knowledge of dissociation in other solvents is so limited that we are scarcely warranted in drawing any general conclusions concerning its nature.^ INFLUENCE OF THE SOLVENT ON THE CONDUCTIVITY OF SOLUTIONS. — The condition of the electrolyte in non-aqueous solutions has just been discussed. Undoubtedly, however, the conductivity of a solution depends to a great extent also on the nature of the solvent ; for HCl, which is a good con- ductor in many solvents, when dissolved in benzene does not con- duct at all. The question then arises, what is there in the nature of a solvent which causes it to yield solutions that conduct elec- tricity. (i) The first explanation offered in answer to this question was stated independently by Thomson^' and by Nernst^ Thev suggested that the power to yield conducting solutions depends on the specific inductive capacity of the solvent, and consequently the greater the dielectric constant of a solvent the greater the con- ductivity of substances dissolved in it. The idea which led up to this rule was, that solvents having high dielectric constants render it more difficult for the charges on oppositely charged ions to neutralize each other on account of the electrostatic attraction 1 Besides Walden's paper just cited, the following paper by Whetham should be con- sulted in this connection : Phil. Mag., (6) s, 279 {1903). 2 Phil. Mag., (5) 36, 320 (1893). 8 Ztschr. phys. Chem., 13, 531 (1894). 146 THE CONDUCTIVITY OF LIQUIDS existing between them. Nernst showed that there was a distinct paralleHsm between the electrolytic conductivity of a solution and the dielectric constant of the solvent, as far as the data on the con- ductivity of electrolytes in different solvents extended at that time. He furthermore pointed out that this parallelism is only relative, that is, that conducting power and dielectric constant are not in strict proportion. An absolute parallelism was hardly to be ex- pected, because other factors undoubtedly also have some influ- ence. Recent experimental data have, however, brought to light numerous exceptions to this rule. Liquid ammonia has a much smaller dielectric constant (16) than hydrocyanic acid (95) or water (81),, but its solutions conduct on an average as well as those in the latter liquids. Sulphur dioxide also yields solutions which are excellent conductors, but its dielectric constant is only 14. Solutions of KI in acetone (D. C, 21) are much better con- ductors than solutions of the same salt dissolved in methyl or in ethyl alcohol (D. C, 32.5 and 27, respectively). However, there are other electrolytes which conduct better when dissolved in either of the two alcohols mentioned than when dissolved in acetone. Attention has already been called to this fact, — ^that is, that certain electrolytes may be better conductors when dissolved in one solvent than when dissolved in another, while certain others conduct better when dissolved in the second solvent than when , dissolved in the first, — which of course shows that the Nernst- Thomson rule is not paramount in determining the power of a solvent to yield conducting solutions. It does, however, appear to be one of the influences affecting the conductivity of solutions, for when applied to solvents of similar constitution it seems to hold. The accompanying table gives the dielectric constants of four primary hydroxyl compounds and of three compounds con- taining the CN radicle. Conductivity measurements show that the conductivity of electrolytes dissolved in the solvents of either j one of these series decreases as the dielectric constant decreases. Dielectric Dielectric Substance. constant. Substance. constant. Water 81 Hydrocyanic acid 95 Methyl alcohol 32.5 Acetonitrile 40 Ethyl alcohol 27 Propionitrile 30 Propyl alcohol 20 NON-AQUEOUS SOlwUTIONS I47 Other explanations which have been proposed to account for the part played by the solvent in the conductivity of solutions will now be rapidly reviewed. (2) Ciamician^ has ascribed dissociative power to the chem- ical nature of the solvent, that is, to substances of certain distinc- tive types. For instance, solvents of the water type containing an hydroxyl group yield solutions which conduct, as do also solvents of the nitrile type containing the CN group. Although this rule seems to hold within limits for many organic solvents, it is en- tirely inadequate when applied to inorganic solvents, as their power to yield conducting solutions seems to be entirely independ- ent of type. (3) Konovaloff^ thinks that only those solvents which react chemically with the solute yield solutions which conduct. Al- though theire may be considerable truth in this general statement, when the exact nature of the reaction is considered, very little evidence of any uniformity has as yet been brought to light. (4) Briihl'' makes dissociative power depend on unsaturated chemical elements in the compound, for example such elements as N, O and S. He ascribes to oxygen a valence of 4. He himself admits that the presence of such an element in a substance does not necessarily imply that it will yield conducting solutions, so tliat the rule is of little value as a generalization. (5) That a certain relation exists between the latent heat of vaporization of liquids, their dielectric constants, and their dis- sociative power has been pointed out by Obach* and further de- veloped by BriihP- (6) That there is a certain parallelism between the coefficients of association of solvents and their dissociative power was first called attention to by Crompton.^ Dutoit, Aston and Friderich^ have investigated this relation more fully, and they have also ' Ztschr.phys. Chem., 6, 403 (1890). See also Cattaneo, /?««rf. Accad. Lincei., (5)4, II, 63 (1895). » Wied. Ann., 49, 733 (1893). 3 Berichte, a8, 2847 and 2866 (1895) ; 30, 163 (1897) ; Ztschr.phys. Chem., 18, 514(1895); a7i 319(1898); 30, 3 (i899). « Phil. Mag., (5) 32, 113 (1891). » Ztschr. I>h.ys. Chem.. 27, 319 (1S98); 30, 42 (1899). »/• Chem. Soc, 71, 925 {1897). ' Dutoit and Aston, Compt. Rend., las, 240 ; Dutoit and Friderich, Bui. Soc. chim., (3) 10, 321 (1898). 148 THE CONDUCTIVITY OP LIQUIDS taken into consideration the coefficients of viscosity of the solvents in this connection. Their conclusions are, first, that electrolytes dissolved in non-polymerized solvents do not conduct, and sec- ondly, that the value of Ax, of the same electrolyte in different solvents is a direct function of the degree of polymerization and an inverse function of the coefficient of viscosity of the solvent. In opposition to this view it may be said that pyridine whose co>- efficient of association is 0.93 yields solutions which conduct well, while electrolytes dissolved in ethylene chloride whose coefficient of association is 1.46 do not conduct at all. If it is held that only those substances are polymerized which possess residual affinities, the relation is at once apparent between this theory and that of Briihl.^ SUMMARY. — None of the above explanations is in itself adequate to account for all the facts which have been brought out in connection with the conductivity of solutions. Each one of them appears in the case of certain groups of solvents to be more or less related to the power to yield conducting solutions. This relation might be of a more general nature if the conductivity of the different solutions and the various physical constants of the solvents were determined under more uniform temperature con- ditions. The influence of temperature on conductivity has been al- ready briefly discussed in this chapter, and it has been shown that the conductivity of a solution becomes very small at the critical temperature of the solvent. All of the physical constants of the solvent, which have been mentioned, vary considerably with the temperature, some of them becoming zero at the critical tempera- ture. Consequently, if all these factors, including the conductivity itself, were investigated at equal fractions of the absolute critical temperature, the parallelism between them would very likely be increased. It is, however, extremely doubtful, whether. even then strict proportionality could be found to exist between them. The conductivity of a solution is apparently not to be referred to the nature of the solvent alone nor to the nature of the solute alone, but rather to the effect of their mutual interaction. Just what the interaction is when a conducting solution results remains 1 For rather complete discussions of this subject see besides the papers already men- tioned, Kohlenberg, /. PAys. Ckem., 5, 384 (1901); and Walden and Centnerszwer, Ztschr. phys. Chem., 39, 558 (1902). NON-AQUEOUS SOLUTIONS 149 yet to be explained. After this interaction has taken place we think we know something of the state of dilute aqueous solutions. Of the inner nature of concentrated aqueous solutions and of the majority of non-aqueous solutions we know on the other hand almost nothing, so that the general problem of the nature of solu- tion remains as yet unsolved.^ TRANSPORT NUMBERS IN NON-AaUEOUS SOLUTIONS.— But few determinations of the relative velocities of the ions in non-aqueous solutions have been made. Hittorf" deter- mined the transport numbers of Cdlj, ZnClj and Znlj in ethyl alcohol, and of Cdlj in amyl alcohol, while Lenz' investigated Cdlj in ethyl alcohol and also in mixtures of ethyl alcohol and water, and Campetti* L,iCl and AgNOj in methyl and ethyl alco- hols. More recently Mather^ has determined the transport num- bers of AgNOj in ethyl alcohol, and Schlundt" that of AgNOg in pyridine and in acetonitrile. Schlundt gives a table containing a resume of the results obtained with AgNOj in different solvents, which is reproduced below. The transport number of the cation is given. Transport Number of the Cation of AgNO., in Different Solvents. Solvent. V =0.42.' i ■> 4 10 16 35 40 Water 0.532 0.500 0.483 0.473 o-475 Acetonitrile 0.383 0.422 0.448 0.473 •••• Pyridine 0.326 0.342 0.390 0.440 Methyl alcohol . 0.533 Ethyle alcohol . 0.405 0.490 In the non-aqueous solvents the transport number of the cation increases with increasing dilution, while in water it decreases. This decrease of the transport number of the cation in aqueous solution has been explained by Noyes' on the assumption that complex anions exist in the more concentrated solutions, which gradually decompose on dilution. Correspondingly Schlundt sug- > In a series of recent papers i,Am. Chem. /.,) 31, 303 and 32, 308 (1904); Ztschr.phys Chem., 49, 385 (1904) ) Jones and Getman present evidence that the exceptional behavior of concentrated solutions is due to the presence of hydrates. 2 Pogg. Ann., 106, 551 (1859). 8 See Ostwald's Lehrbuch d. allg. Ckemie, II, i , p. 618. *Nuovo Cimenio, 35, 226 (1894); Ref Ztschr. phys. Chem., 16, 165. <> Am. Chem. J., 26, 473 (1901). »y. Phys. Chem., 6, 159 (>902). '/. Am. Chem. Soc, 23, 54 (190'). 150 THE CONDUCTIVITY OP LIQUIDS gests that the change undergone on diluting solutions of AgNOg in pyridine and in acetonitrile is due to the existence of complex cations in the more concentrated solutions. The complex cation, he believes, however, is formed by some sort of combination be- tween the AgNOj and the molecules of the solvent. This view is supported by the fact that heat is liberated when AgNOj is dissolved in these solvents. At any rate the nature of the solvent exercises considerable influence on the transport number of an electrolyte. This influence appears to be less, however, in very dilute solutions, since the values of the transport number found in the dififerent solvents tend to approach one another as the dilu- tion increases. CHAPTER XIV. Conductivity of Electrolytes in Mixed Solvents. RESEARCH OF ARRHENIUS.— Investigations of the conduc- tivity of electrolytes in mixed solvents have been almost entirely confined to ascertaining the effect on the conductivity of aqueous solutions produced by the addition of other solvents or vice versa. This is closely connected with the effect produced on the conduc- tivity of aqueous solutions by adding solid non-electrolytes such as sugar and the like. When only small quantities of a nxDn- aqueous solvent are added the effect produced is entirely similar in the tviro cases. Arrhenius^, who was the first to investigate this subject thor- oughly, derived an empirical formula for calculating the change in conductivity of aqueous' solutions due to additions of non-elec- trolytes. Starting from a general equation of the form, in which /„ is the conductivity of the aqueous solution, x the per- centage concentration of the non-electrolyte and a and /? arbi- trary constants, he finds the value of /? is given sufficiently ac- x^ curately by making ;8 = — . The equation then becomes which contains only one arbitrary constant^. Arrhenius found that quantities of a non-conducting liquid not exceeding lo per cent, of the total volume of the solution on being added to an aqueous solution of a good electrolyte decrease the conductivity nearly in proportion to the increase in the viscosity of the medium, a in the above equation represents the specific decrease for a i per cent, addition of the non-electrolyte. This quantity varies according to the nature of the electrolyte and of the non-electrolyte. It is, however, practically constant for cer- tain types of electrolytes in the presence of the same non-elec- trolyte. For instance, for salts of the KCl type in the presence 1 Zlschr. phvs. Chem., g, 4S7 (iSp^)- 2 For further experimental work in connection with this formula, see Holland, IVied. Ann., so, 261 (1893), and Strindberg, Ztschr.phys. Chem., 14, 161 (1894). 152 THE CONDUCTIVITY OP LIQUIDS of ethyl alcohol the value of a varies but little from 0.0235. Since the conductivity decreases nearly in proportion to the increase in the viscosity of the solution, it indicates that the change in con- ductivity is largely due to the diminished speed of the ions rather than to change in the degree of dissociation of the electrolyte. In the case of strong electrolytes the latter is appreciably influ- enced only after the addition of the non-electrolyte considerably exceeds 10 per cent. With weak, electrolytes, however, it was found that the degree of dissociation is considerably affected from: the start. EFFECT OF CHEMICAL UNION BETWEEN THE ELECTROLYTE AND THE NON-ELECTROLYTE.— Hantzsch^ has shown that when the non-electrolyte added has a tendency to form complex molecules with the electrolyte the equivalent conductivity is ab- normally diminished, the effect being most marked when the non- electrolyte is present in exactly the right proportion to form the complex compound. The following results show the effect of adding different quantities of alcohol and of pyridine to ^/jj nor- mal solutions of potassium chloride and of silver nitrate. The coefficients before the formulas of alcohol and pyridine represent the number of molecules added to one molecule of the electrolyte. The conductivity has been recalculated to reciprocal ohms. Effect on the Conductivity of KCl and AgNO, Soi,utions of Adding Alcohoi, and Pyridine. Temperature 25°. z/ = 20 for all solutions. KCl 131-8 AgNO, 116.5 " + 4C2HeO 129.0 (( + 2C,U,0 103.8 " -1- 6 " 127.1 (( + 4 " 102.9 " + 8 " 124.7 " -Hio " 122.2 ** + 2C6H5N 81. 1 l{ + 4 " 76.5 " +4C6H5N 126.2 H + 8 " 71.0 l( + 20 " 63.6 The effect on the conductivity is seen to be the greatest when pyridine is added to the solution of silver nitrate. This is in ac- cord with the fact that heat is liberated when silver nitrate and pyridine are brought together, thereby showing that a chemical union takes place between them. The decrease is relatively the greatest when there are two molecules of pyridine to one mole- ' Ztschr. anorg. Chem., 25, 332 (1900). CONDUCTIVITY OF ELECTROLYTES IN MIXED SOLVENTS 153 cule of silver nitrate, and this is the ratio in which these sub- stances combine. CONDUCTIVITY OF ELECTROLYTES IN AUUEOUS ALCOHOLIC SOLUTIONS. — The effect produced on the conductivity of aqueous solutions by adding ethyl alcohol has been frequently investi- gated. Wakeman^ determined the conductivity of a number of substances when dissolved in mixtures of alcohol and water, especially with a view to finding whether the Ostwald dilution formula applied in such cases. He found that in general it did not hold. Roth^ has since found that neither the formula of Ost- wald, nor of van't Hoff, nor of Rudolphi, applied to the cases in- vestigated by him, but that the following empirical formula of Kohlrausch could be used for interpolating with considerable suc- cess: Ax — A . = criyz. A* In this p and c are constants, which must be found experiment- ally from the data at hand. Most of the investigators in this field have found that when the quantity of alcohol in the solution does not exceed 50 or 60 per cent.'% the equivalent conductivity of dilute solutions of strong electrolytes as related to that of the corresponding aqueous solu- tions is dependent only on the amount of alcohol added and not on the concentration of the solution. This is illustrated by the following table taken from the paper of Cohen*. The conduc- tivity has been recalculated to reciprocal ohms. In A are given the equivalent conductivities at different dilutions of solutions of potassium iodide in water and in mixtures of alcohol and water, and in B the conductivity of the aqueous solution at each dilution is made equal to 100 and the conductivities in the other solutions are given in relative terms. 1 Ztschr. phys. Chem., ii, 49 (1893). 2 Ibid., 42, 209 (1902). ' Throughout the consideration of aqueous alcohol solutions the concentration of the alcohol, unless otherwise indicated, is given in volume percentages. i Ztschr. phys. Chem., as, 30 and 34 C1898). 154 THE CONDUCTIVITY OF LIQUIDS Bquiv AI,ENT ( Conductivity. Ei,ectroi,yte, KCl Temperature 18°. Percentage alcohol. Percentage alcohol. V, 0. 20. 40. 60. V. G. 20. 40. 60. 64 12I.4 •• 45.3 36.8 64 lOO • ■ 37-3 30-3 128 124.0 70.6 46.4 37.8 128 100 56.9 37.4 30.5 255 125-7 7 1. 1 46.6 38.4 256 100 56-6 37-0 30-S 512 127-5 72.0 47.2 39.1 512 ]00 56-s 37-0 30.7 1024 128.3 72-9 47-7 39-7 1024 I(X) 56.8 37-1 30.9 2048 129.2 73-9 48.0 402 2048 100 57-1 37-1 31. 1 The numbers in each cohimn of table B are very nearly con- stant. They, however, show a slight tendency to increase at the higher dilutions, and in fact Roth from careful measurements with solutions oif potassium chloride concludes that the relative conductivity is somewhat dependent on the percentage of alcohol as well as on the dilution^. His results follow : Eqdivai,ent Conductivity. Electrolyte, KCl. Temperature 18° Solvent. Conductivity in water = loo. V. Water. 10^ alcohol. 25^ alcohol. io)( alchol. 25^ alcoh< 30 117-78 88.93 59-68 75-53 50.66 60 120.65 9 [.09 61.04 75-47 50-58 90 122.10 92.22 61.78 75-53 50.61 120 123.00 92-97 62.28 75-59 50-63 150 123.64 93-51 62.65 75-64 50-68 180 124.13 9392 62.94 75-64 50-71 300 125.32 94.98 63-71 75-82 50.84 600 126.61 96.18 64.62 75 99 51-05 Here the numbers in the last two columns are nearly constant, a tendency to increase is however distinctly observed at the last two dilutions. In solutions not so dilute but that the ratio of the conductivity in water to that in a mixture of alcohol and water is constant, the conductivity in a mixture of alcohol and water can be calculated from that in water alone by means of a factor depending only on the percentage of alcohol. This factor seems to be influenced but little by the temperature or by the nature of the electrolyte — provided it belongs to the class of so-called strong electrolytes — as the following table shows. Fjo) 1^20) etc., indicate the factors by which the conductivity of the aqueous solutions are to be multiplied to give the conductivity of a solution containing a percentage of alcohol equal to 10, 20, etc., respectively. ' See in addition a more recent article by Shapire, supporting Roth; Zischr. phys. Chem., 49, 513 (1904). Electrolyte. Temperatnre; Fio.- F20. Fao. P40. KI iS^ .. 0.57 0.37 KI 25 0.73 0-57 0.47 0.40 KCl 25 0.73 0-57 0.47 0.40 NaCl 25 0.75 0.59 0.49 0.41 HCl 25 0.75 0.60 6.48 0.40 NaQHsO^ 18 .. • ■ .. CONDUCTIVITY O? ELECTROLYTES IN MIXED SOLVENTS 1 55 0.35 0.35 0.37 0.32 0.36 Walker and Hambly^ have found practically the same to be true for the conductivity of diethylammonium chloride in aqueous alcohol up to 60 per cent, alcohol. In solutions containing more than 60 per cent, alcohol the factor was found to vary with the concentration, which they ascribed to a change in the degree of dissociation of the electrolyte. Since, however, the factor is not constant at high dilutions. Roth infers that the speed of the ions is also affected by the addi- tion of alcohol. Moreover, he finds that the temperature coeffi- cients increase rapidly with increasing proportion of alcohol and increase slowly with the dilution. For considerable differences of temperature therefore, the factors would not be constant as the above table seems to indicate The transport numbers of some electrolytes in mixture of alcohol and water have been investigated by Lenz^ and by some of Jahn's students.* The addition of alcohol to an aqueous solu- tion of an electrolyte like KCl seems to decrease the transport number of the anion. AaUEOUS ALCOHOnC SOLUTIONS OF MINIMUM CONDUC- TIVITY. — When small quantities of water are added to an alco- holic solution of KI, Cohen found the conductivity was affected in a rather remarkable manner. At dilutions of 64 liters the con- ductivity increased with the amount of water added, as was to be expected, but at dilutions greater than 512 liters the conductivity became less than that of the electrolyte in pure alcohol, as the fol- lowing table shows. The measurements were made at 18°. Percentage of Alcohol. V. 100. 64 27.8 128 3I-I 256 33-9 512 36.7 1024 30-4 2048 38.7 ly. Chem. Soc, 71, 61 (1897). 2 IVied. Beibl., 7, 399 (1883). 8 Ztschr.phys. Chem., 37, 684 (1901). See also Ibid., 4a, 210 (1902). 99- 28.7 OU. 32.9 31-9 34.3 34-3 35-4 36.5 36-4 37-7 36.8 38.5 37-3 IS6 THE CONDUCTIVITY OF LIQUIDS More remarkable, however, is the behavior of aqueous methyl alcohol solutions in this respect as found by Zelinsky and Krapi- win^. The conductivity of the electrolytes, KBr, KI, NH^Br, and NH4I in methyl alcohol is considerably less than in water. They found, however, that the addition of water, up to 50 per cent., to the solutions of these substances in methyl alcohol, in- stead of causing the equivalent conductivity to increase as might be expected, causes it to decrease for all concentrations investi- gated. The results obtained with solutions of KI and of NH^Br are given below by way of illustration. The figures have been recalculated to reciprocal ohms and represent equivalent conduc- tivities at 25°. Conductivity of KI and NH^Br in Methyi, Alcohol, in Water, and IN Mixtures of the Same. Potassium Iodide. Ammonium Bromide. Percentage of Methyl Alcohol. v. 100 98 50 100 50 16 73.8 72.7 66.2 132.7 69.7 65.2 135-6 32 81.4 79-3 68.7 136.7 77-5 68.0 140.5 64 88.0 85.3 70.3 139- 1 84.8 70.4 144.2 128 94.6 91.2 71-9 141. 8 91-5 71.9 147.8 256 lOO.I 95-9 72.8 144.8 96.9 72.8 150.5 512 104.7 99.8 74.2 1470 101.3 73-7 I53-0 1024 io8.g 102.6 75-2 150.2 104.7 74-7 155-2 Jones and Lindsay^ have recently investigated the conductivity of a number of salts in water, in methyl alcohol, in ethyl alcohol, in propyl alcohol and in mixtures of some of these solvents. The measurements were made at both 0° and 25"- They have found a minimum conductivity for all salts investigated in aqueous methyl alcohol solution except for cadmium^ iodide, the conduc- tivity of which was determined only at 25°- Mixtures of ethyl alcohol and water as solvent yield a minimum in the conductivity of all sahs investigated at 0°. At 25° this minimum had disap- peared, at least for 50 per cent, additions of water. The results obtained with lithium nitrate are given in the table below. These as well as all other of Jones and Lindsay's results reproduced in the following pages are expressed in equivalent conductivities and have been recalculated to reciprocal ohms. 1 Ztschr. phys. Chem., 21, 35 (1896). ^ Am. Chem. J, ^ 281 329(1902). CONDUCTIVITY OF ELECTROLYTES IN MIXED SOLVENTS 1 57 Conductivity of LiNOj in Ethyi, Ai,cohoi<, Water, and a 50% Mixture oE the Same. Ato°. At 25". V. Alcohol. Mixture. Water. Alcohol. Mixture. Water. 32 15-2 14.0 53-3 234 36.0 97-9 64 16.6 14.5 54.9 26.5 37-9 100.9 128 18.7 15.2 56.0 29.6 39-5 104.5 256 20.7 15.6 56.9 32.9 41.4 106.3 512 22.8 16.5 58.3 35-4 42.8 108.0 1024 24.8 17.3 59-0 37-9 44.1 109.0 V. Alcohol. Mixture. 16 2.56 14.6 32 64 128 3.00 3-48 3.96 15.3 15-9 16.5 At 25°. Mixture. Water. 36.1 38.2 40.2 42.3 109.4 1 14.3 I18.9 123.5 The conductivity oif the salts investigated in mixtures of pro- pyl alcohol and water exhibit no minimum either at o° or at 25°, as the following table shows. Conductivity op ^SrI^ in Propyi< Alcohol, Water, and a 50% Mixture of the Same. At 0°. Water. Alcohol. 60.3 4.04 62.7 4.71 65.1 5.44 67.2 6.03 No point of minimum conductivity was found for salts dis- solved in mixtures of methyl and ethyl alcohols, but the conduc- tivity of a salt dissolved in a 50 per cent, mixture of these alcohols was found to be less than the mean of the conductivities of the salt dissolved in the two solvents separately. Jones and Lind- say's results with potassium iodide in miethyl and ethyl alcohols are given in the accompanying table. Conductivity of KI in Methyl Alcohoi,, Ethyl Alcohol, and a 50% Mixture of the Same. At 0°. At 25°. Methyl Ethyl Methyl Ethyl V. Alcohol. Mixture. Alcohol. Alcohol. Mixture. Alcohol. 64 63.2 39-2 20.4 88.3 57.8 31.3 128 68.1 42.1 22.8* 94.3 62.4 35.2 256 72.2 44.7 24.2 99-9 66.2 38.4 512 74.5 47.4 26.7 104.9 70.3 41.2 :o24 75.9 50-0 29.2 108.7 74.2 44.1 An adequate explanation of all these facts is diiificult to find. Zelinsky and Krapiwin who investigated the conductivity of aqueous methyl alcohol solutions have suggested that the cause of the low conductivity of such solutions may be due to the union of the molecules of the. two solvents corresponding to cer- tain hydrates of methyl alcohol, as CH3OH + 4H2O or CH3OH + 2H2O. This, however, can scarcely be accepted with- out overwhelming evidence to support it, for we know that the 158 THB CONDUCTIVITY OP LIQUIDS hydrate theory as applied to solutions has become a rather in- genious device, employed at times to explain almost any excep- tional behavior, but as readily discarded when it does not appear to be required. With therefore practically no evidence to support it, this explanation is scarcely probable. We have already seen that one of the theories, which has been suggested to account for the fact that electrolytes conduct only when dissolved in certain solvents, is that the dissociative power of such solvents depends on the polymerization of their molecules. Assuming that this is the true cause of such action, Jones and Lindsay have based upon it an explanation of the conductivity of electrolytes dissolved in mixed solvents. Pure water and pure alcohol have been found by the surface tension method to be asso- ciated liquids, but the molecular weight of alcohol dissolved in water is normal. Furthermore, Jones and Murray^ have recently found that the molecular weight of any one of the three liquids, water, formic acid, or acetic acid, dissolved in any one of the re- maining ones is much less than the molecular weight of the pure substance as determined by the surface tension method. This apparently shows that when two associated liquids are mixed the effect is to lower the association of one or of both of them. This being the case, it seems probable that the conductivity of an elec- trolyte dissolved in a mixture of two solvents in which fewer molecules are associated than in either solvent alone, would be less than the mean of the conductivities when dissolved in each solvent separately. If the polymerization of the molecules of a solvent were really the cause of the conductivity of its solutions, this explanation would be very plausible. But it has already been shown that many substances possess conductivity when dissolved in solvents which are not polymerized at all, so that this explanation of Jones and Lindsay is not universally applicable. It would be interesting in this connection to investigate the conductivity of electrolytes dissolved in a mixture of two non-associated solvents. An ade- quate explanation of such phenomena as the above cannot be ex- pected until our knowledge shall cover all possible varieties of cases of this kind. > Am. Chem.J., 30, 193 (1903). APPENDIX. ExplanaLtion. of Tables. The first seven tables contain the results of the most important conductivity measurements which have been published since the compilation by Kohlrausch and Holborn in 1898 in their Leit- vermogen der Blektrolyte. All conductivities in these tables are expressed in reciprocal ohms, except in Table IX. Concentrations are expressed in equivalents per liter, and dilutions in the number of liters in which an equivalent weight is dissolved. Where conductivity or concentration has been expressed otherwise in the original papers, the results have been recalculated. Table I. — Conductivity of nitric acid by Veley and Manley,^ recalculated to reciprocal ohms by the factor i .063 ; conductivity of ammonia by Goldschmidt ;^ conductivity of the remainder of the electrolytes by Jones and Getman,^ recalculated by the factor 1.066. Table II. — Equivalent conductivities at 18° A, by Kohlrausch and associates* and, B, by Foster.^ These are the most trust- worthy of any conductivities thus far obtained, and they have therefore been made the basis, of the values of A^ and of mi- gration numbers. (See Chapters VII and VIII). Numbers in parenthesis are interpolations. Tables III and IV. — Equivalent conductivities at o" and 95" by Kahlenberg.* Tables V and VI. — Equivalent conductivities, mostly at 25°, by Jones and students.' In these the conductivity of the water used in preparing the solutions was subtracted in every instance. All of the numbers have been recalculated to reciprocal ohms by \Phil. Mag., (6) 3, 119 (1902). 2 Physik. Ztsch., i, 287 (1900). » Am. Chem.J. 27, 443 (1902). * SUzungsber. Kgl. pr. Akad. Wiss-, Berlin, 1899, 665 ; 1900, 1002 ; 1902, 581; 1904, 1215. 6 Phys. Rev. 8, 257 (1899). «/. Phys. Chem., 5, 348 (1901). ' Am. Chem. J., 32, sand no (1899); as. 349 fi9oi); a*. 4^8 (1901); a8, 329 (1902). l60 THE CONDUCTIVITY OF LIQUIDS means of the factor 1.066. Also^ when it was not already the case, the conductivities have been interpolated so as to corre- spond to dilutions which are powers of 2. Table VII. — Specific conductivity of saturated solutions of difficulty soluble salts at 18° by Kohlrausch.^ The conductivity of the water employed in preparing the solutions has been deduct- ed. Some values at other temperatures are given in the original paper. Table VIII. — Similar results by Bottger^ at 20°. Here also the conductivity of the water used has been subtracted. Table IX. — Specific conductivity of pure liquids. This is not an exhaustive collection, for it has been considered to be useless to give all the values thus far obtained for those substances whose conductivity has been frequently determined, as for instance methyl and ethyl alcohols and acetone. Only the lower values have therefore in general been given. Most of the values have been expressed by the observers in mercury units, /, and they are so given here. Values expressed in reciprocal ohms are indi- cated by a *. Table X. — Atomic weights of the more common elements. Table XI — Equivalent weights and electrochemical equivalents, the latter based on the electrochemical equivalent of silver as found by Richards and Heimrod.^ Table XII. — Obach's table for use with Wheatstone bridge. Table XIII. — Obach's logarithmic table for same purpose. Table XIV. — Four place logarithm tables. 1 Zlsch. phys. Chem, 44, 197 (1903). 2 Tbid. 46, 521 (1903). 8 Ibid. 41, 302 (1902). TABLES l6l TABLE I.— CONDUCTIVITY OF CONCENTRATED SOLUTIONS. Nitric Acid, HNOs, 15' 3_ Amtr lonia, NH4OH, 25°. ni. 1 Per cent. K. A- *n. io'k. A- 0.208 1.30 0.064 306.1 0.0109 0.1220 11.19 0.503 0.981 1.698 2.646 3.12 0.152 299.2 0.0219 0.1730 7.90 5-99 0.270 275.2 0.0553 0.2718 4.92 10.13 0.411 242.4 0.1107 0-3843 3-47 1532 0-535 202.0 0.3148 0.6339 2.01 ^•^z? 20. It 1693 0.541 0.7882 1.44 4.766 25-96 0625 131-2 0.666 0.8776 1.^2 5.728 30.42 0.609 106.4 0.817 9510 1. 16 6.490 6.971 7.815 33-81 0.592 91.2 0-935 1.002 1.07 35-90 0.545 78.2 l.oSi I -057 0.978 39-48 0.530 67.8 1.586 1.177 0.742 9.167 45.01 0.466 50.9 2.190 1.270 0.579 10.90 51-78 0.378 34-7 2.995 1.296 0-433 11.22 53-03 0.362 32.3 3-521 1.291 0.367 12.59 58.20 0,297 23.6 4.720 1.218 0.258 13-39 61.20 0-265 19.8 7930 0.870 O.IIO 14.63 65-77 0.206 14.1 9.204 0.791 0.0S6 Ji:ii 69-53 73-82 0.172 115 II.O 6.83 12.89 0.4?* 0.034 1758 76.59 0.0941 5.35 18.22 19.66 78.90 84.08 0.0634 0.0228 3.48 1. 16 Sulphuric Acid, J^H^SOi, 0°. 20.24 86.18 0.0202 1. 00 m. IV. A- 20.66 87.72 0.0136 0.659 2.0 0.2701 135.1 21.26 89.92 0.00814 0-383 3.0 0-3579 118 21.79 9-1-87 0.00394 0.181 4-0 0.4252 106.3 22.45 9432 0.00168 0.07s 5-0 0.4765 0.4968 95-3 22.94 96.12 0.000S5 0.037 6.0 82.8 23.62 98.50 0.00040 0.017 7.0 0.5037 72.0 ""Hi 98.85 0.00033 0.014 8.0 0.5068 63.4 23.88 99-27 0.00043 0.018 9.0 0.4805 53-4 24-15 99-97 0.00018 0.0075 lo.o 0-4635 464 HCL 0.° HNOs, o.o KOH, 0.° NaNOj, 0.° KNO3, 0.° m. K A. •^. A- A. K. A- A I.O 0.2] '.■i6 213.6 0.2078 207.8 0.1208 120.8 0.0431 43- 1 0.1 0533 53- 1.2 O.29I6 1944 02957 197. 1 0.1701 "3-4 0.0590 39-3 o.( 3741 49. 2.0 0.3628 181.4 0.3608 180.4 0.2156 107.8 0.0730 36.5 2.5 0.4060 162.4 0.4143 165.7 0.2595 103.8 0.0825 33-0 3.0 0.4539 151-3 0.4509 150.3 J^CaCls, i D.° J^SrCla, . 3.° J^BaClj, 0.0 m. ^. A- K. A- m. K. A- 1.0 0.0449 44.9 0.1 0.0062 61.9 2.0 0. 0759 38.0 0.0795 39-8 0.2 O.OIII 55-3 3-0 0, ■0993 33-1 0. 1008 33-6 0.5 0.0256 51-2 4.0 0. 1152 28.8 O.II7S 29-S 1.0 0.0476 47.6 5-0 0. .1250 25-0 1-5 0.06S2 45-5 TABI,E II.— EQUIVAI^ENT CONDUCTIVITY OF ELECTRGI^YTES AT i8° {A) m. KCl. KBr. o.ooor 129.05 131. 15 0.0002 128.76 130.86 0.0005 128.09 130-15 o.ooi 127.33 129.38 0.002 126.29 128.32 0.005 124.40 126.40 o.oi 122.42 124.40 O 02 120.00 121.87 0.05 115-94 "7-78 0.1 112.00 114.22 0.2 107.96 110.40 0.5 102.40 105.37 1.0 98.28 . . KL KN03. KSCN. KCIO3. KF. KIOj. V. 129.76 125.49 120.22 11S.63 110.47 97.64 lOOOO 129.50 125.18 120.02 "8.35 110.22 97.34 5000 128.97 124.44 119.38 117.68 109.57 96.72 2000 128.25 123.64 118.64 116.92 108.89 96.04 1000 127.21 122.59 117.65 115-84 107.91 95-04 500 125.33 120.47 115.81 113-84 106.16 93.19 200 123-44 118.20 "3-95 irl.64 104.28 91.24 100 121.10 115.27 I". 59 108.81 101.87 88.64 50 117.26 110.09 107.74 103-74 97-73 84.06 20 113-98 104.77 104.28 99.19 94.02 79.67 10 (110.50) 98.74 (100.70) ll-ll (89-95) 74-34 5 106.20 89.23 95-69 82.60 2 103.60 80.47 91.61 76.00 1 1 62 THi; CONDUCTIVITY OF LIQUIDS TABI- Butyric anhydride 25-0 0.1598* Walden Acetyl chloride . . 25-0 0.953* Walden Acetyl bromide 0.0 2.088* Walden Acetyl bromide . . 25.0 2-,377* Waldent Bromacetyl bromide . 0.0 0.725* Walden Eormamide . 25.0 47.0* Waldent Acetamide . . . 81.0 290.0* Waldenf Niiriles : Cyanogen .... 0.0 <0.007 Centnerszwer Probably a Hydrocyanic acid 0.0 4-73* Kahlenberg and Schlundt non-conduc- Hydrocyanic acid 0.0 4.96 Centnerszwer tor. Acetonitrile 0.0 0.319.')* Waldent Acetonitrile 25.0 0.398* Waldenf Acetonitrile . 25.0 2.0 Dutoit and Friderich Propionitrile 25.0 0.001* Waldent Commercial,o.2 Propionitrile . 25.0 2 Dutoit and Friderich • Butvronitrile . . . . 25.0 1.2 Dutoit and Friderich Hydroxyacetonitrile (Glycolic nitrile) 0.0 5-i6* Waldent Hydroxyacetonitrile (Glycolic nitrile) . 25.0 8.43* Waldent TABLES 169 TABLE IX..— {Continued). Tempera- Authority. Substance. ture. K*or/xiofi Hydroxypropionitrile (Lactic nitrile) . . 0.0 3.16* Waldenf Hydroxy propionitrile (Lactic nitrile) . . 25.0 4.94* Waldenf Hthylene cyanide . . . 60.0 1.50* Waldenf Benzonitrile . . . . 25.0 1.9 Lincoln Benzouitrile 25.0 3.31* Waldenf Benzonitrile 25.0 9.4* Patten Benzyl cyanide .... 26.0 0.40* Waldenf Sulphocyanates and m-ustard oils : Methyl sulphocyanate 25.0 1.46* Waldenf Methyl sulphocyanate . 25.0 7.38* Kahlenberg Ethyl sulphocyanate . 25.0 2.62* Waldenf hyl sulphocyanate . 25.0 4.8* Kahlenberg Amyl sulphocyanate . 25.0 14.7* Kahlenberg Methyl mustard oil . . 50.0 0.33* Waldenf Ethyl mustard oil . . 25.0 100,000 ohms Rt>- 100,000 ohms 170 THE CONDUCTIVITY OF LIQUIDS TABI,E VUl.— {Continued). Kahlenberg : Ztsch. phys. chem., 46, 64 (1903). Kahlenberg and I^incoln :J. phys. Chem., 3, 12 (1899). Kahlenberg and RuhofF: Ibid., 7, 254 (1903). Kahlenberg and Schlundt : Ibid,, 6, 447 (1902). Kohlrausch : Pogg. Ann., 159, 233 (1876). I . . . . . 103.45 E Anions 0.01043 CI 0.4054 Br 0.2387 I - . . 0.07279 F . 0.1S71 OH. . I-I175 CN .. 2.113 NO3 CIO3 0.7113 BrOs . 0-4535 IO3 .. 0.2076 CHO2 . 0.1261 CjHaOa 0.3386 0.5819 ^0.. 0-3293 }4S .. 0-2894 MS,Oi 0.2847 actOi 0-3039 J^COa 1-0711 %CiOi w 35-45 79.96 126.97 19- 17.01 26.04 62.04 8345 127.96 174-97 45-01 .'59.02 8-00 16.03 48.03 58.05 30.00 44.00 0.3671 0.8279 1-3146 0.1967 0.1761 0.2696 0.6424 0.S641 I 3249 1.8116 0.4660 0.6111 0.08282 0.1660 0.4973 0.60 1 1 0.3106 0.4555 TABI^ES 171 TABI76 1.4938 172 THE CONDUCTIVITY OF LIQUIDS TABLE ILll.—^Coniinuai). a I 2 3 4 5 6 7 8 9 60 1.500 1.506 1.513 I.519 1.525 1-532 1.538 1.545 1.551 1.558 61 1.564 I.571 1.577 1.584 I-591 1.604 1. 611 1.618 1.625 62 1.632 1.639 1.646 1.653 1.660 1.667 1.674 1.681 1.688 1.695 63 1.703 I.710 1.717 1.725 1.732 1.740 1.747 1.755 1.762 1.770 64 1.778 1.786 1-793 I.801 1.809 1.817 1.825 1.833 1. 841 1.849 65 1.857 1.865 1.874 1.882 1.890 1.899 1.907 1. 915 1.924 1-933 66 1-941 1.950 1-959 1.967 1.976 1.985 1.994 2.003 2.012 2.021 67 2.030 2.040 2-049 2.058 2.067 2.077 2.086 2.096 2.106 2. 1 15 68 2.125 2.135 2.145 2155 2.165 2.175 2.185 2.195 2.205 2.215 69 2.226 2.236 2.247 2.257 2.268 2.279 2.289 2.300 2 311 2.322 70 2.333 2.344 2.356 2.367 2.378 2.390 2.401 2.413 2.425 2.436 71 2.448 2.460 2.472 2.484 2,497 2.509 2.521 2.534 2.546 2.559 72 2571 2.584 2-597 2.610 2.623 2.636 2.6.50 2.663 2.676 2.690 73 2.704 2.717 2.731 2.745 2.759 2.774 2.78S 2.802 2.817 2.831 74 2.846 2.861 2.876 2.S91 2.906 2.922 2.937 2.953 2.968 2.984 75 3.C00 3.016 3-032 3-049 3065 3.082 3.098 3. 1 15 3.132 3.149 76 3167 3.184 3.202 3-219 3237 3255 3.274 3.292 3.310 3329 77 3.348 3367 3.386 3-405 3.425 3-444 3464 3.484 3505 3.525 78 3-545 3566 3.587 3.608 3.630 3-651 3.673 3-695 3.717 3.739 79 3.762 3.785 3.808 3.831 3.854 3878 3.902 3.926 3.950 3.975 80 4.000 4.025 4-051 4.076 4.102 4.12S 4.155 4.181 4208 4.236 81 4.263 4.291 4-319 4-348 4.376 4-405 4.435 4.464 4.495 4.525 82 4.556 4-587 4.618 '*■*§? 4.682 4-714 5.747 4.780 4.814 4.848 83 4.882 4-917 4.952 4.988 5.024 5.061 5.098 5-135 5.173 5.211 84 5.250 5289 5-329 5-369 5.410 5-452 5.494 5536 5-579 5.623 85 5.667 5.711 5 757 5-803 5.849 5-S97 5.944 5 993 6.042 6.092 86 6.143 6.194 6.246 6-299 6.353 6.407 6.463 6519 6.576 6.634 ll 6692 6.752 6.813 6.874 6.937 7,000 7.065 7.130 7-197 7-264 88 7-333 7.403 7.475 7.547 7.621 7.696 7.772 7.850 7.929 8.009 89 8.091 8.174 8.259 8.346 8.434 8.524 8.615 8.709 8.804 8.901 90 9.00 9.10 9.20 9.31 9.42 9-53 9-64 9-75 9.87 9-99 91 10. II 10.24 10.36 10.49 10.63 10.76 10.90 11.05 11.20 11-35 92 11.50 11.66 11.82 11.99 12.16 12.33 12.51 12.70 12.89 13.08 93 13.29 13.49 13.71 13.93 14.15 14.38 14.63 14.87 15-13 15-39 94 15-67 15.95 16.24 16.54 16.86 17.18 17.52 17.87 18.23 18.61 95 19.00 19.41 19.83 20.28 20.74 21.22 21.73 22.26 22.81 23-39 96 24.00 24.64 25.32 26.03 26.78 27-57 28.41 29.30 30.25 31.26 97 32.33 33.48 34.71 36.04 37.46 39-00 40.67 42.48 44.45 46.62 98 49.00 51.63 54.56 57.82 61.50 65-67 70.43 75.92 82.33 89.91 99 99.00 IIO.I 124.0 141.9 165.7 199.0 249.0 332.3 499.0 999.0 TABLE XIII.— OBACH'S LOGARITHMIC TABLE FOR WHEATSTONE BRIDGE. LOGARITHM OF —2- CORRESPONDING TO a. a. I 2 3 4 5 6 7 8 9 00 CO 7.0004 3019 4784 6038 7011 7808 84S1 9066 > 9582 01 8.0044 8.0462 0844 1196 1523 1827 2111 2379 2632 2871 02 3098 3514 3521 3718 3908 4089 4264 4433 4752 03 4903 .5050 5193 5331 5465 5595 5722 5846 5966 60H3 04 6198 6310 6419 6526 6630 6732 6832 6930 7026 7120 05 7212 7303 7392 Z'*?? 7565 7649 7732 7814 7894 7973 06 8050 Si^' 8202 8276 8349 8421 8492 8562 8631 07 8766 S832 8898 8962 9026 9089 9151 9213 9274 9334 08 9393 9452 9510 9567 9624 96S0 9736 9790 9845 9899 09 9952 9.0005 0057 0109 0160 0211 0261 0311 0360 0409 10 9.0458 0506 0553 0600 0647 0694 0740 0785 0831 0875 11 0920 0964 1008 1052 1095 1138 1180 1222 12^4 1306 12 1347 1388 1429 1469 1549 1589 1628 1667 1706 13 1744 1783 1821 1858 1896 1933 1970 2007 2044 2080 14 2116 2152 2188 2224 2259 2294 2329 2364 2398 2433 TABLES 173 TABIDS yilll.— {Continued). a I 2 3 4 5 6 7 8 9 15 9.2467 2501 2534 2568 2602 263s 2668 2701 2733 2766 16 2798 2831 2863 2895 2926 2989 3021 3052 3083 ^l 31 14 3144 317s 3205 3236 3266 f^ 3326 3355 3385 18 3415 3444 3473 3502 3531 3560 3618 3646 3674 19 3703 7313 3759 3787 3815 3842 3870 3898 3925 3952 20 9-3979 4006 4033 4060 4087 41 14 4140 4167 4193 4220 21 4246 4272 4298 4324 4350 4376 4401 4427 4452 4478 22 4503 4529 4554 4579 4604 4629 46.'i4 4678 4703 4728 23 4752 4777 4801 4826 4850 4874 4898 4922 4946 4970 24 4994 5018 5041 5065 5089 5"2 5136 5159 5182 5206 "5 5229 5252 5275 5298 5321 5344 5367 5389 5412 5435 26 5^57 5480 5502 5525 5547 5570 5592 ^614 5636 5658 ^i 5880 5702 , 5724 5746 5790 5812 5833 5855 5877 28 5898 5920 5941 5963 5984 6195 6005 6027 6048 6069 6ogo 29 6ni 6132 6153 6174 6216 6237 6258 6279 6300 30 9.6320 6341 6362 6382 6403 6423 6444 6464 6484 6505 31 6525 6545 6566 6586 6606 6626 6646 6666 6686 5706 32 6726 6746 6766 6786 6806 6826 6846 6865 6885 6905 33 6924 6944 6964 6983 7003 7022 7042 7061 7081 7100 34 7119 7139 7158 7177 7197 7216 7235 7254 7273 7292 35 7312 733' 7350 73*^ 7388 7407 7426 7445 7463 7482 36 7501 7520 7539 7558 7576 7595 7614 7633 7651 7670 37 7707 7726 7744 7763 7948 7782 7800 7819 7837 7855 38 7874 7892 79" 7929 7966 7984 8003 8q2I 8039 39 8057 8076 S094 8ri2 8130 8148 8167 8185 8203 8221 40 9.8239 8257 8275 8293 8311 8329 8347 836s 8383 8401 41 8419 8437 8455 8473 8491 8509 8527 8545 8563 8580 42 8598 85l6 8634 8652 8669 8687 8705 8723 8740 8758 43 S776 8794 881 1 8829 8847 8864 8882 8900 8917 8935 44 8953 8970 8988 9005 9023 9041 9058 9076 9093 9111 ^i 9128 9146 9164 9181 9199 9216 9234 9251 9269 9286 9304 9321 9339 9356 9374 9391 9408 9426 9443 9461 47 9478 9496 9513 9531 9548 9583 9600 9618 9635 48 9652 9670 9687 9705 9722 9739 9757 9774 9791 9809 49 9826 9844 9861 9878 9896 9913 9931 9948 9965 9983 50 0.0000 0017 0035 0052 0069 0087 0104 0122 0139 0156 51 0174 0191 0209 0226 0243 0261 0278 0295 0313 0330 52 0348 0365 0382 0400 0417 0435 0452 0469 0487 0504 53 0522 0539 0557 0574 0592 0609 0626 0644 o66i 0679 54 0696 0714 0731 0749 0766 0784 0801 0819 0836 0854 55 0872 0S89 0907 0924 0942 0959 0977 0995 1012 1030 56 1047 1065 1083 HOC 1118 1 136 1 153 1171 1 189 1206 57 1224 1242 1200 1277 1295 1313 1331 1348 1366 1384 58 14c 2 1420 1437 1455 1473 1491 1509 1527 1545 1563 59 1581 1599 1617 1635 1653 1671 l68g 1707 1725 1743 60 0.1761 1779 1795 1815 1833 1852 1870 1888 1906 1924 61 1943 1961 1979 1997 2016 2034 2052 2071 2089 2108 62 2126 2145 2163 2I8I 2200 2218 2237 2256 2274 2293 63 2311 2330 2349 2367 2386 2405 2424 2442 2461 2480 64 2499 2518 2537 2555 2574 2593 2612 2631 2650 2669 65 2688 2708 2727 2746 2765 2784 2803 2823 2842 2861 66 2881 2900 2919 2939 2958 2978 2997 3017 3036 3056 67 3076 3095 3"5 3135 3154 3174 3194 3214 3234 3254 68 3274 3294 3314 3334 3354 3374 3394 3fi 3434 3455 69 3475 3495 3516 3536 3556 3577 3597 3618 3638 3659 70 0.3680 3700 3721 3742 3763 3784 3805 3826 3847 3868 71 3889 3910 3931 3952 3973 3995 4016 4037 4059 4080 72 4102 4123 4145 4167 4188 4210 4232 4254 4276 4298 73 4320 4342 4364 4386 4408 4430 4453 4475 4498 4520 74 4543 4565 4588 46U 4633 4656 4679 4702 4725 4748 174 THE CONDUCTIVITY OF LIQUIDS TABLB yini— (.Continued). a I 2 3 4 5 6 7 8 4982 ^ 0.4771 4794 4818 4841 4864 4888 491 1 4935 4959 76 5006 5030 5054 5078 5102 5126 5150 5174 5199 5223 77 ,5248 5272 5297 5322 •5346 5371 mi 5446 5471 78 5497 5522 5573 5624 5650 5702 5728 79 5754 5780 5807 5833 5860 5886 5913 5940 5969 5994 80 0.6021 6048 6075 6102 6130 6158 6185 6213 6241 6269 81 6297 6326 6354 63S2 6411 6440 6469 6498 6527 6556 82 6585 6615 6545 6674 6704 6734 6764 6795 6825 6856 ?3 6886 6917 6948 6979 701 1 7042 7074 7105 7137 7169 84 7202 7234 7267 7299 7332 7365 7398 7432 7466 7499 85 7533 7567 7602 7636 7671 7706 7741 7776 7812 7848 86 7956 7993 80^0 8067 8104 8142 8179 8217 87 8256 8294 8333 8372 8411 8451 8491 8531 8571 8612 88 8653 8694 87.36 8778 8820 8862 8905 8948 8992 9036 89 9080 9125 9169 9215 9260 9306 9353 9400 9447 9494 90 0.9542 9591 9640 9689 9739 9789 9840 9801 9943 9995 91 1,0048 OIOZ 0155 0210 02b4 0320 0376 C433 0490 0548 92 0607 0666 0726 0787 0849 0911 0974 1038 1102 1 168 93 1234 I30I 1369 1438 , 1508 J,'^79 165. 1724 1798 1873 94 1950 2027 2106 21S6 2268 2351 2435 2521 2608 2697 95 279 2S8 297 307 317 327 337 347 358 369 96 380 392 403 415 428 440 467 481 97 510 525 541 557 574 591 609 628 648 669 98 690 713 737 762 789 817 848 880 916 954 99 996 2.042 093 152 219 299 396 522 698 3.000 TABI,B XIV— I 3 Conductivity of non-aqueous solutions, 135 ; influence of solvent on, 145 ; influence of temperature on ... . . . , 141 Cormack. See "Walker Crompton . . . . . . . 147 Dawson and Williams ... 122 D^guisne . . . , . ... 99 Denison, 71. See also Steele * • , . . . ; . Dennhardt . . ... . . . . ' 169 Dielectric constants and conductivity 145, 147 Diesselhorst. See Kohlrausch . . . ; : ; : ; . . . ... Dilution, of solution, 46; unit of , . . i Dilution law, 51, 143. 153 ; some consequences of . . 53 Dip electrodes . . . 17 Dissociation, degree of, 50, 57 ; of electrolytes in mixtures, ixo ; in non-aqueous solu- tions . . . . . 142 Dissociation constant .... . 52 Dissociative power of solvents . . . 145 Double sails 116 Douglas. See Jones. Drucker. See Rothmund. Dullberg . . 119 Dutoit and Aston 147 Dutoit and Friderich . . 138, 147, 169 Electricity carried by a gram-ions 50 Electrochemical equivalents 01' ion . ... . . 170 Electrodes . . . . . . 15 Electrodynamometer . . . . . . . 24 Electrolytes, strong, dilution formulas for, 58 ; and law of mass action ... . 54, 56 Electrolytic vessels . . . . . . . 12 Ende. See Andrews. Equivalent weights of ions .... ... . 170 Erdmann , . . 126 Errors with alternating current method, sources of . . , 25 Euler 59. 130 Eversheim . . . . . . ioi« 141, 142 Fanjcing ... . .... 102 Faraday, 49 ; law of ... . ... 50 Farmer. See Frankland, Flasks, calibration of . . . .... . . . . 44 Formic acid, conductivity of, 52 ; as solvent . . . 137 Foster ... . . . 100, 159 Foussereau. See Bouty. Frankland and Farmer . . 131 Franklin and Kraus ... 130, 138, 141, 169 Frenzel 130, 134, 169 Friderich. See Dutoit. Fritsch . . ....... 132 Fuchs . . ... 8 Fused salts, conductivity of, 132; solidification of .. ...... .... .......... 121 INDEX 179 GALVANOMETER, D'Arsonval, 6; vibrations 24 Gaus. See Abegg. Getman. See Jones. Glass, influence of its solubility on the conductivity of water 43 Godlewski j., Goebel „ Goldschmidt . ■ ■ '3, 159 Goodwin and Thompson . ,2g^ ,30, 138, 169 Gorski. See Laszczynski. Graetz ,jj Graphic representation of conductivity , . . . . .89 Grotthuss An ^ „ . " ... . 49 Gruneisen. See Kohlrausch. Guldberg and Waage .... . 51 Guthrie and Boys .... ... . 5 Hagenbach . . , 141 Hantzsch . . . . _ , ^ ^ ^ ,=2 Hantzsch and Voegelen ... ... .... 169 Hartwig . .169 HeatingeSFect of current .... 25 Heimrod. See Richards. Henderson. See Stroud. Heydweiller. See Kohlrausch. Hiitorf . . ... . .. 64, 68, 75, 149 Hoffmeister . .... .■ . , , . . 113 Hofmann ... . . ... . 104, 116 Holborn. See Kohlrausch. Holland . . . . . , . . igi, 169 Hopfgartner . . . . . . 68, 75. 76, 1 13 Hulett ... . .. 34, 36, 41 Hulett and Allen . . .... . . 34 Hydrocyanic acidras solvent ... . . 136, 138 Induction apparatus . ... ....... 9, 20 Interpolation, methods of . ... ...... . . 89, 92 Ions, definition of, 49; influence of complex, on transport numbers, 78; method.s for determining relative migration of, 65, 68 ; movement of, 61, 64 ; in non- aqueous solutions, 142, 144 ; transport numbers of, 72, 75 ; velocity of . 87, 89 Isohydric solutions . . 104 JAHV ... . . Jahn and Buscfanewski . . Jahn and students . ... Jones and Douglas . Jones and Getman . . . . Jones and Lindsay ... ... Jones and Mackay ... Jones and Murray Jones and students Kablukoff . . . .... Kahlenberg ... Kahlenberg and Lincoln . . Kahlenberg and RuhoflT . Kahlenberg and Schlundt . . ...... Klein ... Kohlrausch, F . . . ... . . I, 8, 12, 14, 34, 41, 43, 48, 51, 52, 61, 64, 77, 78, 85, 99, 119, 123, 125, 128, 153, 159, 160, 170 5< i, 59 . 75, 155 . 76 . 68,72 JOG 138, 156, 55. 157. 149. 159 158, 169 n6. 41 158 159 139. 148, 159, 138, 138 170 170 170 170 116 l8o INDEX Kohlrausch and Gruneisen Kohlrausch and Heydweiller . . Kohlrausch and Holborn Kohlrausch, Holborn and Diesselhorst . Kohlrausch and Maltby Kohlrausch, W . . . . . Konovaloif . ... Krapiwin. See Zelinski. Kraus, 141. See also Franklin. Kiimmel . , . . Kunz . . . ... Kurlbaum. See Lummer. 78 8, 40. 42, 43 76. 86 9S , 122, 159 I. 32. 36 59 132 147 78 100 138, 170 .138. 170 170 149. 155 59 121 I^ASZCZVNSKl Laszczynski and Gorski .... . . I^emnie . ... . , . . Lenz . .... ... I^iebenow I^iebknecht and Nilsen Lincoln, 138, 170. See also Kahlenberg. Lindsay. See Jones. Liquids, single, cause of conductivity of, 133 ; conducting and non-conducting, 131 , conductivity of ... . 128, 130, 167 Lodge ... • . . 69 Loeb and Nernst . , .... 66 Logarithm table .... 174 Loomis . . . . . 14 Lummer and Kurlbaum . . . . . 15 Luther. See Ostwald. Mackay, See Jones. Mcllhiney ... ... ... 11 Magnesium sulphate forcalibrating conductivity vessels , .... 33,35 Magnesium tartrate, conductivity of . . . . . 93 Malstrom .... ... ... . 8 Maltby. See Kohlrausch. Manley. See Veley. Mass action, law of 51. 54 Masson . . . . 69 Mather . . , . ... . .. 68, 72, 149 Methyl alcohol, conductivity of . . . ... ... . 120 Migration of ions. 64 ; methods for determining . . , 65, 68 Migration numbers . . . . . . ' ' 64, 73, 78 Mixed solvents, conductivity in . 151 Mixtures of two electrolytes, analysis of, 125 ; conductivity of .... 104 Molecular weight in non-aqueous solvents ... . 142 Morgan and Hildburgh . . . . . n Murray. See Jones. Neeff's interrupter . . ... ..... ... 20 Nernst, 26, 42, 145, 170. See also Loeb. Nilsen. See Liebknecht. Nitriles as solvents . . . . . . .... 138, 140 Non-aqueous solutions, conductivity of, 135 ; dissociation in, 142, 145 ; influence of temperature on conductivity of, 141 ; transport numbers of . . . . . 149 Novdk ... . . . .170 Noyes, A. A . 55i 68, 73, 75, 76, 77. 149 Noyes and Sammet . . 68, 73 INDEX i8i OBACH, 147 ; tables of . . Ohm, conductivity based on . Ostwald Ostwald and I,uther . Otten . 171, 172 48, 51, i 1, 86, 118, 131, 143, 153 18,43,44 . . . 170 170 15. 170 15 138 44 Patten . . .... Pfeiffer . Platinizing solution ... ... Piperidine as solvent ... Pipettes, calibration of Poiucarfi, 132. See also Bouty. Polarization . . . . 26 Polymerization in non-aqueous solutions ... . .... 144, 158 Potassium chloride, for calibrating conductivity vessels, 33, 34, 35 ; conductivity of . 60 Pressure, influence on conductivity .... 102 Price .... 25 Purity of liquids, determination of . "9 Pyridine as solvent . 138, 140, 149 QinNOLiNE as solvent 138, 140 Ramsay and Shields . .... Resistance capacity, determination of, 32, 36, 37 ; unit of . Resistances, calibration of, 26, 28 ; according to Chaperon, 25 ; graphite, 17 ; standard .... ... Richards and Heimrod .... Rosenheim and Bertheim . ... Roth Rothmund and Drucker . . . Rubens . ... Rubidium nitrate, conductivity of, etc. Rudolph! . . Rudorf ... Ruhoff. See Kahlenberg. Sackur . . . . . ... Sammet. See Noyes. Saposchnikoff* . ..''.... Saturated solutions of difficulty soluble salts, concentration of, 123, 166 . conductivity of ... . . Schall . . Schaller . . Schlamp . Schlundt, 149, 170. See also Kahlenberg. Schrader . .... Self-induction Shapire . . ... Sheldon . . . . 8 Shields. See Ramsay. Siemensunit, conductivity based on .... . . , 2 Skilling . . . ... . . 131 Sodium benzoate, conductivity of . ... .... 85 Sodium chloride, for calibrating conductivity vessels, 33, 35 ; conductivity of . . 60 Solid electrolytes, conductivity of . . . . ... ... 132 Solidification of fused salts ...... .... 121 Solubility of difficultly soluble salts, determination of 123 Solubility of glass, influence on conductivity of water . ...... 43 Solutions, dilution of, 46 ; preparation of ... . . 43 Solvent, influence of, on conductivity . . .... . . 145 134 3 17 50, 160 . . 116 153. 154, 155 56 24 56 ■ 59. 153 no ■ • 59 170 166 15. 170 45 ,97 138 170 xio 25 154 1 82 INDEX 33 44 145 68 74 75 77 57 69 81 68, 75 76 77 61 151 21 5 s6 61 . I 36. 138 Specificgravity and Strength of solutions Specific inductive capacity and conductivity Starck .... . . ... Steele ....;. . '. Steele and Denison ... . . . . * . . . Stbrch Strindberg . , . .... .... String interrupter . . Stroud and Henderson ... ... . ... Strouhal and Barus .... Succinic acid, conductivity of .... Sulphur dioxide as solvent . .... Sulphuric acid, for calibrating conductivity vessels, 33, 35 ; maxima of its conductivity 62 Tables of appendix, explanation of . . 159 Tanimann, 102. See also Bogojawlenski. Telephone, g, 21 ; optical . , . . , 22 Temperature, influence on conductivity of non-aqueous solutions, 141; standard . 4, 96 Temperature coefficients of conductivity, influence of concentration on, 97 ; influence of temperature on, 97 ; at high temperatures, 100 ; use of loi Thermometer, standard . . . . . . 96 Thermostats ... , . .94 Thompson. See Goodwin. Thomson . ........ . 145 Titration by means of conductivity . . 119 Transport numbers, 65 ; effect of complex ions on, 78 ; in non-aqueous solutions, 149; values of . . ..... . . 72, 75 Units, of conductivity, i, 2, 3 ; of resistance capacity 3 Van't Hoff . , . ... Veley and Manley . . . . Vessels, electrotytic ... ... .... .... Vibrations galvanometer . . . Viscosity, coefficient of ..... Voegelen. See Hantzsch. VoUmer . . .... ... 59. 122, 153 159 12,37 24 100, 148 .18, 129, 138, 170 Waage. See Guldberg. Wakeman Walden Walden and Centnerszwer Walker and Cormack . Walker and Hambly Warburg • . . . .... 105, 153 120, 130, 131, 134, 138, 139, 141, 144, 170 . ... loi, 129, 138, 141, 148, 170 . • . . 42, 48 . ■ • • 155 ... . . 8, 170 Water, conductivity of, 40 ; effect of impurities in preparing solutions in, 47 ; purifica- tion of ..... . Weighing, reduction to weight z« vacuo . . Wheatstone bridge, different forms of, :8 ; with direct current, current .... Wfietham Wiedemann ... Wien ... ... Wildermann ... Williams. See Dawson. Williamson . . . .... Wolf . . . ...... Zanninvich-Tessarin . . ..... Zelinski and Krapiwin ... ' . 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