118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. L. ONSAGER 349 GENERAL DISCUSSION; Mr. H. Hartley said that the very close agreement between the experimental values and those calculated on Dr.Onsager’s theory for uni- univalent and uni-divalent electrolytes in water and for a number of uni- univalent electrolytes in methyl alcohol showed that the new theory accounted satisfactorily for the conductivity of completely dissociated electrolytes in dilute solution in different solvents, and that deviations from the theory, such as those found for di-divalent electrolytes in water and for the nitrates in methyl alcohol, was good evidence of ionic associations or of the forma- tion of complex ions in such cases. Calculations made by Mr. R. P. Bell with the data given in the table on p. 399, indicated that a considerable amount of association or complex ion formation occurred in all solvents other than water and methyl alcohol. In view of the great experimental difficulties attending the determination of the activities of many solutions of electrolytes the existence of an ade- quate theory of completely dissociated electrolytes was of much importance to chemists, as the conductivity of a solution could almost always be deter- mined ; in conjunction with Dr.Onsager’s theory the results would give a valuable clue to its electrical condition. Professor T. M. Lowry asked Dr. Onsager through what range of con- centration the deviations he had mentioned extended. Professor Allmand asked whether Dr. Onsager or others could throw light on the following points. (I) What was the nature of the relation be- tween the mobility of an ion in a solution of appreciable concentration (free from non-electrolytes) and the actual macroscopic viscosity of the solution ? 24350 GENERAL DISCUSSION By which, if any, of the following schemes, could the relation be qualita- tively expressed? [Concentration c ; fluidity 4 ; ionic mobility I ; forces acting on ion (interionic and electrophoretic considered together) K.3 (2) ( 3 ) Change in c Change in K Change in c (1) Change in c / \ I / \ K / \ K (b Change in Change in \ / I Change in Change in 9 Change in Change in I 9 Change in C Change in I Schemes (I) and ( a ) would mean that ionic mobility was determined solely by considerations arising out of the Debye-Huckel-Onsager theory and that, leaving out of consideration cases of negative viscosity, the increase in macro-viscosity due to increased ionic concentration had no direct influence on ionic mobility.I n other words if the Stokes’ equation, in its simplest or in a modified form, be applied to the movement of an ion, the viscosity entering would aIways be the viscosity of the liquid medium, free from ions. Scheme ( a ) would indicite, in addition, that the increase i n viscosity due to increase in ionic concentration, as usually measured, was governed by’ the same factors as entered into the Debye-Huckel- Onsager theory. Some mechanism involving preferential adsorption of ions of one sign on the walls of the viscosimeter might be imagined. On the other hand, scheme ( 3 ) would indicate the necessity of applying a so- called viscosity correction (Sutherland ; Bousfield and Lowry ; Washburn) to experimental mobilities before the latter could be compared with the values calculated by applying the considerations of Debye, Huckei, and Onsager.( a ) In considering the diffusion coefficients of aqueous electrolytes of finite concentration from the point of view of the Nernst formula (D=RT x --- 2uv ), it would appear necessary ( a ) to introduce the osmotic I J i V - . I coefficient (b) to use, not mobilities at infinite dilution, but actual “true” mobilities holding for the given concentration conditions. Would these mobilities be the same as those determined by conductivity and true trans- ference number measurements? For it appeared to the speaker that the Debye-Huckel electrophoretic retarding effect, which, according to the authors of the theory, could be regarded )as the action on the movement of the ions of a stream of solvent molecules carried in the opposite direction by ions of opposite charge, would Fpt be operative in cases of diffusion.Diffusion measurements made by Oholm and in his own laboratory appeared to indicate that, whilst the concentra- tion at which minimum values of D occurred could be calculated by the above type.of formula for solutions of KCI, NaCl and LEI, the experimental values of the diffusion coefficients at finite concentrations were always greater than the calculated figures ; the discrepancy might disappear if the correct mobilities to use were greater than the ordinary “ true ” mobilities. Mr. C. F& Bury expressed doubt whether Stokes’ law were applicable to bodies as small as ions. Millikan had investigated its applicability for small particles during the course of his researches on the charge of an electron, and had expressed the opinion that Stokes’ law can only be re- garded as valid, in liquids, for spheres of radii greater than 10-6 cm.Most ions were considerably smaller than this, and radii deduced for them Or would they perhaps be greatcy ?GENERAL DISCUSSION 3 5 7 by Stokes’ law were smaller than their true radii. This probably accounted for the inconsistency of the figures for the degree of hydration of ions ob- tained by Professors Reniy and Ulich, and commented on by Professor Allmand ; and also for the fact that Messrs. Hartley and Raikes found some ions in solution to be smaller than the corresponding ions in crystals. The President asked if Dr.Onsager could indicate, for the benefit of those chemists who were not familiar with the mathematical treatment of this subject, in what way the properties of the solution deviated from those represented by the formula, when the concentration became greater than N/IOO, or whatever the limit of their application might be. For instance, was it the viscosity or some other property of the solution which changed in an unknown way as the concentration was increased? Practical chemists were chiefly interested in solutions of fairly high concentration, and it would be of interest to know what was the physical meaning of the deviations from theory which were found to occur. The Extent of Dissociation of Salts in Water. The equivalent conductivity of an electrolyte changes with increasing concentration of the solution ; in general, this change is due to two factors, to the decrease in ionisation of the solute and to changes in the mobilities of the ions.I n a sufficiently dilute solution the second of these two effects alone will persist and there will be a region in which the solute can be regarded as completely dissociated. The concentration at which this will no longer be the case will depend on the character of both solute and solvent. For the inorganic salts in liquid ammonia or acetone (Dielectric Constant ca. 2 2 ) the effect of incomplete ionisation appears to become apparent below 1 0 - 4 equivalents per litre. I n water (D.C. 8 1 ) we have “weak” electrolytes-phosphoric acid, magnesium oxalate,-where this region is not realisable by experiment ; ‘$ intermediate ” electrolytes such as iodic acid (whose dissociation constant K = o - I ~ ) , which can be regarded as completely ionised at .o o o ~ N ; and “strong ” electrolytes-the uni-uni- valent salts. These latter can be regarded as completely dissociated up to much higher concentrations than ’000 IN, but in moderately concentrated solutions it is to be anticipated that the effect of incomplete ionisation will no longer be negligible. This point has been emphasised in the papers of Onsager2 and MacInnes and Cowperthwaite,3 and in view of their work it seems to deserve closer consideration than it has yet had. The extent of dissociation of bi-bivalent salts will first be considered and the uni-univalent salts will then be briefly discussed.No quantitative treatment of salts of mixed valence types has been attempted since uncertainty as to the character and mobility of possible intermediate ions would render the results of little value. I n discussing incompletely dissociated substances it is necessary to distinguish between the activity coefficient, y, defined by the equation Mr. C. W. Davies (communicated 1 2 t h May, 1927). y = 2 a + (where a+ is the mean ion activity and m the molality of the - m - solution) ; and the quantity f+ - = ion-activity-coefficient and is defined by the equation : f f, .fa, which will be called the mean . mi = a+, - or J. Physical Chcm., 29, g86 (1925). *See p. 341. See p. 400.352 GENERAL DISCUSSION m, being the concentration of ionised molecules in moles per IOOO g.of water (or, in dilute solutions, in moles per litre). This ion-activity- coefficient represents the effect of inter-ionic attraction whereas the stoichiometric activity coefficient involves both this and the degree of dissociation. Bi-bivulent SaZts.-The equation of Onsager connecting the mobility of an ion with the ion-concentration is, for the majority of electrolytes in water, in striking agreement with the experimental data. I n the case of magnesium sulphate, however,-and the same applies to other bi-bivalent salts-the actual decrease in conductivity is greater than that predicted by the theory. This discrepancy is most readily explained by supposing the salt to be incompletely dissociated. The Onsager equation for a bi-bivalent'electrolyte in water at 18' is :- A, = A, -(142*8 + 1.272A0)JCi .* (2) where Az is the sum of the mobilities of cation and anion in a solution in which the equivalent concentration of ions is Ci. If this equation is provisionally adopted, it is possible to calculate from the conductivity data the concentrations and the activities of the ions at each concentration.* Let A be the equivalent conductivity of a salt at total equivalent concentration C, and let C, be the concentration of ions Dresent in the A ci K! = C' solution. The degree of dissociation is given by the ratio Combining this with equation 2 gives:- A, - (142.8 + r.272Ao)JCI . ' (3) A . C A @ = - = ci From this equation it is possible by a short series of approximations to calculate Ci and, by subtraction, C,, the equivalent concentration of un- dissociated molecules.For a bi-bivalent electrolyte the mass action expression is :- where K is the true dissociation constant, and fu-the activity coefficient of the unionised fraction-may be taken as equal to unity in very dilute solutions. The factor 2 is introduced into the denominator to convert the equivalent into molar concentrations. therefore be calculated. To obtain K, use is made of the well-known limiting equation: log y = - A Jc, which has been found to hold for all electrolytes hitherto examined up to a concentration of approximately 0.01 A? If therefore log K' is plotted against Jc, a straight line is obtained which determines the values of K and A. The results of the calculation for MgSO, are plotted in the figure.In this case there is some uncertainty as to the A, value, since the mobilities of Mg" and SO4" at infinite dilution are not known with great accuracy. The method of calculation is that introduced by the writer in discussing weak uni- univalent electrolytes. (y, physical Cheni., 29, 973, 1925 ; and Phil. Mag., 1927) ; Sherrill and Noyes ('jf. Am. Clzem. SOL., 48, 1861, 1926) and MacInnes (ibid., 48, 2068, 1926), have employed a similar method of treatment which, however, involves an addition31 assumption as to the validity of the Debye-Hdckel limiting activity equation. Ii - K' can The ratio __ = - - f, .f5 G In the present case this becomes : log f,. f5 = - 2A Jc,GENERAL DISCUSSION 353 The probable value obtained from conductivity data is 113.4 and the calculations have been made for this value and for several other values lying in this neighbourhood.From the figure it will be seen that the value A, = 113.5 gives the best straight line and this yields the result: K 5 -00612 ; A = 3.66. These values may be regarded with suspicion as depending on the selection of the most appropriate A, value as well as on the validity of the Onsager equation ; but they can be checked to some log^* extent by freezing- point measurements in the following way. The Onsager limit- ing equation breaks down at about ' 0 0 2 N; but once the value of K has been determined, the ion concentrations, acti- vity coefficients and mobilities at the higher concentra- tions can be ob- tained from the re- sults of activity mea- surements. From the equation y2m2 = a,K the value of as is calculated and.if this is as- .I,= 113': I 1 I I *01 +02 003 '04 l/c, + FIG. I.-MgSO,. sumed to be equal to mu, mi and consequently f + and A, are obtained. The validity of the assumption that the activity is equal to the concentration for the undissociated molecules is, of course, uncertain. It seems to be justifiable up to an ion concentration of 0.1 N; but at higherconcentrations the activity is probably appreciably greater than the concentration. The results of this treatment are illustrated for MgSO, in Table I., where the activity values are those obtained by' Lewis and Randall from the freezing-point measurements of Hausrath and others. TABLE I. MgSO,. K = 0*00612, '0001 '0002 '001 ' 0 0 2 .0005 -005 '01 '02 '85 -81 '75 '69 '61 '50 '404 -321 2 2 5 .160 *0000012 '0000043 ~000023 *000078 *00024 -00267 '00673 '0207 '0450 .OOIO *ooorgB *000954 *oor844 .0080 ,01466 '02654 *0586 '0003914 '00352 'I10 *86 '83 '79 '75 '69 '63 '55 *48 *38 '30 5 Lewis and Randall, Thermodynamics," p.344 (1923).354 GENERAL DISCUSSION In column 5 are given the ion concentration values obtained from the conductivity data by the former method of calculation. They agree well with the values in column 4. Conductivity data are also available for ZnSO,, CdSO,, CuSO,, and MgC,O,, and these salts have been treated in the same way as MgSO,. Curves similar to those shown were obtained in each case, and the results are shown in Table 11. TABLE 11. &SO, CdSO, cuso, Mg C*O, ZnSO, 1x3'50 om061 3'7 113.50 0.0045 3 '7 113'90 0'0038 3 '5 113'85 0.0045 3 '3 3'5 107.00 1 0'00037 I I Magnesium sulphate is the strongest of these electrolytes, but its dissociation constant is no greater than that of o-nitro-benzoic acid (K = *0062 at 25").The weakest, magnesium oxalate, is more comparable with formic acid. The A values are more uncertain, as is evident from an inspection of the figure, since they depend so largely on the values adopted for A. and on the accuracy of the conductivity data at extreme dilutions. They are all larger than the value given by the Debye-Hiickel theory, which for a bi-bivalent electrolyte is 2.81. Uni- UnivaZent SaZfs.-The dissociation constants of the uni-univalent salts are much larger than those of the bivalent electrolytes, and the unionised fraction only becomes measurable in more concentrated solutions where the Onsager equation is inapplicable and where the conductivity data are subject to a viscosity correction.Still, approximate values for the extent of ionisation of the common salts seem likely to be of interest, and the figures of MacInnes and Cowperthwaite provide a starting-point. These writers find that hydrogen, lithium, sodium and potassium chlorides in 0.1 Nsolution are completely dissociated, so that in these five electrolytes the mobility changes are not masked by the effect of incomplete dis- sociation. Now the Onsager equation for uni-univalent electrolytes : A = A0 - (50'49 + 0*2238Ao) Jc only holds up to a concentration of o'ooz ; but it has been found that for the chlorides mentioned the deviations from this equation at the higher concentrations are larger the larger the ho value; and that, in fact, the equation, is approximately true for these electrolytes and some others even up to concentrations of 0.5 N a n d beyond.The values found for f (c) are given in the following table : c = '005 'OX '02 '05 'I '2 '5 f ( C ) '07006 '09441 '1246 '1748 '2239 '2789 '3548. I n the equation 7 is the relative viscosity of the solution. This viscosity correction is, of course, purely empirical ; it is the one which gave the bestGENERAL DISCUSSION 355 average agreement for the electrolytes examined. Actually the true viscosity correction is most uncertain and probably vanes from ion to ion: this is certainly the chief, if not the only difficulty in the accurate extension of the limiting equation into higher concentrations.Equation 5 has been applied to the uni-univalent electrolytes quoted by Noyes and Falk in their valuable collection of the data. For six salts the agreement up to 0-5 N i s good, the maximum deviation being 0.4 per cent. (the viscosity correction is in some cases ten times this amount), and these salts are presumed to be completely dissociated. They are: lithium, sodium and potassium chlorides, potassium bromide, potassium thiocyanate and lithium nitrate. For the remainder, the experimental conductivity figures at the higher concentrations become in every case lower than the calculated, and the ratio Aexp./Acalc, is taken as an approximate measure of the degree of dissociation.The dissociation constants can then be calculated, assuming, as before, that C(I - Aexp./Acalc.) = a2, and introduc- ing this value into the equation Pni2/,, = K where y is the experimentally determined stoichiometric activity coefficient. The results are shown in Table III., the activity coefficients being again taken from Lewis and Randall except in thei caseslspecially noted. represents the degree of ionisation and K the dissociation constant derived. TABLE 111. Thallous Nitrate" { 'kX Potassium Potassium Thallous Rubidium Caesium Chlorate * Bromate * Chloride t Chloride t. Chloride t *OI. - - '916 '994 -902 '993 '984 '521 1.40 1'10 - - - a882 '997 '994 1-99 1.40 - - '972 0'300 - - - - '02. '05. '991 3:& '975 '783 '973 '946 '573 '765 .988 '765 '984 '977 '984 1.32 1'12 2-42 1.85 1.42 2-03 - - - - - - *I.'985 '732 *g6 I '723 '957 '917 '591 -692 '984 %g2 '976 -968 '977 3-86 1'37 1-23 3-00 2'00 1-70 2'41 - - '990 '981 5.88 3.18 '5. The constancy of these rather tentative K values is good in view of the enormous effect upon as of small errors in A. or in the derivation of Adc. Of the other electrolytes examined, lithium iodate begins to show the * Assuming that the ion-activity-coefficient is the same as that of potassium nitrate t. Assuming that the ion-activity-coefficient is the same as that of potassium chloride. a t the same concentration. J. Amer. Chcm. Soc., M~ 461 (1912).356 GENERAL DISCUSSION effect of incomplete dissociation at 0.1 N ; its strength is approximately the same as that of rubidium chloride but cannot be safely calculated owing to the magnitude in this case of the viscosity correction.The strength of the fluorides and of the acids also could not be calculated owing to the absence of viscosity data. For the salts that have been examined it will be seen, that salts contain- ing a common anion fall, in strength, in the following order : Li > Na> K > R b > Cs > T1, and that the dissociation constants of those containing a common cation decrease in the order C1> 10, > BrO, > ClO,, NO,. Thallous chloride is an apparent exception. Dr. Onsager replied that the theory accounted for the influence of Coulomb’s forces upon the mobilities of the ions. The square root formula was only an approximation, applicable in great dilutions. At finite con- centrations deviations from that formula must necessarily occur even if no other effects at all were operating.The deviations from the square root law would depend upon the individual properties of the ions, such as the dimensions of the ions, the variation of viscosity with concentration and, particularly, upon the deviations from Coulomb’s law which would probably occur when the distance between two ions became small (‘6 association ” and ‘‘ hydration ”).7 In the conductivity theory no attempt had been made to improve the simplified mathematical treatment of Coulomb’s forces which led to the square root law. However, in the thermodynamic theory such advances had been made. Besides Professor Bjerrum’s investigation * attention should be drawn to the recent papers of Gronwall and Muller.lo As to Professor Allmand’s question regarding viscosity, his scheme (3) was essentially the right one ; however, at greater concentrations the effects of interionic forces and viscosity wouId interfere with each other to a certain extent.There was some uncertainty about the viscosity correction even for dilute solutions ; firstly, because the ions could not be expected to obey Stokes’ law exactly ; secondly, because the composition of the solution sur- rounding an ion would differ from that of the solution in bulk. Though the viscosity correction should of course be taken into consideration for the interpretation of the conductivity curves, it was of minor importance for the testing of the theory, as the deviations from the limiting formula would in general depend more upon the other individual properties of the electrolytes. As to the question regarding diffusion, the activity coefficients should be introduced as had been done by Schreiner.” The mobilities should always be taken as greater than those obtained from the conductance data. Schreiner took the limiting mobilities; this was approximately right for simple electrolytes when there was no diffusion potential and the viscosity correction was negligible. For simple electrolytes, the diffusion coefficient would not be influenced by the effect he (Dr. Onsager) had described as “ionic forces,” because both kinds of ions migrated with the same velocity in the same direction, and need not pass each other. The electrophoresis effect would be zero when there was no diffusion potential, and negligible for binary electrolytes, when the transference member did not differ much from 0.5. The question has been discussed more extensively in Physik. Z., 1927, 28,277-298. Proc. Amer. Nat. A d . Scimt., April, 1gz7. Physik. Z., 1927, 28, 324. 8 Kgl. Uanske Vidensk. Selsk., Mat. f y s . Medd., 7, 9, 1926. Tidsskrift for kemi og berguaesen, 1924.