92
WILLIAM J. ARGERSINGER, JR., AND ARTHURW. DAVIDSON
It shou!d be noted that the solution I1 was formed b y equlhbratmg-part of the solution V with additiow specific precipitate, increasing the relative amount of antibod in the system aa compared to the latter solution. Ghls clearly demonstrates the revenibility of the aggregation reaction. It is thus seen that in the antigen excess region of the reaction between equine antibody and human serum albumin, the solution formed contains several complexes of del%+ antigen-antibody composition. The relative proportions in which these complexes appear depend upon the relative amounts of antigen and antibody in the system. The fact that the relative proportions of these complexes can be altered from a relatively single complex as seen in experiment V to that in experiment I1 by increasing the relative amount of antibody in the system would further indicate the dependence of the composition of the antigen-antibod complexes upon the amounts of antigen and antibody in tKe system. It would thus ap ar that these complexes exist in equilibrium with each o t g r and the amount of free antigen in the system. It does not appear likely that these complexes are polymers of a simple complex, all possessing a single antigenantibod ratio. In such a system, the smallest complex would sLft (probably increase) in molecular weight as the antigen-antibody ratio in the monomer system increases, and the molecular weights of the complexes would be multiples of each other. This does not appear to be the case. We have just described three protein-protein interactions which have recently been studied in our laboratories. A fourth reaction of this t is that of the mercury’salt of merca talbumin, A l b S r O H , with mercaptalbumin, AIbS8. The properties this interaction have been described in some detail by Hughes68 and by Edsall.‘* More recently, we have studied the corresponding reaction where a bifunctional organic mercurial
d
HIHgCH2CH /-H
Vol. 56
>HCH,HgOH
‘CH2-0’ replaces the mercury ion.S0 Although these interactions involve very different systems, and have been studied by different methods, the similarities in the kinds of forces which we call u on to explain the results obtained are most striking. Tge principal forces in the &lipoprotein, y-globulin system, electrostatic in character, are also responsible for the dissociation of the insulin polymers. There is much more specificity in the insulin reaction, however, introduced by the short-range attractive forces which are so important to antigen-antibody and enzyme-substrate interactions. The attractive forces involved in the mercaptalbumin system, while apparently simple in origin, are highly specific. Further studies of such interactions, especially these simpler ones, will do mpch to increase our knowledge of all protein-protein interactions.
REMARKS GERSONKEOELES:It is suggested that the equilibrium
between the various protein species may possibly be influenced by the ultracentrifuge itself when it 18 used to study this equilibrium. For if the partial specific volumes of the reactants differ from those of the products, then under the high pressures attained in the ultracentrifuge, that direction of the reaction should be favored, accordin to Le Chatelier’s principle, which results in a decrease of vofume It is therefore sug ested that the existence of such an effect might be studied %y examining the equilibrium as a function of the speed of the ultracentrifuge. (58) W. L. Hughes, Jr., Cold Spring Harbor Sump. Quanl. Biol., 14, 79 (1950). (59) R. Straessle, J . Am. Chem. Soc., 78, 504 (1951)
EXPERIMENTAL FACTORS AND ACTIVITY COEFFICIENTS IN ION EXCHANGE EQUILIBRIA BY WILLIAM J. ARQERSINGER, JR., A N D ARTHURW. DAVIDSON Department of Chemistry, Unzversity of Kansas, Lawrence, Kansas Received Auguat $0, 1961
In aqueous ion exchange experiments on exchangers such as Dowex 50, the total process has been found to include, in addition to equivalent exchange of ions, both water absorption and electrolyte adsorption by the solid exchan er. Although the quantity of water absorbed and the extent of electrolyte adsorption may be determined and correctei for, yet analysis of each of the equilibrium phases for both components provides the best data for the calculation of exchange equilibrium constants. The equilibrium system consists of a non-ideal liquid electrolyte solution and a non-ideal solid resin solution. Mean activity coefficients for the mixed electrolytes when available, may be combined with exchange data forethecalculation, through the Gibbs-Duhem equation, of both the equilibrium constant for the exchange process and the acti?ty coefficients of the resin com onents as functions of com osition. These activity coefficients, a t a fixed resin composition, should be inde endent of tge ionic strength of the e ibrium aqueous phase. The constancy of resin activity coefficients has been veriied for the Na-H exchange system a t g e e ionic strengths. The mean value of the e uilibrium constant for this system is 1.69. Similar calculations have been made for the Ag-H system a t 1 M ionic strength. %ere the resin activity coefficients are greater than unity, and the value of the equilibrium constant has been found to be 13.7.
Even though the mechanism, kinetics and equilibrium of many cation exchange systems have been studied,l-a and reports of applications of cation exchange in both industry3 and are exceedingly numerous, yet few investigations of exchange reactions have been carried out under (1) A. W. Davidson, W. J. Argersinger, Jr., R. W. Stoenner and W. K. Lowen, Teohnical Report to the O5ce of Naval Research, NR
057158, Feb., 1949. (2) E. P. Gregor, J . Am. C h m . Soc.. 73, 642 (1951). (3) F. C. Nachod, “Ion Exchange,” Academic Press Inc., New York, N. Y.. 1949. (4) R. E. Connick and 8. W. Mayer, J . Am. Chem. Soc., 78, 1176 (1951). (5) R. J. Myers. “Advances in Colloid Science,” Vol. I, Interacience Publishers Inc., New York, N. Y., 1942.
rigorously simple and reproducible conditions with the primary aim of det,ermining the true thermodynamic equilibrium constant for the process. A program of such investigations of exchange systems involving some of the more important uni- and bivalent cations was initiated in this Laboratory some time ago. In the course of the study a large amount of exchange data for fairly concentrated solutions has been obtained,’ the total process occurring in exchange has been to some degree clarified, and a start has been made toward the determination of activity coefficients (8) W. K. Lowen, R. W. Stoenner, W. J. Argerainger. Jr., A. W. Davidson and D. N. Hume, J . Am. Chem. 8oc., 73,2666 (1951).
Jan., 1952
ACTIVITYCOEFFICIENTS IN ION EXCHANGE EQUILIBBIA
in the exchanger phase, and from these the true equilibrium constant for the exchange process?S8 The initial research involved exchange of simple univalent cations on the phenolsulfonic acid-formaldehyde resin known as Dowex 30.9 It was soon established, however, that this exchanger is not entirely stable , especially toward oxidizing agents such as silver ion in acid solution. Consequently, all subsequent work has been done on Dowex 50,'O a sulfonated polystyrene polymer, which is stable even in concentrated acid or salt solutions and is not oxidized by silver ion or similar oxidants in these solutions. From considerations of practical utility, the measurements were made for the most part in solutions of unit ionic strength. In the first series of investigations, initial and equilibrium concentrations of both cations were determined, in accord with rather common practice, in the solution phase only; the equilibrium composition of the entire system was calculated from these data, together with the known initial number of equivalents of solid exchanger. It w&s observed, however, that in general the concentration increase of a cation in solution exceeded the concentration decrease of the other exchanging cation. The discrepancy was not due to decomposition of the resin, as had been the case with Dowex 30 as exchanger, but was later found to arise principally from absorption of water, or of solution, by the partially dried resin. In the simpler exchange systems the sole assumption of water absorption accounted for the change in ionic strength of the solution during exchange, and permitted the calculation of exchange equilibrium quotients, to be d e 5 ignated as K,. I n exchange reactions involving silver and thallous ions, however, the variation in ionic strength could not be so readily explained. The discrepancy between the concentration changes for the two ions was generally smaller than in exchanges involving hydrogen and alkali metal ions, and decreased, changing sign, with increased proportion of silver or of thallous ion in the solution. Adsorption of the silver or thallous ion on the resin was thus indicated. In these exchanges, then, a constant amount of water absorption wrts assumed, and the experimental concentration data were used to calculate the amount of adsorbed silver or thallous ion, the equilibrium composition of the solid exchanger, and the equilibrium quotient for the process. The equilibrium quotient, the proper quotient of ionic molalities in the solution and resin component mole fractions in the solid phase, was found not to be constant, but to vary reguIarly with equilibrium resin composition. The variation may be attributed to two sources: the non-ideal nature of the liquid electrolyte solution, and the non-ideal nature of the solid exchanger solution. The former is easily corrected for, a t least in principle, by the use of ordinary mean activity coefficients for the elec(7) W. J. Argersinger, Jr.. A. W. Davidson and 0. D. Bonner, Tranr. K a n a Acad. Sci., 63, 404 (1950). (8) A. W. Davidson, W. J. Argereinger. Jr.. W. I(. Lowen, R. W. Stoenner and 0. D. Bonner. Final Report to the O5ce of Naval Rssearch. NR 057158. Feb.. 1950. (9) W. C. Bauman. Ind. En#. Chem., 38, 46 (1946). (LO) W. C. Bauman and J. Eichorn, J . Am. Chem. am., $9, 2830 (1947).
93
trolytes in the solution. However, there are but few cases in which such coefficients are known for mixed electrolyte solutions, especially at ionic strengths as high as unity. Hence, by extension of the Lewis ionic strength principle, the appropriate ratio of mean activity coefficients of the exchanging electrolytes was assumed constant at constant ionic strength, and equal to the proper ratio of the coefficients of the separate electrolytes each in its own pure solution. This assumption naturally does not improve the results so far as constancy with respect to composition change is concerned, but the actual values, Ka, obtained for the equilibrium quotient by the application of this correction may be regarded as having greater validity than the uncorrected K m values. For solutions containing alkali metal ions and hydrogen ions, mean activity coefficients are known as functions of composition at constant total ionic strength, and these may be used to calculate improved values of the equilibrium quotients. The values so obtained are somewhat more nearly constant, but still exhibit a trend as the equilibrium composition of the system varies, which must be due to the variation from constancy of the proper ratio of activity coefficients of the components of the solid exchanger solution. In the first investigations, attempts were made to use empirical Margules expansions" for the resin activity coefficients, but with little success. The range of values of the equilibrium quotients K m and Kal and their values for equimolar final resin compositions, are given in Table I for each of a number of exchange reactions with Dowex 50 in solutions of approximately constant unit ionic strength a t 25'. In each case, the quotient applies to the reaction in which the first ion of the pair replaces the second in the resin. TABLE I EQUILIBRIUM QUOTIENTS IN EXCHANGE REA~IONS Exchange reaction Sodium-hydrogen Ammonium-hydrogen Silver-hydrogen Thalloun-hydrogen Thallouaammonium Nickel-hydrogen Calcium-hydrogen Calcium-nickel
Km
Ka
0.9- 1 . 6 1.4- 2.4 1.1- 2 . 2 2.2- 4.4 4.0- 6.2 13 -20 4.7- 6 . 0 21 -27 2.7- 3 . 9 5.1- 7 . 4 1.0- 6 . 0 4.0-24 5.5-17 24 -72 1.7- 3 . 5 1.8- 3 . 6
-
Km at Ka N = 0.5 N 1.33 1.56 5.4 5.3 3.3 3.0 9.5 2.4
at 0.5 2.25 3.15 18 24
6.3 12 42 2.5
In each case the experimental data give K , as a function of equilibrium resin composition. Some apparent hysteresis was observed in the last three systems, presumably primarily because of the uncertainties involved in the calculation of the resin composition solely from solution concentration measurements. The effect of the nature of the anion was found quite negligible, At the completion of this first series of investigations it was decided, in view of the uncertainty in calculation of resin composition, that a detailed study of simple systems should be undertaken in order to determine experimentally the several distinct factors involved in the usual exchange process. Of particular interest were the previously postulated water absorption and electrolyte adsorption effects which, with the solution composi(11) J. Rielland, J . SOC.Chem. Ind., 64, 232T (1935).
94
WILLIAM J. ARGERSINGER, JR., AND ARTHUR W. DAVID.SON
tion, establish the equilibrium composition of the resin phase. For the study of water absorption, the ammonium-hydrogen exchange on Dowex 50 a t 25’ in solutions of constant unit ionic strength was chosen. In all exchange experiments the initial pure resin had been dried, for convenience, to an arbitrary degree, and the previous results had indicated the occurrence of water absorption by such partially dried resins. Direct measurements of water uptake, by both the ammonium and the hydrogen forms of the resin, were made by complete dehydration of water-saturated samples. Each pure resin was found to have a characteristic reproducible total capacity for water. The capacity is independent of particle size, within limits, and independent also of the previous history of the resin with respect to either exchange or drying. The capacity of the mixed resins is ,a linear function of the composition on a mole fraction basis. Indirect calculations of water absorption from the change in total ionic strength of solution during exchange are generally in good agreement with these direct measurements. In the exchange reactions involving silver or thallous ions, it had been necessary to postulate electrolyte adsorption as well as water absorption in order to explain the observed changes in ionic strength during exchange. This effect was more carefully studied not only in the silver-hydrogen exchange, but also in the ammonium-hydrogen exchange; for it was now found to be more general than had been supposed (although much more pronounced in the silver system than in the ammonium system). The equilibrium resin in an exchange experiment was filtered off with suction, superficially dried by gentle pressing between filter papers, and then washed with pure water. The electrolyte removed from the resin by washing in this manner is termed (‘adsorbed electrolyte”; this arbitrary designation, although certainly not entirely correct, is neverthelem convenient from the experimental viewpoint. Such “adsorbed electrolyte” may indeed consist in part merely of adhering solution, but in most cases the results indicate in addition the presence of more firmly bound material. Since similar washing of the pure forms of the resin indicated no appreciable exchange under these conditions, the experimentally determined composition of the washed resin was taken as its equilibrium composition in the exchange reaction. In every case the h a 1 analysis of the washed resin corresponded to a total exchange capacity in agreement, within the small experimental error, with that of the initial resin. The washings froh the resin were analyzed for both cations involved in the exchange. The total amount of electrolyte adsorbed, and the ratio of the amounts of the two cations, both vary with the composition of the resin and that of the solution. Typical experimental results are shown in Table I1 for the silver-hydrogen exchange system. It should be noted that these data refer to adsorption by a mixed resin from a mixed solution; the concentration of silver ion in the solution increases from zero to 1 M as the mole fraction of silver resin increases from zero to unity.
Vol. 56
TABLE I1 ELECTROLYTE ADSORPTION IN SILVER-HYDROQEN SYSTEM AT UNIT IONIC STRENGTH Mole fraotion of
Ag resin at
equilibrium
0
0.177 .477 ,701 .815 .935 .981 1 .000
Equivalent of A g + adsorbed per equv. of resin
Equivalent of H + adaoTbed per eqmv. of resin
Total equivalent adsorbed per eqmv. of resin
....
0.0098
0.0098
.0116 .0147 .0219 .0275 .OB9 .0223
.0122 .0161 .0261 .0373 .0565 .o800 ,0909
0.0006 .0014 .0042
.ma .0276 .0577 .0909
....
Similar results were obtained for the ammoniumhydrogen system, but here the magnitude of adsorption, of the order of 0.030 equivalent of total electrolyte per equivalent of resin, is much more nearly constant. In view of the differences in nature between the two resin pairs, this difference was not unexpected. The problem of the direct determination of the magnitude of this postulated adsorption is complicated by the fact that in such experiments exchange must generally occur also. It is planned, however, to study the uptake of electrolyte from mixed solutions by resin mixtures carefully made up in each case to the appropriate equilibrium composition. In this way it is hoped that exchange will be avoided, or a t least drastically reduced, and that adsorption on such equilibrium resins may be directly determined. However, the measurement of adsorption of a single electrolyte by a particular resin of constant composition, over a range of concentration of the electrolyte in solution, seems to be unattainable, particularly if the ionic strength is to be maintained constant. A third factor which must be considered in determining the equilibrium resin composition from measured changes in solution concentrations, is the change in solution volume resulting from the exchange af electrolytes of different apparent molal volumes. In the silver-hydrogen exchange in nitrate solutions, since the densities of l M solutions of silver nitrate and nitric acid are nearly identical, this effect is negligible. I n the ammonium-hydrogen exchange in chloride solutions, however, the apparent molal volumes of the two electrolytes in 1 M solution differ by about 2%; so that in an exchange experiment in which considerable exchange occurs, there is observed an appreciable volume change, approximately proportional’to the extent of exchange. The results of these studies have thus shown that the total equilibrium composition of an exchange system is determined not only by the extent of simple ion exchange, but also by absorption of water by the exchanger, by adsorption of electrolyte by the exchanger, and by the variation in apparent molal volume of the solute during exchange. These three factors, which in general are neither negligible nor compensating, invalidate any attempt to calculate resin compositions directly from measurements of changes of solution concentrations alone. As a typical illustration, in one run in the ammoniumhydrogen investigation the equilibrium mole frac-
.-
ACTIVITY COEFFICIENTS IN ION EXCHANGE EQUILIBRIA
Jan., 1952
95
So long as the exchanger may be considered a tion of ammonium resin as calculated from the observed change in ammonium ion concentration in solid solution of the two forms of the resin, not only solution was 0.756, while the value calculated from the equilibrium constant for the exchange process, the observed change in hydrogen ion concentration but also the activity coefficients of the resin compowas 0.865. On t,he other hand, the value computed nents should be independent of the ionic strength from measured concentration changes and electro- of the aqueous medium. The constancy of activlyte adsorption, with corrections for volume changes ity coefficients has been tested with data for three due to water absorption and to the difference in ap- sets of exchange experiments in the sodium-hydroparent molal volumes of the solutes, was 0.850, and gen system with Dowex 50 a t 25", at constant ionic the experimentally obtained value, from direct strengths, respectively, of 1.0 M , 0.3 M and 0.1 M . analysis of the resin, was 0.849. While it is thus pos- The equilibrium composition of each phase was sible to calculate the equilibrium resin composition determined directly by analysis for both compofairly closely, it is scarcely more difficult, and prob- nents; thus explicit consideration of the compliably more accurate, always to determine the compo- cating factors previously discussed was unnecessary. sition experimentally. This has been done in all The experimentally determined values of the equilibrium quotient K , were converted to values of the our subsequent work. As has been mentioned, the equilibrium quotients apparent equilibrium constant Ka by the use of acdetermined from experimental exchange data vary tivity Coefficient data for sodium chloride-hydrowith the composition of the exchange system, be- chloric acid solutions from the literature.Ia The cause of the non-ideal nature of both liquid and values of K , and of fNa and f ~ the , activity coefsolid solutions. If the activity coefficients of the ficients of the resin components, are given in Table electrolytes in the aqueous solution are available 111. as functions of composition, however, it is possible TABLE I11 to calculate from the exchange data the true equili- EQUILIBRIUM CONSTANTS AND RESINAcrrvIiTY COEFFICIENTS brium constant and the activity coefficients of the IN SODIUM-HYDROGEN EXCHAXGE O N DOWEX 50 AT 25" resin components.'~l2 Ionic Rtrength = 1.0 M 0.8 M 0.1 M fraction For a simple univalent ion exchange we may de- Mole of Naresio /Nn fI! /N. fn S N ~ SII fine the equilibrium quotient K,,,, the apparent 0.879" 1.000 0.881" 1.OOO 0 . 0 0.865" 1.000 equilibrium constant K,, and the true equilibrium .850 1.OOO ,881 1.0oO .1 .867 0.999 constant K as . S i 9 1.000 ,881 1.OOO .2 .870 .999 A + + B Res B f + A Ros ,883 0.997 ,881 1.OOO .3 ,876 .9W In these expressions m represents molality in the aqueous solution, N mole fraction in the solid exchanger phase, y mean electrolyte activity coefficient (X is the anion in the solution), and f activity coefficient of resin component on a mole fraction basis, with pure resin as the standard state. The differential form of the logarithmic relation between K and K, may be combined with the Gibbs-Duhem equation at constant temperature and pressure for the solid solution phase
-
d I U ~ A d In fB = - d In K . NAd In fA NBd h fB = 0
+
These two differential expressions may readily be solved as simultaneous equations for d In f~ and d In f ~ .Integration with the boundary conditions f~ -+ 1 as NA+ 1 andjB -+ 1 as N B + 1 gives the results 111 K., d KA In fA = - N g 111 K, + InjB
= N A I n K.,
-
x4 lNA In K , d
x.4
Finally, substitution of these values in the init,ial logarithmic equation for the true equilibrium constant yields In K = In K, d AT*
"r
Since Ka is known as a function of resin composition, i.e., of NA,the values of In f ~In,.fB and In K may readily be obtained by graphical integration. (12) E. Htrgteldt, E. Ekedahl and L. G. RillBn, Acta Chem. Scund., 4, 556,828,829 (1950).
a
.4 .5 .6
.884
.i .8 .9 1.0
.933
.894
.909 .964 ,986 1.OOO
,992 .Y83 ,963 ,916 ,836
.520
,887
,883 0.999
.940
.995 ,984 .960 .91i
,066
,847
,989
,735 ,983 ,583" 1.OOO
.89Y ,917
,232" 1.OOO
,894
,912 ,936 ,961
.992 ,965 ,920
,848 ,745 .505"
Extrapolated values.
As is indicated by Table 111, the agreement among the values of the equilibrium constant for the three sets of experiments is reasonably good. Except a t the very ends of the composition range, where some extrapolation is required, the agreement among the values of the activity coefficient at any given composition is also satisfactory. The over-all correspondence seems to justify the treatment of the exchanger phase as a non-ideal solid solution, in which the variation of log f N a and log f~ with composition cannot be described by simplc one-term Margules expressions. It should he remarked that exchanges involving ions of higher valence may l x treated in an exactly analogous manner, if the equi\dent fraction in the resin phase, instead of the mole fraction, is used as independent variable for the integration.'^'^ The extension of the method to exchanges other than the sodium-hydrogen system requires a knowledge of solution activity coefficients. Of particular interest was the silver-hydrogen exchange; here, however, the requisite activity coefficient data (13) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New York, 1950.
96
WILLIAM J. AICBERSINGER, JR., AND ARTHURW. DAVIDSON
were not available in the literature. Since the evaluation of K , from the exchange data involves only the ratios of coefficients, rather than the individual values, a single set of measurements of the electromotive forces of appropriate cells will suffice to give the needed information. The use of the usual hydrogen gas electrode is prevented by ordinary chemical reaction between silver ion in acid solution and gaseous hydrogen; for this reason, as well as for experimental convenience, the glass electrode was chosen as a substitute. Cells were set up of the general type
TABLE IV SILVER-HYDROGEN EXCHANGE ON DOWEX 50 AT 25" Ionicstrength 1 M; K = a%L%@.!!
a4+aaR-
Mole fraction of A g resin
0.0 .1 .2 .3 .4
.5 .6 .7 .8
where a represents activity, m molality and y mean activity coefficient. In principle, experimental measurements of the electromotive forces of such cells as a function of total ionic strength of the mixed solution should permit the evaluation of the constant Eo by means of obvious extrapolation techniques.lg In practice, however, such evaluation is interfered with by the so-called "acid error" of the glass electrode; the quantity Eo varies slowly with acid strength of the solution." Hence, the glass electrodes were calibrated in hydrochloric acid solutions, and the Eo values so obtained were assumed to be valid for nitric acid solutions of the same acid strength. Although this assumption 'could not be tested by direct experiment, the error is believed to be slight. The ratio of the mean activity coefficients of nitric acid and silver nitrate was then determined as a function of solution composition from theexperimental electromotive force data for solutions of const,ant total ionic strengths of 1.0, 0.5,0.2 and 0.1 M. In each study the mole fraction of silver nitrate in the mixed solute wm varied from 5 to 95%. In the more concentrated solutions, the activity coefficient ratio is far from constant, changing by 44% over the range 5 to 95% silver nitrate. In the dilute solutions, however, the ratio is nearly constant, changing over the range mentioned by about 1% only. In all cases the rate of variation of the ratio is very much less ovcr the intermediate composition range than a t the ends of the scale; in other words, the ionic strength principle holds well under these conditions even at relatively high ionic strengths. Data for the silver-hydrogen exchange on Dowex 50 a t 25" were obtained for solutions of approximately constant total ionic strength of unity. The equilibrium resin composition waa determined from direct analysis of the washed resin by exhaustive exchange; the effluent solutions, as well aa the equilibrium solution samples, were analyzed by standard methods for hydrogen ion and silver ion. The exchange data were combined with the independently obtained solution activity coefficient data to calculate values of Ka, the apparent equilibrium constant, from which in turn the activity coefficients of the resin components and the true equilibrium constant were derived by graphical integration. The results are summarized in Table IV. (14) Af. Dole. "The Class Electrode," John R'iley and S o u , Inc.. New York, N. Y., 1941.
Vol. 56
.9 1.0 a Extrapolated values.
= 13.7at 25"
JA*
1.42" 1.35 1.29 1.24 1.19 1.16 1.12 1 .os 1.05 1.02 1 .oo
fE
1.00 1 .oo 1.01 1.02 1.05 1.07 1.12 1.18 1.29 1.53 3.05.
In contrast with the behavior of the sodium-hydrogen system, the activity coefficients of the resin components in the silver-hydrogen system are found to be greater than unity.I2 This difference may be due to the greater dissimilarity between the silver and hydrogen resins, as compared with the sodium and hydrogen resins. Similar experiments t o determine activity coefficient ratios and exchange data for the computation of exchange equilibrium constants are planned for other systems to which the present methods are applicable. These include, for example, exchange reactions involving mercurous, cadmium, zinc and thallous ions. In certain systems, the necessity for separate exchange solution analyses and activity coefficient ratio determinations may be obviated by the use of electromotive force measurements on the exchange solution itself, to give directly the a p propriate ratio of solution activities. Some work of this nature has been reported by Marshall and Gupta.I5 In addition to the obvious direct applications of equilibrium constant data of the sort here discussed to ordinary ion separations, a t least two other applications may be mentioned. Since each actual ion exchange process may be regarded as an ordinary chemical reaction, it is possible to calculate the equilibrium constant for a given exchange from those for two other independent processes which may be combined to give the exchange under consideration. Such "triangular" relationships have been tested for the ammonium-thallous-hydrogen and calcium-nickel-hydrogen systems, with fairly good results. Finally, if the resin activity coefficients are independent of solution ionic strength, and depend only on the composition of the solid phase, then it should be possible, once these coefficients have been determined for a given exchanger, to apply them in the determination of mean activity coefficients in mixed electrolyte solutions at any ionic strength of interest. However, since the liquid soIution contains three components, the GibbsDuhem equation for this solution contains a third term involving the activity of water; hence such a calculation would require additional information such as vapor pressure or freezing point data. (15) C. E. Afarsliall and R. 8. Gupta. J . Soe. Clrem.
(1933).
Id.. 62, 433
