THERMODYNAMIC PROPERTIES IN THE EXCHANQE OF SILVER WITH SODIUM IONS
2295
Thermodynamic Properties in the Exchange of Silver with Sodium Ions in Cross-Linked Polystyrene Sulfonate Cation Exchangers1
by F. Vaslow and G . E. Boyd Oak Ridge Natwnal Laboratory, Oak Ridge, Tennessee 57851
(Received FebTUaTy 9, 1966)
Standard free energy and enthalpy changes, AGO and AH", respectively, for the exchange reaction of silver ion in dilute aqueous solutions with sodium ion in a series of cross-linked polystyrenesulfonic acid type cation exchangers were estimated from equilibrium selectivity coefficient and heat of exchange measurements at 25". The standard entropy changes, AS", derived from AGO and AH", showed that the selective uptake of Ag+ ion was accompanied by an entropy increase. The AH" values were either small or zero except with the most highly cross-linked exchanger; the magnitude of the decrease in AGO therefore was governed by the magnitude of TAS". The unusual behavior of silver ion, in contrast with other singly charged cations where A G O is governed by the enthalpy decrease, was explained in terms of "site-binding" of Ag+ by the sulfonate groups of the exchanger. The strongly selective uptake of trace quantities of silver was attributed to a charge-transfer interaction of Ag+ ion with the benzene groups in the exchanger.
Silver ions in dilute aqueous solution are known to differ significantly from the alkali metal cations in their ion-exchange reactions with strong-acid type cation exchangers. Thus, the selective uptake of Ag+ in its exchange reactions with Na+ ion is appreciably larger than expected either on the basis of the ionic (crystal) radii or on the basis of the effective radii of the two hydrated ions which are nearly the same.2a The similarity of these two cations in aqueous solution is reflected also by their hydration entropies, which have been estimated as -15.8 and -14.5 eu for gaseous Ag+ and Na+, respectively.2b The free energies of hydration for the same ions are -106 and -91.5 kcal mole-', respectively, so that if ion-exchange selectivity is obtained because of more complete cation hydration3 in the dilute external solution than in the resin phase, sodium should have been the preferred ion. However, several types of measurements suggest that ion-water interactions by themselves do not determine the ionexchange behavior of Ag+ ion. (a) The small osmotic coefficients of very lightly cross-linked silver polystyrene sulfonate4relative to the coefficients for salts with other cations show that Ag+ ion interacts strongly with the sulfonate group. (b) The relatively large penetration (Donnan invasion) of the silver forms of cross-linked
cation exchangers by anions from an external aqueous solution5requires that Ag+ ion be extensively associated. (c) The electric conductivities6and self-diffusion coeffic i e n t ~for ~ singly charged ions in cross-linked sulfonic acid exchangers have shown that the mobility of silver is much less than that of sodium ion, whereas in aqueous solutions the situation is reversed, thus indicating strong binding of argentous ion in the exchanger. A distinctive feature in the behavior of silver ion compared with other singly charged cations is its strongly preferred uptake, especially by highly cross-linked sulfonic acid exchangers, when it is present in trace concentrations in aqueous solutions. The results of several ob-
(1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) (a) E. R. Nightingale, Jr., J. Phys. Chem., 63, 1381 (1959); (b) W. M. Lhtimer, J. Chem. Phys., 23,90 (1955). (3) D. C. Whitney and R. M. Diamond, Inorg. Chem., 2 , 1284 (1963). (4) B. A. Soldano and Q. V. Laran, J. Am. Chem. SOC.,7 7 , 1331 (1955). (5) J. F. Duncan, Proc. Roy. SOC.(London), A214, 344 (1952). (6) E.Heymann and I. J. O'Donnell, J. CoZZoid Sci., 4, 405 (1949). (7) G. E. Boyd and B. A. Soldano, J . Am. Chem. SOC.,7 5 , 6091 (1953).
Volume 70, Number 7 July 1966
F. VASLOW AND G. E. BOYD
2296
servers*-'' are in agreement on this effect, for which as yet no explanation has been given. The calorimetric and equilibrium selectivity coefficient measurements reported in this paper were undertaken to determine if information on the heat and entropy of the exchange of silver ion would aid in the elucidation of the nature of its binding by cation exchangers. The preferential uptake of the alkali metal cations has been found to be accompanied by the evolution of heat and by a decrease in e n t r ~ p y . ' ~ JThis ~ result has been interpretedI3 as indicating that the binding of these cations was nonspecific (ie., ion atmosphere binding) and that ion-pair formation (ie., site binding) in the sense that the cation and the anionic exchanger group possessed a definite structure involving one or more water molecules probably did not occur. During the course of our work, Redinha and Kitchenerl* published a calorimetric study on the silver-sodium and silver-hydrogen ion-exchange reaction in several cross-linked polystyrenesulfonic acid exchangers. However, their work on the former system was much less extensive than ours, and the interpretation given below differs in several respects.
Experimental Section The calorimeterwas the same as in our measurements15 of the heats of exchange of the halide ions in variously cross-linked strong-base anion exchangers, except for the temperature-sensing element which was changed from a 36-junction copper-constantan thermocouple to a pair of 2 W o h m thermistors connected to the opposite sides of a bridge circuit. A highly stable sensitivity of about 15pdegwas realized with the thermistors,which compares favorably with that observed with the multijunction thermocouple. The over-all reliability of the calorimeter system was checked by measurements of the heat of solution of NaCl(c) and of the heats of dilution of HC1 solutions of accurately known concentrations. Excellent agreement with literature values was obtained. Strong-acid cation exchangers of the Dowex-50 type (polystyrenesulfonic acid) nominally croposs linked with 1, 4, 8, 16, and 24% divinylbenzene (DVB) and with exchange capacities of 5.18, 5.24, 5.06, 4.73, and 4.64 mequiv/g of dry HR, respectively, were employed. Selectivity coefficients, DNa+Ag+J for the uptake of Ag+ by the sodium form of the exchangers were measured at 25" with aqueous NaN03-AgNOs mixtures at a constant ionic strength of 0.1 M . The distribution of silver ion between the exchanger and the equilibrium aqueous electrolyte mixture was measured with 270-day ll0Agand 15-hr 24Natracers. The variation of DNafAg+, with the equivalent fraction of the preferred Ag+ ion in the exchanger, Z A ~ + ,is shown in Figure 1. The Journal of Physdcal Chemistry
f00.0
%
.O
4%
A
A
Y
'*O
of,
2 ;
a 013
u
OL
1 ,
a a
1%
015
0
Oi6
;7
0:s 019
3
1.0
EQUIVALENT FRACTION, XAp+
Figure 1. Selectivity coefficients for the silver-sodium ion exchange at 25' with variously cross-linked Dowex-50. (Data for filled symbols taken from ref 9.)
Results and Discussion Certain general features of the dependence of the selectivity coefficients (Figure 1) and of the differential heats of exchange (Figure 2) on the cross linking and ionic composition of the cation exchangers may be noted. The selectivity coefficientsshowed a regular increase with cross linking and were nearly independent of the equivalent fraction of silver, X A +,~in the exchanger except for a marked increase in the uptake of Ag+ by the most highly cross-linked exchangers below X A ~ += 0.1 to 0.2. There were no selectivity coefficient cross-overs or inversions in contrast, for example, with the K+-Na+ and Cs+-Na+ ion-exchange systems16 and many others. The measurements on the 8% DVB exchanger were in (8) (a) E. Hogfeldt, E. Ekedahl, and L. G. Sillen, Acta Chem. Scdnd., 4, 1471 (1950); (b) E.Hogfeldt, ibid., 6, 610 (1952); (c) E. Hogfeldt, ibid., 7, 561 (1954). (9) G.E. Boyd, B. A. Soldano, and 0. D. Bonner, J. Phys. Chem., 58, 456 (1954). (10) G.E. Wilson, A. W. Davidson, and W. J. Argersinger, Jr., J. Am. Chem. Soc., 76,3824 (1954). (11) (a) 0.D.Bonner and V. Rhett, J. Phys. Chem., 57,254 (1963); (b) 0. D. Bonner and W. H. Payne, ibid., 58, 183 (1954); (c) 0.D. Bonner, {bid., 58, 318 (1954). (12) E. H. Cruickshank and P. Meares, Trans. Faraday SOC.,53, 1289 (1957). (13) G. E. Boyd, F. Vaslow, and S. Lindenbaum, J. Phy8. Chem., 68,590 (1964). (14) J. S. Redinha and J. A. Kitchener, Trans. Faraday SOC.,59, 575 (1963). (15) F. Vaslow and G . E. Boyd, J. Phy8. Chem., in press. (16) G . E. Myers and G . E. Boyd, ibid., 60, 521 (1956).
THERMODYNAMIC PROPERTIES IN THE EXCHANGE OF SILVER WITH SODIUM IONS
4 000
2297
were estimated by graphical integrations (Figure 2). Standard heats of cation exchange, AH", for the hypothetical reaction
h
NaR (a = 1, eq 0.1 N NaN03)
+
--+
A
AgN03 (as, a = 1) AgR (a = 1, eq 0.1 N AgN03) NaN03 (as, a = 1) nHzO (a, = 1)
+
were derived by correcting the integral heats by the difference in the relative apparent molal heat contents, &,, of the two 0.1 N aqueous solutions
AH" = AH -
A$L
A value of A+L = dL(NaN03) - h(AgN03) = 56 cal mole-' at 25" was estimated with data taken from a recent compilation. Standard free energies, AGO, were computed from the data in Figure 1 with the formula
- AGO
excellent agreement with previous determinationsgin the composition range 0.06 < X A g t < 0.95. The more extensive measurements made in this research for XA*+ < 0.06, however, revealed a nearly twofold increase in the selectivity coefficient as the amount of silver in the exchanger approached zero. The DNatAgtvalues for the nominal 16% DVB also are in good agreement with other on the same preparation. The relatively large selectivity coefficients exhibited by the nominal 1% DVB cross-linked preparation are consistent with the view that Ag+ ion is one of the most strongly bound of all the singly charged cations formed by the group I elements. The dependence of the heats of exchange (Figure 2) on cross linking and exchanger composition contrasts with the behavior of the equilibrium selectivity coefficients already noted. For high cross linking and small silver ion loadings, the reaction was strongly exothermic. However, over most of the composition range except for the nominal 24% DVB preparation it was weakly endothermic. In the nominal 1% DVB cross-linked preparation the exchange reaction was athermal within the experimental error. Integral heats of exchange, defined by
AH = L1@AH/Z)xag+)dxag+
=
L1
2.303RT
log DOdxAgt
where Do is the experimentally measured equilibrium selectivity coefficient corrected for aqueous electrolyte solution activity coefficients. The required values for this correction, -yk2(NaN03)/rk2(AgN03) , which did not exceed 3%, were derived for an ionic strength of p = 0.1 following Robinson and Stokes.'* Standard-state thermodynamic quantities for the exchange of Ag+ with Na+ ion in variously cross-linked polystyrene sulfonates are given in Table I. The data in the table show that the selective uptake of silver ion was governed by the entropy increase in its ion-exchange reaction. The standard heat was small and was either positive (ie., heat absorbed) or negative or zero, whereas AS" became progressively more positive with increasing exchanger cross linking. The heat and free energy measurements of Redinha and Kitchener14 on nominal 4.5 and 8% DVB cross-linked polystyrene sulfonates gave standard entropy increases of 1.8 and 2.6 eu, respectively. A value of 3.5 eu may be derived from their results with a 16% DVB exchanger. All of these values agree reasonably well with corresponding entries in Table I. Interestingly, the measurements by these authors also show that Ah'" for the silver-hydrogen ion exchange is much less positive than for the exchange with sodium ion and that the selective uptake of silver ion was determined by the enthalpy decrease. (17) V. B. Parker, "Thermal Properties of Aqueous Uni-univalent Electrolytes," National Standard Reference Data Series, National Bureau of Standards, NSRDS-NBS 2, Washington, D . C.,1965. (18) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth and Co. Ltd., London, 1955, p 440.
Volume 70,Number 7 July 1966
F. VASLOWAND G. E. BOYD
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Table I : Standard Free Energies, Heats, and Entropies of Exchange at 298.2' of Silver with Sodium Ion in Variously Cross-Linked Polystyrene Sulfonates Nominal CrOEE
-AGO,
-AHo,
AS',
linking, 7% DVB
koa1 mole-1
kea1 mole-'
cal deg-1 mole-1
1 4 8 16 24
0.30 0.56 0.83 1.23 1.47
0.00 -0.04 -0.11 0.12 0.34
1.0 2.0 3.1 3.7 3.8
Our results with the nominal 8% DVB exchanger (Table I) have been combined with the AGO, AH", and &So values reported earlier13on the same exchanger to give additional thermodynamic quantities for the exchange of Ag+ with H+, Li+, K+, and Cs+ ions (Table 11). These results show that the selective uptake of silver ion in exchange reactions with strongly hydrated cations (i.e., Li+, H+) is governed by the enthalpy decrease, while with weakly hydrated cations (ie., Cs+) the entropy increase is the determinant. The small, slightly negative AS" in the exchange of Ag+ for Li+ ion suggests that the partial dehydration of silver ion on entering the exchanger was compensated by the more complete hydration of lithium ion when the latter is displaced into the dilute aqueous electrolyte phase. In the exchange of Ag+ with Cs+ ion probably only a small, negative entropy change is associated with the displacement of the latter ion into the aqueous phase, so that most of the entropy increase (Table 11) can be assigned to the dehydration of Ag+ as it enters the exchanger and interacts with the sulfonate exchange groups. The net absorption of heat accompanying the silver-cesium ion exchange possibly mirrors the energy to dehydrate Ag+ ion, while the net heat evolution in the exchange with Li+ is a consequence of the relatively large energy release when the latter ion becomes fully hydrated.
Table I1 : Thermodynamic Quantities in the Exchange of Silver Ion with Other Singly Charged Cations in a Nominal 8% DVB Cross-Linked Polystyrene Sulfonate - AQO,
-AHo,
Exchange system
kea1 mole -1
koa1 mole -1
ASO, eu
Ag +-Li + Ag +-H + Ag +-Na + Ag +-K + Ag +-CS +
1.19 1.06 0.83 0.58 0.51
1.35 1.07 -0.11 -0.66
-0.5 0.1 3.1 4.1 4.6
The Journal of Physkal Chemistry
-0.88
The foregoing discussion emphasizes the role of ionsolvent interaction in ion-exchange selectivity, and this must be regarded as an oversimplification; other entropy and enthalpy changes such as those in the copolymer network of the exchanger, etc., undoubtedly contribute to the net observed AS" and AH". These other changes, however, are believed to be small compared with the ion-solvent contributions, and this may justify our interpretation. The interaction of silver ion with the sulfonate groups of the exchanger has appeared to be stabilized by the entropy increase caused by the release of water of hydration. It is possible, although not likely, that the sulfonate group may substitute for water in the primary coordination sphere of the highly stable A ~ ( H z O )ion.19 ~+ However, in its interaction with silver ion, the sulfonate ion may very well lose its water of hydration. Recent information on thermodynamic quantities for ion-pair formation by silver with sulfate ion in aqueous solutions is relevant. Hopkins and W~lff,~O in a calorimetric study of the equilibrium Ag+(aq)
+ S0d2-(aq) = AgS04-(aq)
have found AH" = 1.5 f 0.3 kcal mole-'. This result, when combined with the value for the association constant, pK = 1.3 determined by Righellato and Davies,Zl gives AS" = 11 eu. Additional ion pairs formed by silver for which thermodynamic information is available are Ag103(aq)22and AgC1;23their standard enthalpy and entropies of association are 5.14 f 4.54 kcal mole-' and 20.3 f 14.7 eu and -2.7 kcal mole-' and 6 eu, respectively. The association of silver ion in aqueous solutions therefore appears to be accompanied by an entropy increase and usually by the absorption of heat. The large selectivity for silver ion present in tracer concentrations observed in this and in other work with highly cross-linked exchangers does not appear to have been caused by an entropy increase but, rather, by a marked lowering of the enthalpy. This behavior can be explained if silver ion forms a charge-transfer complex with the benzene rings of the ion exchanger. There is spectroscopic evidence for silver ion complex formation (19) The possibility that the silver species in the exchanger was Agla+ rather than Ag+ ion is considered unlikely in view of the report by D . N. Waters and L. A. Woodward, J. Chem. Soc., 3250 (1954), that no Raman effect assignable t o the double argentous ion was observed even in concentrated (8.4 M ) aqueous solutions of &NO& (20) H. P. Hopkins, Jr., and C. A. Wulff, J . Phus. Chem., 69, 9 (1965). (21) E. C. Righellato and C. W. Davies, Trans. Faraday Soc., 26, 592 (1930). (22) J. J. Reinier and D. S. Martin, Jr., J. Am. Chem. Soc., 7 8 , 1833 (1956). (23) J. H. Jonte and D. S. Martin, Jr., ibid., 74, 2052 (1952).
TERNARY LABELED ALANINE-ALANINE-WATER SYSTEMS
with polystyrene in alcoholic solutions.24 The chargetransfer energy for each of two benzene-silver bonds formed in the silver perchlorate-benzene complex has been estimated as ca. 16 kcal mole-' of silver ion.2s While this Ordinarily does not form in the presence Of water, when the benzene rings and Ag+ ions are con-
2299
strained to favorable configurations as might occur in highly cross-linked exchangers, the formation of such charge - transfer complexes is conceivable. (24) D. F.Evans, J . Chem. Phys., 24,1244 (1956). (25) H.G. Smith and R. E. Rundle, J . Am, Chem. SOC.,80, 5075 (1958).
Measurements of the Intradiffusion Coefficients' at 25" of the Ternary Systems (Labeled L-ct-Alanine)-(DL-ct-Alanine)-water and (Labeled @-Alanine)-( pAlanine)-Water
by J. G. Albright2 DiffusionResearch Unit, Research School of Physical Scklaees, Auatralian NatWnaE University, Canberra, Australia, and the Institute for EnResearch. University of Wisconsin, Madkon, Wisconsin 63706 (Received January $1, 1966)
Intradiffusion coefficientshave been measured at 25" for the systems (labeled ca-alanine)(Dca-alanine)-water and (labeled Balanine)-(P-alanine)-water over concentration ranges of 0.0-1.5 and 0.0-5.0 moles/l., respectively. The four diffusion coefficients for these ternary systems are calculated at a series of concentrations from the intradiffusion coefficients obtained in this study and some previously reported data for the mutual-diffusion coefficients. The results show that at higher concentrations in the system with &alanine the cross-term diffusion coefficients may be an appreciable fraction of the main-term diffusion Coefficients. Thermodynamic transport coefficients related to solute-solute interaction and to solvent-solute interaction have been calculated and discussed.
Introduction In recent years interest has developed in the study of isothermal diffusion in three-component systems. It is hoped that such studies will help yield a better understanding of the complex transport phenomena which occur in biological systems as well as improve the understanding of diffusion in industrial processes. A system composed of a solvent containing two solutes which are chemically equivalent but isotopically different constitutes a three-component system of particular interest. In this case the four diffusion coefficients, which are necessary to describe a three-com-
ponent system, may be calculated in a simple manner from the values of the intradiffusion coefficients and mutual-diff usion coefficients for the system.a Data (1) The term intradiffusion was introduced and explicitly defined in ref 3. IntraMusion coefficients are equal to tracer-diffusion coefficients for the systems described here where the unlabeled solute is chemically equivalent to the labeled solute. (2) The experimental work reported in this article was performed by the author while visiting the laboratory of Dr. R. Mills at the ANU during the tenure of the NIH Postdoctoral Fellowship No. 4-F2GM-19,747-02. Subsequent tceatment of the data was performed at the author's present addreas, Institute for Enzyme Research, and supported in part by Public Health Service Research Grant AM06177 from the Institute of Arthritis and Metabolic Diseases.
Volume 70, Number 7 July 1966
