Relationship between Solvation as Expressed by the Walden Product and Cation Exchange Selectivity in Water-Dimethylsulfoxide Robert Smits, Pierre Van den Winkel, and D. L. Massart Pharmaceutical Institute, Vrije Uniwrsiteit Brussel, Paardenstraat, 67, B-I640 Sint Genesius Rode, Belgium Jean Juillard and J. P. Morel Laboratoire d’e‘tude des interactions solutes-solvants-Groupe France
de Chimie Physique, Unicersite de Clermont, B.P. 45, 63-Aubi&re,
The importance of solvation in establishing the selectivity of a strongly acidic cation exchanger is investigated in a mixed solvent. The systems used are Rb+/H + and MgZ+/H+ in dimethylsulfoxide (DMSO)water. The variations of the weight distribution coefficient, KD, and the difference of the Walden products, 6(Aotlo), of the exchanging ions as a function of the DMSO content are compared. The correlation between the KD and the s(Aoq0) curves is excellent up to a DMSO concentration of 70%. It is concluded that solvation determines the selectivity in solvents that consist mainly of water but not in a solvent that consists mainly of DMSO.
IN WATER, the order of selectivity of strongly acidic cation exchangers for a series of metal ions such as the alkali metals is the same as the order of the Stokes radii. This suggests the importance of solvation as a factor determining the selectivity of these ion exchangers. Several authors (1-8) have implicitly or explicitly incorporated solvation as a parameter in ion exchange selectivity theories. The selectivity usually increases when one uses mixed aqueous organic solvents. Therefore, these media are important for analytical ion exchange (for example: 9-13) and a better understanding of the reasons for their higher selectivity is necessary. In this communication we study the relationship between solvation and selectivity in an aqueous organic binary. Several fundamental studies concerning cation exchange in mixed solvents have already been carried out. Fessler (14), among other authors, came to the conclusion that there is a relationship between dielectric constant and selectivity in aqueous alcoholic media. This led several authors such as
Sakaki (25) to try to explain selectivity in binary solvents in terms of bulk dielectric constants. Such theories are too simplified as was established by several authors. Fessler (7) recognized the importance of relative activity coefficients, relating water to mixed solvents, to explain the change in selectivity when an organic solvent is added to water. Ohtaki and Kakihana (16) obtained an equation containing hydration numbers and molar volumes. A qualitative agreement was obtained between experimental and calculated values. The quantitative failure is probably due to the fact that it is difficult to define unambiguously a quantity such as a hydration number. Pauley (27) tried to explain qualitatively the observed variations in selectivity by the occurrence of simultaneous variations in the Coulombic attraction forces between functional group ion and counterion and in the solvation of ions. We limited our study of the correlation between solvation and selectivity to the water-rich zone, because characteristic minima, maxima, and inflection points are observed in this zone for a number of physicochemical quantities related to solvation. This is due to the non-monotonous evolution of the solvent structure in this range. The Belgian team having experience with chromatography in dimethylsulfoxide (DMSO)-water media (28) and the French team having carried out physicochemical (19, 20) studies in the same mixtures, water-DMSO was chosen for this study. Distribution coefficients of Rb+ and MgZ+ in DMSOwater were determined. To explain the observed variations in selectivity for the exchanges Rb+/H+ and Mg*+/H+, we correlated these changes with changes in the Walden products, h o q u , for the ions in the same media. The variations of the Walden product that occur when the solvent changes, are classically attributed to variations in certain aspects of the solvation of the ions.
(1) G. Eisenman, “Membrane Transport and Metabolism,” A.
Kleinzeller and A. Kotyk, Ed., Academic Press, New York, N.Y., 1961, p 163. (2) G. Eisenman, Biophys. J . Suppl., 2 (2), 259 (1962). (3) G. N. Ling, “A Physical Theory of the Living State,” Blaisdell, New York, N.Y., 1962. (4) J. Pauley, J . Amer. Client. Soc., 76, 1422 (1954). ( 5 ) A. Ghodstinat, J. L. Pauley, Teh-Hsuen Chen, and M. Quirk, J . PIiys. Chem., 70, 521 (1966). (6) R. M. Diamond and D. C. Whitney in “Ion Exchange,” Vol. 1, J. A. Marinsky, Ed., Marcel Dekker, New York, N.Y., 1966. (7) R. G. Fessler and H. A. Strobel. J . Phys. Chem., 67,2562 (1963). (8) D. Reichenberg in “Ion Exchange,” Vol. 1, J. A. Marinsky, Ed., Marcel Dekker, New York, N.Y., 1966. (9) J. Korkisch and S . S. Ahluwalia, Tularzru, 14, 155 (1967). (10) J. Korkisch! F. Feik, and S. S. Ahluwalia, ibid., p 1069. (11) J. Korkisch and E. Klakl, ibid., 16, 377 (1969). (12) F. W. E. Strelow and C. Baxter, ibid., p 1145. (13) F. W. E. Strelow, C. R. Van Zyl, and C. J. C. Bothma, Anal. Cliim. Acra, 45, 81 (1969). (14) R. G . Fessler, Ph.D. thesis, Duke University, Durham, N.C., 1958.
EXPERIMENTAL
Ion Exchange. RESIN. Dowex 50 W-X8, 200400 mesh, hydrogen form resin was used throughout the experiments. Before use, the resin was allowed to swell, was purified, washed, dried, and stored in a vacuum desiccator over PzOS. REAGENTS.The DMSO was spectrograde. All other reagents were reagent grade. @Rb, obtained from S.C.K. Mol (Belgium) was used to prepare a Rb-stock solution with a specific activity of 100.000-200.000 counts per minute and per ml. (15) T. Sakaki, Bull. Cliem. Soc. Jup., 28,217 (1955). (16) H. Ohtaki and H. Kakihana, ibid., 40,2536 (1967). (17) J. L. Pauley, D. D. Vietti, C. C. Ou-Yang, D. A. Wood, and R. D. Sherrill, ANAL.CHFM.,41, 2047 (1969). (18) R. Smits, K. Larsen, and D. L. Massart, J . Cliromatogr., 59, 237 (1971). (19) J. P. Morel, Bull. Soc. Cliim. F r . , 1968, 896. (20) Zbid., 1967, 1405.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
339
Table I. X
zwlw
A0
and hOyOof RbCl and MgClz in Water-DMSO Ao?o(W1. cm2.mole-'. A 0 ( C1. an2.mole-') poise) RbCl MgC1z RbCl MgC1z
0
259.2 210.2 167.0 131.4 101 .o 76.4 58.6 50.2 49.7 58.0
153.6 125.3 101.1 79.6 62.4 47.7 37.2 30.9 28.8
10 20 30 40 50
60 70 80
90 100
1 368 1.393 1.414 1.401 1.401 1.367 1.288 1.164 0.988 ~
2.308 2.337 2.336 2.313 2.267 2.189 2.029 1.888 1.702 1.545
0.690
34.55
F. Calmes-Perrault and Y . Doucet, C.R. Acad. Sei., Ser. C, 271 (14), 780 (1970).
distribution coefficient was calculated from the elution curve using Equation 2
100
20
IO
30
40
50
60
70
80
.
90
/.*OHSO
Figure 1. Comparison of differences in Walden product and log KO as a function of the weight per cent dimethylsulfoxide For Rb,
6Aoqo =
Aoqo(RbC1) - Aoqo (HCI), for Mg, 6,ioqo
=
112
A'qo(MgC12) - Aoao(HCI)
Procedure. The absorption by the resin is expressed as weight distribution coefficients, KD, defined by Equation 1 amount of element per gram dry resin KD = amount of element per ml solution (1) - activity per gram dry resin activity per ml solution They were determined by batch and column methods. In batch experiments, exactly-weighed 1.OOO-gram samples of the dry, pretreated resin were equilibrated with 1 ml of the metal stock solution (containing 0.33 mequiv of the metal ion) and 25 ml of a solvent mixture consisting of lOO-O% of hydrochloric acid 1-12M and 0-100% of the appropriate organic solvent. The mixture was then mechanically shaken 0.2 O C until equilibrium was reached. a t 25.0 Mg*+ was determined by automatic colorimetric titration. The resin was filtered off and 5 ml of the solution was pipetted into a titration vessel, evaporated to dryness, and titrated with EDTA using Eriochrome Black T as indicator, a t a wavelength of 665 nm. For the determination of R b , 2 ml of the solution were counted on a NaI crystal. The results were corrected for solvent uptake by the resin using the mean value (0.6 ml) as determined by Janauer (21). In column experiments, a column was packed with 1.0000 g of the dry resin. After conditioning, 500 p1 of a mixture containing 2 mg of Mgz+was adsorbed on top of the resin and eluted a t a flow-rate of 0.2-0.3 mlimin. The effluent was collected in fractions, which were titrated with EDTA. The
*
(21) G. E. Janauer, ~MI'Ic~ocIII'IM. Acta, 6, 11 11 (1968). 340
where p = specific volume of the ion exchange resin, i = void fraction of the column, V = geometrical column volume, and Vmsx = volume required to elute the maximum of the peak, corrected for dead volume. Conductometry. The conductance measurements were performed using a Tacussel CMO2 cell in combination with a Beckman R C 18A conductivity bridge. The electrode cell was placed in a double envelope glass vessel, the temperature of which was maintained a t 25.00 f 0.01 "C. This vessel was large enough to reduce side effects and Parker dielectric losses to a negligible level. In this way, a determination of the resistance with an accuracy better than 0.1 was possible. T o an exactly weighed amount of solvent, successive volumes of stock solution of the salt under investigation were added with a microburet under constant stirring. The stock solution of RbCl was prepared by weighing the dry salt. The MgC12 stock was obtained by dilution of a concentrated aqueous solution, the concentration of which was determined by a Fajans titration. Aqueous solutions of KC1 were used for determination of the cell constant. A O data were obtained from the conductometry results for RbCl solutions by using the Fuoss-Onsager Equation 3 A = ,io- S.\/,
+ Ec log c + Jc
(3) With the following procedure, a first approximation of -10 was obtained by graphic extrapolation to c = 0 of the plot repThis yields values of S and E which are resenting A us. &. only functions of .io, the viscosity, and the dielectric constant of the bulk solution. Knowing S and E, the value of A' equal to A' = A
+ S&
- Ec log c
+ Jc
= .io
(4)
is calculated for each value of c. -10 and J are evaluated by a least square treatment of the data [A' us. c]. By iterative calculation, substituting -4'I in Equation 3, a quick convergence for the A 0 was obtained. For MgC12, the lack of a convenient equation for 2-1 electrolytes, led us to use the Onsager limiting law. Thus, values for this salt given in Table I were obtained from linear The concentration range involved extrapolation of d us. mole 1.-l. was between 1 and 5 X
4,.
RESULTS AND DISCUSSION
In Table I, the experimentally determined values of the limiting equivalent conductivity, .io,of RbCl and MgC12 are
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
given as a function of the weight per cent, X,of DMSO in the mixture. The values of Aovo were obtained using the viscosity interpolated from the data of Cowie and Toporowski (22) and Sears, Jurch, and Sands (23). These values are in agreement with .i0(MgCl2) = 258.8 for X = 0 as determined by Shedlovsky and Brown (24) and AO(RbC1) = 153.67 for X = 0 as determined by Kunze and Fuoss (25). As stated in the experimental part, we have measured distribution coefficients, K,, instead of selectivity constants, K H A . For the exchange A+ + H+
+
K~
+
=
[=]/A+
and
where [-] designates concentrations in the resin phase. We preferred the measure of KO instead of K H Afor several reasons. The external concentration [H+] is kept constant. On the other hand, the resin is for a very large part (>93 %) in the H+ form and the swelling of the resin varies only slightly over the range of solvents considered ( p maximum: 2.42, minimum: 2.32), so that [PIcan be assumed constant. Therefore, KD is proportional to K H Aand the experimenally easier measurement of KD is preferred. More important is that the measurement of K D instead of K H A becomes necessary, if one wants to avoid interference from the combined ion exchange solvent extraction effect (CIESE effect), described by Korkisch (26). This author has shown that differences can exist in the composition of the external and internal solvent phases so that a liquid/liquid extraction effect can be superimposed on the ion exchange. Janauer (27) has shown that, if one uses a resin in the HT-form and limits the exchange to a small fraction of the capacity, no CIESE effect occurs in DMSO-water. In this case one cannot obtain accurate selectivity values because one has to determine very small changes of [F] The .measurement of K D does not suffer from this difficulty. Figure 1 represents the KD-values of Rb- and Mg2+. Two zones are observed: X < 40% and X > 40%. Case 1. X < 40%: K D goes through a minimum. The same phenomenon has for example been observed for the K D of Rb'/H" in water-dimethylformamide and water-isopropanol (28). By comparison of the results obtained by Samuelson (29) in water and by Janauer (21) in water-DMSO mixtures, the existence of this minimum is confirmed for Mg2-. Results obtained by the same authors, show that it exists for Ca*+ but not for Ba2+or Sr2+. The presence of this minimum is independent of the concentration of the acid as shown in Figure 2 . The minimum is also independent of the anion, present in the external phase: the curves for Mg2+ in water-DMSO-HCI, water-DMSOHNOJ, and water-DMSO-HC104 are nearly identical (18). (22) J. M. G. Cowie and P. M. Toporowski, Can. J. Chem., 39,2240 (1961). (23) P. G. Sears, G. R. Jurch, and D. E. Sands, T r a ~ sKentucky . Acad. Sci., 28, 10 (1967). (24) T. Shedlovsky and A. Brown, J. Amer. Cliem. SOL.,56, 1066 (1934). (25) R. W. Kunze and R. M. Fuoss, J . Phys. Cliem., 67,914 (1963). (26) J. Korkisch, Separ. Sci.. 1, 159 (1966). (27) G. E. Janauer. H. E. Van Wart, and J. T. Carrano, ANAL. CHEW.42, 215 (1970). (28) R. Smits, unpublished results, 1972. (29) 0. Samuelson. "Ion Exchange Separations in Analytical Chemistry," Wiles, New York, N. Y . , 1963, p 306.
3.16 N HCL
1
3.95 H HCl
0
10
20
30
40
50
60
70
%S
Figure 2. Distribution coefficient of Rb as a function of the composition of the external phase (% S = weight per cent dimethylsulfoxide) Therefore, one can exclude the possibilities of complex formation and almost certainly also of the formation of ion pairs in the external phase. It is difficult to situate the minimum exactly because experimental errors of the order of 1-2% cannot be avoided in this sort of measurement. Anyhow, it is clear that the minimum observed coincides approximately with the faint maximum observed in the Walden product (Table I). The mean Stokes radius of a solvated salt being inversely proportional to AOq0, it seems that a correlation exists between this radius and KD, so that a minimum in KO corresponds to a minimum in solvation. In fact, K, involves an exchange of two ions. Therefore, it is suitable to compare KD with the difference of the Walden products, S ( A 0 v " ) of both ions. This has been done in Figure 1 . This procedure has the additional advantage of eliminating the influence of the anion. One observes that in the X < 40% region, the KO and S(Ao,o) curves are very similar. Case 2. X > 40%: KD increases monotonously until a composition X = 70% is reached and then decreases. This maximum was also found by Janauer (21) for Mg2+, C a 2 + , Sr2+, and Bat+. This author remarked that the maximum is situated at a composition where many other physicochemical parameters go through either a minimurn or a maximum or show the largest deviation from ideal behavior. The most significant are the viscosity (22) and the heat of mixing (30). This composition corresponds approximately to 2 moles H 2 0 :1 mole DMSO, and therefore one has concluded that privileged complexes of the form 2 H 2 0 . , 1 DMSO exist. (30) J. Kenttamaa and J. J. Lindberg, Acra Chern. Sra/?d.B; 33, 98
(1960).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
341
The ~ ( L ~ O V O curve ) increases also until X = 70% is reached and then remains nearly constant. To explain these findings one must take into account that the distribution coefficient, K,, depends on the chemical potentials of the ions in the two phases, i.e. on the solvation in the resin and in the external phase. Resin Phase. The interactions with the active sites of the resin should not remain identical when one changes the solvent, since ion-ion interactions depend on the local dielectric constant of the solvent and on the solvation. It is, however, not possible to reach a conclusion about the variations in the resin because the solvent structure in the resin is probably not the same as in a normal solvent phase. Diamond and Whitney ( 6 ) developed a “competitive solvation” theory in which they present a number of reasons that for strong cation exchangers these interactions should be less important than interactions in the external phase. If one accepts their conclusions, this means that one has to try and explain the variations of KD in mixed solvents exclusively by changes in the external phase. External Solvent Phase. The classical continuous medium theories predict that A070 must be a constant. Variations that do occur, are classically attributed to variations of the structure of the medium resulting in variations in solvation. It should be noted here that the exact significance of variations of A O ~ is O not completely understood. In classical hydrodynamic theories, ions were treated like rigid spheres moving in a continuum. More recent and sophisticated treatments, which take into account the reorientation of the solvent dipoles in the field of ions were carried out by Boyd and Zwanzig (31). In the relations obtained, static and high frequency dielectric permittivities as well as relaxation time of the solvent appear. Such relations were shown to explain reasonably well experimental results in aprotic media (32) but not in water-rich media (33). In particular they cannot predict the existence of a A O ? O maximum in this region in water-alcohol mixtures (33) and even in water-dioxane mixtures (34). Anyway, even if more sophisticated theories would be relevant in such mixtures, these theories would make use of parameters related to solvent properties and structure and consequently to the solvation ability. Therefore, in the state of our knowledge, we think that it is still worthwhile to (31) R. Zwanzig, J. Chem. Phys., 52, 3625 (1970). (32) R. Fernandez-Prini and G. Atkinson, J . Phys. Chem., 75, 239 ( 1971). (33) J. Juillard, J. P. Morel. and L. Avedikian, J . Chim. Phys., 69, 787 (1972). (34) R. L. Kay and T. L. Broadwater, Electrochim. Acta, 16, 667 ( 1972).
342
consider the Walden product as a quantity significant for ion solvation, As discussed before, the correlation between the S(AO~,) curves and the KD-curves is excellent up to 70% organic solvent content. This suggests that solvation in the external phase is the more important selectivity-determining factor for exchanges between strongly acidic cation exchangers and mixed solvents. Diamond and Whitney (6) state in their “competitive solvation” theory that the two most important factors which determine the selectivity of cation exchangers are solvation in the external phase and the structure of the external phase, in this order. Our findings corroborate their conclusions. However, since solvation and structure of the solvation medium are completely interdependent phenomena, it is in our opinion preferable to make no distinction between them. The correlation between ~(AOVO) and K Dbreaks down above 70% DMSO. In the authors’ opinion, the most probable explanation is that the medium up to 7 0 z DMSO (ix., mole fraction of water 165%) can be thought to consist preponderantly of water in which a number of the water molecules have been replaced by DMSO molecules. At high DMSO concentrations, the solvent consists on the other hand predominantly of free DMSO and DMSO-water associates. This means that one has to distinguish two differently structured phases: water-rich media and DMSO media. Since Diamond and Whitney’s arguments to explain the interactions in the resin of lesser importance depend largely on the existence of a highly structured and strongly solvating phase, the conclusion that the external phase determines the selectivity is not necessarily true in a solvent other than water. In such a solvent, it is very well possible that solvation is no longer the factor which determines the selectivity; more precisely, it is our opinion that the Walden product is not the best way to account for it. The chemical potentials of the ions in the external phase probably allow a thermodynamically more rigorous explanation of the variations in selectivity and can be used over the whole range of hydro-organic mixtures (35). ACKNOWLEDGMENT
The Belgian authors thank the Fonds voor kollektief en fundamenteel onderzoek for financial assistance and Miss A. D e Schrijver for technical assistance.
RECEIVED for review June 5 , 1972. Accepted October 13, 1972. (35) Preliminary and unpublished results.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
