J. Phys. Chem. 1982, 86, 135-139
by the formation of this shell. Accordingly, the Si4++" stituted shell has catalytic properties very much different from those of pure magnetite. The phenomenon of H20induced migration of silica and the catalytic properties of this Si4+-substitutedshell will be a d d r e d in parts 315and 416 of this series, respectively.
135
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. In addition, we acknowledge the support of the National Science Foundation through research grant ENG-7911130.
Nonaqueous Ion Exchange. 4. Application of Gupta's Equation for Mixed-Solvent Ion Exchange to Some Unl-Univalent Exchanges in Methanol-Water Mixtures John W. Taylort and Howard A. Strobel' Paul M. Qos chemlcel Laboratory, Lbpartmnt of Chembby, Duke UniversHy, Durham, North Carolina 27706 (Recsived: June 29, 1981; In Final F m : September 21, 1981)
The thermodynamic analysis by Gupta [ J . Phys. Chem., 75,1152 (1971)l of mixed-solvent ion exchange has been successfully applied to some uni-univalent ion exchanges at 30 "C in methanol-water mixtures across the solvent composition range. These systems comprised two cation exchanges, Na+/H+ and Na+/Li+,with Dowex 50 X8 and one anion exchange, I-/Cl-, with Dowex 1X8. Selectivity coefficient data are reported for the I-/Cl- exchange as well as solvent uptake from methanol-water mixtures for pure iodide and chloride forms of the resin. In the cation-exchange systems selectivity trends were found to be determined mainly by salt and medium effect activity coefficient ratios in the external solution phase. By contrast, it was found that resin phase activity coefficients contributed significantly to the selectivity trend in the I-/C1- exchange.
Introduction Attention to the role of solvent in ion exchange is yielding insights that help to provide a better description of the overall phen~menon.'-~ Further, shifting from ion exchange in a single solvent, usually water, to exchange in mixed solvents such aqueous-organic systems often effecta dramatic and useful enhancement in sele~tivity.*~ Early theory for ion exchange dealt mainly with singlesolvent When such theory was extended to interpret exchange in mixed solvents, new attention had to be given to the exchange of solvent components between phases as well as to medium effect activities. It is the purpose of this paper to apply the rigorous thermodynamic treatment of mixed-solvent ion exchange developed by Gupta'O to some uni-univalent exchanges in methanol-water mixtures. Insofar as the authors are aware, this presentation will offer its first application over solvent composition ranges in which selectivity changes distinctively. Systems exhibiting different trends with solvent composition will be used: a cation exchange showing a selectivity maximum, Na+/H+, and another showing a monotonic trend, Na+/Li+, and an anion exchange showing a selectivity minimum, I-/Cl-. Earlier, Gupta applied his theory to the Na+/H+, Li+/H+, and K+/H+exchanges up to 80 mol % methanol" and in pure methanol,12in effect passing over the region of selectivity maximum a t about 80 mol %.13 As will be shown, the theory does fit each trend succeasfuuy and provides insight into the factors contributing to the trend. It will be helpful to trace briefly the development of theory in mixed-solvent ion exchange. In an extensive series of M+/H+ exchanges in methanol-water, ethanolwater, and methanol-ethanol mixtures over the entire solvent composition ranges, Fessler and Strobel13found 7U.S. Food and Drug Adminstration, Rockville, MD 20857. 0022-365418212086-0 135$0 1.2510
selectivity maxima in most systems. They interpreted results on the basis of a simplified Gibbs-Donnan approa~h.~J~ Subsequently, Gupta15offered a semiempirical theory for mixed-solvent exchange based on the model developed by Gaines and Thomas.l6 He focused attention basically on the activity of a single-solvent component, water. He was soon challenged by Starobinets and co-workers, who propo_aedadding to his equation a medium effect activity ratio fOH+/fOM+ for the resinate ions, thus including the effect of the organic solvent." They buttressed the presentation by applying their equation successfullyto the Na+/H+ exchange in MeOH-H20 mixtures for which they had determined selectivity and solvent up-take data up to 70 mol % methanol. Resourcefully, they approximated (1)D. Reichenberg in "Ion Exchange",J. A. Marinsky, Ed., Marcel Dekker, New York, 1966,Vol. 1, p 235. (2)R. M. Diamond and D. C. Whitney in "Ion Exchange",J. A. Marinsky, Ed., Marcel Dekker, New York, 1966,Vol. l. (3) Y. Marcus in "Ion Exchange and Solvent Extraction",J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, 1973,Vol. 4,pp 46-75. (4)G. Wiegner and H. Jenny, Kolloid Z., 42,268 (1927). (5)G. J. Moody and J. D. R. Thomas, Analyst, 93,557 (1968). (6)H.P.Gregor, J. Am. Chem. Soc., 73,642 (1951). (7)E. Glueckauf,h o c . R. SOC.London, Ser. A , 214, 207 (1952). (8)G. E. Boyd and B. A. Soldano, 2.Elektrochen., 57, 162 (1953). (9)L. W. Holm, Ark. Kemi, 10,151,445,461(1956). (10)A. R. Gupta, J . Phys. Chem., 76, 1152 (1971). (11)D. Nandan,A. R. Gupta, and J. Shankar,Indian J. Chem., 10,285 (1972). (12)D. Nandan and A. R. Gupta, J. Phys. Chem., 79, 180 (1975). (13)R. G.Fessler and H. A. Strobel, J. Phys. Chem., 67,2562(1963). (14)F. G. Donnan, 2.Phys. Chem., 168A,369 (1934). (15)A. R. Gupta, J. Phys. Chem., 69,341 (1965). (16)G. L. Gaines, Jr., and H. C. Thomas, J. Chem. Phys., 21, 714 (1953). (17)G. L. Starobmeta, L. V. Novitakaya, L. 1. Sevost'yanova,Russ. J. Phys. Chem., 42,575 (1968).
0 1982 American Chemical Society
136
The Journal of Physical Chemistty, Vol. 86, No. 1, 1982
the resin medium effect activity coefficient ratio by the ratio for the counterions at the solvent composition existing in the resin phase. Gupta'O then developed the rigorous theory being applied in this paper. Simultaneously, Starobinets and coworkers18presented exchange and solvent uptake data for additional uni-univalent cation exchanges in MeOH-H,O up through 90 mol % methanol. They secured quite satisfactory agreement between experimental selectivities and those predicted by their modified version17 of Gupta's semiempirical treatment.15 Still more recently, El-Prince and Babcocklg returned to Gaines and Thomas16 and developed a more direct integration procedure for dealing with solvent. They acknowledged Gupta's treatmentlo but suggested that an adequate theory of binary solvent ion exchange required a second solvent term in the Gibbs-Duhem equation. On the basis of a preliminary analysis we believe Gupta's final equation is equivalent to that of El-Prince and Babcock. For the present study, cation-exchange data have been taken from Fessler and Strobel13(selectivitieswith Dowex 50 X8 cation exchange resin at 0.1 m external concentration and 30 "C) and Clappm (solvent uptake values of pure cation resinate forms). In addition, selectivity data were determined for the Cl-/I- exchange between Dowex 1X8 anion-exchange resins and 0.1 m external solutions in methanol-water mixtures and for solvent uptake of chloride and iodide forms of the resin at 30 "C. Experimental Section Materials. Reagent grade methanol was dried by standard procedure.21 Deionized water was used. Reagent grade NH4Cl and NH41were used without additional purification. These salts were dried at 110 "C before use. Dowex 1 X8 anion-exchange resin in the chloride form was conditioned by washing successively with 1 M NaOH deionized water, methanol, deionized water, and sufficient 1M HC1 to reconvert it to chloride form. The resin was cycled three times. It was dried at 50 "C for 3 days and then screened with ASTM 40 and 100 mesh sieves. The iodide form of resin was prepared from the chloride by columnar techniques using 1 M NaI solutions. Equilibration and Analysis. Solvent uptake was measured by a difference determination technique. It appeared to give results experimentally undistinguishable from the earlier vacuum distillation procedure.22 A batch of 2 g of resin pre-swollen in water at 30 "C and centrifuged to constant weight22and 3 g of methanol-water mixture prepared by weight from analytical grade solvents were weighed into an equilibration tube which was then sealed. Samples were tumbled for at least 48 h in a 30 f 0.1 "C air bath. Samples that had lost no more than 5 mg of weight during equilibration were opened for analysis. The external solution was analyzed for water by Carl Fischer titration. The resin was quantitatively transferred to a centrifuge tube specially constructed from a 20-mL plastic syringe. A small hypodermic syringe served as a "wash bottle" in the transfer. After centrifugation to constant weight the resin was again transferred quantitatively to a tared weight bottle and its weight was established.
(18) G. L. Starobinets, A. B. Chizhevskaya, L. I. Sevost'yanov, Russ. J . Phys. Chem., 45, 1767 (1971). (19) A. M. El-Prince and K. L. Babcock, J . PhYs. C h e w 79, 1550 i l OVCI
(IUI",.
(20) W. L. Clapp, M.A. Thesis, Duke University, 1966. (21) R. W. Gable and H. A. Strobel, J. Phys. Chem., 60, 513 (1956). (22) K. A. Boni and H. A. Strobel, 2. Phys. Chem. (Frankfurt am Main), 87, 169 (1973).
Taylor and Strobel
TABLE I : The Selectivity Coefficient kIlCl in Methanol-Water Mixtures at 30 "C .~ - XMeOH [I-l/m [Cl-llm XI -_______ 1.00 0.0069 0.094 0.50 0.10 0.0078 0.091 0.50 0.30 0.0118 0.091 0.50 0.51 0.0137 0.085 0.51 0.71 0.0123 0.085 0.51 0.80 0.0112 0.087 0.51 0.91 0.0085 0.089 0.49 0.99, 0.0080 0.089 0.50
hiC1
13.8 11.7 7.5 6.4 7.2 8.0
10.0 11.1
The calculation of solvent uptake could be carried out straightforwardly with these data since the initial resin sample was either vacuum dried or equilibrated to constant weight with water or methanol. In the latter type, the solvent content was known from a vacuum distillation determination on a representative sample. Note that both initial and equilibrium weighta of external and internal resin phases were known and the equilibrium composition of the external solution had been determined. Resin capacities were determined by displacement of the ion present with an appropriate electrolyte by standard pro~edures.'~Values found were RC1,4.02 mequiv g-', RI, 2.92 mequiv 8'. For selectivity coefficient determinations each sample was made up with 30 g of solvent, 3 mequiv of the preswollen resin (in water, usually), and sufficient NH4Cl and NHJ to give a 0.1 m external solution phase. Weights of resin forms used were those estimated to give at equilibrium a resin ion fraction of 0.5. To overcome a tendency toward formation of triiodide ion, iodide salt was added to the system last and rapidly dissolved. In this way a local excess of iodide was avoided and no characteristic triiodide color developed. Sample tubes were wrapped with aluminum foil to keep out light. After sealing, samples were tumbled for a minimum of 24 h at 30 f 0.1 "C. Both external solution and resin phases were analyzed. The external phase solvent composition was found by Karl Fischer titration. Total external electrolyte was determined by potentiometric titration of a 10-mL aliquot with standard silver nitrate to the chloride end point. The concentration of iodide was then found by a periodate oxidation technique.23 The sixfold enhancement in sensitivity this method provides was desirable since iodide concentration ranged as low as 0.005 m. The overall reaction was shown to be quantitative in methanolic media by running standards. By monitoring the external electrolyte concentration at equilibrium (note in Table I it averages 0.1 f 0.01 m as expected) it is estimated that invasion electrolyte was at most 3% of the exchange electrolyte. To complete the analysis the resin was transferred to a short column equipped with a fritted glass disk, rinsed under suction with deionized water to remove excess external electrolyte, and then eluted with 1M sodium nitrate until a negative silver nitrate test was obtained. The collected effluent was potentiometrically titrated with standard silver nitrate and first derivative end points for chloride and iodide were observed. The ion fraction could then be calculated. Results and Discussion Selectivity and Solvent Uptake Data. In Table I values of the selectivity coefficient kI c1are listed as a function of methanol mole fraction in external Dhase. ~h~~~ values at 0.5 ion fraction of resin are considered reliable
tie
(23) P. W. Jensen and A. L. Crittenden, Anal. Chen., 26,1373 (1954).
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
Nonaqueous Ion Exchange
J
-i
12-
1
-
n
137
phase ion i are defined with respect to infinite dilution in the solvent used, and aiRand f i R for the resinate species iR are defined with reference to the swollen pure resin form in equilibrium with an infinitely dilute solution of the corresponding salt in that solvent.27 Further, kBIAis the selectivity coefficient or concentration equilibrium constant for the exchange. In his approach to mixed-solvent ion exchange, Gupta'O began with the Gibbs-Duhem relationship and modeled his treatment closely after that of Gaines and Thomas.16 He showed that the equilibrium constant in any particular solvent, s, may be written as
RT In KBA(s) = p 0 m ( s ) - p0BR(s) + p0B+(s) - p0A+(s) (2) where poi is the standard chemical potential for species i in solvent s. A similar equation can be stated in water. By combining these expressions with the standard definition of the free energy of transfer for the species i, AGto(i) = p?(s) - p?(w) = RT In f?,he obtained for the selectivity in solvent s relative to that in water
+
log KAB(s)= log KAB(w) AGt"(AR) - AGt"(BR) + AG,"(B+) - AGto(A+) (3) 2.303RT Flgure 1. The swelllng moles of water and methanol per equivalent of chloride and Iodide resins in methanol-water mixtures vs. external solvent composition X w : (0)A,, chloride form; (A) , ,A chloride , ,A IodMe form. form; (W) A,, IodMe form; (A)
to &4%. In addition, they are believed to reflect integral selectivities for the I-/Cl- exchange in methanol-water mixtures since selectivities in methanol-water are found to vary approximately linearly with ion Other data important in characterizing the exchange are solvent uptake of iodide and chloride forms of Dowex 1 X8; these are graphed as a function of mole fraction of water in Figure 1. Values interpolated from the curves are believed reliable to f4%. The RC1 uptake values are in good agreement with measurements by Kim, Born, and Lagally%for the same resin form. It is believed that any alteration as a result of electrolyte invasion under the conditions of the selectivity determination is within experimental error. As is evident from Figure 1, more water is taken up by both RC1 and RI resins than methanol and more of both solvents by RC1 than RI. These solvation differences are interpretable in terms of the greater polarity of water (at 25 OC, CH0 = 78.5, C M ~ = H 32; p ~ =p1.85 D; p ~ = 1.66 a ~ D) and the greater charge density of chloride ion (crystallographic radii are rcl- = 0.181 nm and rI-= 0.217 nm). Marcus and Naveh have discussed these and other factors affecting solvation of anion-exchange resins a t some length.26 Theory. For a representative cation-exchange reaction between an ion-exchange medium R and external solution in a particular solvent, AR B+ BR + A+, the thermodynamic equilibrium constant is defined as
+
-
where activity ai and activity coefficient f i of the external
To evaluate the free energies of transfer for ions in the external phase it is only necessary to recall that AGto for an electrolyte, say AC1, is the sum of the cationic and anionic contributions. Thus AGto(BC1)- AGto(AC1) is an unambiguous measure of AG," (B+) - AGto (A+). Gupta then evaluates the term for the difference free energies of transfer of the resinate ions. In order to do this each dry monoionic resin form is chosen as a reference state. The free energy of resin swelling is then regarded as the sum of two stages: (1) each dry resin form sorbs water at a, = 1, taking up n,moles of water per equivalent; (2) then organic solvent is gradually added maintaining equilibrium until state (ad,a3 is reached. The final result, adapted to the Na+/H+ exchange, may be seen subsequently as eq 4. Application of Gupta's Theory. The thermodynamic equilibrium constant KAB, or an approximation thereof, must of course be evaluated in mixed solvents and water to apply Gupta's theory, as well as terms on the right-hand side of eq 4. Choice of the resin standard states as given abovel6J7leads to formulation of log KABin any solvent in terms of kaBIA,the selectivity coefficient corrected for activity effects in the external phase (see below) as log KAB = log kaBIAaA, where the integration adjusts k$lA for loading of the resin, i.e., for variation of resin phase activity coefficients with resin ion fraction. Fortunately, an alternative procedure is often available. In many cases plots of In k*B/A.vs. f~are reasonably linear and the integral may be a p p r o m t e d by the value of h kaBIAat 0.5 ion fraction of resin.lJ3J8 Further, correction of the selectivity coefficient kBIAto kaglAmay be made by use of the simple ratio of mean activity coefficients at low concentration (50.1 m); i.e., mixed electrolyte effects on activity may be neglected. Thus, log KAB = 1% (kB/A)O.B - 2 1% f & A X / f & B X Gupta identifies log KBA(s)as log Kmk;in his terms log kBIAbecomes log k-. Using this simplication in his find equation, eq 15,'O making the approximations just indi-
~~~
(24)J. W.Taylor, PbD. Dissertation, Duke University, 1978. (25)J. I. Kim, H.-J. Bom, H. Lagally, J. Znorg. Nucl. Chem., 37,1259 (1975). (26)Y . Marcus and J. Naveh, J. Phys. Chem., 73,591 (1969).
(27)(a) E.Ekedahl, E. Hogfeldt, L. G . Sillen, Acta Chem. Scand., 4, 556,829,1471(1950); (b)W.J. Argersinger, A. W. Davidson, and 0. D. Bonner, Trans. Kans. Acad. Sci., 53, 404 (1950).
138
The Journal of Physical Chemistry, Vol. 86, No. 1, 7982
Taylor and Strobel
TABLE 11: Calculated and Experimental Selectivity Coefficients for Cation Exchanges in MeOH-H,O Mixtures at 30 " C ...
.
A. Na+/H+Exchangea ~-
.___
fl%
2 log -
fEE1
XhleOH
~
~
log kmix calcd exptlC
2 log-f"HC1 foNaC1
0.040 0.096 0.193 0.322 0.407 0.481
0.1 0.3 0.5 0.7 0.8 0.9
..~-
-0.36 -0.98 -1.50 -1.86 -1.84 --1.61
_____I__
ciMeOH
XJ'H,O
itotal
Eb
-0.12 -0.37 -0.62 -0.85 - 0.97 -1.08
0.06 0.19 0.37 0.61 0.71 1.08
- 0.06 -0.18 -0.25 - 0.24 -0.16 0.00
0.50 1.06 1.49 1.72 1.61 1.31
..~_
~.
___
0.44 0.88 1.24 1.48 1.45 1.31
0.36 0.71 1.01 1.25 1.31 1.15
0.42 0.43 0.51 0.71 1.03 1.12 1.205
0.35 0.45 0.54 0.70 0.88 0.97 1.02
B. Na+/Li+Exchange"
0.1 0.2 0.3 0.5 0.7 0.8 0.9
-0.004 0.009 0.009 0.017 0.026 0.034 0.042
-0.206 - 0.262 -0.384 -0.624 -0.940 -0.996 - 1.100
- 0.04 -0.10 -0.15 -0.27 -0.37 -0.42 -0.48
0.01 0.04 0.05 0.13 0.25 0.34 0.39
0.45 0.49 0.61 0.85 1.15 1.20 1.31
-0.03 -0.06 -0.10 -0.14 -0.12 - 0.08 -0.09
Columns represent terms from eq 4. Note ''i" subscripts have been omitted from activity ratios t o simplify notation. Integrals below refer t o designated combination of integrals evaluated on basis of solvent uptake data of Clapp." E= E = log k , - 2 log 2 log f 3 $ I C l / f o N a C 1 . Data from Fessler and Strobel;13log k , = 0.18. log k , - 2 log 2 log f o L i C l / f NaC1. e Data from Fessler and Strobel;13log k , = 0.24.
fzg/
fg&/ffa&-
fra$l-
TABLE 111: Calculated and Experimental Selectivity Coefficients for the I-/Cl- Exchange in MeOH-H,O at 30 O log f"c1 ~
XMeOH
..- - ____
.-
_____
0.1 0.2 0.3 0.5 0.7 0.8 0.9 a
f"1
0.062 0.163 0.254 0.349 0.420 0.460 0.540
____
2: JMeOH
clH,O
J'total
Eb
-0.46 -0.81 -0.97 -1.18 -1.35 - 1.46 -1.58
+ 0.26
- 0.20
+1.41 t 1.66 t 1.90
-0.34 -0.32 -0.17 t 0.06 + 0.20 + 0.48
1.08 0.98 0.89 0.79 0.72 0.68 0.60
+ 0.47 + 0.65 + 1.01
See eq 4 for pairs of integrals and entire set of integrals combined.
cated, and adapting the equation to the Na+/H+ exchange in MeOH-H,O, gives eq 4, where (kmix)0,5 and (k,)o.5 are 1%
____-
(kmix)0.5
= log
(kw)0.5
- log @kI/f&!l)
-
concentration selectivity coefficients at a given solvent composition and in water, respectively, at a resinate ion fraction of 0.5, f i - is the salt effect activity coefficient of species i referred to infinite dilution in mixed solvent, ii, and ii, are moles of methanol and water per equivalent of resin sorbed by a particular resinate form at a given solvent composition, and a[ is the activity of species i at equilibrium. Note that the term (log kw)o.5 includes Gupta's first solvent sorption step from dry resin to resin fully swollen with water. For each of the other exchanges appropriate modifications were made to eq 4. Values of mean salt effect activity coefficients and medium effect activity coefficients f " H a were obtained from Oiwa,28the corresponding values for NaCl and LiCl from Akerlof,B and for HI from Bates.% (28)I. T.Oiwa, Sci. Rept. Tohoku Uniu., First Ser., 41, 129 (1957).
E = log k , - log
calcd
c a
log kmix exptlC
_ _ _ _ _ . _ _ _ _ ~ _ _
0.88 0.64 0.57 0.62 0.78 0.88 0.95 f"cl/f"I.
1.05 0.97 0.85 0.79 0.79 0.86 0.95
Log k , = 1.14.
Solvent activity data were obtained from Butler.31 In applying eq 4 the integrals involving water were evaluated graphically by constructing plots of A, vs. log a, using the solvent uptake data of Clapp.20 The data of Clapp agree within experimental error with those of Starobinets and ceworkersls and those of Nandan, Gupta, and Shankar.32 A cut-and-weigh procedure was used to determine area. Integrals involving rtMeOH were evaluated in similar fashion except that extrapolation to a M a H = 0 (log aMeOH = -m) was avoided by extrapolating iiMeOH vs. log U M ~ O Hto values of TtMeOH = 0 in the manner of Gupta.'O Results are presented in Tables I1 and 111. Agreement between experimental and calculated values of log kmixas shown in the tables is very reasonable considering the extrapolations involved. For the Na+/H+ system, the largest differences (0.2 in log k,) occur above 0.5 mole fraction methanol but for the Na+/Li+ and I-/Clexchanges agreement is best in this region. Gupta and co-workers reported a similar degree of agreement." A second observation is that Gupta's theory correctly predicts the selectivity trends and locations of extrema: (29)R.G.Bates in "Hydrogen-BondedSolvent Systems",A. K. Covington and P. Jones, Ed., Taylor and Francis, London, 1968,p 61. (30)G . Akerlof, J.Am. Chem. Soc. 52, 2353 (1930). (31)J. A. V. Butler, D. W. Thomson, and W. H. Maclennan, J.Chem. Soc., 674 (1933). (32)D. Nandan, A. R. G u p t a , and J . Shankar,Indian J. Chem., 10, 83 (1972).
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
Nonaqueous Ion Exchange
a fairly sharp Na+/H+ selectivity maximum in the 70-80 mol % methanol range, a much broader I-/Cl- selectivity minimum in the middle composition range, and a selectivity rising monotonically with increasing methanol content in the Na+/Li+ exchange. What can be surmised about the relative contribution of different terms to the selectivity? The value of eq 4 is that it allows this assessment to be made. For the two cation exchanges it is clear from Table I1 that external phase activity coefficient ratio changes are the dominant influence. Column E, which reports the value of log k, corrected for these activity changes, reliably identifies the maximum for the Na+/H+ exchange and the monotonic increase in the Na+/Li+ exchange. The contribution of the resin phase may be seen from Table I1 to be quite modest. Combining the pair of integrals relating to methanol gives a consistently negative value. Note that this result must follow since the methanol activity is approximately equal to its mole fraction and NaR resin sorbs fewer moles of methanol at a given composition than HR. By contrast the pair of integrals involving water (HR also sorbs more moles of water than NaR) is always positive. As is evident from Table 11for the Na+/H+ system the s u m of integral terms is significant and negative in sign, while for the Na+/Li+system the s u m is relatively insignificant (swelling differences are comparatively small for metallic resinate forms). I t should be observed again that even though the contribution of the resinate terms is significant for the Na+/H+ system, the selectivity trend is predicted successfully by use of external phase activity coefficients alone. Before assessing contributions to the I-/Cl- exchange selectivity, it should be noted that the calculation of the resin terms in Table I11 are based on data obtained in this work. Values of the log f"I/f"cl term were calculated from AGt0 data for corresponding hydrohalic acids.%" Finally, while necessary data for the salt effect external phase term, 2 log ~ N HI / ~ N H , C ~ were , not found, it is expected that this term will be small since it is known from conductivity studies33that ion pairing for both anions is small even at 1 M concentrations. It is of interest now to assess the contribution of the various terms to the magnitude of the anionic selectivity ~
~
139
coefficient. From Table 111,it appears that both phases contribute significantly. In any event, it may be seen from column E that "correction" of log k, for the external phase medium effect activity coefficient ratio results only in a value that decreases monotonically with rising mole fraction of methanol. In this case, then, it is the addition of this term to integral terms reflecting the contribution of the resinate ion medium effect that gives rise to the selectivity minimum.
Conclusion Gupta's treatment, then, seems to describe at least semiquantitatively observed trends in ion-exchange selectivity in the different uni-univalent exchange systems examined in methanol-water mixtures. Some uncertainty results from the graphical extrapolations required in its use and somewhat more is generated by neglect of the effect of mixed electrolyte in the exterior solution. The importance of this theory is that it allows a fuller assessment of contributions of resin phase factors to selectivity. In terms of wide application, Gupta's equation can be used for prediction when medium effect activity coefficients for the ions involved and solvent uptake curves for resinate forms are known. Salt effect activity coefficients for the external solution will usually also be required. Such data are in short supply. Free energy of transfer data, from which medium effect activity coefficients may be calculated, are regretably available for only a modest number of electrolytes in few solvent systems though the volume of such data is increasing. A possible help with respect to solvent uptake data is that while such data are timeconsuming to obtain experimentally, in some aqueousorganic systems uptake curves have been found to conform to an empirical expression of the type26p34 log (fiw/%)
= p 1% (X,/X,) - k
(0.2 > X,> 0.8)
where r ~and , ii, are moles of water and organic solvent per resin equivalent, X, and X, are external phase mole fractions of water and organic solvent, and p and 12 are empirical constants. I t may therefore be possible to approximate some solvent uptake curves by measuring relatively few experimental points.
~~~~
(33) R. L. Kay, J. Am. Chem. SOC.,82,2099 (1960); J. L. Hayes and R. L. Kay, J. Phys. Chem., 69, 2420, 2787 (1965).
(34)
H.Ruckert and 0.Samuelson, Acta Chem. Scand., 11,303 (1957).
