Cation Exchange Selectivity in Aqueous-Organic Solvent Mixtures, and Solvation in the External Phase Robert Smits and Desiri! L. Massart* Pharmaceutical Institute, Vrde Universiteit Brussel, Paardenstraat 67, 6- 1640 Sint-Genesius-Rode, Belgium
Jean Juillard and Jean-Pierre, Morel Laboratoire d'Etude des Interactions Solutes-Solvants, Groupe de Chimie Physique, Universite de Clermont, Les Cezeaux, BP 45, F-63 170, France
The Importance of solvation in the external phase in establishing the selectivity of a strongly acidic cation exchanger is investigated in a large number of mixed water-organic solvent systems. The exchange behavior of Dowex 50W-X8 200-400 mesh resins is investigated for the systems Rbf/ H+, Na+/H+, Ag+/H+ and LI+/H+, The relationship between selectivity coefficients Ri!$ and transfer free energy factors fi(M+ H') Is studied. An excellent correlation between both quantities is found for crystalline zirconium phosphate, indicating that the selectivity of an ion exchanger can indeed be predicted from variations of Glbbs free energies of transfer. The agreement is not so good for organic sulfonic cation exchangers. This can be explained by effects In the resin phase. A simple model is presented, permitting estimation of the variations with organic solvent content of the chemical potentlais in the resin phase, knowing the quantities of organic solvent absorbed. These considerations lead to a simple model which allows a nearly quantitative explanation of the selectivity behavior of cation exchangers in mixed solvents.
mean that a rigorous relation exists between the transport and thermodynamical properties of the ions in solution. Assuming that the properties of the internal (resin) phase are not influenced by the addition of organic solvent, an elementary thermodynamic treatment shows that a simple relationship exists between changes of the standard free energy of exchange for the exchanged cations, and the changes in chemical potentials of the ions in solution (8). The general equation for the thermodynamic equilibrium constant of an uni-univalent cation exchange reaction (A+ B+ F! B+ A+) can be written as
The study of ion exchange in solvents other than pure water started about 25 years ago. Systematic investigations ever since demonstrated the interesting properties of aqueous-organic solvent mixtures for the separation of metal ions. Considerable effort has been given to quantitatively explaining ion exchange equilibria in mixed solvents. A rigorous theoretical thermodynamic treatment of the selectivity behavior in these media is very difficult. Such formal thermodynamic approaches have been developed through the efforts of a number of authors (1-4).In contrast with these rather elaborated theories, which mostly require several parameters very difficult to obtain experimentally, the present study was undertaken with the thought of being able eventually to predict qualitatively and semi-quantitatively selectivities of cation exchange resins. I t is general knowledge among ion exchange researchers interested in physicochemical aspects that there exists a causal relationship between the selectivity exhibited by an ion exchange resin, and solvation in the external (nonresin) phase. However, as recognized by some authors (5, 6) and also by ourselves (7, 8), the influence of solvation in the external phase has to be of paramount importance in establishing the selectivity behavior of cation exchangers. In a first attempt (7), we tried to correlate variations of the affinity of a strongly acidic cation exchanger with variations of the Walden product ( A O ~ O ) of the exchanging ions as a function of the organic solvent content. The systems used were Rb+/H+ and Mg2+/H+ in dimethylsulfoxide (DMSO)-water. However, this should be regarded more as a correlation than as a causal relationship. The latter would
RT In K , = (pug+ - p i + ) + ( p i + - &+)
-
458
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
+
+
K, =
dB+ * aA+ ~
dA+ * a B +
(1)
the bars indicating the exchanger phase. The chemical potentials of the ions in both phases can be defined by pi = 1 :
+ RT In ai
(2)
The standard chemical potential p! is thereby defined in the classical way as the hypothetical state where, a t unit concentration, the ionic activity coefficient approaches unity. The thermodynamic equilibrium constant can be expressed (€?) by an equation of the type (3)
bars again indicating the exchanger phase. When going from an aqueous solution to a solution in another solvent mixture, Equation 3 yields
RT S6 In K , = S 6 ( p t +- p i + ) - s6(&+ - p i + )
(4)
The notation s6 A stands for the variation of A when going from water to solvent S, i.e. A = SA - "A
(5)
w referring to water and s to the solvent mixture S. It has been shown previously (8) as a first approximation that, when using the rudimentary assumption that the properties of the internal phase are not influenced by the addition of organic solvent (Le. s6(&+ - p i + ) = 0), the variation of the thermodynamic equilibrium constant is due only to the change of standard chemical potentials of the exchanged ions in solution. Equation 4 can then be written as
RT
In K , = sG(p;+
-pi+)
(6)
Introducing the transfer (free energy) factor gt, an undimensioned quantity (8) s6pB AG$) g J i ) = -(7) RT In 10 RT In 10 where AG,8(i) represents the standard Gibbs free energy of transfer of ion i when going from water to solvent S. Equation 6 can be written in the form
SG(l0g K,) =
-A&,
amount of element (activity) per gram dry resin (10) amount of element (activity) per ml solution was calculated. This distribution coefficient was then corrected by taking into account the absorption of solvent by the resin, yielding a new weight distribution coefficient K D (corr). Use was made of the mean value (0.6 ml) as determined by Janauer ( 1 5 ) . Knowing both volumes and densities of the added water, organic solvent, mineral acid, and metal stock solutions, the weight percent of organic solvent and the total weight of solvent present in each batch experiment was evaluated. Finally, from these data, a selectivity coefficient KE: was computed, defined by
(8)
K D=
where
6Mt = gt(A+) - g t ( B + )
(9)
The quantities 6&, c a n be obtained from solubility, vapor pressure or s t a n d a r d electrode potential measurements. In o r d e r to be able to d e t e r m i n e b o t h t h e validity and the limits of s u c h a t r e a t m e n t , extensive m e a s u r e m e n t s of Gibbs free energies of transfer for different ion-pairs i n different water-organic solvent m i x t u r e s were carried out. T h e res u l t s h a v e been presented elsewhere (9-13). The p r e s e n t p a p e r r e p o r t s the results for the exchange behavior of sulfonic cation exchange resins i n the same hydroorganic mixt u r e s , a n d s t u d i e s the relationship between both types of measurements.
KE: - !M+.
cH+ C H + CM+
(11)
where E and c stand for concentrations in the resin and solution phase, both expressed as mequiv/g dry resin and mequiv/g solvent, respectively. Values of K D , K D (corr), and KE: were drawn as a function of the weight percent X of organic solvent, and values a t 0, 5 , 10, . . . , 85% weight interpolated. Corresponding values of the volume fraction of the organic co-solvent 42 in the mixture were calculated as previously described (IO) a t each of these solvent compositions, assuming that the presence of metal salt and mineral acid does not alter the volume fraction of the organic co-solvent. Some of the above mentioned experiments were repeated using a slightly different procedure. A stock solution of the appropriate metal ion (chloride form) was prepared. Exactly weighed amounts of pure organic solvent were transferred into a previously weighed measuring flask. Then 5 ml metal stock solution and x ml hydrochloric acid were added, and the mixture was diluted to the mark. Weight percent of organic solvent was calculated, and 25 ml of the solvent mixtures (again containing 0.33 mequiv metal ion) were equilibrated with 1.0000-g amounts of the dry, pretreated resin. Both procedures yielded approximately the same results, indicating that errors due to volume contraction were negligible. Distribution coefficient measurements of Li+ in water-organic solvent mixtures were carried out using the last mentioned procedure. Lic was determined by flame spectrometry using an Eppendorf flame photometer.
EXPERIMENTAL Materials. Dowex 50W-X8 of 200-400 mesh was used. Before use, the resin was allowed to swell, it was washed several times with 3-4 M HC1, water, and water-organic solvent mixture, dried a t 60 "C, and then stored in a vacuum desiccator over P205. The capacity of the hydrogen resin was determined in the usual way (14)by acid-base titration and was found to be 5.23 mequiv/g dry resin. Chemicals and solvents were all reagent grade, except for acetonitrile, dimethylsulfoxide, sulfolane, and dimethylformamide which were spectrograde, and were used without further purification. s6Rb, 22Na (chloride form), and lloAg (nitrate form) obtained from SCK Mol (Belgium) were used to prepare stock solutions with a specific activity of about 150 000 counts per minute and per ml. Procedure, In all Rb+, Na+, and Ag+ batch experiments, exactly weighed 1.0000-g samples of the dry, pretreated resin were equilibrated with 1.00 ml of the appropriate metal stock solution (containing 0.33 mequiv/ml of the metal ion), x ml water, y ml organic solvent, and z ml of concentrated hydrochloric acid, where x y z = 25 ml (nitric acid was used instead for all Ag+ batch experiments). The mixture was mechanically shaken a t 25.0 f 0.2 OC until equilibrium was reached. Then 2.00-ml aliquots of the solution were removed and y-counted. Samples of solutions prepared in the same way as described above (but without adding any resin) were also counted to give the initial tracer activity. All calculations were carried out using a Fortran computer program. After correction for background activity, the weight distribution coefficient, KD, defined by Equation 10
+ +
RESULTS The ion exchange absorption o n Dowex SOW-X8 resin ( H + f o r m ) f r o m aqueous-HC1 (or HNOs)-organic solvent mixtures was s t u d i e d for Rb+, Na+, Li+, and Ag+ ions. Alt h o u g h the numerical value of the t h r e e equilibrium coefficients m e n t i o n e d i n the experimental p a r t was n o t t h e s a m e , in all cases broadly t h e s a m e values were o b t a i n e d for the q u a n t i t i e s log K D , log K D (corr), and s6 log KE: (at a given solvent composition) which a r e i n fact t h e quan-
-
Table I. Change of t h e Logarithm of t h e Selectivity Coefficient Kgb,' (as Defined b y Equation l l ) , si3 (log KBb+'), When Going f r o m an Aqueous 1.97 N HC1 Solution of R b + to a 1.97 N HCl Solution of R b + in Water-Organic Solvent Mixtures
7.~wt organic solvent 5
Methanol 0.04 Ethanol 0.00 1-Propanol 0.02 2-Propanol -0.04 tert-Butyl -0.04 alcohol Acetone 0.00 Acetonitrile 0.06 Tetrahydro0.00 fur a n Dioxane 0.06 Ethylene gly- 0.00 col monomethylether Dimethyl -0.04 sulfoxide Sulfolane -0.02 Dimethyl -0.23 formamide Urea -0.16
10
1s
20
25
30
3s
40
0.08 0.00 0.03
0.11
0.16 0.09 0.09
0.20 0.16
0.00
0.03
0.05 0.09
0.25 0.24 0.16 0.13 0.16
0.30 0.33 0.21 0.21 0.22
0.36 0.42 0.28 0.31 0.32
0.04 0.15 0.07
0.07 0.20 0.12
0.13 0.24 0.18
0.20 0.28 0.25
0.28 0.32 0.32
0.36 0.46 0.55 0.63 0.72 0.80 0.89 0.97 0.35 0.39 0.42 0.45 0.49 0.52 0.56 0.59 0.41 0.49 0.58 0.68 0.78 0.89 1.00 1.12
0.16 0.02
0.23 0.04
0.31 0.07
0.37 0.14
0.43 0.20
0.51 0.60 0.70 0.78 0.86 0.93 0.99 1.04
0.04
0.08
-0.04
-0.06 0.02 0.11
0.04 0.10 0.00
0.04 0.06 -0.04 -0.04
0.11
45
SO
SS
60
0.45 0.58 0.70 0.82 0.51 0.61 0.72 0.83 0.35 0.44 0.53 0.64 0.42 0.53 0.65 0.80 0.42 0.53 0.65 0.78
65
70
75
0.92 1.02 1.16 0.96 1.13 1.34 0.80 0.97 1.17 0.95 1.13 . . . 0.93 1.07 1.19
0.27 0.34 0.42 0.48 0.54 0.60 0.65 0.70
-0.09
-0.09
-0.02 -0.34
-0.38
-0.34
0.05 0.08 0.09 0.12 0.14 0.18 0.21 0.23 0.26 0.29 0.31 -0.30 -0.23 -0.16 - 0 . 0 8 0.00 0.07 0.14 0.20 0.26 0.33 0.41
-0.41
-0.51
-0.58
-0.66
0.00
-0.09 0.01
-0.04
-0.02
-0.66
-0.71
-0.71
0.16 0.22 0.29 0.38 0.46 0.54 0.60
..,
...
...
...
...
...
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
... 459
Table 11. Change of Logarithm of the Selectivity Coefficient K$"+C (as Defined by Equation ll), s6(log K!:'), When Going from an Aqueous 1.98 N HCl Solution of Na+ to a 1.98 N HCl Solution of Na+ in Water-Organic Solvent Mixtures % wt organic solvent 5
Methanol Ethanol tert-Butyl alcohol Tetrahydrofuran Dioxane Dimethylsulfoxide Dimethylformamide
-0.02 -0.03 -0.02 0.03
10
-0.02 -0.03 -0.02
0.10
0.00 0.05 -0.02 -0.04 -0.09
-0.18
15
20
25
30
35
40
45
50
55
60
65
0.00 0.00 0.01
0.04 0.07 0.05
0.11 0.16 0.09
0.18 0.30 0.17
0.26 0.40 0.27
0.34 0.52 0.38
0.41 0.63 0.50
0.49 0.73 0.62
0.57 0.85 0.77
0.64 0.98 0.92
0.73 1.12 1.09
0.82 0.91 1.28 1.52 1.13 . , .
0.12
0.18
0.20
0.26
0.32
0.40
0.49
0.56
0.66
0.77
0.85
0.97
1.16
0.10 0.14 -0.05 -0.06
0.21 -0.06
0.30 -0.03
0.38 0.01
0.46 0.06
0.56 0.12
0.64 0.19
0.72 0.29
0.82 0.94 0.48 0.56
1.04 0.61
0.65
-0.23
-0.19
-0.14
0.01 0.08 0.17
0.27
0.36
0.50 0 . 5 4
-0.23
tities of interest to us. Since, neglecting activity coefficients both in the external and the internal phase, by definition the value of KEi for monovalent cations has to be the closest possible approximation of the thermodynamic equilibrium constant K,, we will use wherever possible values of the selectivity coefficient KE: for further discussion. Distribution results for Rb+ obtained in this work are summarized in Table I, where values of s6 log K$b+'for the transfer from an aqueous 1.97 N HC1 solution to a solution in mixed water-organic solvent up to 75% weight are tabulated. An average selectivity coefficient KEY of 2.2 a t 0 mol % organic solvent has been found. Corresponding values of KD and K D (corr) a t the same solvent compositions were 6.0 and 6.6, respectively. The corresponding distribution results for Na+ are given in Table 11. Average values a t 0% weight organic solvent for K D ,K D (corr), and KEB;' were respectively 2.3, 2.8. and 0.88. Table I11 summarizes the calculated values of s6 log KK for Ag+ ions for the transfer from an aqueous 1.11 N "03 solution to a solution in mixed water-organic solvent. Here the average values for the different equilibrium coefficients in pure water-minera1 acid media were 12.1, 12.5, and 2.6, respectively. Finally, Table IV shows some preliminary results for the distribution of Li+ ions. Some of the above mentioned experiments were also reconcentration. I t appeated using another HC1 (or "03) peared that the molarity of mineral acid, although having a big influence on the absolute value of the selectivity coefficient, had only little influence on the values of log KZ; especially a t intermediate and high concentrations of organic co-solvent. The minimum in the curve log KE: vs. weight percent organic solvent systems, in most cases, seemed to be a little less pronounced a t lower concentrations of mineral acid. Furthermore, in most cases its position seems to shift somewhat to lower organic solvent content when the mineral acid concentration is increased.
DISCUSSION A great number of approaches have been proposed in the literature in order to interpret the observed selectivity relationships of ion exchangers towards cations in mixed aqueous-organic solvents, and to predict ion exchange selectivities from independent physicochemical data. One of the oldest, but up to now most employed, treatments assumes that the dielectric constant D of the mixed solvent could be used for this purpose (16-18). However, by plotting the values of log KE;, reported in the present article, as a function of l / D (figures not shown here), it seems clear that no satisfying correlation between both sets of data can be found, so that the dielectric constant is not the best way to 460
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
-0.07
0.44
70
75
...
account for the observed variations in selectivity. Another useful approach is due to Eisenman (19). Although his theory is difficult to summarize in a few words, its principal merit is the fact that thermodynamics of hydration and solvation are considered as of key importance in explaining ion exchange processes. The same holds for the competitive solvation theory of Diamond and Whitney (6). This theory considers selectivity as a competition among external phase co-ion, internal phase co-ion, and solvent molecules in each phase for solvating the exchanging ions of interest. Our theory has started from the same ideas. By making the assumptions (which are discussed later in more detail) that structure and solvation in the resin phase are lower and that solventsolvent interactions in the resin can be neglected, we arrive a t the proposed models. In this connection, it is worth noting that Gupta and coworkers (20), starting from a very formal thermodynamic treatment of ion exchange phenomena containing several terms inaccessible to experimentation, found results very similar to ours. After introducing several approximations, they determined an equation where the variation of selectivity with the solvent is explained by medium effect terms (proportional to our gt's) and an empirical parameter. They were not able to check their equation systematically because of lack of sufficient data. Data for the Gibbs free energies of transfer for different ion pairs in various aqueous organic media having been given elsewhere (9-13), the relationship between gt's and selectivity coefficients will now be investigated. Two approaches will be discussed. First Approach. It has been shown previously (8) that, assuming that the properties of the internal phase are not influenced by the addition of organic solvent (i.e., s6(pt+ p i + ) = 0 or maybe even s6 p t = 0), the variation of the thermodynamic equilibrium constant K , should be given by Equation 8. If, furthermore, it may be assumed that log K" N s6 log K , (or YM+ = YH+ and y ~ =+y ~ + )a ,relationship of the type follows. This neglect of activity coefficients may be justified by the fact that the molarity of mineral acid in the external phase has only very little influence on the values of log KE: (see "Results" section of this article). In this connection, a very similar approach by Fessler and Strobe1 (21) is worth noting; according to these authors, a better approximation would, however, be to use equilibrium coefficients taken a t 0.5 resin ion fraction. A still better approximation would be to use equilibrium
15
mmmmooms. vi
\c
"c?p'.?Y".?1
0 0 0 0 0 0 0 0
I
I /
10
05
(Dms.*o*am Lo
?@???S?"?
0 0 0 0 0 0 0 0
I
I I
00
Figure 1. &(Rb+-H+) as a function of (+) Methanol, (A)ethanol,
s6 log @ti
(I)1-propanol, (I 2-propanol, ) (0) tert-butanol,
(e)acetonitrile,
(0) tetrahydrofuran, ( 0 )dioxane, ( X ) ethylene glycol monomethylether, ( 0 )dimethylsulfoxide, ( 0 )sulfolane, (9)dimethylformamide. and ( 0 )urea.
(€ acetone, I)
vi
0s.cDaoC-mC.1
??1?1?"? I I I
0 0 0 0 0 0 0 0
woc.la0ms.s.
4 ?91???"-' 0 0 0 0 0 0 0 0 I
I I
coefficients obtained by integration over all resin compositions (22, 23). The determination of this more rigorous equilibrium coefficient would, however, involve too much work for a study covering several ions and fourteen solvents. To be able to study in more detail the deviations from the proposed relationship between gt and KH"+'data, values of gt(M+-H+) (=gt(M+) - gt(H+) =gt(M+,C1-) gt(H+,Cl-)) as a function of s6 log KE: were plotted. From Equation 12 it follows that, for all the solvents studied, one straight line, with a slope equal to 1,should be expected. In Figure 1, values of gt(Rb+-H+) are plotted as a function of s6 log K a y . Although most of the plotted curves after a while show a tendency to parallel each other, the slope A
2
u3mmoacomo ???????@? 0 0 0 0 0 0 0 0 I 1 I I
2.0
-
*u30.10ms.mo
-
????"?-'"
-
????"?1" 0 0 0 0 0 0 0 0 I I I 1
vi
c
1.5-
0 0 0 0 0 0 0 0
I I
I 1
mmOOm"0
~
1.0 -
I
rlmm0mc.lt-el Lo
~
Oo o Oo Oo Oo m.O oOorol 1
I l l
I /
I
0.5-
0 0-
1.0
0.6
Figure 2. g;(Na+-H+)
as a function of
*6 log I($+
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
461
Table IV. Change of the Logarithm of the Weight Distribution Coefficient K D (Li+) (as Defined by Equation l o ) , s 6 log KD, When Going from an Aqueous 1.03 N HCI Solution of Li+ to a 1.03 N HCl Solution of Li+ in Water-Organic Mixtures % wt organic solvent 10
5
Methanol 0.00 Ethanol 0.06 tert-Butyl alcohol 0.06 Dioxane 0.04
20
15
0.00 0.01
25
0.01 0.02 0.28 0.37 0.33 0.41 0.17 0.22
0.12 0.20 0.14 0.23 0.08 0.13
45
30
35
40
55
60
65
0.05
0.12 0.56 0.56 0.32
0.19 0.65
0.24 0.28 0.75 0.84
0.32 0.92
0.39
0.63 0.37
0.71 0.78 0.41 0.46
0.88 0.51
0.36 1.02 0.99 0.56
0.46 0.48 0.27
being nearly equal to 1, different curves are obtained for each water-organic solvent system. The behavior of dioxane-water systems being nearly ideal, too large values of 9 log KEY (yielding curves which lie underneath the line which we expected) are found for the systems acetonitrilewater and sulfolane-water, whereas for all other solvent systems the s6 log K$b+'values are too low (yielding curves above the ideal straight line). The largest deviations are obtained for dimethylsulfoxide, dimethylformamide, and urea. It is very interesting to note that the sequence of the curves in Figure 1 is very similar to the one obtained by plotting g,(Rb+-H+) as a function of the volume fraction dz of organic solvent. The same holds for the exchange of Na+-H+ (see Figure 2) and Li+-H+ (see Figure 3). From Figure 4, where values of gt(Ag+-H+) are plotted as a function of 8 6 log K#, another interesting point arises: here the curve corresponding to the water-dimethylsulfoxide system goes into the opposite direction, log K# being negative for (in the majority of cases) negative values of gt(Ag+-
H+). The conclusion from this comparison between gt and
KH"+'data is that, in general, the agreement between both is acceptable but that only a semi-quantitative correlation between selectivity behavior and transfer functions seems to exist. Deviations are occurring and it seems to be impossible to exactly compensate for them simply by using a more correct selectivity coefficient (8). We have already stated in a previous article (8) that it is improbable that the effect of the resin could be completely eliminated. Indeed, by putting %(&+ - &+) = 0 in Equation 3, it was thought that the effect on the standard chemical potentials of the ions in the internal phase would be less important than in the external phase. In a first approximation, these effects were therefore neglected. However, when trying to
50
75
80
0.42 1.29 1.38
0.44 1.38 1.57
70
0.41 1.11 1.21 1.11 1.21 0.60 0.63
0.67
refine our theory, it seems that it is necessary to take these effects into account. Not only is there the fact that ion exchangers are known to swell when brought into contact with different solvent mixtures, but also there is the problem that, with mixed solvents, another variable, namely the solvent selectivity of the ion exchanger, appears. These factors bring on serious modifications to the medium considered. Therefore it seems reasonable to attribute the deviations of the experiment from theory to modifications of the resin- or internal phase, making it necessary to introduce a correction term in Equation 8. This correction term should be equal to zero, and consequently Equations 8 and 1 2 should hold, whenever the resin phase can indeed be regarded as an independent, unmodified phase. This should, for example, be the case for an ion exchanger such as zirconium phosphate, which is generally accepted not to swell to such an extent as ordinary synthetic organic cation exchangers do. Indeed, ion exchange phenomena with inorganic ion exchangers of the type zirconium phosphate take place in cavities of such small dimensions, that it seems impossible for the liquid phase in the exchanger to build up any structure. In a study on the selectivity behavior of crystalline zirconium phosphate in mixed aqueous organic media, Massart (24) determined weight distribution coefficients of Rb+ ions in several water-hydrochloric acid-organic solvent mixtures. Distribution results were all expressed as a function of percent volume of organic solvent. This way of expressing results made it difficult for us to convert them exactly into the concentration scale used in this work. Neglecting the presence of mineral acid, we estimated the corresponding values of the volume fraction 42, and have plotted values of s6 log K D as a function of 9; (Ag*)-g;(H*l
/+
'd I
1
I
0
0.5
10
Figure 3. &(Li+-H+) as a function of
462
'6
'dlog K;:+
log K D
log &(Li+)
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
...
I -0.5
Figure 4. &(Ag+-H+)
I
1
0
0.5
as a function of 6 ' log @$+
1 1.0
*
gt(Rb+-H+). The resulting curves are shown in Figure 5 . Except for the systems dimethylformamide-water and dimethylsulfoxide-water, all plots now coincide, resulting in one straight line as expected from Equation 12. A special case are the systems dimethylformamide-, dimethylsulfoxide-, and urea (25)-water. Large deviations are found for these solvent systems. The only explanation we can offer is a very special type of interaction between the organic co-solvent and the ion exchanger. Although we have no further proof yet for this assertion, in our opinion a strong bond-formation of the type P-0-H . . . O=S< between the hydrogen atom of the fixed ionic group and the negatively charged part of the organic solvent dipole should be the cause of this special behavior, resulting in a kind of "blocking" of the active groups of zirconium phosphate. More extensive investigations in this connection will be carried out. This brings us to the point as to how to estimate the occurring deviations from theory for the synthetic organic exchangers, in order to be able to correct for them. Another approach was developed to achieve this. Second Approach. We again assume that log KH"+'N s6 log K , (or TM+ = ?H+ and Y M + = YHC), Furthermore, the ion exchange resin phase can be treated as a mixture of dry resinate R and free absorbed solvent 3. Assuming that the standard chemical potential ,$ of an ion i in the ion exchange resin phase varies linearly with the volume fraction between the standard chemical potential of free solvent of the ion in the pure dry resinate I? and the standard chemical potential spB in the pure free solvent one can write (13) p; = $ R . Rp; + 4 s . s&fl
s,
s,
Substituting this value of ,ii: in Equation 3 yields, in water RT In " K , = "(&+ - p i + )
*&log KD
Figure 5. gf(Rb+-H+) as a function of s6 log Kd(Rb+), zirconium phosphate. Weight distribution coefficients calculated from Ref. 24
'6 log K , = [gt(B+)- gt(A+)] - 0.6[gt(B+) - gt(A+)] (17)
+
where gt(i) is the transfer factor of ion' i for the transfer from water to mixed organic solvent in the free solvent of $R(Rpi+ - ' M i + ) -k $iv(Wpi+ - i v p t + ) (14) the exchanger phase. We thereby accept that this factor and in solvent S gt(i) is equal to the corresponding factor gt(i) in an external phase of the same composition. RT In S K , = s(pL+ - p i + ) As a first consequence of this model, it can be mentioned $ R ( ~ & + - R&+) & ( s p ~ + - spi+) (15) that the correction for swelling will be more important the However, by approximation we may state that the volume more co-solvent will be absorbed. The correction will be fraction of absorbed solvent only slightly depends upon the negligible when only water is absorbed by the resin, and composition of that solvent. Fessler and Strobe1 (21), for a when the quantity of this absorbed water remains constant. pure Dowex 50-X8 hydrogen-form resin, reported ratios of Furthermore, from our model, it follows that for an ion exswollen volume/dry volume of 2.5, 2.3, and 2.4, respectively, changer which does not swell, there will, of course, not be in pure water, methanol, and ethanol. Bonner (26) has any correction for swelling. measured the solvent uptake of this same resin in mixtures The validity of Equation 17 can be checked by analyzing of water-ethanol and water-dioxane. By expressing his rethe data on exchanges in dimethylsulfoxide-water, methasults in terms of ml solvent per equivalent weight of resin, nol-water, and acetone-water mixtures, for which reliable for ethanol-water (respectively dioxane-water) mixtures data on solvent selectivity are available. Values of f , the containing 0, 25, 50, and 75% weight organic solvent, a mole fraction of organic solvent in the internal solution value of 206, 224, 222, and 209 (respectively, 206, 220, 221, phase, as a function of x , the mole fraction in the external and 194) ml solvent per equivalent weight of resin can be phase, for the dimethylsulfoxide-water system were intercalculated. In addition, from a study by Van Wart and Japolated from solvent partition data with Dowex 50W-X8 nauer (27) on the equilibrium swelling of Bio-Rad AG 100-200 mesh H+-form resins, as reported by Janauer and 50W-X8 hydrogen-form resins in dimethylsulfoxide-water co-workers (Figure 1 of Ref. 28). Corresponding values in media, we could interpolate (from Figure 1 of Ref. 27) water-methanol solvent mixtures were interpolated from values of 1.19, 1.28, 1.29. 1.33, 1.35, 1.33, and 1.28 ml/gram data given by Nandan, Gupta, and Shankar for the Dowex dry resin, values corresponding to external solvent compo50W-X8, 20-50 mesh hydrogen form resin (29). Finally, sitions, respectively, of 0, 0.10, 0.20, 0.30, 0.40, 0.50, and values of % as a function of x in water-acetone solvent sys0.60 mol fraction of dimethylsulfoxide. From the above retems for a resin of 8% DVB were obtained by interpolation sults, it therefore follows that a mean value of $ s ( ~ $ ~ ) from the data reported by Davies and Owen ( 3 0 ) for resins equal to 0.6 may be adopted. Reintroducing the transfer of different cross-linkage (2:25, 5.5, and 10%DVB). notation s 6 for the transfer from water to solvent mixture S, In Figure 6, we have plotted values of gt(M+-H+) - 0.6 Equations 14 and 15 yield g,(M+-H+) as a function of s6 log KE:. Values of g,(M+H+)were interpolated from g,(M+-H+) vs. x curves, taking RT S6 In K , = s 6 ( p k + - p i + ) - & 9(&+- ai+) (16) into account the previously mentioned literature data for or selective solvent uptake.
+
+
ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
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ation. This is no doubt one of the reasons why no complete correlation was obtained. In addition, although a nearly quantitative explanation of the selectivity behavior in mixed solvents is obtained for uni-univalent exchange, this should not necessarily be true for multivalent ions. Indeed, the selectivity coefficient being a close approximation to the thermodynamic equilibrium constant for monovalent cations in dilute solution, multivalent cations, on the contrary, can show activity coefficients in the external phase which are very far from unity even in relatively dilute solutions.
ACKNOWLEDGMENT The Belgian authors thank A. De Schrijver for technical assistance.
LITERATURE CITED G. L. Gains, Jr., and H. C. Thomas, J. Chem. Phys., 21, 714 (1953). A. R. Gupta, J. Phys. Chem., 69, 341 (1965). A. R. Gupta, J. Phys. Chem., 75, 1152 (1971). A. M. El-Prince and K. L. Babcock, J. Phys. Chem., 79, 1550 (1975). C. H. Jensen, A. Partridge, T. Kenjo. J. Bucher, and R. M. Diamond, J. Phys. Chem., 76, 1040 (1972). (6) R. M. Diamond and D. C. Whitney, in "ion Exchange", Vol. 1. J. A. Marinsky, Ed., Marcel Dekker, New York, 1966. (7) R. Smits, P. Van den Winkel, D. L. Massart, J. Juillard, and J.-P. Morel, Anal. Chem., 45, 339 (1973). (8)J. Juillard, J.-P. Morel, R. Smits, and D. L. Massart, J. Chim. Phys., 3, 522 (1973). (9) R. Smits. D. L. Massart. J. Juillard, and J.-P. Morel, Bull. SOC. Chim. Belg.. 82, 511 (1973). (10) R. Smits, D. L. Massart, J. Juiilard, and J.-P. Morel, Electrochim. Acta, in press. (11) R. Smits, D. L. Massart, J. Juiilard, and J.-P. Morel, Electrochim. Acta. in press. (12) R. Smits, D. L. Massart, J. Juiilard, and J.-P. Morel, Nectrochim. Acta, in press. (13) R. Smits. D. L. Massart, J. Juillard, and J.-P. Morel, in preparation. (14) J. Inczedy in "Analytical Applications of ion Exchangers", Pergamon Press, Oxford, 1966. (15) G. E. Janauer, Mikrochim. Acta, 6, 1111 (1968). (16) R. G. Fessler, PhD. Thesis, Duke University, Durham, N.C., 1958. (17) G. M. Panchenkov. V. J. Gorskov, and M. V. Kukianova, Zh. Fiz. Khim., 32, 361, 616 (1958). (18) T. Sakaki, Bull. Chem. SOC.Jpn, 28, 217 (1955). (19) D. Reichenberg, "ion Exchange", Vol. 1. J. A. Marinsky, Ed., Marcel Dekker, New York, 1966. (20) A. R. Gupta, M. R. Ghate, and J. Shankar, lndian J. Chem., 5, 316 (1967). (21) R. G. Fessler and H. A. Strobei, J. Phys. Chem., 67, 2562 (1963). (22) E. Ekedahi, E. Hogfeldt, and L. G. Sillen, Acta Chem. Scand.. 4, 556, 828, 1471 (1950). (23) W. J. Argersinger, Jr., A. W. Davidson, and 0.D. Bonner, Trans. Kansas Acad. Sci.. 53, 404 (1950). (24) D. L. Massart. Talanta, 20, 358 (1973). (25) R. Smits. preliminary unpublished results. (26) 0. D. Bonner, J. Chem. Educ., 34, 174 (1957). (27) H. E. Van Wart and G. E. Janauer, J. Phys. Chem., 76, 41 1 (1974). (28) G. E. Janauer, H. E. Van Wart, and J. T. Carrano, Anal. Chem., 42, 215 (1970). (29) D. Nandan. A. R. Gupta, and J. Shankar, indian J. Chem., I O , 83 (1972). (30) C. W. Davies and B. D. R. Owen, J. Chem. Soc.. 1676 (1956). (1) (2) (3) (4) (5)
M' '61og K,,+
Figure 6. gt (M+-H+)
- 0.6 gt (M+-H+)
as a function of "6 log K$
(0)Ag+/H+ in dimethylsulfoxide-water, ( 0 )Na+/H+ in dimethylsulfoxidewater, (9) Rb+/H+ in dimethylsulfoxide-water, (I) Li+/H+ in methanolwater, ()I Rb+/H+ in methanol-water, Na+/H+ in methanol-water, (a) Ag+/H+ in methanol-water, (V)Ag+/H+ in acetone-water, (A)Rb+/H+ in acetone-water
(8)
From Figure 6, it appears that now a much better correlation between selectivity coefficients and transfer quantities has been achieved. As contrasted with what was found for ion exchange phenomena on crystalline zirconium phosphate (for which an acceptable explanation has already been given by invoking a special interaction between the fixed ionic group and the solvent dipole), even the'previously strongly deviating curves for the dimethylsulfoxidewater systems now show a tendency to coincide. This is not surprising a t all, since it is exactly this system which exhibits the smallest solvent selectivities. Since some not always satisfactory approximations had to be made, it is not surprising that the correlations are not perfect! I t should be remembered that we are working with measured selectivity coefficients K#Z instead of thermodynamic equilibrium constants K , so that a perfect correlation cannot be expected. Furthermore, resin invasion, although it is not negligible, was not taken into consider-
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ANALYTICAL CHEMISTRY, VOL. 48, NO. 3, MARCH 1976
RECEIVEDfor review July 1, 1975. Accepted November 18, 1975. The Belgian authors thank the "Fonds voor kollektief en Fundamenteel Onderzoek" for financial assistance.
