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SELECTIVITY COEFFICIENTS OF METHACRYLIC ACID
263
STUDIES ON ION EXCHANGE RESINS. XV. SELECTIVITY COEFFICIENTS OF METHACRYLIC ACID RESINS TOWARD ALKALI METAL CATIONS B Y HARRY P. GREGOR,MARYJANEHAMILTON,' RAMESH -1.
o X A 2 AND
FABIAN BERNSTEIN3
Contribution jrorti the Department of Chemistry of the Polytechnic institute of Brooklyn, New York Received M a y 36,I966
The selective uptake of lithium, sodium and potassium by a series of methacrylic acid cation-exchange resins of various divinylbenzene contents was measured; the general order of preference was lithium > sodium > potassium. This preference became more marked as the degree of cross-linking increased, or as the degree of neutralization of an given resin increased. This resin behavior was compared with the association evidenced by the alkali metal acetates. Calues of relative alkali metal resinate activity coefficients were compared with analogous acetate values, giving fairly good agreement. Also, integration of the Gibbs-Duhem equation for a two-component system led to a simple expression which correlated the selectivity coefficients with the DVB content of the resin and the composition of the resin phase. base and also for the reference cation (potassium) by means of the flame photometer (Perkin-Elmer, Model 52 A). The distribution coefficient could then be calculated. Since only one of the competing cations in but one of the phases (solution) was determined directly, the other terms being calculated by difference, this procedure gave the least precise results and was for this reason restricted to systems where Kd was near unity and where FK, the mole fraction of exchange cations (excluding hydrogen) in the resin phase was about 0.5. Where more accurate Kd determinations were required the total base and the potassium content of the resin were also determined. Here the exchange cations were eluted from cent,rifuged resin with an excess of standard hydrochloric acid. The accuracy of Kd as determined in this manner was considerably improved because two of the four concentration t e r m were determined directly. Potassium-sodium exchange (Fig. 2) was measured at different p H levels by passing a large excess of a phosphate buffer solution containing mixtures of sodium and potassium Procedures .-The same methacrylic acid-divinylbenzene copolymers were used in this study as in the previous one4; a t an ionic strength of about 0.2 through a 0.1-g. bed of resin until equilibrium was reached. The resin was rinsed for details of the preparation and conditioning procedure8 quickly with a small amount of water and the cations eluted the reader is referred to this earlier paper. with an excess of standard acid and determined flameThe practical (molal) selectivity coefficient Kd for the photometrically. cation-exchange process where cation (2) is displaced from Selectivity coefficients for resin systems at different dethe resin phase by cation ( 1 ) originally present in the solu- grees of neutralization a,defined as moles of base added per tion phase is defined as mole of resin acid (Fig. 3) were determined by shaking the hydrogen form resin with different amounts of equimolar mixtures of potassium chloride and the hydroxide of either lithium or sodium. After equilibration, the potassium where an upper case letter ( M )denotes the molality of an content of both the resin and solution phases was deterion in the resin phase, calculated from the water content. mined. A lower case letter ( m ) is the molality of the corresponding All data reported are equilibrium values. Systems were ion in the solution phase. The relationship between Kd shaken in every case for twice the period of time required and the true thermodynamic equilibrium constant for the to obtain equilibrium. Where the Kd values were very exchange processes has been described .6 large or very small, equilibrium was approached from both Selectivity coefficients were determined using three simi- directions. All experiments were carried out a t room temlar techniques. The selective uptake of two cations from peratures (24-26') unless otherwise stated. The systems solutions of their hydroxides (potassium-lithium, Fig. 1 ) were kept carbonate-free. The use of inert plastic bottles was measured by weighing air-dried hydrogen form resin (of eliminated errors due to sodium contamination from glass. known moisture content) into inert plastic bottles, adding a The accuracy of the Kd values was set by that of the flame standard solution containing the two cations as their hy- photometric determination of potassium which was accurate droxides, and shaking to equilibrium. A 3-4 fold excess of to f1%. Kd values in the range of 0.2 to 5 were accurate base over resin acid (in terms of equivalents) was used. The to within f3%. When the mole frltction of potassium in volume of base was sufficiently large so that errors due to the resin was low, Kd values maintained this latter accuracy, water sorbed by the resin were negligible. After equilib- but when X'Xwas high (> 0.9) the Kd values were probably rium, the solution phase was filtered off and analyzed for total accurate to but *lo%. When two bases were used, the solution concentration (1) A portion of this work is abstracted from the thesis of Mary was kept in the range 0.03-0.04 M ; when basechloride Jane Hamilton, submitted in partial fulfillment of the requirements solutions were employed to give systems of different degrees for the degree of Master of Science in Chemistry, Polytechnic Institute of neutralization the concentration range was 0.01-0.05 M. of Brooklyn, June, 1950. In these concentration ranges the total capacity of the resins (2) A portion of this work is abstracted from the thesis of Rameah was fairly constant, although where necessary corrections J. Oaa, submitted in partial fulfillment of the requirements for the were made for changes in capacity.' For potassium-sodium degree of Master of Science in Chemistry, Polytechnic Institute of exchapge the solution ionic strength was 0.2. Brooklyn, June, 1952.
A previous paper in this series4described the uptake by carboxylic acid cation-exchange resins of various bases from solutions of different concentrations and ionic strengths, where the pH of the solution phase, the absorptive capacity and the swelling of the resins were measured. This behavior was correlated with the general properties of polymeric electrolytes. This contribution describes the selective uptake of one cationic species over another by these resin systems with lithium, sodium and potassium, where the resin acid is neutralized t o different degrees and coefficients measured at different temperatures. Experimental
(3) A portion of thie work is abstracted from the Dissertation of Fabian Bernstein, submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry, Polytechnic Institute of Brooklyn, February, 1952. (4) H. P. Gregor, M. J. Hamilton, J. Becher and F. Bernstein, THIS JOURNAL, 69, 874 (1955). (5) H. P. Gregor and J. I. Bregman, J . Colloid Sei., 6, 323 (1951).
Results Selectivity coefficients for the exchange of potassium with lithium (from 0.03-0.04 M solutions of their hydroxides) with different resins are shown in Fig. 1. The selective uptake of potassium meas-
H. P. GREGOR, M. J. HAMILTON, R. J.
264
O Z A AND
F. BERNSTEIN
Vol. 60
same at the different mole fractions (X',) studied, in agreement with the earlier observations that the capacity at the same degree of neutralization and ionic strength was the same to alkali metal cations.4 At pH levels of 6 , 7 and 8 the corresponding capacities in millimoles/g. were: DVB 0.5-6.7, 9.7, 11.5; DVB 2 4 . 5 , 7.2, 9.2; DVB 16-1.4,2.6,4.6. The selective uptake of potassium over sodium and lithium at different degrees of neutralization cy of resin DVB 6 is shown in Fig. 3. Here the total concentration of the solution phase was 0.01-0.05 M . Values of pH at differentdegrees of neutralization were as follows: cy = 0.2, pH 6.5; .0.4, 7.0; 0.65,7.4; 0.85,8.7.
& 2.9 2.7 2.5 2.3 2.1: 1.9
0
0.2
0.4
0.6
0.8
17
1.0
Xi. Fig. 1.-Selectivity coefficients for potassium-lithium exchange from base solutions a# a function of the fraction of resin exchange sites occupied by potassium. Resins are: 0,DVB 0.25; A, DVB I; 0,D V S 2; A, DVB 16; 0, DVB 24.
1.5
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.3 1.6
Q.
ured against sodium from buffer solution a t pH 7 Fig. 3.-Variation of specific external volume of resin is given in Fig. 2. Determinations were also per- DVB 6 in alkali metal states with degree of neutralization CY (right-hand ordinate), and Kd as a function of CY for potassium-lithium and potassium-sodium exchange. potassium ( 0 ); exCations are: lithium (A), sodium (o), change, shown dotted.
0.2
-0.2
- 0.4 0.2
0.4 0.0 0.8 1 n k. Fig. 2.-Selectivity coefficients for potassium-sodium cschange in buffered Rolutions at pH 7. Resins are: m, DVB 0.5; 0 ,DVU 2; A, DVB 1G. 0
formed a t p H G and 8; a t all three pH levels the data were substantially the same, usually within experimental error. The total capacity of the resins ill the mixed potassium-sodium state was the
The selective uptake of potassium over lithium from 0.03-0.04M solutions of their hydroxides with resins DVB 0.25, 1, 2! 16 and 24 was measured a t 4" in addition to the measurements a t 25". I n every case no significant variation in Kd was observed, nor was any consistent trend seen to occur. Since AH is therefore nearly zero, one can conclude that appreciable changes in enthalpy such as those which correspond to changes in hydration of the lithium ion are not taking place, or that such changes as do occur compensate for one another as regards enthalpy contributions. Discussion Figure 1 shows that fully neutralized methacrylic acid resins show a low order of preference for potassium over lithium when the resin phase is rich in lithium ( X k E 0.1). With potassium-rich resins this preference is reversed and the resin prefers lithium over potassium t o a marked degree. Further, these effects are relatively weak for resins of low degrees of cross-linking, increasing in magnitude as the cross-linking increases. With potassium-sodium exchange (Fig. 2) the resins also show a decrease in potassium selectivity
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Mar., 1956
SELECTIVITY COEFFICIENTS OF METHACRYLIC ACID
as the mole fraction of potassium in the resin phase increases. The order of preference is low, being 2 : 1 or 1:2 in the range examined. Here the low cross-linked resins show the strongest preferences, that for sodium. Figure 3 shows KG, and Kfi for resin DVB 6 a t different degrees of neutralization. At a! = 0.2 the resin prefers potassium but at a 2 0.4 this preference is reversed, in the order of Li > Na > K. Figure 3 also shows the swelled volumes V e of these resin^.^ Selectivity is favored for those ions giving smaller resin volumes; this behavior is consistent with that generally observed with cation and anionexchange systems.6u6 The thermodynamic equilibrium constant for potassium-lithium exchange is
where rKisthe single cationic activity coefficientand A , the activity of water in the resin phase, and where g moles of water are transferred from the solution t o the resin phase per mole of each cation being exchanged. As a first approximation, the solvent term and the pressure-volume term can be set equal to zero. I n dilute solution phases ratios of solute molalities are nearly equal t o ratios of aGtivities ; the expression above therefore considers only solution molalities. It then becomes
285
Harned and Owen7 discuss this problem and suggest that the reversal is due to solvent interaction with the ions (“local hydrolysis”) which results in association between anion and cation through the solvent dipole. The data of Fig. 1 for Kfi can thus be explained qualitatively in terms of the assumptions made above. In Fig. 4,the mean activity coefficients of the alkali metal acetates are plotted against their molalities.’ It can be seen that in general the values for potassium are higher, but that if the resin is largely in the lithium state, Le., the molality of lithium is large compared to potassium, ’)’LiAc > Y K A ~and by analogy r L i R would be greater than r K R . This effect would be enhanced as the total molality increases, that is; as the degree of crosslinking increases. Thus for small values of X k there would be a preference for potassium, but for intermediate and large values of Xfc there would be a cross-over and the resin would prefer lithium.
1.2
t-
1.1 1.o
go.9 Multiplying and dividing by the activity coefficient of the resinate (R) which is being treated here as a 1-1 electrolyte leads to the expression
where r K R is the mean activity coefficient of the potassium resinate, etc. K d can then be calculated if mean activity coefficients of the resinate are known. These values are not available, but nevertheless a comparison can be made on the basis first of the assumption that the molality of a cationic species in the resin phase will vary linearly with its mole fraction. Thus if the molalities a t Xt;, = 0 and X k = 1 are known, the molality a t any value of Xk can be determined. Further, it is assumed that there is little, if any, interaction between the lithium and potassium resinates. At a given molality, then, the mean activity coefficient of the alkali resinate is independent of the concentration of other resinates present. Further, it is assumed that the ratio of the mean activity coefficients of the lithium and potassium resinates may be approximated by the corresponding ratio of the mean activity coefficients of the lithium and potassium acetates. The order of the activity coefficients of the alkali salts of the halogen acids is reversed in the alkali hydroxides and acetates. The general order for chlorides, bromides and iodides is Li > Wa > K. For the acetates and hydroxides it is K > Na > Li. (6) H. P. Gregor. . I . Belle and R. A. Marcus, J . Am. Chern. Soc., 77, 2317 (19.55).
0.8
0.7
3
0.5 0 O O 6
Fig. 4.-Mean
1
2
3
4
m. molal activity coefficients of alkali acetates in aqueous solution.
In view of the assumptions made above, Table I was constructed and the K d values for the various DVB resins compared with (YLiAc/YKAc) .* For resin DVR 1, there is essentially no agreement; K d decreases slightly with X k while ( Y L ~ A ~ / Y K A ~ ) ’increases slightly. The data for resin DVB 2 show reasonably good agreement except that the calculated values are somewhat low; there is excellent agreement with resin DVB 16. There is also fairly good agreement with the DVB 24 data, and here the calculated values are somewhat high. With resins DVB 16 and 24 where high osmotic pressures are present, the pressure-volume term is appreciable and would make for an increased preference for lithium. Obviously, calculations of this type are useful only for qualitative comparisons. They do show a relationship between the mean activity coefficients (7) H. 8. IIarned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Reinhold Puhl. Corp., New York, N. Y.. 1950.
It. J . 0 z . t A N D F. BERNSTEIN TABLEI EXPERIMENTAL AND CALCULATED SELECTIVITY COENWCIENTS BOR POTASSIUM-LITHIIJM I
