0. D. BONNER AND FRANCES L. LIVINGSTON
530
VOl. 60
CATION-EXCHANGE EQUILIBRIA INVOLVING SOME DIVALENT IONS BY 0. D. BONNERAND FRANCES L. LIVING ST ON^^^ Department of Chemistry, University of South Carolina, Columbia, South Carolina Received October $1, 1066
Equilibrium studies involving cupric, barium, strontium and calcium ion on Dowex 50 resins of approximately 4, 8 and 16% divinylbenzene content have been made while maintaining a constant ionic strength of approximately 0.1 Selectivity coefficients have been measured at various resin loadings. The characteristic maximum water uptake of the resin in thew ionic forms is reported.
A summary of the results of studies of ionexchange equilibria and maximum water uptake of Dowex 50 resins of 4, 8 and 16% DVB content involving the common univalent cations has been reported previously.s An extension of this study to polyvalent cations and their inclusion on the same selectivity scale should furnish information on the effect of charge, hydration, ion pair formation, etc., in the ion-exchange process. Experiments of this type are now underway and data on exchanges involving cupric ion and three of the alkaline earth cations are reported herewith.
Experimental The methods of equilibration and separation of aqueous and resin phases for exchanges of univalent ions have been described in detail .4 The same experimental procedures were followed in these exchanges also with two exceptions. A longer period of time for equilibration is necessary for exchanges involving polyvalent cations. At least two days was allowed for each of these equilibrations. Also in exchanges involving ions of different valence types such as the cupric-hydrogen and silver-cu ric exchanges, the resin phase must be as free as possible ofadhering solution before washing with distilled water for subse uent analysis. This precaution is necessary because of &e great effect which dilution of a solution containing the two ions in a given concentration ratio will have upon the equilibrium composition of the resin phase. The resin composition must of necessity change in such a manner, upon dilution, so as to offset the change in the ratio cB+/cz& (see equation 4 below) and maintain the constancy of the equilibrium constant. In preparation for analysis the resin phase was first exhaustively eluted with either ammonium chloride or barium nitrate solutions. Aliquots of this effluent and also of the solution phase were then analyzed for both ions being exchanged. The concentration of hydrogen ion in the presence of cupric ion was determined by titration with Rtandard alkali, brom phenol blue serving as an indicator. Cupric ion concentration was determined by the titration of the iodine liberated upon the addition of potaasium iodide with standard thiosulfate. Silver ion concentration was determined potentiometrically, standard sodium chloride serving as the titrant or radiometrically, using Ag1l0 as a tracer. Calcium, strontium and barium were determined gravimetrically as the oxalate of the former and sulfate of the latter two ions. The precipitation of strontium sulfate was accomplished from a 50% alcoholic solution.
Discussion and Results In exchanges of univalent ions the exchange reaction has been expressed by the equation (A+)o
+ (B+)i = (A+)i + (B+)o
where A+ and B+ are the cations involved in the exchange and the subscripts i and 0 represent the (1) These results were developed under a project sponsored by the United States Atomic Energy Commission. (2) Part of the work described herein was included in a thesis submitted by Frances Livingston to the University of South Carolina in partial fulfillment of the requirements for the degree of Master of Science. (3) 0.D. Bonner, THISJOURNAL, 59, 719 (1955). (4) 0.D. Bonner and V. Rhett, ibid., 57, !264 (1953).
resin phase and the outside solution, respectively. The thermodynamic equilibrium constant, K , and the selectivity coefficient, IC, are related to the concentrations of the ions, C, and their activity coefficients, y, by the equation For many of the exchange reactions which have been studied the activity coefficient ratio y ( g +lo/ Y(A+),, is unknown in mixed aqueous solutions. Dilute aqueous solutions (ionic strength = 0.1) have therefore been used and this ratio has been regarded as unity. This procedure has seemed preferable to applying a partial correction obtained by assuming the values of Y A + and Y B + to be the same as in pure solutions. The equilibrium constant may then be calculated from the equation6 log K =
K
log k d N
(2)
where N is the molar fraction of the resin associated with A+. For exchange reactions between two divalent ions or between a divalent and a univalent ion the reactions may similarly be represented as
+ '/z(N++)i = '/z(M++)i + ' / ~ N + + ) o '/~(M++)O + (B+)i = '/z(M++)i + (B+)o
'/z(M++)o
and
Values of the equilibrium constants for the various exchanges may then be calculated which are directly comparable with those for exchanges between univalent ions, and cations of all valence types may be included in a single selectivity scale. The expressions for the equilibrium constants are
and
The equilibrium constant for the exchange reaction between two divalent ions may be calculated from equation 2. The constant, K , for the exchange of a divalent ion and an univalent ion may be calculated from the equation6 log K = JO1 log k dX ( 6 ) 0. D. Bonner, W. J. Argorsingcr and A. W. Davidson, J . Am. Chem. S O C . 74, , 1044 (1952).
(6) W. J. Argersinger, A. W. Davidson and 0. D. Bonner, Trans. Kans. Acod. Sci., 53, 404 (1950).
P
CATION-EXCHANGE EQUILIBRIA INVOLVING DIVALENT IONS
May, 1956
Mole % calcium resin
er exchan e: A, 16% DVB; B, 8% D$B; c, 42 DVB. k5.- mcu++ N c e ~ e s r mea++ NCUR~~~
Fig, 1.-Calcium-cop
Mole
Oh
strontlum resin.
53 1
Mole % barium resin.
Fig. 3.-Barium-co
per exchange: A, 16% DVB; B, 8% bVB; C, 4% DVB.
Equivalent % Cupric resin
Fig. 2.-Strontium-copper exchange: A, 16% DVB; B, 8% DVB; C, 4% DVB.
Fig. 4.-Cupric-hydrogen exchange: A, 16% DVB; B, 8% DVB; C, 4% DVB; D, 4% DVB (NO; media). k = - mB+z NC~R~S,
where X is the equivalent fraction of the resin associated with ion M++ (equation 4). The quantity Y ~ + / Y $ + + has a probable value’ of about 1.2 f 0.2 but will vary for each pair of ions studied. This ratio was therefore neglected in. the
present calculation of K for these exchanges as was done for exchanges involving only univalent ions. The value of K may be corrected for any exchange involving ions for which activity coefficient in mixed aqueous solutions are known. The experimental data for these exchanges are presented graphically in Figs. 1-5 as a plot of k ,
mcu++
(7) I. M. Klotz, “Chemical Thermodynamics,” Prentiee-Hall, Inc., New York, N. Y.,1950, p. 332.
N%R~B
0. D. BONNER AND FRANCES L. LIVINGSTON
532
Equivalent Ye Sllvrr r i r i n .
Fig. 5.-Silvercupric exchange: A, 16% DVB; B, 8% DVB; C, 4% DVB.
k=-
~cu++
mL+
N'AER~S NcuR~.~
the selectivity coefficient as a function of resin composition. The equilibrium constants have been calculated and are given in Table I. The affinity of the resins for the ions studied is Ba > Ag > Sr > Ca > Cu > H for resins of 4 and 8% DVB content and Ag > Ba > Sr > Ca > H for the TABLE I TABLE OF EQUILIBRIUM CONSTANTS Exchange system
Ba-Cu Sr-Cu Ca-Cu Ag-Cu(NOa-) Ag-H( NOs-)o Cu-H(NOj-) Cu-H( C1-) Cu-H( calcd.) Previously reported.
K 4%DVR
8%DVB
l6%DVB
2.24 1.45 1.26 1.52 3.08 1.99 1.92 2.03
2.95 1.72 1.40 2.35 5.84
4.60 2.30 1.71 5.47 13.4
2.38 2.49
2.38 2.45
Vol. 60
16% DVB resin. These and other divalent ions will be included in the same selectivity scale with the univalent ions when their position is verified by other exchanges between univalent and divalent ions. The effect of the anion, even in fairly dilute solutions, upon the activity coefficients in the solution phase is apparent in the cupric-hydrogen exchange. An equilibrium constant of 1.92 is obtained for this exchange when cupric chloride and hydrochloric acid solutions are used but the constant is 1.99 when cupric nitrate and nitric acid solutions are used. This effect is to be expected since in solutions of the pure electrolytes the activity coefficient of hydrochloric acid is greater than that of nitric acid while the activity coefficient of cupric nitrate is greater than that of cupric chloride. This effect is of further interest in the triangular comparisons. Upon completion of the silver-cupric exchange a value of the equilibrium constant for the cupric-hydrogen exchange may be calculated since data on the silver-hydrogen exchange are available. It is found that rather satisfactory agreement is obtained for the 4% DVB resin when the nitrates of the various cations are used in all exchanges. The constants for the cupric-hydrogen exchange on 4, 8 and 16% DVB resins using cupric chloride and hydrochloric acid differ, however, from the calculated value by about 5%. Since the discrepancy in the observed and calculated values of K for this exchange on 8 and 16% DVB resins are of similar magnitude, it is believed that the same explanation is applicable. The maximum water uptake data (Table 11) show that the same pattern for divalent ions that was observed for univalent ions. The water uptake is smaller for ions for which the ion-resin affinity is greater. Comparisons of water uptake data for univalent with those of divalent ions does not appear t o be profitable a t this time. TABLEI1 MAXIMUM WATER UFTAKEOF DOWEX 50 RESINSIN VARIOUS FORMS (G./MoLE) IONIC Ion
4%DVB
8%DVB
16%DVB
Ba++ Sr++ Ca++ cu++
333 499 563 643
245 307 319 369
194 227 230 277
s
