984
HARRY P. GREGOR, OSCARR. ABOLAFIA AND MELVIN H. GOTTLIEB
Vol. 58
ION-EXCHANGE RESINS. X. MAGNESIUM-POTASSIUM EXCHANGE WITH A POLYSTYRENESULFONIC ACID CATION-EXCHANGE RESIN' BY HARRYP.GREGOR,OSCARR. ABOLAFIA~ AND MELVINH. GOTTLIEB Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, New York Received February I O , I964
The practical (molal) distribution coefficient for magnesium-potassium exchange with a polystyrenesulfonic acid cationexchange resin is 0.14 f 0.02 for a wide range of solution phase normalities (0.001-1.0) and resin phase compositions (FK = 0.01-0.78). Also, truly monofunctional resins show exactly the exchange capacity toward magnesium as they do toward univalent cations.
This paper describes the selectivity coefficients obtained for magnesium-potassium exchange with a 10% cross-linked polystyrenesulfonic acid resin. The cationic composition of the resin phase was varied within wide limits, as was the ionic strength of the equilibrating solution. While polyvalent cation-exchange processes have been studied, notably by Bauman and Eichhorq8 Boyd, Schubert and Adamson, Kressman and Kitchner,6 Marinsky,6 Duncan and Lister,' and Hogfeldt, Ekedahl and these studies usually were carried out at a single ionic strength, or with no variation in the composition of the resin phase, or with a resin which was not monofunctional and could conceivably undergo specific reactions with some of the cations. Also, most of these studies employed the heavier alkaline earth metals or other cations where complications due t o ion-pair formation with the sulfonic acid group might supervene, as pointed out by Gregor. g#lo
Experimental Resin.-The exchange studies were carried out with polystyrenesulfonic acid resins having about 10% cross-linking (Dowex-50, Dow Chemical Co.). The conditioning procedures were described in an earlier paper in this series." Procedures.-All experiments were performed using a small amount of resin (0.5-1 g.) in a small column. A large excess of solution was assed through this column until equilibrium was reachez as evidenced b an analysis of the effluent. In several instances, equigbrium was approached from both directions; the same state resulted. The ionic composition of the resin phase was determined by drawing off the excess solution b applyin suction for a few moments, followed b passing tgrough a few ml. of distilled water, and then ecting the resin with concentrated ammonium chloride solution. Where concentrated equil(1) The authors thank the Office of Naval Research for the support given this work. (2) A portion of this paper is abstracted from the thesis of 0. R. Abolafia, submitted in partial fulfillment of the requirements for the degree of Master of Science in Chemistry, Polytechnio Institute of Brooklyn, May, 1950. (3) W. C. Bauman and J. Eichhorn, J . A m . Cham. Soc., 69, 2830 (1947). (4) G. E . Boyd, J. Schubert and A. W. Adamson, ibid., 69, 2818 (1947). (5) T. R . E. Kressman and J . A. Kitchner, J . Chem. SOC.,1201 (1949). (6) J. A: Marinsky, Office of Naval Research Report, NR-026-001 (1949). (7) J. F. Duncan and B. A. J. Lister, Diaca. Faraday Soo., No. 7,104 (1949). (8) E. Hogfeldt, E . Ekedahl end L. G. Sillen, Acta C'hem. Scond., 4, 829 (1950). (9) H. P. Gregor, F. Gutoff and J. I. Bregman. J . Colloid Sci.. 6, 245 (1951). (10) H. P. Gregor and M. Frederick, Ann. N . Y . Acad. Sci., 67, 87 (1953). (11) H. P. Gregor, J. I. Bregman, F. Gutoff, R. D. Broadley. D. E. Baldwin and C. G. Overberger, J . Colloid Sci., 6 , 20 (1951).
ibrating solutions (1 molal) were used, the resin phase was separated by the centrifugation techniquee since the nonexchange electrolyte content is appreciable at these concentrations, and wm included in the resin phase composition. The centrifugation technique also was used when resin volumes were determined. All data were obtained for systems at room temperature (24-26'). Potassium was determined by flame photometer (PerkinElmer, Model 52A), using calibration curves made up using appropriate concentrations of magnesium and ammonium chloride, which interfere in the determination. Magnesium was determined by the Schwarsenbach titration method. Duplicate determination agreed within f 1%. Capacity Measurements.-The capacity of these resins is the same to all low molecular weight univalent cations or mixtures thereof at low concentrations, as was described in an earlier paper." However, in this earlier study i t was observed that in dilute solution the magnesium capacity was significantly larger (5.23 meq./g.) than for univalent cations (4.90 meq./g.), and that this excess capacity decreased gradually as the resin composition was varied in favor of the univalent ion (potassium). It was thought that complex ions as MgOHf might be responsible. These results were obtained using a sample of the commercial resin (Dowex-50) which was quite black. I n the present study this point was re-examined using resin DVB 10, prepared in this Laboratory," which had a light amber color; it was found that this resin capacity was the same. toward both magnesium and potassium and all mixtures of these ions. As a check on the earlier work, a column of the same blaok resin used in the earlier study was placed in the hydrogen state, then treated with an excess of 0.1 N potassium chloride; 4.90 meq. of hydrogen ions was eluted. When the same column in the hydrogen state was treated with excess 0.1 N magnesium chloride, 5.12 meq. of hydrogen was eluted although the magnesium capacity was 5.23 meq. The difference between the equivalents of magnesium absorbed and of acid eluted by magnesium may be due to hydrolysis or the presence of acid absorbing groups in the resin. The differences exhibited by these two resins are probably due to the presence of weak acid groups, presumably of the carboxyl type, which appear to be present in the black, commercial type resins. The Dowex-50 titration curves do show a small inflection at about pH 7, which is absent in the DVB 10 resin. The presence of these groups may be explained by the degradation of the polymer which is known to result from strong sulfonation rocedures which leave the product charred. Samples of %owex-50 obtained recently are lighter in color and more monofunctional, showing only 3% more capacity to magnesium than to the univalent ions. Both resin samples (Dowex-50) showed the same selectivity, within experimental error. Wet Weights.-The specific volume Ver (centrifuged volume of 1 gram of hydrogen resin) of the resin samples in various exchange states is shown in Fig. 1 as a function of XK', the potassium equivalent fraction (equivalents of POtassium per total equivalents present) in the resin The corresponding weight of solvent Wwr, calculate?!:; the centrifuged weight and the resin composition, is also shown. The curves are regular. The larger volume of the magnesium form resin is presumably the result of the larger hydrated molar volume of the magnesium ion. Distribution Coefficients.-Results of the determinations of distribution coefficients are shown in Table I for values obtained at four different normalities of the equilibrating solution, 1.0, 0.1, 0.01 and 0.001 N . The f i s t column
Nov., 1954
EXCHANGE WITH ACIDCATION-EXCHANGE RESIN
MAGNESIUM-POTASSIUM
985
gives X K , the potassium equivalent fraction of the equilibrating solution, the second, XK' and the third the calculated practical (molal) distribution coefficient
0.8 Here m is the molality and "a" the molal activity. Values of mr for ion species present in the resin phase were calculat&d from the weight of the solvent in the centrifuged resin.
TABLE I
I .44
.*
2
B DISTRIBUTION COEFFICIENTS FOR MAGNESIUM-POTASSIUM EXCHANGE K
K
XK
XKr
0.74 .68 .50 .29
1.0 N 0.72 .64 .48 .32
0.98 .74 .68 .50 .29
0.1 N 0.78 .39 .36 .25 .13
0.99 .87 .32
0.01 N 0.52 .28 .040
0.14 .12 .12
0.98 -50 .25
0.001 N 0.20 .029 .010
0.16 .12 .16
~
~
1.39
0.7
0.17 .18 .16 .12 '
0.12 .15 .14 .12 .13
0.6 0
1.33 0.5
1
XK'. Fig. 1.-Specific centrifuged wet weight WWr(0) and wet volume V,r ( 0 )for a polystyrencsulfonic acid resin (Dowex-50) as a function of the potassium equivalent fraction XK'. Exchange capacity, 5.20 meq./g. as hydrogen form resin. Total normality of solution phase 0.01.
-
A sample calculation of Kdm from a typical experiment is as follows: Consider the line of data in Table I where the solution normality is 0.1, XK = 0.74 and X K ~ = 0.39. While the value of K p does not depend upon the extensive properties of the resin phase, a given amount of resin is taken as a basis for calculation. Here we select the "specific" amount of resin, i.e., one gram of dry, hydrogen resin. ~ From Fig. 1 the total capacity is 5.20 meq./g., and at X K = 0.39 the specific weight of water in the resin phase is 0.73 g. Then the moles of potassium in the resin are 0.39 (0.00520) or 0.00203, the moles of magnesium 0.61 (0.00520)/2 or 0.00159. Since the water content is 0.73 g., the resin phase molality of potassium is 2.78, of magnesium is 2.18. The solution phase molalities are 0.074 for potassium, 0.013 for magnesium. Then Kdm(neglecting solution activity Coefficients) is (0.074)2 K d m = _A 2 18 (2.78)2 0.013 = The solution phase molal activity coefficients for the cationic species were calculated from the weight of the solvent in the centrifuged resin. The molal activities are for the cationic species. These were calculated on the assumption that in potassium chloride solutions ?'+ = 7- = ?'*,that in mixtures of potassium and magnesium chlorides TAKC' is the same as in solutions of potassium chloride of the same total ionic strength, and that under the same conditions ?',argclz is the same as for magnesium chloride solutions of the same total ionic strength. Accordingly, Yyg++ and YK+can be calculated. This method is described by several authors, see, e.g., Sollner and Gregor.12 I t should be noted that this type of calculation is very approximate. The value of the term u ~ K + / u M calculated ~++ in this manner does not differ by more than 25% from the value calculated using concentrations. (12) K. Sollner and H. P. Cregor, THISJOURNAL, 61, 2Q9 (1947).
Discussion Exact expressions for equilibrium constants in ion-exchange processes are known. l s , l 4 Similar expressions for polyvalent ion-exchange processes are easily derived. Neglecting solvent transport and pressure-volume free energy terms, if one assumes that the standard chemical potential of each diffusible species is the same in both resin and soluiion phases, it follows that for divalent (A)-monovalent (B) cation exchange in an ideal system, using mole fractions
where K d N is the rational selectivity coefficient; the cationic activities in this and following expressions are expressed in a consistent frame of reference for expressing composition, namely, rational, molal, etc. For real systems, the experimentally determined value of K d N is then a function of deviations from ideal behavior. Subject to the simplifying assumptions made earlier, and if the activity coefficients in the resin phase are constant, and if other effects as ion-pair formation do not supervene, KdN should be sensibly constant. Assuming that the resin phase contains only the resinate salts and solvent (neglecting non-exchange electrolyte which is a micro-component in dilute solutions)
where the n's refer to numbers of moles.. Similarly, one can define the practical (molal) selectivity coefficient Kd*
(13) H. P. Cregor, J . Am. Chsm. Soc., 73, 642 (1951). (14) H. P. Cregor and J. I. Bregman, J . Colloid Sci., 6, 323 (1951).
986
HARRYP. GREGOR, OSCARR. ABOLAFIA AND MELVINH. GOTTLIEB
VOl. 58
vr
or KdC because Q is proportional to or t o Wwr, except that it does not vary with resin phase composition. For most exchange processes there is a change in where the volume term V is the molar volume of Wwf, the specific weight of sorbed water, with XK'. Whde this factor is part of the Kdm and KdN exthe resin phase. If both resin and solution phases are ideal and pressions, this change is usually not significant. dilute, all three Kd'S are unity. For concentrated Values of Wwrfor a similar resin in different states and ideal systems, only KdNwould be unity. How- taken from the data of Gregor, Gutoff and Bregever, even at the total molalities which prevail in man9 is as follows: H, 0.88; Li, 0.88; Na, 0.77; DVB 10 resins, ( W L K ~= 8 at XK?= l), terms for the K, 0.66; NH4, 0.G7; Ag, 0.46; Mg, 0.86; Ca,0.77; solvent are so much larger than other terms that Sr, 0.72; Ba, 0.62. For magnesium-potassium exthe numerical values of Kd are not very different. change, Wwr varies from 0.66 (K state) to 0.86 The same is, of course, true for real systems. For (Mg state), a variation of only *150/o. For calexample, using the numerical values used 'previ- cium-magnesium exchange the variation is zero. Therefore only relatively small errors will result ously from a neglect of changes in WWralone. 1.59 (lS)40.5 (0.074)2 1000 Table I shows that the molal selectivity coeffiK d m = [ ( m 7 + i m 1 mX(18)55.5 cient KgMgis remarkably constant over the wide (0 ) ~55.6 1 solution concentration range from 1.0 to 0.001 N , K~= N [=(1.59 2.03 40.511~ 0 .0.1037 4 X (2.03)2 and over a wide range (XK' = 0.01-0.78) of resin The two expressions differ only by the factor 40.5/ compositions. First, it is important to point out 55.5 in the Kdmexpression and (40.5 3.62)/55.6 that the numerical value of Kd is determined to a -in the KdN expression, or by about 8%. Relatively minor extent by the choice of units, and that it small differences would also be found when using contains a solvent term. The fact that Kdmis less than unity does then not mean per se that the resin the KdCexpression. shows a preference for potassium, any more than it Both KdNand Kdmrequire the same data for their calculations; however, the practical (molal) ex- means the converse. The fact that K d m is constant over a wide range pression is employed here because of its wider usage. The use of KdCis less attractive, because it of solution concentrations is consistent with ionrequires volume data in addition. Some earlier exchange equilibria in general.14 However, Kdmis also constant at different values of X K ~ .In almost authors have simply used numbers of moles, as all cases of cation exchange, the selectivity coef~ as the equivalent fraction of ficient K B decreases the reference ion XA' increases. A typical example of this effect is to be found for potassium-tetrabut In this expression Kd becomes a function of the methylammonium exchange with sulfonic resins amount of resin taken. This factor has been cor- of different degrees of cross-linking. l4 The princirected for by later authors who introduced the capa- pal exception to this effect occurs when Kd is unity city Q of the resin, and used the expression for a particular exchange process, i.e., neither ion is preferred. With potassium-magnesium exchange, one is then led to the conclusion that here neither ion is sorbed selectively, and as a result Kd does not This latter expression is somewhat analogous to vary with XK'. and the rational (molar) selectivity coefficient
+
+
+
Kdm
