J. Phys. Chem. 1980, 84, 165-169
of interactions would tend to increase the specific volume of the solution, leading to positive values of the coefficients b? (Protein-protein interactions through hydrogen bonds would presumably be accompanied by smaller volume changer3 of uncertain sign. It is difficult to conceive of any reason ]toexpect especially compact or expanded hydrogen bonded1 structures will either form or disappear when protein-protein contacts are made through hydrogen bonds idone.) It is therefore not at all surprising that bz has been found to be positive. The fact that the effects of the higher coefficients bj 0' > 2) are not detectable suggests that no additional special effects on the volume of water occur when cluster of three or more protein molecules interact. This is perhaps somewhat surprising. At a concentration of 0.4 g of protein per gram of solution t,he volume fraction of protein is about 33%. ]For more or less spherical protein molecules 60 A in diameter the layers of water between the protein molecules (assuming for simplicity that these are uniformly distributed on the average on a simple or face centered cubic lattice) would be only of the order of 10-20-A thick (corresponding to only 3-7 water molecules). One might have expected that when the layers of water between the protein molecular surfaces become this thin, the properties of the water (and especially its density) would be significantly changed. Such an effect might have been expected to have appeared in the form of detectable contributions by the coefficients beyond b2 when c is of the order of 0.4. We see! no signs of such contributions. In this connection measurements of the specific heats of lysozyme-water mixtures by Yang and Rupley6 show a highly linear dependence of the specific heat on c from
165
c = 0 to c = 0.72. Evidently no effect of even a pairwise protein-protein interaction on the heat capacity (the equivalent to our b2 term in a power series expansion of the specific heat in terms of the weight fraction, c) could be detected in these measurements. It would thus appear that the water in lysozyme solutions as concentrated as c = 0.72 (containing only 0.39 g water per gram of protein) is not very different from pure water. It is also interesting that the value of b2 for oxyhemoglobin is considerably smaller than the values found for BSA and ovalbumin. The magnitude of b2 thus shows a certain amount of specificity. The fact that different values of b2 were found for different batches of ovalbumin (subject to very different storage conditions) is also intriguing. Acknowledgment. This work was supported by a grant from the National Science Foundation (PCM76-175104). The donation of blood by the American Red Cross is much appreciated.
References and Notes (1) J. Bernhardt and H. Pauly, J . fhys. Chem., 79, 584-590 (1975). (2) J. Bernhardt and H. Pauly, J . fhys. Chem., preceding article iin this issue. (3) R. E. Benesch, R. Benesch, and S. Yung, Anal. Biochem., 5 5 , 245-248 (1973). (4) (a) K. Linderstrom-Lang and H. Lanz, C.R. Trav. Lab. Carisberg, Ser. C h i . . , 21, 315-338 (1938); (b) J. Rasper and W. Kauzmann, J . Am. Chem. Soc., 84, 1771-1777 (1962); (c) D. W. Kupe, "Physical Principles and Techniques of Protein Chemistry", S. J. Leach, Ed., Part C, Academic Press, New York, 1973, pp 1-75. (5) G. Ogunmola, W. Kauzmann, and A. Zipp, froc. Nati. Acad. Sci. U . S . A . ,73, 4271-4273 (1976). (6) P.-H. Yang and J. A. Rupley, Biochemistry, 18, 2654-2661 (1979).
Mechanism of Ion Exchange in Zirconium Phosphates. 28. Calorimetric Determination of Heats of Rb+-H+ Exchange on a-ZrP Lennart Kullbergt and Abraham Clearfield" Department of Chemistry, Texas A&M University, Coi/ege Station, Texas 77840 (Received July 5, 1979) Publication costs assisted by Texas A&M University
The thermodynamics of the Rb+-H+ exchange on zirconium phosphate have been studied. The heats of the exchange on three samples of widely different crystallinities have been determined calorimetrically. For the most crystalline exchange the reaction is exothermic with virtually constant heat changes up to 75% rubidium loading. For that reaction, the enthalpy change was found to be -2.25 kcal per mole of rubidium (1cal = 4.184 J) and the corresponding entropy change -36 eu (1eu = 4.184 J K-l mol-l). In the case of the nearly amorphous exchanger, the reaction is initially exothermic, but then the heat function passes through a broad maximum and becomes progressively more endothermic. A maximum value of AHo, = -3.3 kcal per mole of exchanger was obtained at 45% of exchange. For the amorphous exchanger the Rb+-H+ exchange isotherm has also lbeen determined. The exchange reaction is reversible and the equilibrium constant was found to be 2.8 X
Introduction In preceding papers in this series, the effect of crystallinity of the exchanger on M+-HS (M' = Li+, Na+, K+, Cs+)exchange of a-zirconium phosphates (a-ZrP) was examined. Ion exchange isotherms and calorimetric heats of exchange have been determined on samples varying from amorphous to highly ~rystalline.l-~ Very few thermodynamic data on Rb+-H+ exchange on a-ZrP have been reported to date. Alberti et aL8 determined the isotherm for the exchange on crystalline a-ZrP, On leave from L u n d University, Lund, Sweden. 0022-3654/80/2084-06 65$0 1.OO/O
Zr(HP04)2.H20,and Hasegawa and Tomitag reported distribution coefficients for the same exchanger. 'Two studies with amorphous zirconium phosphate have been carried out. From the temperature dependence of the Rb+-H+ exchange reaction Baets16,1° working with trace quantities, and Amphlett et a1.,l1 studying the exchange up to a loading of 1.3 mequiv/g, determined enthalpies and entropies of exchange.12 Therefore, to complete the thermodynamic study on alkali metal ion exchange on a-ZrP the present Rb+-H+ exchange study was undertaken. Heats of exchange were calorimetrically determined for three a-ZrP samples of 0 1980 American Chemical Society
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The Journal of Physical Chemistry, Vol. 84, No. 2, 1980
Kullberg and Clearfleld
different crystallinities. For the amorphous sample, the exchange isotherm was also determined. All measurements were performed at 25 “C.
Experimental Section Chemicals. Reagent grade chemicals were used. The zirconium phosphate samples used in this study, 0.5:48, 4.5:48, and 12:336, were the same as those described in the previous Water contents were redetermined as loss of weight on ignition to 800 “C. Ion-Exchange Studies. Equilibrations of exchanger 0.5:48 with titrant (RbCl+ RbOH) or (RbC1 HC1) were carried out by a batch technique at an ionic strength, p , of 0.1 M and 25.0 f 0.1 “C as described bef0re.l The solution to solid ratio was 100 mL/g “anhydrous” exchanger and equilibration times were 4-5 days. For the titrations in the reverse direction preweighed samples were first exchanged to 70% load with RbCl RbOH and shaken for 48 h. Higher loadings were found to introduce appreciable phosphate hydrolysis in the exchanger. The requisite amount of HC1 was then added and the whole equilibrated for an additional 2-3 days. After equilibration the pH was measured on the filtrate with a Fisher Accumet Model 144 pH meter fitted with a Fisher microprobe combination electrode. For determination of the amount of hydrogen ion and phosphate an aliquot of the filtrate was potentiometrically titrated with standardized NaOH. Another aliquot of the filtrate was passed through a strongly acidic, cation exchange resin (Dowex 50W-X8) to exchange Rb+ in solution for H+. The effluent was subsequently titrated with base. Calorimetric Measurements. A constant temperature environment type LKB 8721-1 reaction solution calorimeter was used. The calorimeter has been described in detail in a previous paper.3 The heat measurements were made by using a titration technique in which 0.3 g of a-ZrP -t80 mL of 0.1 M RbCl in the reaction vessel was titrated with a 0.1 M RbOH + 0.1 M RbCl solution. For each addition (1.00 mL) of titrant, the heat change was recorded. A total of -20 mL of titrant was added in each titration series. This was enough to cover the whole range of exchange. An amorphous a-ZrP sample equilibrated with a 0.1 M RbCl solution exchanges a significant amount of rubidium for hydrogen. For a crystalline sample, the extent of exchange is small, although not negligible. In order to measure the heat for this exchange, the calorimetric procedure described previously was used.3 In brief, 0.3 g of finely ground exchanger in the hydrogen form was weighed into an ampoule and water (0.5-0.6 mL) was added to eliminate heat of wetting effects. The ampoule was then sealed and put into the calorimeter where also 80 mL of a 0.1 M RbCl solution was introduced. After temperature equilibration, the ampoule was broken and the heat change for the reaction between exchanger and rubidium ions was recorded. After each calorimetric determination the extent of exchange was determined by analyzing the solution.
+
+
Calculations Ion Exchange. Aliquots of the filtrate were potentiometrically titrated with NaOH. From the base added to pH 5.2 the sum, A, of the amount of hydrogen ions and the amount of phosphate in the filtrate was obtained. The amount of phosphate, B, was obtained from the amount of base required to change the pH from 5.2 to 8.0. In this range H2P04-is converted to HPOd2-. The total amount of hydrogen ions released by the exchange reaction is then given by ( A- B + C) where C is the amount of OH- added. When HC1 was used instead of RbOH, the term C refers
to the amount of HC1 added and its sign is negative. The rubidium ion uptake was obtained from the difference of base consumed in titrations on samples of the filtrate before and after passing through the strong acid cation exchanger. Treatment of Calorimetric Data. The standard heat of partial exchange, AH”,, refers to the reaction
-
HH-nsHH20-t- aHzO + 2xRbC1Rb2,H2-2xnsMH20+ (a + nsH- nsM)H20 2xHC1 (1)
+
Bars refer to the counterions inside the exchanger. In this equation, one formula weight of mixed exchanger containing 2x equiv of Rb+ is formed from 1mol of zirconium phosphate in its pure hydrogen form. All reactants and products are in their standard states. That is, the mixed exchanger is in equilibrium with an infinitely dilute solution of RbCl and HC1 in the right proportions to maintain the composition of the exchanger. The pure hydrogen ion and rubidium ion forms of the exchanger are in equilibrium with infinitely dilute solutions of HCl and RbC1, respectively. nSHrepresents the number of moles of water in one formula weight of zirconium phosphate (E) while nsM denotes this value for the mixed exchanger. When x = 1, we obtain the standard heat of complete exchange, AH”. However, since the exchanger greatly prefers hydrogen ion, it is necessary to add rubidium hydroxide in order that the entire range of rubidium ion uptake may be covered. Thus, the reaction for which the heat is measured is
+
-
HH-n,H(u)H20 + 2nRbCl + 2yRbOH vH,O Rb2rH2-2,nsM(U)H20 + (u + nsH(u)- nSM(”) 2y)H20 2(n - x + y)RbCl + 2(x - y)HC1 (2) ~
+
+
where nSH(”) and nsM(u) are the numbers of moles of water in one formula weight of exchanger before and after exchange, respectively. Then, following the procedure developed p r e v i ~ u s l yone , ~ can show that
+
AH”, = AHx - 2yAH0N - 2(x - y)$L(M”HCi) 2(x - Y)$L(M’R~c~) + ~ Y ~ J L ( M ’ R ~(3) oH) In this equation, AHx is the measured heat of reaction, is the heat of neutralization, 2y is the equivalents of‘ RbOH consumed by the exchange reaction, and c$L denotes the relative apparent molar heat contents of the indicated species and molarities. Values of AHoNand dJL were determined in separate calorimetric experiments. Thus from heats of dilution of RbOH (a 0.1 M RbOH + 0.1 M RbCl solution was added to a 0.1 M RbCl solution), $ L(MRboH) was obtained. With the same titrant added to a 0.01 M HC1 + 0.1 M RbCl solution the heat of neutralization, - A H O N = (13.53 f 0.05) kcal/mol, was obtained. This value is in good agreement with literature data. The “best” heat of neutralization value at 25 “C and zero ionic strength seems to be -13.34 kcal/mol.13 However, our value was used because it refers to the present experimental conditions. The 4 terms of HC1 and RbCl in eq 3 are both negligible (C0.05 kcal/mol). In most cases, these two terms are zero because x = y, cf. eq 3. The AHz values were calculated by dividing the measured heat effects by the amount of water free exchanger. It is to be noted that the measured heat effect, Qn,expt, is given by A H O N
n Qn,expt
=
Qs
+
1=1
(4)
where Q, is the heat effect for adding a-ZrP to 0.1 M RbCl and Q, are the heat effects obtained in the titration, i.e., for adding base to the slurry of exchanger -t- 0.1 M RbC1.
The Journal of Physical Chemistry, Vol. 84, No. 2, 1980 167
Ion Exchange in Zirconium Phosphates
7-7111
7
7
8
2
LL. I 8
_-IL-LL
i
6
4
2
0
2
4
6 rreq
nieq
01
8
02
03
04
OH7g
06
07
08
09
10
x Rb
Figure 1. Potentiometric ion exchange titration curve for sample 0.248. Titrant: forward direction, 0.1 M RbOH 4- 0.1 M RbCl or 0.1 M HCI 4- 0.1 M RbC1 (open circles); backward titration, 0.1 M HCI (filled circles). The amounts of O K and HS added are calculated per gram of anhydrous ZrP.
1
IO
05
-
Figure 3. log K, vs. equivalent fraction of rubidium ion in the solid for sample 0.5:48.
I
4
I
T
i
06
07
08
ncal/mol ZrP
i
8 6 UH
4
4
2
01 1
2
3
4
5
6
w /g
The mole fraction of rubidium ion in the exchanger, X R ~ , has been calculated by dividing the amount of hydrogen ion released by the theoretical exchange capacity of zirconium phosphate, 7.54 mequiv/g, based on the totally anhydrous form ZrP207.
Result $1 Ion Exchange Studies on Sample 0.548. The raw titration data are shown in Figure l. Because of the large uptake of Rb+ by sample 0.5:48 when equilibrated with 0.1 M RbCll the curve was extended to lower Rb+ loads by additions of HC1. Corrected titration data are shown in Figure 21, which gives the actual hydrogen ion release and rubidium ion uptake as a function of pH. The extent of hydrolysis is given by the solid line at the far left. The data show a one-to-one correspondence between hydrogen release iind rubidium uptake. Thus, the ZrP sample behaves as a perfect exchanger. The phosphate release is small in acid solution. However, it increases considerably at pH > 6 . As seen from Figure 2, the data for the forward and backward titration agree, which shows that the exchange reaction is reversible. Thus, it is possible to calculate its equilibrium constant. The reaction can be written Ei d- Rb'(aq) + m b f H+(aq) (5) I _ I -
where represents exchanger 0.5:48 and RRb represents the rubidium exchanged state. The thermodynamic equilibrium constant for this reaction is then = aRbaH+/zHaRb+
03
04
05
09
R Rb
7
Figure 2. Corrected potentiometric titration curve for sample 0.5:48. Symbols are as follows: Rb+ uptake (0),H+ release (0). Open symbols for forward direction, filled symbols for backward direction. Solid line at left represents phosphate release. All quantities calculated per gram of anhydrous ZrP.
PRkjq
02
(6)
where the barred quantities represent activities of the ions
Flgure 4. Standard heats of partial exchange as a function of rubidium ion loading for exchanger 12336. Circles and squares represent two different titration series.
in the solid phase and the unbarred ones of the ions in the aqueous phase. Let Kc = X R b a H + / F H a R b + (7) where X refer to equivalent ionic fractions in the exchanger. Then, if the change in water content of the gel during the exchange is small14 log K@$ = S l0 l o g Kc dXRb
A plot of log Kc vs. X R b is shown in Fi ure 3. From the 5:4f area under the curve, a value of @Rb,H = 2.8 x was obtained. For this evaluation, extrapolations at low and high loads had to be made, which detracts from the accuracy of the determination. However, the given value is estimated to be accurate to within 20%. Heat Data on Sample 12336. The AHoxvs. ion uptake curve for this crystalline exchanger is given in Figure 4. Thermal equilibrium after addition of base was achieved in 3-4 min for loadings up to 60%. Beyond that point progressively longer times were required for equilibrium. No measurements were performed at X R b > 0.85 because of the slowness of reaction and the increasing hydrolysis effect. The AHo,curve, shown in Figure 4, is virtually linear up to a loading of 75%. A t higher loading the heat, of reaction is small. The change of the slope of the curve at 75% of loading coincides with the complete conversion of a-ZrP to phase H0.5Rb1.5reported by Alberti et al.s They also report that a solid solution is formed up to 25% of Rb+ loading. From the AH", curve it is evident that there is no difference in the heat of the exchange reaction below and above 25% of uptake. The Rb+-H+ exchange reaction on crystalline a-ZrP is not reversible so that it is not legitimate to derive eqlui-
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The Journal of Physical Chemistry, Vol. 84, No. 2, 1980 I
I
I
I
I
I
I
I
Kullberg and Clearfield
I
I
I
I
03
04
I
I
I
!
l
0 5
06
07
08
09
-&Hi kcal/mol ZrP
4l 2
I
I
I
I
I
I
1
I
0
1
2
3
4
5
6
7
01
02
8
-
XRb
meq OH-/g
Figure 5. Potentiometric ion exchange titration curve for sample 12:336 (circles) and for sample 4.548 (dashed line). Filled circles represent values determined by batch technique. The amount of base added is calculated per gram of anhydrous ZrP.
Figure 6. Standard heats of partial exchange as a function of rubidium ion loading for exchanger 4.5:48. Circles and squares represent two different titration series.
librium constants. However, following a procedure previously invoked for Na+-H+ e ~ c h a n g e ,one ' ~ can think of the first part of the ion exchange reaction as being ideally 2/3HH.Hz0
+ Rb+ + nHZO +
'/3Ho,SRb1,5(1.5n + 1)HzO + H+ (9)
KktfV
=
aRbaH*/aHaRb+aWn
(10)
In the range G75% of Rb+ loading one solid of constant composition is converted to another of constant composition. If we choose as the standard reference state an activity of 1 for the ions in the pure solids, we get where the equilibrium constant is expressed per mole of Rb+. In order to determine this equilibrium constant, the pH titration curve, shown in Figure 5 , was run. The curve was recorded in a dynamic titration by using a 0.1 M RbCl + 0.1 M RbOH solution as titrant. Points were taken at 1-h intervals. From experiments made by batch technique (2 days of shaking) it was shown that the system came very close to equilibrium within 1h for loads up to X R b = 0.75, see Figure 5. The curve exhibits a pronounced plateau (0.1 C X R b C 0.75) with an approximately constant pH, indicating the presence of two phases. When the pH at the midpoint of the plateau, pH 7.4, and an a R b + (for p = 0.1) of 0.076 are used, an equilibrium constant of 5.2 X lo-' results. This leads to a free energy of 8.6 kcal per mole of rubidium for the exchange reaction, cf. eq 9. The enthalpy change for the same reaction, obtained from the AH", curve, is -2.25 kcal per mole of rubidium. From the relation A S = -(AG - AH)/T (12) the entropy change was found to be -36.4 eu. The estimated errors in AG and AH are 0.3 and 0.1 kcal/mol, respectively. This gives an error for AS of 1.5 eu. Heat Data on Sample 4.5:48. The heat of exchange for this sample, characterized as semicrystalline, is strikingly similar to that for the crystalline sample, cf. Figures 4 and 6. The same behavior was shown in the Na+-H+ exchange on a-ZrP where the heat curve for sample 4.5:48 was almost identical with that for a fully crystalline sample. Also the pH titration curve for the rubidium exchange on exchanger 4.5:48, shown in Figure 5 as a dashed line, is similar to the pH curve for the exchange on a-ZrP, 12:336. However, for sample 4.5:48 the plateau of the curve is not reached until 1.5 mequiv of OH-/g has been add_ed. This indicates that there is a solid solution range up to X R ~ = 0.2.
01
02
03
04
05
0 6
07
38
09
XRb
Figure 7. Standard heats of partial exchange as a function of rubidium ion loading for exchanger 0.548. Open circles and squares from titrations, filled circles by ampoule technique.
Heat Data on Sample 0.5:48. The AH", function for this almost amorphous ZrP, see Figure 7, is significantly different from those of the two more crystalline ones. In this instance, the curve is smooth and the heat function, being exothermic throughout the whole exchange, goes through a broad maximum with a maximum value at X R b = 0.45. Beyond 50% of uptake the exchange rate became progressively slower with loading, affecting the precision of the measurements. Thus, at a loading of 65%) attainment of equilibrium required up to 1 h. This, in combination with the increase of phosphate release at higher rubidium loadings, limited the range of the study to X R b C 0.7. The Rb+-H+ exchange on 0.5:48 is reversible. From the corrected selectivity coefficients, Kc, see eq 7 and Figure 3, the differential free energies of exchange, AGx, were calculated from the relationship -AGx = RT In Kc (13) The differential heats of exchange, AR,,were obtained from the slopes of the curve in Figure 7 multiplied by a factor of 0.5. This factor arises because the AHo, values of Figure 7 are expressed in kilocalories per mole of exchanger while the fix values are given in kilocalories per mole of Rb+.16 The differential entropies of exchange were calculated from eq 12. The differential quantities are plotted in Figure 8.
Discussion For ion exchange reactions such as the ones described here, the observed entropies, AS", can be divided into two terms as1' A s " = As,, + (So, - S'M) (14) where (SoH- SoM) is the difference in entropies of the exchanging ions and AS,, represents the entropy difference between the cation and hydrogen ion forms of the ex-
Ion Exchange in Zirconium Phosphates
01
C 2
0 3
04
05
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The Journal of Physical Chemisrty, Vol. 84, No. 2, 1980 109
06
07
08
09
I O
XRb
Flgure 8. Differential quantities of exchange as a function of rubidium ion loading for exchanger 0 5 4 8 .
changer. That is, ASex reflects changes in hydration of the exchanger and differences in lattice distortion of the two forms of exchanger. For Rb+ the difference S O H - so^ is equal io -16.5 eu.18 The Rb+-€l+ exchange reaction on crystalline a-ZrP up to 75% of exchange is accompanied by an entropy change of -36.4 eu (calculated per mole of rubidium). Therefore, for this reaction AS,, = -19.9 eu. Alberti et al.8 found that the rubidiuni exchanged phase contains 2 mol of water, i.e., the phase can be written H0.5Rbl5m2H20. This means that 1mol of water is added to the exchanger during the exchange. In line with the discussion in a previous paper? one can assume that the “freezing” of 1 mol of water will cause an entropy decrease of -6.1 eu. The entropy contribution due to difference in lattice distortion of the two forms (of exchanger should not be large. Thus, the highly negative entropy term suggests that the uptake of water by the exchanger during the exchange reaction is higher than the proposed one. In order to clarify this discrepancy, a determination of the water contents of the Rb+ exchanged phase was therefore performed. A sample with a rubidium loading of 75% was dried over a saturated NaCl solution (relative humidity, RH = 0.76). The weight loss at ignition to 800 “C was 6.02%, which gives a formula of H0.(,Rbl,51H20. Alberti and co-workers conditioned their s(mpleover a saturated solution of BaC1, (RH = 0.90) before determination of the water contents. Thus by slightly lowering the aqueous pressure (from a RH of 0.90 to 0.76) 1 mol of water is removed from the exchanger. Therefore, it is very plausible that the water contents of the exchanger in solution is higher than when conditioned over the BaC12solution. -- The large interlayer distance, 10.6 A, found for the Ho.5Rbl,5nH,0phase also indicates that at least 3 mol of water are present in this phase,19giving support to the conclusions drawn from the AS value. The Rb+-K+ exchange on amorphous ZrP could not be carried out to completion. An extrapolation of the AH”, . _ -
curve to x = 1was deemed to give a very unreliable result. Therefore, AH and A S for the overall reaction could not be determined. However, the differential thermodynamic quantities can be used to gain insight into the exchange process. The differential heat of exchange, being strongly exothermic at low Rb+ loading, decreases continuously with loading (Figure 8). This can be accounted for on the assumption that in amorphous ZrP the size of the cavities is not uniform as in the crystals but varies over a range of values. The most favorable exchange sites presumably are located in the largest cavities. Thus, initially the RbS need not shed its water of hydration. However, as the rubidium ions enter smaller and smaller cavities, they must give up a progressively larger share of the hydration sphere resulting in a steady decrease of --ARx. The differential entropies for the rubidium exchange 011 sample 0.5:48 are negative throughout the exchange although slowly increasing with loading. TJp to 50% of exchange the entropy change is fairly constant, averaging about -22 eu. From eq 14 we obtain AS,, -5 eu. ‘This shows that the water uptake by the amorphous Zrk in the Rb+-H+ exchange is small. The same behavior was found for the Cs+-H+ exchange on sample 0.5:48.4 A discussion and comparison of the results of this c;t,udy with results of our previous thermodynamic studies on alkali metal ion exchange on a-ZrP will. be presented iir forthcoming papers in this series. 5:
Acknowledgment. This work was slipported by the Robert A. Welch Foundation under Grant 55204 for which grateful acknowledgment is made. References and Notes A. Clearfield, A. Oskarsson, and C. Oskarsson, Ion Exch. Membr., 1, 91 (1972). A. Clearfield and A. Oskarsson, Ion Exch. Membr., I,205 (1974). A. Clearfield and L. Kullberg, J . Phys. Chem., 78, 152 (1974). A. Clearfield and L. Kullberg, J. Phys. Chem., 78, i812 (1974). A. Clearfield and D. A. Tuhtar, J . Phys. Chem., 80, 1296 (1976). A. Clearfield and D. A. Tuhtar, J . Phys. Chem., 80, 1302 (1976). A. Clearfield, G. A. Day, A. Ruvarac, and S.Milonjic, J. Phys. Chem., submitted for publication. G. Alberti, U. Costantino, S. Allulli, and M. A. Massucci, J . Inorg. Nucl. Chem., 37, 1779 (1975). Y. Hasegawa and I. Tomita, Bull. Chem. SOC.Jpn., 43, 301 1 (‘1970). L. Baetslb, J. Inorg. Nucl. Chem.; 25,271 (1963). C. B. Amphlett, P. Eaton, L. A. McDonald, and A. J. Miller, J . fnorg. Nuci. Chem., 26, 297 (1964). Ehets6 reports AH= -9.7kcal/mol and AS = -25 eu for the Rbt-Ht exchange on a-ZrP while Amphlett et ai. found that ANand PSvary with the composition of the exchanger. Mean values for AH and AS for the exchange up to a loading of 1.3 mequiv/g were found to be -7.6kcal/mol and -25 eu, respectively. I. Grenthe, H. Ots, and 0. Ginstrup, Acta Chem. Scand., 24, 1067 (1970). W. J. Argersinger, Jr., A. W. Davidson, and 0.D. donner. Trans. Kan. Acad. Sci., 53, 404 (1950). A. Clearfield and A. S.Medina, J . Phys. Chem., 75, 3750 (‘1971). The total exchange capacity of a-ZrP is 2 equiv per formula weight. H. S. Sherry, “Ion Exchange”, Vol. 11, Marcel Dekker, New Yolk, 1968. D. R. Rosseinsky, Chem. Rev., 65,467 (1965). G. Alberti, Acc. Chem. Res., 11, 163 (1978).
