11112
A.
Clearfield and L. H. Kullberg
n the Mechanism of Ion Exchange in Zirconium Phosphates. XII. Calorimetric Determination of Heats of Cesium Ion-Hydrogen Ion Exchange"" Iearfield" and L. H. Kuiibergqb Department of Chemjstry, Ohio University, Athens, Ohio 4570 I (Received March 20, 1974)
The heats of Cs+-H+ exchange on two samples of zirconium phosphate of different crystallinities have been determined calorimetrically. The reactions are initially exothermic. The nearly amorphous sample attained a maximum value of AH,' = -4.5 kcal/mol of exchanger at about 55% of exchange. At higher loadings the reaction became progressively endothermic. The high initial preference of amorphous zirconium phosphate for Cs+ relative to other alkali metal cations stems from the greater exothermicity of the reaction. For the more crystalline exchanger -AH,"increased linearly up to 75% of exchange whereupon the reaction became endothermic. This indicates the formation of an exchanged phase with 1.5 mol of Cs+ per formula weight of exchanger. The results of this study are compared to those of a similar one carried out previously for the Na+-H+ system.
htroduetion Addition of phosphoric acid or a soluble phosphate to an aqueous solution of a zirconium(1V) salt yields an amorphous, insoluble gel commonly termed "zirconium phosphate." This gel may be converted to a crystalline phase by boiling in strong phosphoric acid.2 The crystals are zirconium bis(monohydrogen orthophosphate) monohydrate, Zr(HPQ&H20, referred to as a-zirconium phosphate or a-ZrP. By proper coiitrol of acid concentration, temperature, and contact time it is possible to produce a-ZrPwith almost any desired degree of ~rystallinity.~-~ Interest centers on these products because they exhibit ion-exchange properties. The crystallinity of the exchanger has a marked influence upon its ion exchange behavior. Thus, it is important that the exchanger phase be well characterized in relation to the observed ion-exchange properties. Lack of recognition of this fact has led to conflicting results being reported by different investigators. A case in point is provided by the Csi-H+ exchange system. In Table I are collected pertinent thermodynamic data derived from Ce+-H' exchange isotherms as reported in the literature.6-10 Part of the disparity in these values is due, no doubt, to differences in the crystallinity of the exchanger. However, it should also be recognized that differences arise from the choice of exchange capacity ascribed to the zirconium phosphates. These points have been discussed a t length p r e v i ~ u s l y . ~ J ~ J ~ This paper is part a systematic examination of the ionexchanger properties of zirconium phosphates. In this connection exchangers with different degrees of crystallinity were prepared and characterized as to crystallite size, composition, and dehydration characteristic^.^ Ion-exchange isotherms and calorimetric heats of Na+-H+ exchange have been determined on these s a m p l e ~ . ~Subsequently J~ the exchange isotherms for the Cs+-H+ system were also determined.*l In this paper we report on the heats of exchange for the Cs+-H:+ ,3ystem and the insight these provide into the exchange process.
Experimental Chemicals. Cesium chloride solutions (prepared from Fisher Certified Q X 1 ) were standardized by exchange onto ~~~~~~~
The Journal of Phpiciii Chemistry, Vol. 78, No. 78, 1974
a cation exchange resin in the hydrogen form followed by titration of the liberated acid. Cesium hydroxide was prepared by passing a 2 M CsCl solution through an anion exchange column in the hydroxide form. The cesium hydroxide solution was then diluted and standardized against NBS potassium acid phthalate. In the preparation of the hydroxide solutions care was taken to avoid C02 uptake by using a nitrogen atmosphere. The zirconium phosphate samples used in this study, 0.5:4$ and 4.5:48, were the same as those described in the previous studies.5JlJ2 Water contents were redetermined as loss of weight on ignition to 800'. Calorimetric Measurements. The calorimeter and calorimetric procedures were identical with those described previously.12 A quantity (0.14-0.40 g) of the exchanger in its hydrogen form was weighed into a thin-walled 1-ml glass ampoule. Before weighing the zirconium phosphate was ground in an agate mortar. To prevent heats of wetting during the reaction a small volume (0.5-0.7 ml) of water was added to the exchanger in the ampoule. By this procedure only negligible ( 0.87 because of the slowness of the reaction and the high hydrolysis effect. Examination of the titration curve (Figure 2 ) reveals an initial sharp rise in pH with Cs+ uptake to about 0.8 mequivlg. In this region the Cs+ goes into solid solution.11 However, before the curve levels out a new phase, WHF(Cs-H), is observed. Apparently these changes are
mxo
and a t X c s >* 0.7 almost 30 min was required. This fact coupled with the increasing hydrolysis limited our measurements to N 0.8. At low cesium ion loadings the selectivity for this ion is quite high and a cesium ion mole fraction of 0.25 was reached without the addition of base. Thus to obtain points at lower loading IJome EICl had to be added. Since the CsC-H+ exchange reaction has been shown to be reversible for 0.5:48 and the isotherm determined, values of the corrected selectivity coefficients KcCs+IH+ were available.ll Thus it was possible to calculate the differential free energies of exchange, AGx, from the relationship
.xes
The Journal of Physical Chemistry. Vol, 78. No. 18, 1974
Calorimetric Deiermination of Heats of Cs+-H* Exchange
1815
not reflected in the enthalpy term since the AHx curve is an unbroken straight line. 7-
Discussion In determining accurate values of AHx" two possible sources of error had to be considered, the effect of hydrolysis and the t"rtainty in the values for the relative apparent molal heat contents. However, these later values are small so that their total contribution to eq 2 is of the order of 0.1 kcal. Thus, even a large uncertainty in one of these quantities would introduce a very small error into the AHxo values, Similaply the enthalpy changes for the hydrolysis reactions are small and are known with good accuracy.lZJ6 Therefore, the error due to hydrolysis is very small, i.e., 50 call mol-l. In conclusion we estimate our overall errors to be of the same order of magnitude as for the Na+-H+ study,12 namely, about :k2% s t OW to moderate loads rising to f 4% at high loads. Some very ix~terestingconclusions concerning the mechanism of exchange can be drawn from the thermal data and these are dismssed befew for the individual exchangers. Sample 4.5:1&. The change from exothermic to an endothermic reaction occurs at a loading of 75% for this exchanger. This corresponds exactly to 1.5 mol of Cs+ per mole of exchanger. 11, is also known from the previous ionexchange studg'l that along the relatively flat portion of the titration curve (Figure 2) two solid phases are present. They are the original 4.5:48 containing some Cs+ statistically distributed axid a new exchanged phase called WHF(Cs-W). The interlayer spacing of this phase varies from 11.0 to 11.6 depending upon the Cs+ content. At loads approaching 75% the WHF phase is the only one present except for a r~mallamount of another phase with interlayer spacing 13.4 A. This latter phase is thought to represent the fully exchanged phase, but hydrolysis and disordering of the crystal lattice become too severe at higher loads to allow positive identification. The sequence of exchange reactions can then be represented by the following scheme Xr(WP04)pHzC
-AH;
Kcal/mole ZrP
-
c S+
ZlrCs,H2 - y(P04)2 .X'H20
-
cs+
(solid solution formation) cs'
4)2nx"!d,0 WIIF(Cs- H\
Zr(CsPOd)z*X"'H,O (5) 13.6-A phase
A rational for the formation of the WHF phase has been given based on structural concepts.ll In the ammonium ion exchanged phase four NH4+ groups surround each P-0exchange site and are In turn coordinated by four such oxygens and one water molecule.l7 The cation-cation distances range from 3.43 to 3.88 A. If cesium ions ( P = 1.69 A) replaced the ammonium ions in the lattice, the electrostatic repulsions would increase because of the very closeness of the ions. This repulsion could be diminished by further increasing the interlayer distance. However, the distance separating the negatively charged oxygens in directions parallel to the layers is fixed at about 5.3 A.l8 Thus, irrespective of the interlayer separation crowding in the case of the large Cs+ would be imere. An easy way to alleviate this crowding is to replace only 1.5 of the two hydrogens by cesium ions. Then only three Cs+, on the average, are required to pack around each 0- site. Both the titration curve and the LAX0 curve tend to corroborate this supposition. No evidence is observed for the formation of an inter-
Figure 5. Standard heats of partial exchange as a function of cesium ion loading for semicrystalline a-ZrP (4.5:48). The dashed line denotes similar data for Na+ exchange (ref 12).
mediate phase (except for a small amount of initial solid solution formation) such as the half-exchanged phase formed in the Na+-H+ system. Why the cesium ions do not form such a phase might become clear if the structure of the half-exchanged phase were known. Loadings of greater than 75% require packing four Cs+ around each oxygen with consequent high electrostatic repulsive effects and larger steric barriers to diffusion. These effects are reflected in the slower rates of thermal change, the endothermic nature of the reaction, and the higher extents of hydrolysis accompanying these higher loadings. In the case of sodium ion exchange on a-ZrP, it was shown that the enthalpies for sample 4.5:48 were almost the same as those for the fully crystalline exchanger. Furthermore, the titration curve for 4.5:48 resembles that of a more crystalline sample 12:24.3 Thus, the experimental results for 4 5 4 8 can be taken as representative (or nearly so) of Cs+ exchange on a crystalline exchanger. If the assumption is made that the exchange reaction is microscopically reversible and the treatment given previously for Na+ is followed,lgthen KCs+/H+
(6 1
,+/acS+
Using the pH at the approximate midpoint (Xes = 0.45) of the curve, 7.75, and the acs (for = 0.1) of 0.076, yields an equilibrium constant of 2.3 X lop7.This leads to a free energy of +9.0 kcal/mol for the hypothetical reaction Zr(HP04),*H,0(cr) + 1.5Cs*(aq) ZrCsi.sH,.,(PO,)z.HzO
+
1, 5Bt(aq) (7)
The enthalpy for this reaction is -5.3 kcal and the calculated entropy is of the order -50 eu. Thus, highly unfavorable entropy effects are responsible for the large positive AGO value. This stems from two main causes. The ordering of water molecules in hydrating 1.5 mol of protons which enter the aqueous phase and a similar high ordering of Cs+ in the crystal lattice. The former effect should amount to about 1.5(-17.2) eu or -25.8 eu (vide infra). Sample 0.5:48. The equilibrium constant for Cs+-H+ exchange on 0.548 has been given previouslyll as K = 2.0 X The Journal of Physical Chemistry, Voi. 78, No. 18. 1974
A. Clearfield and L. H. Kullberg
1816
TABLE I: Literature Data for Cs+-H+Exchange on a-ZrPa Method of determination of AGO, kcal/mol
AH', kcal/mol
-2.60
-10.01
-0.93
-8.8
Temp, "C
Crystallinity
dK/dT (5-70')
20
dK/dT (25-40')
25 25
Semicrystalline Amorphous Semicrystalline Semicrystalline Semicrystalline
AH
CO "03 -0.38
-4.5
-0.59
-10.3
Calorimetry
25
dK/dT (50-200')
50
Loading, mequiv/g
Ref
5/3
Trace
6
NR NR
1.32-1.64 0 57-0.63
7 8
NR
2.02
9
1.96
2.12
10
200
.+2.67 a
P/Zr
AGO and AH' are given in kcal/mole of Csf loaded. b Mequiv/g of air dried a-ZrP.
Thus; the overall exchange reaction is highly unfavorable leading to A.G29s0 = $6.4 kcal molv1. Because the reactions coudd not be carried to completion enthalpies and entropies for the overall reaction are not available. However, the differential thermodynamic quantities can be used to gain some insight into the exchange process. Initially the free energy is negative as a result of the high exothermic character of the exchange reaction. However, the exothermicity steadily decreases with loading while the entropy remains relatively unchanged. Thus, a parallel increase in AlC, accompanies the enthalpy changes. At a loading of X c s 0.6 thle reaction becomes endothermic with a larger slope than the preceeding exothermic reaction. However, the eintropy values also turn upward sharply so that there results only a small further increase of the free energy* These results can be accounted for on the assumption that in amorphous or weakly crystalline gels of a-ZrP the size of the cavities is not uniform (as in the crystalsls) but varies over a range of values.12t20The cesium ions initially occupy the most favorable sites. The high negative enthalpy must result. from the hydration and dehydration of the exchanging ions. Consider the hypothetical reaction
=
H'(g)
+
Cs' (as)
-
H' (as)
+
Cs' (g)
(8)
for which AM = -197.8 kcal/mol.21 This high enthalpy value is partially offset in the ion-exchange reactions by the bond breaking and bond making accompanying exchange and by the fact that the hydrogen ion is probably partially hydrated in the gel. The most, favorable exchange sites presumably are situated in the largest cavities. Thus, initially the Cs+ need not shed any of its water of hydration. However, as the cesium ions enter small!er and smaller cavities they must give up P progressively larger share of the waters of hydration resulting in ,a steady decrease of AR,. There i s exactly 1 mol of cavities per formula weight of a-ZrR.ls Thus, when > 0.5, a second cesium ion begins to enter the cavities with consequent crowding of the cations. Severe electrostatic repulsion forces must come into play and progressively increase in magnitude as smaller cavities are 'filled. These repulsions eventually become the dominant factor resulting in the observed rapidly increasing endotheirmicity of the reaction. Coincident with this crowding, the gel katl.ice becomes more disordered as evidenced by the eventual destruction of its X-ray powder patternll and the high release of phosphate to the solution. These effects must be partly responsible for the upturn of the AS, curve.
xes
The Journal of Physical Ghe,mistry, Vol. 78, No. 18, 1974
Comparison with Previous Work. Initially cesium ion is greatly preferred to sodium ion by gel 0.5:48. Reference to their respective ax and AS, values12 shows that this preference is an enthalpy effect. The enthalpy change for the exchange reactions can be thought to result from three processes, namely, (i) the heat consumed in bond breaking as when H+ is released from the exchanger, (ii) the heat released in the formation of bonds to the incoming cation, and (iii) the enthalpy changes accompanying hydration and dehydration. This last term is closely equivalent to the enthalpy change for reaction 8 which for Na+-H+ exchange is -163.8 kcal mol-l. Thus, in order for the sodium ion exchange to be more exothermic than the corresponding Cs+ exchange, the contribution from term ii must be of the order of 34 kcal molp1. A value of this magnitude is certainly not achieved. Presumeably the cations initially locate at the center of the cavity and since the gel is in a swollen condition,ll the anion-cation distance is very large. This is equivalent to a weak anionic field strength based on the model of Eisenman.22Thus cesium ion should be preferred. However, as a second cation enters the cavities, the cations are forced closer to the anionic sites. In addition the gel layers move closer together with loading so that the anionic sites approach more closely to the cations. Thus the anionic field strength increases with loading whnch results in a reversal of preference. This viewpoint is somewhat supported by the fact that, in crystalline a-ZrP, t,he selectivity sequence for the reaction
is Na+ > Li+ > K+.23-25This corresponds to sequence X in the selectivity series predicted by Eisenman's theory and indicates that a fairly strong anionic field strength is operative.21 For ion-exchange reactions such as the ones described here, the observed entropies, ASo, can be divided into two terms as26
where ( S H O - S M O ) is the difference in entropies of hydration of the exchanging ions and ASex represents the entropy difference between the cation and hydrogen ion forms of the exchanger. Values of AS,, reflect (i) changes in hydration accompanying the reaction and (ii) the differences in lattice distortion of the two forms of the exchanger.
Complex Solubilities of AgX in 3-Methyl-2-oxazolidone For CS+the diffeirence SH’- SM’is equal to -17.2 eu.27 The differential entropy change for cesium ion exchange on gel 0.5:48 is fairly constant, averaging about -26 eu up to 8 c s = 0.6 (Figure 4). Therefore AS,, = -9 eu. The corresponding value for sadium ion exchange was -17 eu.12 This lower entropy is expected since Cs+ having less efficiency in binding water would bring less water into the exchanger. Nancollas and Til& also found that AS,, values show significant increases with increasing cation size when exchanged into an erisentially amorphous zirconium phosphateO9 Comparison of our results with those collected in Table I is instructive. To get some idea of the crystallinities of the exchangers we compared uptake of Cs+ from 0.1 M CsCl as reported in ref 6-10 with those of our exchangers.11 Our results for equilibration of 1.0 g of exchanger with 100 ml of 0.1 M CsCl were 1.45 mequivfg for 0.5:48,0.62 mequivfg for 0.8:48, 0.30 naequiv,’g for 2.5:48, 0.13 mequivlg for 3.5:48, and 0.03 meqjuivfg for 4.548. Somewhat greater uptakes were observed in the calorimetric study because of the greater volume to solid ratio. From these uptakes we concluded that all the exchangers used to obtain the results listed in Table 1 are close to 0.5:48 in behavior. On this basis the values reported in the table are reasonable. Baetsle and Ruvarac working with trace quantities obtained a AH which is almost identical with our Ai!lx value a t zero load. Amphlest, et a!., working over a broader portion of the isotherm report a somewhat lower enthalpy. Nancollas and Tilak’s measured AH compares very well to our value a t the same loading, i.e., -3.6 kcal mol-l at 2 mequivfg. Similarly the free energies reported only refer to that limited portion of Ihe isoSherm where cesium ion is preferred by the exchanger and therefore are negative or onlx slightly positive.
1817
References and Notes (1) (a) This work is part of a cooperative research program jointly sponsored by The National Science Foundation and the Swedish Natural Science Research Council. The Swedish portion is under the direction of Professor Sten Ahriand, Lund University, Lund, Sweden. The present work was supported by NSF Grant No. GP-8108.(b) Postdoctoral Fulbright Fellow, Lund University, Lund, Sweden. (2) A. Clearfield and J. A. Stynes, J. lmrg. Nucl. Chem., 26, 117 (1964). (3) J. Albertsson, Acta Chem. Scand., 20, 1689 (1966). (4) S. Ahrland, J. Aibertsson, A. Alnas, S. Hemmingsson, and L. Kullberg, Acta Chem. Scand., 21, 195 (1967). (5) A. Clearfield, A. Oskarsson, and C. Oskarsson, Ion Exchange Membranes, 1, 91 (1972). (6) L. Baetsie, J. lnorg. Nucl. Chem., 25, 271 (1963). (7) C. B. Amphlett, P. Eaton, L. A. McDonald, and A. J. Miller. J. lnorg. Nucl. Chem., 26,297 (1964). (8) J. P. Harkin, G. H. Nancollas. and R. Paterson, J. lnorg. Nucl. Chem.. 26, 305 (1964). (9) G. H. Nancollas and B. V. K. S. R. A. Tilak, J. Inorg. Nucl. Chem., 31, 3643 (1969). (10) A. Ruvarac, Bu//. Boris Kidric lnst. Nucl. Sci., 20,33 (1969). (11) A. Clearfield and A. Oskarsson, Ion Exchange Membranes, in press. (12) A. Clearfield and L. H. Kullberg, J. fhys. Chem., 78, 152 (1974) (13) J. GrenthB, H. Ots, and 0. Ginstrup, Acta Chi” Scand., 24, 1067 (1970). (14) H. S. Harned and B. B. Owen, “Physical Chemistry of Electrolyte Solutions,” Reinhold, New York, N. Y.. 1957, p 707. (15) S. R. Gunn, J. Phys. Chem., 69,2902 (1965). (16) K. S. Pitzer, J. Amer. Chem. SOC.,59, 2365 (1937). (17) A. Clearfield and J. M. Troup, J. Phys. Chem.. 77, 243 (1973). (18) A. Clearfield and G. D. Smith, Inorg. Chem., 8,431 (1969). (19) A. ClearfleldandA. S. Medina, J. fhys. Chem., 75,3750 (1971). (20) A. Clearfield, G. H. Nancollas, and R. H. Blessing, “Ion Exchange and Solvent Extraction,” Vol. 5, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, N. Y., 1973, pp 37-38. (21) G. H. Nancolias, “interactions in Electrolyte Solutions,” Elsevier, New York, N. Y., 1966. pp 120-125. (22) G. Eisenman, Biophys. J., 2, 259 (1962). (23) A. Clearfield. W. L. Duax, A. S. Medina, G. D. Smith. and J. R. Thomas, J. Phys. Chem., 73,3424 (1969). (24) A. Clearfield and J. M. Troup, J. fhys. Chem., 74, 314 (1970). (25) A. Clearfield, W. C. Duax, J. M. Garces, and A. S.Medina, J. Inorg. Nucl. Chem., 34,329 (1972). (26) H. S. Sherry “ion Exchange,” Vol. II, J. A. Marinsky, Ed., Marcel Dekker, New York, N. Y., 1968. (27) D. R. Rosseinsky, Chem. Rev., 65,467 (1965).
Complex Solubilities of the Silver Halides in 3-Methyl-2-oxazolidone ark Salomon Power Sources TechnicalArea, U. S. Army Electronics Technology and Devices Laboratory, Fort Monmoufh, New Jersey 07703 (Received April 75, 1974) Public.ationcosts assistedby the U.S. Army Electronics Command, Electronics Technology and Devices Laboratory
The complex solubilities of the silver halides have been determined in the aprotic solvent 3-methyl-2-oxazolidone. The results appear to be typical of the general behavior of aprotic solvents toward the solubility of the silver halides. 3-Methyl-2-oxazolidone is an interesting solvent in that it is practically isodielectric with water, is stable in the presence of metallic lithium, will dissolve appreciable amounts of alkali metal salts, and is completely miscible with water.
Introduction Propylene (carbonate (PC) and dimethyl sulfoxide (DMSO) are popular aprotic solvents for use in electrolyte
solution studies mainly because of their high dielectric constants and ease of purificati0n.l Recently Huffman and Sears2 have described the physical properties of a series of heterocyclic carbamates which exhibit properties similar to The Journal of Physical Chemistry, Vol. 78, No. 18, 1974
