Abraham Clearfield and Dinko A. Tuhtar
1302
On the Mechanism of Ion Exchange in Zirconium Phosphates. 16. Calorimetric Determination of Heats of Li+-H+ Exchange Abraham Clearfield' and Dinko A. Tuhtar' Department of Chemistry, Ohio University,Athens, Ohio 45701 (Received December 1, 1975) Publication costs assisted by the Petroleum Research Fund
The heats of Li+-H+ exchange have been measured calorimetrically on zirconium phosphates of different crystallinities. For the most crystalline exchanger the reaction is exothermic up to about 50% Li+ uptake. This is followed by a mildly endothermic reaction to about 77% lithium loading and a more highly endothermic reaction a t still higher loading. These heat effects correspond t o the formation of three separate exchange phases identified earlier by x-ray methods. In the case of the nearly amorphous exchanger the reaction is initially very slightly exothermic but soon becomes endothermic. The overall enthalpy is AH' = 2.57 kcal/mol and the entropy, AS' = -10.6 eu. Qualitative explanations for the enthalpy and entropy effects are presented and the results compared to those obtained with other alkali metal cations.
Introduction In the preceding paper in this series the effect of crystallinity of the exchanger on Li+-H+ exchange of a-zirconium phosphates (a-ZrP) was examined.* Three lithium ion containing phases of approkimate composition ZrLio.9-1.o4 H I.1-o.9dP04)2-4H201 phase LiH, ZrLil.33-1.5oH0.67-0.5(P04)2.4H20, phase A, and Zr(LiP04)~4HzO,phase F, were obtained with a highly crystalline a-ZrP exchanger. As the crystallinity of the exchanger decreased the composition ranges became broader for each phase until with the least crystalline exchanger only a single solid solution was observed. Calorimetric studies have been found to yield valuable information on the exchange p r o c e ~ s . : For ~ , ~ example, with highly crystalline exchangers sharp breaks in the AH,' vs. loading curves were obtained a t the phase boundaries. Furthermore, in those cases where the reactions are reversible, enthalpy measurements permit evaluation of the differential entropies of exchange. Comparison of such data for a series of ions provides valuable insight into the exchange process. For these reasons we have undertaken the present study. Experimental Section
Calorimetric Measurements. All solutions were prepared and standardized as described in the previous paper and the exchangers were the same ones described and characterized therein.2 The calorimetric procedure has also been descrihed in detail:',4 so that only a brief sketch will be presented here. A constant temperature environment type I,KR 8721-1 reaction solution calorimeter with associated thermostat, temperature sensor, and calibration unit was used. A small quantity (0.14-0.40 g) of finely ground exchanger in the hydrogen form was weighed into an ampoule and water (0.5-0.7 ml) added to eliminate heat of wetting effects. The ampoules were then sealed and placed into a four-pronged holder. This holder, which also served as a stirrer, was lowered onto a sapphire tipped glass pin to break the ampoule without interrupting the stirring. For most of the experiments the reaction vessel contained 100 ml of a 0.1000 M LiCl C mM LiOH solution, where 0 < C < 10. After each calorimetric determination the extent of exchange was determined by analyzing the solution.*J
+
The Journal of Physical Chemistry, Vol. 80, No. 12, 1976
T r e a t m e n t of Experimental Data. The standard heat of partial exchange, AH,', refers to the reaction H~ZN~"*O(S) 2XLiCl(aq)
+
+ mH20 e Li2xH2-2xZNsMH20(s) + ,(. + NsH - Ns')H20 + 2XHCl(aq)
(1)
In eq 1 a formula weight of mixed exchanger containing 2X mole of Li+ is formed from 1 formula weight 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 LiCl and HC1 f'n the right proportions to maintain the composition of the exchanger. The pure hydrogen ion and lithium ion forms of the exchangers are in equilibrium with infinitely dilute solutions of HCl and LiC1, respectively. 2 denotes one formula weight of the anionic framework of the exchanger while NsH represents the number of moles of water in 1 formula weight of zirconium phosphate (H2Z) and NsMdenotes 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 lithium hydroxide in order that the entire range of lithium ion uptake may be covered. Thus, the reaction for which the heat is measured is
+
+
H2ZNsH(")H2O(s) 2NLiCl(aq) VH20 2YLiOH(aq) e LiSxH2-2,ZNsM'H20(s) ( V NsH(V) - Ns' 2Y)HzO 2(N - X Y)LiCl(aq) 2(X - Y)HCl(aq) (2)
+
+
+
+
+
+ +
In eq 2 NsH(V) and NsM'are the number of moles of water in 1 formula weight of exchanger before and after the exchange, respectively. Then following the procedure developed previously,:' it can be shown that AHxO = AHx - 2YAHh.O - 2(X - Y)@L(M"HcI) + 2(X - Y)@I,(M"L,cI) ~Y@I.(M'I,~oH)(3) In eq 3 2Y is the number of moles of LiOH consumed by the exchange reaction, AHNO is the heat of neutralization a t 25 "C and infinite dilution, AHx is the measured heat of reaction, and @I, denotes the relative apparent molar heat contents of the indicated species and molarity. The values
1303
Mechanlsm of Ion Exchange in Zlrconlum Phosphates
/ -
It
I -3
iI
-4
I.
-*
\I
"
I
\
\
I
-51
-4 -5L-, I
-6
01
02
03
04
05
06
07 ,
08
09
10
-9
01
of the relative apparent molar heat contents were taken from the compilation of Harned and Owen6 and that for A H N O , -13.34 kcal/mol, from the work of GrenthB and associates.s Under the experimental conditions used in the calorimetric study phosphate release to the solution was negligible for all exchangers except 0.5:48.2 In this case the maximum release was 0.052 mM/g of exchanger a t p H 6.0. At this p H most of the phosphate ion is in the form of H2P0d2- so that the hydrolysis reaction occurring is in the main
+
H2P04- H20 G HPOd2- H30+ (4) The enthalpy change for this reaction is 0.8 kcal/mol or a total heat effect of 0.042 cal/g in the worst case. Since the measured enthalpies are of the order of 8-10 cal/g, neglect of hydrolysis is not serious.
Results Crystalline S a m p l e s 12:48 a n d 12:384. The AH,' vs. ion uptake curves for these exchangers are given in Figures 1 and 2. At lithium ion loadings of less than 50% the heat effects were usually completed within 5 min. However, progressively longer times were required a t higher loadings. = 0.8, 20 min was required to achieve a For example, a t steady state in the resistance vs. time curve for exchanger 12:48 and 60 min for 12:384. In these cases the RegnaultPhaundler method9 rather than Dickinson's method was used to calculate the experimental heats of reaction. Even so measurements at very high loadings, requiring more than 1 h time, were deemed unreliable and omitted from the curves. Besides the slowness of the reactions another feature of the experimental observations is worthy of note. At xl,j> 0.5 a second small jump in resistance was always observed a t times close to the completion of the reaction. This indicates that a second reaction is superimposed upon the first ion-exchange-neutralization reaction. This heat effect may result from the sudden crystallization of one of the exchanged phases (most likely phase A). This point is under investigation.
x~j
03
04
05
-
06
07
OB
09
10
X L,
XL,
Figure 1. Standard heats of partial exchange as a function of lithium ion loading for exchangers 12:384 (open circles) and 4 . 5 4 8 (filled circles).
+
,
02
Flgure 2. Standard heats of partial exchange as a function of lithium ion loading for exchangers 12:48 (open circles) and 0 . 5 4 8 (filled circles).
The AH,' vs. lithium uptake curves for 12384 and 12:48 each exhibit three distinct slopes. This correlates well with the ion-exchange titration data.2 The first exothermic reaction is due to the conversion of a-ZrP to phase LiH. When this process is complete, an endothermic reaction ensues in which phase LiH is converted to phase A. The final highly endothermic portion of the curve corresponds to the formation of the fully exchanged phase F. Although no major differences in the curves for the two exchangers are observed smaller heat effects are noted with the less crystalline exchanger 12:48. Also the maximum in the curve occurred a t = 0.53 for 12:48 as apposed to xl,j= 0.5 for 12:384. Exchanger 4.5:48. The AH,' curve for this exchanger (Figure 1) departs from that of the more crystalline samples in that it exhibits only a single endothermic region. At first thought this might seem surprising since 4.548 forms the same three phases as the more crystalline samples. However, as was pointed out previously,2 the composition ranges of the exchanged phases increase with decreasing crystallinity. Thus, a rather smooth transition from one phase to the other seems to occur according to the A H X o values. This seems plausible for the conversion of phase LiH to phase A judging from the titration curve.2 However, it is somewhat surprising when applied to the formation of phase F since a distinct plateau was observed in the titration curve for this phase change. Exchanger 0.5:48. Lithium ion exchange on this almost amorphous exchanger is accompanied by almost negligible heat effects up to about 40% of exchange (Figure 2). At higher loading the AH,' curve exhibits a negative slope characteristic of an endothermic reaction. Since the Li+H + exchange reaction has been shown to be reversible, values of the corrected selectivity coefficients were available from the ion-exchange titration data.2 Thus, it was possible to calculate the differential free energies of exchange defined as
x~j
- A e x = RT In KcI*lIH
(5)
where KCLiIH is the corrected rational selectivity coefficient The Journal of Physical Chemistry, Vol. 80. No. 72, 1976
Abraham Clearfield and Dinko A. Tuhtar
1304
Along the first plateau one solid of constant composition is converted to another (the half-exchanged phase) of constant composition. Thus the activities of the ions in the solid are constant and
DIFFERENTIAL QUANTITIES OF EXCHANGE, kcol/rnole Li'
K[y/{4 = aH+/aL;+aw:i
(11)
Thus, from the pH of the plateau Ki,?g4is calculated t o be 2.3 X and AGO = 3.6 kcal/mol. The heat of reaction, from Figure 1, is taken to be -2.69 kcal/mol from which the entropy is determined to be -19 eu. No real thermodynamic significance is to be attached to these values but they afford some insight into the exchange process. For purposes of this discussion it will be more instructive to compare ASEX' values since these represent entropy differences between the corresponding ionic forms of the exchanger. That is, ASEX' reflects changes in hydration of the exchanger accompanying the reaction and differences in lattice distortion of the two forms of the exchanger. Sherry has shown1° that ASEX'
=
-(SHO
-sMo) + Aso
(12)
where S H O - S M O refers to differences in entropies of the hydrated ions for the hypothetical reaction 01
02
03
0.4
05
-
06
07
08
09
IO
H+(g) + M+(aq)
XL,
Differential quantities of exchange as a function of lithium ion loading for exchanger 0.548. Figure 3.
for Li+-H+ exchange with sample 0.5:48. The differential heats of exchange are readily obtained from the standard heats of partial exchange by the relationship (6)
Af?, = b A H x 0 / A f i l ~ , ;
Finally, the differential entropies of exchange can then be calculated from
AS,
= -(AC,
- ARx)/T
(7)
These differential quantities are plotted in Figure 3. The integral heat of complete exchange, A I I O , is defined as
AHo = J AI?, dXLi
(8)
I t was evaluated as the area encompased by the H , vs. XL;curve in Figure 3, which amounted to a value of +2.57 kcal/mole. From the previously determined value of the equilibrium constant, 6.2 x AGO is calculated to be +5.74 kcal/mol. The standard entropy of exchange derived from these two quantities is then -10.6 eu.
Discussion The appearance of three distinct slopes in the AH,' VS. XI,^ curves of 12:384 and 12:48 confirms the ion-exchange data that three distinct phases form as lithium ion replaces hydrogen ion. These ion-exchange reactions are not reversible so that it is not legitimate to derive equilibrium constants for them. However, following a procedure previously invoked for Cs+-H+ exchange, one can think of the first ion-exchange reaction as being ideally Zr(HPO&HzO(s)
+ 3H20 + Li+(aq)
s;!
+
ZrLiH(P04)~.4H20 H+(aq) (9) and
KC'$4 = a H+tir,ilaLi+tiHa w3 The Journal of Physical Chemistry, Vo/. 80, No. f2, 1976
(10)
-
H+(aq) + M+(g)
(13)
For M+ = Li+ this entropy difference is 2.4 cull so that ASEX' = -21.4 eu. This large negative entropy mainly arises from the binding of 3 mol of water by the exchanged phase. By way of comparison the corresponding ASEX' value for formation of the half-exchanged sodium ion phase was -25.9 eu. In this case 4 mol of water was fixed by the new phase. The greater negative entropy effect per mole of water for Li+ may stem from the smaller interplanar spacing of the lithium phase and the tighter binding of the water by lithium ion compared to sodium ion. Additionally the observed enthalpy for the formation of phase LiH (-2.69 kcal/mol) is less than half that (-6.9 kcal/mol) for the half-exchanged sodium ion phase. This is to be expected because of the high heat of hydration of lithium ion. Thus, the enthalpy for reaction 13 is -137.7 kcal/mol when M+ is Li+ and -163.8 kcal/mol for Na+. The observed decrease in enthalpy for Li+ exchange relative to Na+ exchange more than compensates for the slight entropy increase so that lithium ion is less preferred by crystalline a-ZrP than is sodium ion. For the gel exchanger 0.5:48 the differential entropy is initially relatively constant a t about TAS, = -4.6 kcal/mol = -15.4 eu. or Enthalpies and entropies of exchange are now known for three alkali metal ions on exchanger 0 . 5 4 8 permitting some interesting comparisons to be made. In each case the initial exchange reaction is exothermic but as the loading increases becomes endothermic. Cesium ion exchange is initially the most exothermic but eventually becomes the most endothermic. Lithium ion exchange is the least exothermic and a t the same time becomes the least endothermic. Sodium ion exchange gives enthalpy values which lie between those of Cs+ and Li+. Over the exothermic region of exchange the entropies have high negative values and remain relatively constant. Lithium ion exchange has the highest and cesium ion the lowest entropy values. As the reaction becomes more endothermic the entropies increase with those for Cs+ and Na+ hecoming highly positive (Cs+ > Na+). After an entropy increase from 40 to 60% of exchange, further exchange of Li+ is accompanied by an en-
s,
Mechanism of Ion Exchange in Zirconium Phosphates tropy decrease (Figure 3). The net result of these effects is an initial weak field selectivity sequence Cs > Na > Li which changes with loading to a strong field selectivity sequence I i > Na > Cs. The nearly amorphous gel 0.548 may be considered to be a weak field exchanger in the sense of Eisenman's theory.12 This gel swells in contact with water to an interlayer spacing of 11.2 A.5 Thus, initially the incoming cations need not approach the negative sites closely but may surround themselves with the excess gel water. The electrostatic effect is therefore small and the reaction is dominated by the hydration effect.12 This explains the observed order of the enthalpies and entropies. The hydrogen is mainly covalently bonded to phosphate oxygens (although it has been proposed that some is present as ions to account for the swelling of the gel5). Thus, on displacement to the solution it hydrates binding a large number of water molecules in the process. Conversely, cesium ion binds water weakly and upon entering the gel experiences a small net change in hydration. In addition it is only weakly attracted to the negative fixed group. T h e net effect is a large negative entropy and enthalpy. Lithium ion binds water strongly and this ion likely suffers a loss of water to the solution on exchange. Thus, the initial entropy and enthalpy values are expected to be less negative. As the loading increases, the cations are crowded closer together (especially beyond 50% of exchange). Lithium ions, because of their small size, can approach the negative fixed groups closely and thus stay relatively far apart from each other. The much larger cesium ions cannot easily surround the negative sites as the crowding of three or four cations around each fixed groupl3 sets up large cation-cation repulsions. I t is postulated then that this repulsion effect creates progressively greater internal disorder, i.e., a progressively greater randomization of cations and water molecules. Thus, the entropy progressively increases and the enthalpy decreases. As the size of the incoming cation decreases so does the degree of disorder so that with Naf a smaller increase in entropy and a less endothermic reaction is observed. However, Li+ is so small that it is able to produce a near saltlike arrangement about the negative sites and hold the water molecules in
1305
fixed positions. Thus, the entropy does not become positive in the latter stages of exchange. Also the lessened repulsion and closer approach to the negative sites result in a smaller endothermic effect. These ideas will be given a more quantitative expression when the entire series of exchange reactions with alkali metals has been completed. Our results may be compared to those of an earlier calorimetric study carried out on a weakly crystalline ( 4 . 5 : 48) zirconium p h 0 ~ p h a t e . lT~h a t study used empirically determined exchange capacities obtained without use of added LiOH. Thus, a much lower range of ion uptake was examined, Le., less than 1 mequiv/g. The enthalpy was found to be -1.1 kcal/mol and the entropy -10.0 eu. Our data for 0.5:48 are in the same direction but of somewhat different magnitude when taken over the same loading. Because of the differences in preparation of the two exchangers better agreement is not to be e ~ p e c t e d . ~
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work.
References and Notes (a) Portions of this paper were taken from the Ph.D. Thesis of D. A. Tuhtar, presented to the Department of Chemistry, Ohio University, June 7, 1975. A. Clearfield and D. A. Tuhtar, J. Phys. Chem., preceding paper in this Issue. A. Clearfield and L. H. Kullberg, J. Phys. Chem., 78, 152 (1974). A. Clearfield and L. H. Kullberg, J. fhys. Chem., 78, 1812 (1974). A. Clearfield, A. Oskarsson, and C. Oskarsson, Ion Exch. Membr., 1, 205 (1974). H. S. Harned and 6.6.Owen, "Physical Chemlstry,of Electrolyte Solutions", Reinhold, New York. N.Y., 1957, p 707. I. Grenthb, H. Ots. and 0.Glnstrup, Acta Chem. S c a d . , 24, 1067 (1970). K. S. Pltzer, J. Am. Chem. Soc., 59, 2365 (1937). I. Wadso, Sci. Tools, 13, 33 (1966). H. S. Sherry, "Ion Exchange", Vol. 11, Marcel Dekker. New York, N.Y., 1968. D. R . Rosseinsky, Chem. Rev., 65,467 (1965). G. Eisenman, "Glass Electrodes for Hydrogen and Other Cations", Marcel Dekker, New York, N.Y., 1967, pp 70-75. A. Clearfield and A. Oskarsson, Ion Exch. Membr., 1, 205 (1974). G. H. Nancollas and 6.V. K. S. R . A. Tilak. J. Inorg. Nucl. Chem., 31, 3643 (1969).
The Journal of Physical Chemistry, Vol. 80, No. 12, 1976
