3834
I ( .E. BECKER, S. LINDENBAUM, AND G. E. BOYD
changes by nearly five orders of magnitude when e varies from 30 to 140. This is about 1000 times as great an effect as that predicted by the simple es relationship.
Effects of such an order can be observed otherwise only when ions of various charges are used in the electrolytic coagulation (Schube-Hardy rule).
Thermodynamic Quantities in the Exchange of Lithium with Cesium Ion on Cross=LinkedPhosphonic Acid Cation Exchangers1
by K. E. Becker, S. Lindenbaum, and G. E. Boyd Oak Ridge National Laboratory, Oak Ridge, Tennessee 17851
(Received May 14,1966)
Calorimetric measurements showed that heat was absorbed in the preferential uptake of lithium ion from dilute alkaline aqueous solutions in exchange reactions with cesium ion in cross-linked nuclear and methylene phosphonic acid type cation exchangers. Standard free energies, AGO, heats, AH", and entropies, AS", of exchange were -0.33 and -0.72 kcal mole-', 0.89 and 1.20 kcal mole-', and 4.1 and 6.4 eu, respectively. As with crosslinked polymethacrylic acid ion exchangers, the increase in AS" was attributed principally to the decrease in Li+ ion hydration in the exchange reaction. Site binding of Lif was postulated as the cause for the preferential uptake of this ion by phosphonic acid type cation exchangers.
The order of the preferred uptake of the alkali metal ions from their dilute aqueous solutions by strong-acid cation exchangers, Cs+ > Rbf > Kf > Na+ > Li+, has been shown to be reversed in weak-acid exchangers of the p~lymethacrylate~-~ and polyphosphonate2J types. The selective absorption of the lighter alkali metal cations by carboxylic acid exchangers was found14moreover, to be accompanied by the absorption of heat and an increase in entropy, whereas with strong-acid exchangers (Le., cross-linked polystyrenesulfonic acid) the preferential uptake of the heavier cation occurred with the evolution of heat and a decrease in entropy.6 These observations have been interpreted as indicating that ion-water interactions are of primary importance in determining the alkali metal cation selectivity sequence with polystyrenesulfonate exchangers; with polymethacrylates, ionpair formation between Li+ (and possibly Naf) ion and the carboxylate exchange group has been assumed. The Journal of Physical Chemistry
The specific interaction between Li+ and COO- may obey the "localized hydrolysis" mechanism proposed by Robinson and Harried' and result from the fact that the density of electric charge on a carboxylate group is greater than on a sulfonate group. Accordingly, it was of interest to examine the thermodynamics of the lithium-cesium ion exchange with a cation exchanger in which the electric charge density was even greater. The phosphonate exchange group resembles (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) J. I. Bregman, Ann. N. Y. Acad. Sci., 57 [3], 126 (1953). (3) H. P. Gregor, M. J. Hamilton, R. J. Oza, and F. Bernstein, J. Phys. Chem., 60,263 (1956). (4) S. Lindenbaum and G. E. Boyd. ibid., 69, 2374 (1965). (5) J. Kennedy, J. Marriott, and V. J. Wheeler, J. Inorg. Nzccl. Chem., 2 2 , 269 (1961). ( 6 ) G. E. Boyd, F. Vaslow, and S. Lindenbaum, J. Phgs. Chem., 68, 590 (1964). (7) R. A. Robinson and H. S. Harned, Chem. Rev., 28, 419 (1941).
EXCHANGE O F Li+ WlTH
CS’
ON
CROSS-LINKED PHOSPHONIC ACIDCATION EXCHANGERS
the sulfonate group in that three oxygens are combined in it but differs in that, when fully ionized, it carries two rather than one negative charge.
Experimental Section Materials. ‘Two types of phosphonic acid exchangers were used : a polystyrene-divinylbenzene cross-linked (5.5% DVB) preparation, -CH-C~HK-PO(OH)~,in which the phosphonate groups were attached to a benzene nucleus, and a polystyrene-divinylbenzene cross-linked (5.5% DVB) methylene phosphonic acid exchanger, -C:H-C6H4CH9PO(OH)2, in which the phosphonate was separated from the benzene ring by a methylene group.S The ion-exchange capacities of these preparations were determined by shaking their acid forms which had been pretreated to remove impurities and unreacted monomers with a measured excess of standard SaOH solution for periods up to 7 days and back-titrating an aliquot of the supernatant solution with etandard HCl. Values of 5.50 and 5.75 mequiv/g of dry hydrogen form resin were obtained for the nuclear and methylene phosphonic acid exchangers, respectively. Our experience, and that of others12r5has indicated that these exchangers are stable in the presence of alkaline aqueous solutions and that their exchange capacity remains constant during experiment. The homo-ionic lithium and cesium salt forms employed as starting materials in the calorimeter reactions were prepared by treating the acid forms with an excesE. of aqueous LiOH or CsOH solution, respectively. ‘The preparation of these solutions has been de~cribed.~ Calorimetric Measurements. A description of the calorimeter and its associated measuring circuits has been presented in other publications from this laborat ~ r y . ~The : ~ procedure and methods of analysislO were identical with those described for the exchange of Li+ with Cs+ ion on polymethacrylate ion exchanger^.^ The reaction temperature was 25.00”, and the exchange reaction was conducted with aqueous LiOH CsOH solution3 at an ionic strength of 0.1 A!. The heat of opening of the calorimeter pipet, which initially contained the exchanger, was determined as 0.010 f 0.005 cal. This correction was applied to the observed heat effect expressed in terms of 1 cal = 4.184 joules. The performance of the calorimeter was checked by measurements of the heat of solution of KCl(c) in water and of tris(hydroxymethy1)aminomethane (THAM) in 0.100 N HCl. A heat of solution to infinite dilution for KC1 of 4134 j= 12 cal mole-’ was found, which may be compared with a recently proposed “best va1ue”l’ of 4115 f 10 cal mole-l. An average vstlue of -7118 f 18 cal mole-’ was
+
3835
measured for the heat of solution of THAM at a final concentration of ca. 5 g 1.-’. This may be compared with the value of -7107 cal mole-’ recently reported by Gunn.I2
Results and Discussion Selectivity Coeficients. Selectivity coefficients computed from the measured equilibrium concentrations of Li+ and Cs+ ions in the aqueous solution and in the exchanger phases after the calorimetric experiments are plotted in Figure 1 as a function of the equivalent fraction of lithium ion, X L ~ + ,in the exchanger. With both phosphonic acid exchangers log DCs+Li+ was a linear function of X L ~ + . Both exchangers showed a strong preference for Li+ over most of the range in xLi+; however, there was a selectivity inversion a t large (0.8-0.9) lithium equivalent fractions where cesium was the preferred cation. A similar reversal was observed with polymethacrylate exchangers4 a t slightly lower values of X L +.~ Heats of Exchange. The measured heats of partial exchange are shown in Figure 2 by a chord for each experiment. The curves for the differential heat of exchange, AB = ( b H / b x ~ i +are ) , the best least-squares fit through the midpoints of the chords. With the nuclear phosphonic acid preparation, AR was linear with respect to X L ~ +whereas , the data for the methylene phosphonic acid exchanger were better fitted by a quadratic equation. The preferred uptake of lithium ion was accompanied by the absorption of heat over most of the composition range. The absorption of small amounts of Li+, however, gave an evolution of heat with both exchangers. From the magnitudes of AI7 at X L ~ += 0.0 and x L i + = 1.0, it may be predicted that at temperatures above 48” lithium ion mill be selectively absorbed over the entire composition range. Standard-State Thermodynamic Values. Standard enthalpies, AH”, free energies, AGO, and entropies, AS”, of exchange were calculated for the hypothetical reaction CsR(a = 1, equil with 0.1 N CsOH) LiR(a = 1, equil with LiOH(aq, a = 1) 0.1 N LiOH) CsOH(aq, a = 1) nHzO(a, = 1)
+
+ +
(8) The authors are indebted to Dr. I. M. Abrams, Diamond Alkali Co., Western Division, Redwood City, Calif., for providing these materials. The nuclear phosphonic acid exchanger is commercially available as Duolite ES-63. (9) S. Lindenbaum, J . Phys. Chem., 7 0 , 814 (1966). (10) The authors thank M. Ferguson of the ORNL Analytical Chemistry Division for the flame spectrophotometric determinations of lithium and cesium. (11) V. B. Parker, “Thermal Properties of Aqueous Uni-univalent Electrolytes,” National Standard Reference Data Series, National Bureau of Standards, Washington, D. C., 1965, NSRDS-NBS 2. (12) S. R.Gunn, J . Phus. Chem., 69,2902 (1965).
Volume 70,Number 18 December 1966
K. E. BECKER, S. LINDENBAUM, AND G. E. BOYD
3836
- A G O
=
2.3RT
log Do dxLi+ S,l
The required DOvalues were obtained by correcting the observed selectivity coefficients (Figure 1) by the activity coefficient ratio, r*z(CsOH)/ri2(LiOH), which was evaluated for aqueous 0.1 m mixtures following the method outlined by Robinson and Stokes.14 This correction did not exceed 5%. Standard-state thermodynamic quantities for the exchange of lithium with cesium ion on a nuclear and on a methylene phosphonic acid are summarized in Table I, where it may be observed that the entropy increase accompanying the uptake of Li+ ion was sufficiently large to overcome the increased enthalpy required and thus give a free-energy decrease for the
' H Y L E N E PHOSPHONIC ACID t ' 2
0.7
W
0.6 LL
LI
W
s
0.5
'0
0.4
2
0.3
W _I
% c3
3
0.2 0.f
3500 0.0
- 0.f
3000
t--u
--o.2 0'30
.i
2500
.2
.3
.4
.5
.6
.7
,0
.9
2000
METHYLENE PHOSPHONIC ACID I
-CH,CGH,'
CH,PO(OH),
EQUIVALENT FRACTION, XLi,
I500
Figure 1. Selectivity coefficients for the exchange of Li+ with Cs+ in nominal 5.5% DVB cross-linked phosphonic acid ion exchangers.
-
z
I000
Z
500
.-m i
c
0
L
where n is the number of moles of water lost (or gained) by the exchanger. The desired standard enthalpy changes, AH O , were derived from the integral heats of exchange, AH, corrected by the difference, A&, = -50 cal mole-', in the relative apparent molal heat contents between the 0.1 N LiOH and 0.1 N CsOH solutions. Integral exchange heats, defined by AH = L'(ai\H/~XLi+)dZLi+
were evaluated by integrating the empirical leastsquares equations fitted to the data of Figure 2. Corrections to the differential heat of exchange, @AH/ dxLit), for changes in the ionic strength from its initial value of 0.1 N because of the loss or gain of water by the exchanger during the ion-exchange reaction and for thermal effects caused by the mixing of aqueous electrolytes were always sufficiently small to be neglected.Ia Standard free energy changes were found by graphical integration of the corrected selectivity coefficients, Do,according to the equation The Journal of Physical Chemistry
0
11
a
-500
2000 1500
4000 500 C
I
.1
I
I
I
I
I
I
I
I
. 2 .3 .4 .5 .6 .7 .8 .9 E Q U I V A L E N T F R A C T I O N , XLi+
I
LO
Figure 2. Differential heat of exchange of Li+ with Cs+ ion in nominal 5.5% DVB cross-linked phosphonic acid exchangers.
(13) Changes in the heat contents of the ion exchanger caused by changes in its swelling are included in the standard heat of exchange, AHa, as defined. (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth & Co., Ltd., London, 1955, p 440.
EXCHANGE OF Li+ WITH Cs+ ON CROSS-LINKED PHOSPHONIC ACIDCATIONEXCHANGERS
Table I: Standard Free Energies, Heats, and Entropies of Exchange at 2982°K of Lithium with Cesium Ion on Nuclear and on Methylene Phosphonic Acid Type Cation Exchangers -AGO,
-AHo,
Exchanger
kcal mole -1
kcal mole-1
A!Y, eu
Nuclear phosphonic Methylene phosphonic
0.33 0.72
-0.89 -1.20
4.1 6.4
reaction. Interestingly, the magnitude of the increase in enthalpy and entropy depended on the acid strength of the phosphonate group: the weaker the acid, the greater the selectivity for Li+ over Cs+ ion.15 This result suggests that the observed increases in AH” and AS” cannot be attributed entirely to a decrease in the hydration of Li+ ion when it is absorbed by weakacid type cation exchangers. As with cross-linked polymethacrylic acid exc h a n g e r ~ it , ~ appears necessary to assume that there is a specific association between lithium ion and the phosphonate group of the exchanger (ie., “site-binding”). It is postulated that this interaction involves a water molecule as an intermediary between Li+ and P032-as in the “localized hydrolysis” hypothesis previously employed by Robinson and Harned’ to account for the reversal in the activity coefficient sequence of the alkali metal salts in aqueous solution from that for the halides when the anion is a proton
3837
acceptor. The second acid dissociation constants for phosphonic acids are quite small, indicating that the ion, -PO&-, is a much weaker acid than acetic acid. An activity coefficient reversal between the sodium and potassium mono- and disalts of phosphoric acid has been reported,16and this may be understood on the basis of the “localized hydrolysis” mechanism for ion association. The binding of Li+ ion in the association complex would be expected to increase as the proton accepting strength of the -P0s2- group increases. Thus, the stronger binding of Li+ by the methylene phosphonic acid compared with the nuclear phosphonic acid exchanger can be anticipated. Dilatometric measurements” with doubly charged polyvinylphosphonates in aqueous solution have revealed that a relatively large volume increase accompanies the replacement of tetramethylammonium by lithium or by sodium ions. This result is consistent with the entropy increase (Table I) found by us if it is assumed that a partial dehydration of the Li+ ions accompanies their interaction with the structurally bound P032-groups. (15) p-Methylbenzenephosphonic acid shows pK1 = 1.98 and pKz = 7.2 according t o H. H. JaffB, L. D. Freedman, and G. 0. Doak, J . Am. Chem. SOC.,7 5 , 2209 (1953). whereas for propanephosphonic acid ~ K =I 2.4 and pK2 = 8.2, respectively. Corresponding values for phosphoric acid are pK1 = 2.1 and pKz = 7.1, respectively. (16) G. Scatchard and P. C. Breckenridge, J . Phys. Chem., 58, 596 (1954). (17) U. P. Strauss and Y. P. Leung, J . A m , Chem. Soc., 87, 1476 (1965).
Volume 70,Number 12 December 1966
