2374
S.LINDEKBAUM AND G. E. BOYD
Thermodynamic Quantities in the Exchange of Lithium with Cesium Ion on Cross-Linked Polymethacrylate Ion Exchangers'
by S. Lindenbaum and G. E. Boyd Oak R i d g e Natwnal Laboratory, Oak Ridge, Tennessee
$7831
(Received January 28, 1966)
Calorimetric measurements showed that heat was absorbed in the selective uptake of lithium ion from dilute aqueous solutions in an exchange reaction with cesium ion on crosslinked polymethacrylic acid (PhIA) ion exchangers. The standard entropies of exchange, AS", observed with nominal 1 and 15% divinylbenzene cross-linked preparations were 1.8 and 6.2 e.u., respectively. The magnitude of TAS" showed that it was the increase in entropy which caused the standard free energy of exchange to be negative. The increase in AS' was attributed to a decrease in the hydration of Li+ ion in the exchange reaction. It was proposed that the alkali metal cation affinity sequence Lif > Naf > K + > R b + > Cs+ for PALA exchangers resulted from "site-binding" of the lightest members.
One of the central problems in the understanding of the ionic selectivity exhibited by synthetic organic ion exchangers is that concerned with the nature of the binding of ions by the ionogenic groups in these materials. In our previous study2 of the free energy, enthalpy, and entropy of exchange of Ka+ with H+, Li+, K+, and Cs+ ions i n cross-linked polystyrene sulfonate exchangers it was found that the preferential uptake of these cations from dilute aqueous solutions was accompanied by the evolution of heat and by a decrease in rintropy. The magnitude of the standard free energy decrease, - A F " , was determined by the difference between the lowering of the enthalpy, A H " , and the decrease in AS". Therefore, the ionic selectivity was governed by the lowering of the energy of the exchanger. The affinity sequence of the alkali metal cations in their exchange reactions i n aqueous solutions a t 25" on cross-linkcd polymethacrylic acid (PRIA) exchangers is known3 to be the reverse of that with polystyrene sulfonates where Csf > Rbf > I N a + > Lif. It, has seemed probable that the cause for this inversion was related to the type of biIldiIlg of these catiorls with the carboxylate groups of the exchanger. Accordingly, the relative signs and magnitudes of AH" and AS" for the reactions are of interest. ;\'leasuremerits of selectivity coefficients, D M + ~ for + , the exchange of polassiiim with lithium and with sodium ion The Journal of Physical Chemistry
on cross-linked PMA exchangers have been reported. A strong dependence of D M + ~on* cross linking and on the mole fraction of potassium, zK+, in the exchanger was found, and reversals in the strength of ionic binding were observed in the I 0.45 with all but the most lightly cross-linked preparation. Potassium-lithium selectivity coefficients measured at 4" with four differently cross-linked PRIA exchangers were found not to differ from the values determined at 25" indicating that AH" was nearly zero. This latter result is unexpected, and, therefore, we have made calorimetric measurements of the heats of exchange of Csf with Li+ ion as a function of zL1+ for nominal 1 and 15% divinylbenzene (DVB) cross-linked PJIA exchangers. Equilibrium selectivity coefficients also were determined, and the derived A S " values showed that it was the increase in entropy which determined the selective uptake of Lif ion.
(1) Presented before the Division of Colloid and Surface Chemistry,
149th National Meeting of the American Chemical Society, Detroit, Mich., April 1965. Research sponsored by the U . S. Atomic Energy Commission under contract with Union Carbide Corp. (2) G . E . Boyd, F. Vaslow, and S . Lindenbaum, J . Phys. Chem., 68, 590 (1964). (3) J. I. Bregman, Ann. N . Y. Acad. Sci., 57[3], 126 (1953). (4) H . I?. Gregor, 34. J. Hamilton, R. J . Oza. and F. Bernstein, J . Phys. Chem., 60, 263 (1956).
THERMODYNAMIC QUANTITIES IN
THE
EXCHANGE OF LITHIUMWITH CESIUMION
2375
and 7.72 mequiv./g. of dry H form, respectively, were found. To minimize hydrolysis problems the exchanger Calorimetric Measurements. The calorimeter used always was weighed in the H form and converted to the in the heat of exchange measurements was identical Li or Cs form in the calorimeter pipet by adding an in many respects with that previously e m p l ~ y e d . ~ , ~ excess of LiOH or CsOH and adjusting the final conTemperature changes were followed with two 2000-ohm centration of the supernatant solution to 0.1 N . In thermistors possessing a temperature coefficient of the course of these operations, the swelling of the Cs -3.9%/deg. placed on opposite arms of a Wheatstone form was observed to be distinctly greater than that of bridge. The other two arms of the bridge were decade the Li form.g resistance boxes. The unbalanced current from the The LiOH and CsOH solutions were prepared by bridge was amplified with a d.c. breaker amplifier treating the corresponding chloride salt solutions with (Bgckman >lode1 14) and recorded as a function of time silver oxide, filtering, and diluting to volume. on a 100-mv. Leeds and Xorthrup Speedomax recorder. The temperature sensitivity of the calorimResults and Discussion eter was approximately 15 X lo+'. The electrical energy input to the calorimeter heater used in the caliHeats and Free Energzes of Parttai Exchange. The bration was determined by voltage drop and current dependence of the differential heats of exchange, measurements with a Type K-3 Leeds and Yorthrup of Li+ with Cs+ ion for the nominal 1 and 1.5% DVB potentiometer. The length of the heating period was cross-linked PMA exchangers on the equivalent fraccontrolled by an electrical timer which was activated tion of Li+ ion in the exchanger is shown in Figures 1 simultaneously with the heater current. The overand 2. Heat was absorbed over the entire range of all performance of the calorimeter system was checked compositions in the more lightly cross-linked preparafrom time to time by measurements of the heat of solution, whereas heat was evolved for the uptake of small tion of KCl(c) Values i n good agreement with those amounts of lithium ion by the Cs form of the 1.5% reported by Somsen, Coops, and Tolk6 were obtained. DVB exchanger. A marked dependence of Ai? on XL,+ was exhibited by both preparations, and with the The measurements of the heats of the exchange reachighly cross-linked exchanger the reaction was strongly tion of Li+ with Cs+ ion were performed with ca. endothermic when only microamounts of Cs+ ion 10 mequiv. of the wet, swollen P N A exchanger initially remained ( L e . , Z L ~ += 1.0). in either the Li or the Cs form contained in the sample pipet. The calorimeter was filled with 500 ml. of The compositional dependence of the selectivity coefficient, D C ~ . ~ for " , the exchange reaction is shown aqueous 0.1 N LiOH or CsOH solution, or with mixtures in Figure 3 where it may be rioted that a selectivity of these electrolytes. The exchange reaction was rapid reversal occurred with both preparations when xL,+ and appeared to reach completion in fewer than 4 min. exceeded ca. 0.70 to 0.75. Thus, small quantities of after initiation as judged by the temperature history Cs+ ion were taken up preferentially by the homoof the calorimeter. ionic Li forms. At the conclusion of the calorimeter experiment, an Standard Heats, Free Energies, and Entropies of Exaliquot of the equilibrium aqueous phase was taken. The nieasurements shown in Figures 1-3 were change. The exchanger was separated from the solution by employed to estimate the standard enthalpies, A H o filtration, rinsed with ethanol, and eluted with HC1 solufree energies, AF", and entropies, AS", of ion exchange tion to remove all Li+ and/or Cs+ ions. The eluate for the hypothetical reaction and equilibrium aqueous phases were analyzed for lithium and caesium by flame spectr~photometry.~ The number of equivalents of cation involved in the exchange reaction, the composition of the equilibrium ( 5 ) G. E. Boyd and F. Vaslow, J . Chem. Eng. Data. 7 , 237 (1962). exchanger, and the selectivity coefficient for the ex(6) G. Somsen, J. Coops, and M .F,Tolk, Rec. traz. chim.. 82, 231 (1963). change reaction were computed from these measure(7) The authors are indebted to T . C. Rains of the O R N L Analytical ments. Chemistry Division for these determinations which were performed with a precision in the Li+/Cs+ ratio of better than 1 % . Materials. Spherical polymethacrylic acid type (8) These materials were supplied through the generosity of the cation-exchanger preparations nominally cross linked Rohm & Haas Co., Philadelphia, Pa., by Dr. R. Kunin. with 1 and 15% divinylbenzene (DVB) were used.8 (9) Measurements on a nominal 6% DVB cross-linked I'MA exTotal exchange capacities were measured after prechanger by H. P. Gregor. M .J. Hamilton, J. Becher, and F. Bernstein, J . Phys. Chem., 59, 874 (1955), have shown t h e volume of the K form treatment of the ''as received" acid forms to remove to be greater than either the Li form or Na form which swelled t o the unreacted monomers and impurities. Values of 11.13 same extent approximately in dilute aqueous base solutions.
Experimental
An,
Volume 69, .Yumber 7
J u l y 1966
2376
S. LINDENBAUM AND G. E. BOYD
+
1, equil. with 0.1 N CsOH) LiOH (aq., a = 1) LiR (a = 1, equil. with 0.1 N LiOH) CsOH (as., a = 1) nHzO (a,
CsR (a
=
+
+
2800
1)
=
The integral heat of exchange is given by AH
I
""1 - y L
and it was evaluated by graphical integrations of the differential heats given in Figures 1 and 2.
'
400
-400
I
4 / 1
(600
(dAH/&Ll+)dXLi+
J
/
/ - I
2000
S,'
=
t
-
L
/ .4
0
.2
.3 .4 .5 .6 .7 EQUIVALENT FRACTION, x L i +
.8
1.0
.9
Figure 2. Differential heats of exchange of L i + and Cs+ ion in nominal 15y0DVB cross-linked P M A exchanger. Open circles indicate midpoints of chords for heats of partial exchange.
0
0.1
I
I
0.2
0.3
I 0.4 0.5 0.6 1
I
I
EQUIVALENT FRACTION
,
I
0.7 0.0 xLi+
I
1
0.9
4.0
1
Figure 1. Differential heats of exchange of L i + with Cs+ ion in nominal 1%>DVB cross-linked P M A ion exchanger. Open circles indicate midpoints of chords for heats of partial exchange.
Standard heats, AH", for the Lif-Cs+ exchange reaction were derived by correcting the AH values by the appropriate difference in the relative apparent molal heat contents, q5L, of the two 0.1 N aqueous solutions. Corrections for heats of swelling arid for the heat of mixing of elcctrolyte a t p = 0.1 in the actual exchange reaction were assumed to be negligibly small. Standard free energies, AF", were computed from the corrected selectivity coefficients, Do, with the formula
h
"I \ 0.5
3 0.5 1 0.1
0.2
0.3 0.4 0.5 0.6 0.7 0.8 EOUIVALENT FRACTION, xLi +
0.9
1.0
Figure 3. Selectivity coefficients for the exchange of L i + with Cs+ ion in cross-linked PMA ion exchangers.
1
--AF" = 2 . 3 R T L log DOdxLri
The required values of Do were obtained by correcting the observed DCsiL1+ by the activity coefficient ratio, y ~ 2 ( C s O H ) / y ~ z ( L i O Hfor ) , the aqueous 0.1 N electrolyte mixture. The thermodynanlic quantities are summarized in Table I. The primary observation to be drawn from the entries in Table I is that the selectivity shown by the The Journal of Physical Chemietry
PMA exchangers for Li+ ion was determined by the entropy rather than the energy change. The uptake of Li+ ion is accompanied by a n increase in the energy, but this is over-balanced by the entropy increase to give a free energy decrease. This interplay of thermodynamic quantities may be contrasted with that for the reaction of Li +and Cs+ ions on cross-linked polystyrenesulfonic acid (PSSA) exchangers. The uptake of the
THERMODYSAMIC QUANTITIES IN
THE
EXCHANGE OF LITHIUMWITH CESIUM ION
Table I : Thermodynamic Quantities for t h e Exchange at 298.2”K.of Li+ with C s + I o n in Cross-Linked Polymethacrylate Ion Exchangers Crosslinking
AH,
A+L,
AH‘,
AFO,
7~DVB
cal. ciole-1
oal. mole-’
c d . mole-’
cal. mole-’
- 50 - 50
404
-134
1.8
1220
-621
6.2
1 .o 15
454
1270
AS’, e.u.
preferred cesium ion by the Li form of a nominal 16% DVB cross-linked PSSA preparation is accompanied by a strong lowering of the energy of the exchanger (AH” = -2890 cal. mole-’) and by an entropy decrease (AS’ = -6.9 e.u.).z The enthalpy decrease, however, is larger than TAS”,and AF” is negative. Nature of the Ionic Binding in P M A Exchangers. I t will be of interest to speculate briefly on possible causes for the entropy increase in the exchange of Li+ for Cs+ ion in cross-linked PMA exchangers. The type of ionic binding cannot be the same as with PSSA exchangers where the alkali metal cations appear to retain their primary hydrations and to interact electrostatically with the structurally bound sulfonate anions.2 To account for the preference of Li+ ions it appears necessary to assume that a specific association exists between them and the carboxylate groups of the exchanger or that “site-binding” of Li+ occurs. The evidence that interaction of alkali metal and alkaline earth metal ions with anionic polyelectrolytes takes place with the release of water molecules from the solvated participating species has been reviewed recently, and dilatometric measurements with linear polymethacrylate have shown that a volume increase of ca. 3 ml. equiv.-’ occurs in the system when tetramethyl-
2377
ammonium counterions are replaced by Lif or K a + ions.l0 If water is released in “site-binding,” an appreciable positive contribution to AS” also would be expected.“ The positive AS” values found in this research therefore may be taken as supporting evidence for “site binding’’ of Li+ ion by PMA exchangers.12 The question whether or not the carboxyl group replaces water and enters the first coordination sphere of the ion cannot be decided from the evidence available. It is possible that the interaction displaces only the more loosely bound water in the outer coordination layer and that an ion association involving a water molecule as an intermediary between Li+ and COO- occurs. This latter hypothesis (“localized hydrolysis” mechanism) has been employed by Robinson and Harned13 to account for the reversal in the sequence of activity coefficient values for aqueous solutions of the alkali metal salts when the anion is a proton acceptor (i.e., formate, acetate, fluoride, etc.). The greater ability of carboxylate compared with sulfonate groups to “complex” with the “smaller” alkali metals has been cited14also to explain the reversal in concentrated aqueous lithium salt solutions in the order of elution of these cations from a polymethacrylic acid exchanger. ~
~~~~~~~
(10) U. P. Strauss and Y. P. Leung, J . Am. Chem. Soc., 87, 1476 (1965). (11) The increase in entropy for the release of water by crystalline hydrates is 9.4 e.u.; cf., W. M. Latimer, “Oxidation Potentials,” Prentice-Hall, New York, N. Y.,1952,p. 364. (12) The deswelling of the exchanger on going from its Cs form to its Li form gives a positive contribution to A S o because of an increase in the configurational entropy of the molecular network. An estimate of the deswelling entropy with the Flory-Rehner theory for uncharged, cross-linked polymers indicates the contribution is only 0.1-0.2e.u., however. (13) R.A. Robinson and H. S. Harned, Chem. Rev.,28, 419 (1941). (14) D. C. Whitney and R. M. Diamond, Znorg. Chem., 2, 1284 (1963).
Volume 69,Number 7 July 1966
