HEATCAPACITY CHANGES IN ION-EXCHANGE REACTIONS
Heat Capacity Changes in Ion-Exchange Reactions.
2651
The Exchange
of Tetra-n-butylammonium with Sodium Ion in Cross-Linked Polystyrenesulfonatel by G. E. Boyd, Q. V. Larson, and S. Lindenbaum Oak Ridge National Laboratory, Oak Ridge, Tennessee 87880 (Received February d8, 1968)
Calorimetric measurements of the temperature dependence of the standard enthalpy of ion exchange, 4H0, were performed for the reaction in dilute aqueous solution of tetra-n-butylammonium with sodium ion in a lightly cross-linked sulfonated polystyrene type of cation exchanger. Between 15 and 35" the value of AH" decreased from 2.39 to 1.38 kcal equiv-' corresponding to an average standard heat capacity change, 4Cp0 = -53 =t9 cal equiv-1 deg-1. The sign and magnitude of 4Cp0 are consistent with the hypothesis that large, singly charged organic cations such as the tetra-n-alkylammonium ions in aqueous solution produce an extensive ordering of the water structure in their vicinity. The prediction of 4Cp"values for the exchange reactions in dilute solutions of singly charged cations (and anions) with one another is discussed.
Calorimetric2-12 measurements on ion-exchange reactions between dilute aqueous electrolyte solutions and organic ion exchangers have shown that these reactions are accompanied by an enthalpy change, the magnitude of which is dependent on (a) the charge on the ions, (b) their electronic and/or molecular structures, (c) the nature of the ionogenic group, and (d) the cross-linking of the exchanger. The enthalpy change, if it is truly a thermodynamic property, must vary with the temperature so that ion-exchange reactions must also be accompanied by a heat capacity change. Only fragmentary information is available on the sign and magnitude of the heat capacity change in ion-exchange reactions, and this comes entirely from temperature coefficient determinations. Measurements13J4 with 8 and 16% DVB cross-linked polystyrenesulfonates on the variation of ion-exchange equilibria with temperature between 0 and 100" have shown that generally log K , os. T-' curves are not linear and hence that the standard enthalpy change, AH", is not independent of temperature. The heat capacity change, AC,", thus inferred from the change in AH", appears to be either zero or positive and small, although in the exchange of thallium with hydrogen ion AC," = 12 cal equiv-l deg-'. Temperature coefficient measurements on cation-exchange reactions with 12% DVB cross-linked polystyrenesulfonate over a wider interval (ie., 0-200") but with one ion only a t tracer concentrations have been reported by Kraus and Raridon.lS The ACp' values obtained from a "least-squares best fit" of the data, assuming ACpf itself was independent of temperature, were always positive and sometimes as large as 20 cal equiv-' deg-'. The temperature dependence of AH" revealed by the measurements of Bonner and the temperature coefficients recently
reported by Starobinets and Soldatov16 suggest that AC," also varies with temperature. However, equilibrium constants were measured only a t 20 to 25" intervals from 0 to loo", and corrections for the temperature-dependent activity coefficient ratios of the ions in the aqueous phase either were ignored or were estimated crudely. The magnitude and even the sign of the temperature dependence of AC," therefore is highly uncertain. I n this research the calorimetric measurement of AH" a t a series of temperatures near 25" was undertaken in an attempt to derive more reliable values of (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) (a) G. E. Boyd, F. Vaslow, and S. Lindenbaum, J . Phys. Chem., 68, 590 (1964); (b) S. Lindenbaum and G. E. Boyd, ihid., 69,2374 (1965). (3) F. Vaslow and G. E. Boyd, ihid., 70, 2295, 2507 (1966). (4) K. E. Becker, S. Lindenbaum, and G. E. Boyd, ibid., 70, 3834 (1966). (5) G. E. Boyd and A . Schwarz, ihid., 71, 1355 (1967). (6) G. E. Boyd, F. Vaslow, and S. Lindenbaum, ibid., 71, 2214 (1967). (7) G. E. Boyd and Q. V. Larson, J . Amer. Chem. SOC.,89, 6038 (1967). (8) 0. D. Bonner and J. R. Overton, J . Phys. Chem., 65, 1599 (1961). (9) E. H. Cruickshank and P. Meares, Trans. Faraday Soc., 53, 1289 (1957). (10) D. S. Flett and P. Meares, ;hid., 62, 1469 (1966). (11) W. R. Heuman and D. Patterson, Can. J . Chem., 44, 2139 (1966). (12) J. S. Redhina and J. A. Kitohener, Trans. Faraday Soc., 59, 516 (1963). (13) 0. D. Bonner and L. L. Smith, J . Phys. Chem., 61, 1614 (1957). (14) 0. D. Bonner and R. R. Pruett, ibid., 63, 1417, 1420 (1959). (15) K. A. Kraus and R. J. Raridon, ihid., 63, 1901 (1959). . , (16) G. L. Starobinets and V. S. Soldatov, Russ. J . Phys. Chem., 37, 153 (1963). Volume 7.9,Number 7 J u l y 1968
2652 AC," and to determine if the latter showed a temperature dependence. The exchange reaction between tetra-n-butylammonium ion, B u ~ Y +, in 0.01 N aqueous solution with sodium ion in a sulfonated polystyrene exchanger was used. Because of the large size of the Bu4N+ ion, a lightly cross-linked ( i e , , 0.5% divinylbenzene) polystyrenesulfonate cation exchanger was employed that a rapid exchange reaction leading to the establishment of an equilibrium in which all the sulfonate groups participated would be realized.
Experimental Section Heat Measurements. The calorimeter, thermal measurement techniques, and experimental procedure were closely similar to those described in earlier reports from this laboratory' except that less exchanger was used (e.g., ca. 1 mequiv) and a smaller concentration in the aqueous electrolyte phase was employed ( p = 0.01 M ) so that heat of dilution corrections, A ~ L would , be negligibly small compared with the integral heat of ion exchange. Measurements were performed at 15, 20, 25, 30, and 35" with the exchanger initially in an homoionic form ( i e . , as NaR or as BuJXR). Two and sometimes four determinations were made at each temperature. A correction of 0.011 cal exothermic was applied for the heat of opening of the pipet which initially contained the ion exchanger. The calorimeter was submerged in a stirred 60-1. water bath whose temperature was maintained constant to =tOo.O0lofor periods of 1-2 hr. Longer term temperature drifts were read to 0.002" on a 5" range Beckman thermometer. A calibrated NBS mercury-inglass thermometer (range, -1 to 51" in 0.1') was used to estimate the absolute temperature of the thermostat. The temperature of the stirred calorimeter solution was set above that of the thermostat for convenience in establishing a uniform drift rate. This increment, AT, was determined from the difference in resistance, AR = Ro - Rt, of the calorimeter thermistor measured when immersed in the bath, Ro, and in the assembled and stirred calorimeter, Rt. The approximate equation, AT = (T2/B)(AR/Ro), was employed. A plot of log Ro us. T-l was accurately linear from 15 to 35" and yielded a slope of B = 0.389 X lo4. The reaction temperatures thus are believed to have been known to =k0.05". The over-all reliability of the calorimeter system was established by measurements of the heat of solution of tris(hydroxymethy1)aminomethane (THAM) in 0.1 N HC1 solution. After small heat of dilution and heat capacity corrections, a value of 7095 & 7 cal mol-l at 25.00' and 0.04 m final concentration was obtained which is in good agreement with the value of 7104 cal mol-' by Irving and Wads617 and of 7107 cal mol-' by Gunn.'* The temperature coefficient of the heat of solution of THAM estimated from calorimetric measurementsl7 at 20, 25, and 30" is 40 cal deg-l mol-'. The Journal of Physical Chemistry
G. E. BOYD,Q. V. LARSON, AND S. LINDENBAUM As a further test of our calorimeter, the heat of solution of THAN was measured at 30'. A value of 6916 k 30 was obtained in good agreement with the value 6904 f 3 cal mol-l by Irving and Wadso. Chemical Analyses. The number of milliequivalents of exchange reaction was determined on concluding the thermal measurements by analysis of the exchanger and the mixed aqueous electrolyte in the calorimeter for sodium and tetra-n-butylammonium ions. Sodium ion concentrations were determined by flame spectrophotometry with a precision of ca. k l % ; tetra-nbutylammonium ion was measured by amperometric titration7 with sodium tetraphenylboron to ca. 201,. The total milliequivalents of ion exchanger in the calorimeter were found by titration of the acid form after its quantitative recovery and conversion by elution with 100 ml of 0.2 N HN03. The purity of the ion-exchange reaction (ie., the absence of interferences from other ionic impurities) was established by material balances from the chemical analyses of the exchanger and aqueous electrolyte. The source of the largest error in the calculated heats of exchange was in the determination of the milliequivalents of reaction. The uncertainty in the calorimetric measurements was 0.4% or less, while that in the analyses of the exchanger for the amount of E a + or Bu4N+ ion taken up varied from 1 to 2%. The precision of the heat of exchange therefore was ca. 2%, although at several temperatures the measurements were better than this.
*
Experimental Results The experimentally determined heats of partial exchange, &, were plotted as chords against the initial and final values of the equivalent fraction of Bu4N+ S the chord-area method ion in the exchanger, Z ' B ~+,~ and was applied to find the differential heat of ion exchange, A B = d&/dxBuANt,and also the integral ion-exchange enthalpy, AH, defined by AH = JIAR dxBu4N+. The standard enthalpy change, AH", for the hypothetical ion-exchange reaction in which the products and reactants are in their standard states NaR(a
+
1, equil with 0.1 N NaCl) Bu4SCl(aq, a = 1) BurNR(a = 1, equil with 0.1 N Bu4NC1) NaCl(aq, a = 1) nHzO(a, = 1) =
+ +
+
was obtained from the relation: AH" = AH A ~ L where A& is the relative apparent molal heat content difference, $q,(Bu4NC1) - &,(NaCl), which was taken to be negligibly small for = 0.01 N solutions. The values of AH" plotted against temperature in Figure 1 show that the standard enthalpy of exchange (17) R. J. Irving and I. Wadso, Acta Chem. Scand., 18, 195 (1964). (18) S. Gunn, J . Phys. Chem., 69, 2902 (1965).
2653
HEATCAPACITY CHANGES IN ION-EXCHANGE REACTIONS
The standard apparent molal heat capacity for sodium ion is known,20 +"C,(Na+) = 11.1 eu,while that for tetra-n-butylammonium ion may be derived from the experimental measurements of Wen.21 However, an extrapolation to infinite dilution from the 25" value, +CP(Bu4NBr) = 270 f 2 cal deg-l mol-1 at 0.1988 m, must be made. We have utilized the equation for a 1-1 electrolyte
+cp- +"C,
AJrn'/"[(l 3. m * ' y ~(m'/')/3] - 2.30313Tz[(2/T)(dB/dT) (d2B/dTz)3m (2)
1
1
25 TEMPERATURE, *C
20
I
I
30
35
1
Figure 1. Temperature dependence of the standard enthalpy of exchange, AH ', of tetra-n-butylammonium with sodium ions in 0.5y0divinylbenzene cross-linked polystyrenesulfonate.
AHo = 3605 - 92-72
+ 0.804t2
+ 1.61t
Discussion The standard heat capacity change in the tetra-nbutylammonium-sodium ion-exchange reaction is unusually large and negative in contrast with all other reactions involving the exchange of singly charged cations in organic ion exchangers. However, the apparent molal heat capacity, $IC,, of aqueous solutions of Bu4NBr are known from the measurements of Frank and Wen19 to be quite large, whereas the @Cpfor NaBr solutions is small (ie., +"C, = -22.8 eu). Accordingly, AC, for the conversion of sodium form exchanger to the tetra-n-butylammonium form can be expected to be large provided other effects do not enter. The standard heat capacity change, AC,", in the conversion in fact is simply related to the +Cp difference for the two resinates when the cross-linking of the ion exchanger is light
+
(1)
(3)
where A , = 0.511, Thus, with A J = 10.4 cal deg-' mol-l, dB/dT = 7.2 X loda,and d2B/dT2= -13.6 X one calculates form = 0.1988 = 9.4 eu
(4)
from which 4"C,(Bu&Br) = 261 rfi 2 eu. The value +"C,(Bu4N+) = 295 f 2 eu is then obtained by subtracting the value for bromide ionz0 +"C,(Br-) = -33.9 eu from 261 i 2 eu. Equation 1 becomes
AC," = +CP(Bu4KR) - +C,(NaR)
which, for 25", gives AC," = -53 rfi 9 cal deg-l mol-'. The heat capacity change itself is slightly temperature dependent and increases by approximately 1.6 eu deg-l.
AC," = +CP(Bu4NR) - +C,(NaR) +"C,(Na+) - +"C,(Bu4N+)
+ = (2.303/3)A,m"2~(m"") - (2.303/2)Bm
4Cp - +"C,
where t is the temperature in degrees Centigrade. The standard errors in the constants were 108, 9.1, and 0.179, respectively. The standard heat capacity change, AC,', is given by AC," = dAHO/dt = -92.7
+
first proposed by Guggenheim and PrueZ2to join the available data to the limiting Debye-Hiickel slope. The quantities, dB/dT and d2B/dTz, were estimated from the correlation diagrams of Pitzer and Brewerz3 with the value of B = -0.25 for aqueous solutions of Bu4NBr estimated at m = 0.1 from the osmotic coeficient a t this concentrationz4with the equation
1of Bu4N+ with Na+ ion decreased by approximately 1000 cal equiv-' as the temperature increased from 15 to 35". The decrease in AH" with temperature followed the least-squares quadratic equation
=
- 284
f
2 (1')
To estimate approximately the difference +CP(Bu4NR) - +C,(NaR) = A4C,, we note that an examination of available heat capacity data for aqueous solutions of the alkali metal salts20 shows that A&, is nearly independent of the nature of the anion over a wide concentration range. Thus, we shall assume +C,(IYaR) = +C,(NaBr) and +CP(Bu4NR) = #CP(Bu4SBr), respectively. The concentration at which $C,(NaR) and +CP(Bu4NR)are to be taken needs justification. There is reason to believe that the "effective concentration" in the double layer of cations about the negatively charged polyelectrolyte chains of the cation exchanger is of the order of 4-5 m based on heat of ion-exchange (19)H.Frank and W. Y. Wen, Discussions Faraday Soc., 24, 136 (1957). (20) V. B. Parker, "Thermal Properties of Aqueous Uni-univalent
Electrolytes," National Standard Reference Data Series, NSRDSNBS 2, National Bureau of Standards, U. S.Government Printing Office, Washington, D. C., 1965. (21) W. Y.Wen, Ph.D. Thasis, University of Pittsburgh, 1957. (22) E. A. Guggenheim and J. E. Prue, Trans. Faradau Soc., 50, 710 (1954). (23) K. S. Pitzer and L. Brewer in G. N. Lewis and M. Randall, "Thermodynamics," McGraw-Hill Book Co., Inc., New York, N. Y., 1961,pp 396,397. (24) S.Lindenbaum and G. E. Boyd, J . Phys. Chem., 68,911 (1964). Volume 78, Number 7 July 1968
G. E. BOYD,Q. V. LARSON, AND S. LINDENBAUM
2654 m e a s ~ r e r n e n t sand ~ ~ other studies.26 Therefore, assuming an effective localized concentration m = 4.0, the value &,(NaBr) = 3.8 may be taken from the literature, while @C,(BudNBr) = 220 eu may be found by extrapolating the 25" measurements of Frank and Wen.19J1 Thus, AdC, = 216 eu and AC," = 216 284 = -68 eu. If m = 2.0 is assumed, ACpo = -40 eu. It is clear therefore that a large and negative standard heat capacity change in the exchange reaction of Bu&+ with Na+ ion is to be expected. It is of interest to note that only a relatively small fraction of the total heat capacity (ie., 284 eu) of the BudN+ ion is released when it is bound by the ion exchanger. However, this large, complex hydrocarbonlike ion may be estimated to possess an internal heat capacity of as much as 150 eu; this will not be lost when the ion is taken up by the exchanger. Further, as Frank and Wenlg have pointed out, the ca. 130-eu difference between the internal and the total heat capacity of the ion must be assigned to the interaction of the ion with water. This interaction decreases when Bu4N+ ion leaves its dilute solution and is bound by the exchanger. Actually, of course, this ion does not entirely leave its water environment; even when it is held by the polyelectrolyte it will interact with the water structure in its vicinity. An appreciable overlap of the "hydration" cospheres must occur, however, so that a negative and relatively large heat capacity change will accompany its replacement of sodium ion in an ion-exchange reaction. The relatively large increase in the standard entropy, AS", previously reported7 and the large, negative AC," found in this research are consistent with the view of Frank that
tetra-n-butylammonium ion should be regarded as a "water-structure producer" of a special type. In conclusion, we note that eq 1 may be employed to predict the approximate magnitude of AC,' for many ion-exchange reactions in exchangers of large crosslinking. A comparison of predicted and observed values is presented in Table I where it was assumed that R- = NOa-. All things considered, the agreement between columns 4 and 5 is surprisingly good, particularly when it is remembered that the "observed" AC,' values were for the exchange of trace amounts of alkali metal ion in either the pure hydrogen or pure sodium form of cross-linked polystyrenesulfonate. Table I: Estimation of Heat Capacity Changes a t 298.2"K in Ion-Exchange Reactions with Eq 1 and the Apparent Molal Heat Capacities of Aqueous Nitrate Solutions
Reaction
A(bCp)
Na-Ha K-Ha Rb-Ha CS-Ha K-Nab Rb-Nab Cs-Nab
25.8 16.8 15.3 14.0 -6.0 -8.5 -9.5
Nb'Cp)
11.1 5.2 3.3 1.9 -5.9 -7.8 -9.2
Calcd ACpO
Obsd's
14.7 11.6 12.0 12.1 -0.1
9.3 11.4 11.3 15.5 1.1 0.4 0.9
-0.7 -0.3
Computed for hydrogen resinate molality of 2.6. puted for N a R molality of 2.95.
A(&'
' Com-
I
The Journal of Physical Chemistry
(25) G. E. Boyd, I?. Vaslow, A. Sohwarz, and J. W. Chase, J . Phys. Chem., 71, 3879 (1967). (26) 0.D. Bonner and 0.C. Roger, ibid., 65, 981 (1961).
