THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS OF ~-ETWLBENZENESULFONIC ACID
3879
Thermodynamic Properties at 25' of Aqueous Solutions of p-Ethylbenzenesulfonic Acid and Its Alkali Metal Salts. Comparisons with Cross-Linked Polystyrenesulfonate Type Cation Exchangers'
by G. E. Boyd, F. Vaslow, A. Schwarz,2 and J. W. Chase Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
Oak Ridge National Laboratory, Oak Ridge, Tennessee $7880 (Receined April 13, 1967)
Molal osmotic and mean molal activity coefficients, $I and y, and apparent molal heat contents, C$L, of aqueous solutions of p-ethylbenzenesulfonic acid (p-EBSA) and its alkali metal salts were determined at 25" for a wide range of concentrations. The strength of the acid was inferred to be less than that of "03, and evidence was obtained for ion-pair formation with the cesium salt. The concentration dependence of 41, was unusual in that values above the Debye-Huckel limiting slope were observed with all but Cs p-EBS. Calculations of solvent relative partial molal entropies, SI - &', indicated that the p-ethylbenzenesulfonate anion possessed "water structure forming" properties. Free energies of dilution, AGD, were computed from 4 and y, and the differences between these were compared with the standard free energy changes, AG,,", for ion-exchange reactions between the alkali metal cations and hydrogen ion in cross-linked polystyrenesulfonic acid type cation exchangers. Differences in 41,were also compared with standard heats of cation The concordance between the various thermodynamic quantities indiexchange, AH,,'. cated that the analogy between concentrated electrolyte mixtures and cation exchangers was valid.
The objective of this research has been to conduct the measurements necessary for a comparison of the differences in the thermodynamic properties at 25" of aqueous solutions of the alkali inetal salts of p-ethylbenzenesulfonic acid with the standard enthalpies, free energies, and entropies of ion exchange for the corresponding cations in cross-linked polystyrenesulfonic acid type cation exchangers. Justification for this comparison lies in the existence of numerous analogies in the equilibrium behavior of organic ion exchangers with concentrated aqueous electrolyte solutions. The electrochemical properties of sulfonic acid groups in cross-linked polystyrenesulfonates, for example, appear to be virtuaIly the same as those for the same groups in low molecular weight analogs such as in p-ethylbenzenesulfonic acid or p-toluenesulfonic acid. The pH titration curves for the cross-linked polymer acid and its heat of neutralization indicate strong acid behavior. Further, Raman spectral3 and nmr4 measurements on poly-
styrenesulfonic acid and on ethylbenzenesulfonic acid have shown that the amount of associated hydrogen ion must be quite small. Comparisons between the thermodynaniic properties for alkali metal cation-exchange reactions and those for concentrated aqueous alkali metal chloride solutions have been attempted.6ve However, only a poor correspondence was observed for several reasons. The properties of aqueous alkali metal salt solutions are strongly dependent on the nature of the anion, as may (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) Radiochemistry Department, Israel Atomic Energy Commission, Soreq Nuclear Research Center, Yavne, Israel. (3) S. Lapanje and S. A. Rice, J. Am. Chem. SOC.,8 3 , 496 (1961). (4) L. Kotin and M. Nagasawa, ibid., 83, 1026 (1961). (5) E. Cruickshank and P. Meares, Trans. Faraday SOC.,53, 1299
(1957). (6) 0. D. Bonner and J. R. Overton, J . Phys. Chem., 65, 1599 (1961).
Volume 71, Number 1.2 Noaember 1967
Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
3880
be seen by comparing the activity coefficients and apparent molal heat content values for the chlorides with those for the nitrates. Comparisons of the properties of concentrated electrolyte solutions with those of cation exchangers therefore should be made with aqueous solutions of the “model compounds.” Further, in one instance5 it was mistakenly assumed that a hydrostatic pressure exists inside a cross-linked ion exchanger. Consequently, the free energies and heats of dilution for the alkali metal chloride solutions were corrected by estimated free energies and heats of compression (or decompression), respectively. In acttuality, the pressure in an ion-exchange gel is the same as the ambient pressure, which is usually 1 atm. A probe placed in the gel, for example, would not register a pressure different from that outside the gel. The free energy of the molecular network of an ion exchanger varies with its volume; formally this variation has the units of pressure and the derivative has been termed the “swelling pressure,” although a better term would have been the “strain free energy.”’ The lithium, sodium, potassium, and cesium salts of the “model” compound, p-ethylbenzenesulfonic acid, were employed in this investigation of the analogy between cat,iori exchangers and concentrated electrolyte solutions. Llolal osmotic coefficients, 4, for these salts in aqueous solution were measured with the gravimetric isopiestic vapor pressure comparison method and with a vapor pressure o s m ~ m e t e r . ~These .~ determinations were employed to compute mean molal activity coefficients, y, and free energies of dilution, AGD, as a function of concentration. Calorimetric determinations of the heats of dilution of aqueous solutions of the acid and its alkali metal salts also were made and values of their apparent molal heat contents, qh,, as a function of concentration were derived. The values of AGD and c p ~thus obtained were employed to estimate freeenergy differences, A (AGD) , and enthalpy differences, A$L, for comparison vith standard free energies and enthalpies of cation exchange.
Experimental Section Materials. The synthesis of p-ethylbenzenesulfonic acid and its lithium and sodium salts have been described.l0 Measurements of the infrared and nmr spectra of the barium salt of the acid indicated at least 99% para substitution. The potassium and cesium salts were prepared from the barium salt, which was converted by ion exchange to give an aqueous solution of the acid which was neutralized with pure K2C03or CSZCO~,respectively. The salts were recrystallized from and vacuum-dried at 6oo* Equivalent weights, determined by titration of the The Journal of Physieal Chemistry
G. E. BOYD,F. VASLOW,A. SCHWARZ, AND J. W. CHASE
acid released when solutions containing known weights of salt were passed through a deep bed of H-form cation exchanger, were 224 and 318 for the potassium and cesium salts compared with theory values of 226 and 317, respectively . Osmotic Coeficient Determinations. The gravimetric isopiestic vapor pressure comparison apparatus and techniques employed in measuring the concentrations of the model compound solutions in vapor pressure equilibrium with standard sodium chloride solutions have been described. l1 Concentrated stock solutions of the alkali metal p-ethylbenzenesulfonates were made up by weight, and weight burets were employed in the preparation of more dilute solutions as required. A vapor pressure osmometer was employed in the measurements with solutions of concentrations less than 0.5 m. The precision of these measurements was lower than with the gravimetric technique, particularly below 0.1 m; however, the speed and convenience with which determinations can be made on dilute solutions are important advantages. Approxiniately 6-S min was needed for the system to come to a steady-state temperature difference and give a constant resistance reading. Repetitive measurements were made and the data were averaged to increase precision. Molalities of the isopiestic NaC1 and alkali metal p-ethylbenzenesulfonate solutions of 25” observed with the gravimetric technique are presented in Table I. Molal osmotic coefficients were computed from these data with vxmxdx =
Yr?nr+r
(1)
where the number of ions, Y = 2, m x is the sulfonate molality, 4x is its osmotic coefficient, and m, and +r are the molality and osmotic coefficient of the reference electrolyte (NaCl), rsepectively. The osmotic coefficients given in Table I1 were computed with the equation (W)x
(ARx/ARr) (?n4>r
(2)
where (AR,/AR,) is the measured resistance ratio. Values for the osmotic coefficient, Cp,, of the reference electrolyte solution (NaC1) at 25” were computed from m, with the equation12 (7) For a further discussion see 3. J. Hermans, “Flow Properties of Disperse Systems,” North-Holland Publishing Co., Amsterdam, 1953, Chapter 111. (8) 0. D. Bonner and 0 . C. Rogers, J . Phys. Chem., 65, 981 (1961). (9) G. E. Boyd, A. Schwara, and S. Lindenbaum, ibid., 70, 821
(1966). (10)S. Lindenbaum and G. E. Boyd, ibid., 71, 581 (1967). (11) S. Lindenbaum and G. E. Boyd, ibid., 68, 911 (1964). (12) E.A. Guggenheim and J. C. Turgeon, Trans. Faraday Soc., 51, 747 (1955).
THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS OF ~-ETWLBENZENESULFONIC ACID
1 - q5 = 0.3903m1f'cr(m'f')- /3m
(3)
using@ = 0.15. Mean molal activity coefficients were calculated from the osmotic coefficients with the Gibbs-Duhem equation. The required integrations were performed numerically with a CDC 1604 digita,l computer. The
3881
Table 11: Osmotic Coefficients for Dilute Solutions from Vapor Pressure Osmometer Measurements at 25" mK p~~~
4K p-EBB
~C,,EBS
*Cs p E B S
0.02129 0.04998 0.10000 0.14996 0.19954
(0.9368) 0.9379 0.9165 0.9011 0.8865
0.10012 0.15001 0.19420
0.9044 0.8868 0.8642
Table I: Molalities of Isopiestic Solutions at 25'
Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
mNsC1
Li p-EBS
Na p-EBS
K p-EBS
Cs p-EBS
...
0.2150
...
0.3596
0.3973 0.4316 0.4561
... ... ...
0.4150
... ... ...
... ...
0.4840 0.5170
0.5143 0.5499
0.4646 0.4886 0.5947
... 0.5128 0.6375
0.4953 0.5274 0.6641
... ...
0.7270
0.7678
... ... ... ...
...
...
...
0.8788 1.097
0.9646 1.213
1.180
1.310
...
1.690
1.855
2.085
2.227
0.1994 0.3493
0.6674 0.6862 0.7837
1
.
.
...
0.8187 0.8732 0.9937
...
...
1.008
1.135
1.101 1,208 1 I221
...
...
1.548
1.939 1.974
... ...
...
...
...
...
... ...
...
...
3.167
2.723 3.218
...
...
... ...
...
...
4.927
4.849
3.006 3.085
...
...
1.4525 1.537 1.764
2.0905 2.441
2.084 2.1635 2.211
...
2.533 2.741 2.971
3.751
3.3845 3.385 3.392
4.520
4.009 4.155 4.210
5.410
4.808 5.1195
...
... ...
...
...
... ...
...
4.026
...
... ...
... ...
... ... ...
5.874
...
7.873
... ...
7.894
...
... ... ...
...
*..
...
... ...
... ...
...
,..
...
...
...
...
3.346
...
6.9405
...
9.473
...
10.044 11.739 12.624
necessary extrapolation of the $ x values to zero concentration was performed with eq 3 with /3 taking the valuesO.ll, 0.08, -0.055, and -0.19 =t0.03 for the lithium, sodium, potassium, and cesium salts, respectively. A value, /3 = -0.047, derived from the measurements of
Bonner,l3 was employed for the acid. Osmotic and activity coefficients computed for interpolated concentrations are given in Table 111. The concentration dependence of the measured osmotic coefficients including those for the acid is exhibited in Figure 1, where it may be seen that the sequence of values for the p-ethylbenzenesulfonates taken at a constant concentration resembles that for the corresponding nitrates. Interestingly, the sodium and potassium salts were relatively insoluble; the sodium salt in fact was the least soluble alkali metal p-et,hylbenzenesulfonate. Culorimetric Measurewnts. The calorimeter and accessories employed in the heat of dilution measurements have been de~cribed.'~Several improvements to the electrical measuring circuits were eff ected,16 thereby increasing the temperature sensitivity to approximately 15 pdeg. Solutions of accurately predetermined concentration were measured into the Calorimeter pipet from weight burets. The initial volume of water in the calorimeter was ca. 500 ml accurately measured by weight; the final concentration after dilution was less than 0.01 m in all cases. Over-all checks on the calorimetric system were made by measuring the heat of solution of KCl(c). The reaction temperature was 25.2" and the results are expressed in terms of the defined calorie (i.e., 1 cal = 4.1840 absolute joules). Corrections to the observed heats for "dilution to infinite dilution," 41,(rnr),were computed with the equation proposed by Guggenheim and Prue'* following a procedure outlined elsewhere." In this procedure requisite values of the coefficient (dB/dT) were obtained from the correlation between (dB/dT) and (Bax - B K C ~computed ) from the values of B m = (13) 0. D. Bonner, G. D. Easterling, D. L. Wefit, and V. F. Holland, J . Am. Chem. SOC.,7 7 , 242 (1955). (14) G. E. Boyd and F. Vaslow, J. Chem. Eng. Data, 7 , 237 (1962). (15) 8. Lindenbaum and G. E. Boyd, J. Phus. Chem.. 69, 2374 (1965). (16) E. A. Guggenheinl and J. E. Prue, Trans. Faraday Soc., 50, 710 (1954).
(17) G. E. Boyd, J. W. Chase, and F. Vaslow, J. Phys. Chem., 71, 573 (1967).
Volume 71, Number 19 .Vovember I967
G. E. BOYD,F. VASLOW, A. SCHWARZ, AND J. W. CHASE
3882
Table 111 : Osmotic and Activity Coefficients for Interpolated Molalities of Aqueous Alkali Metal Salt Solutions of pEthylbenzenesulfonic Acid a t 25” -Li
9
Y
+
0.1 0.2 0.3
0.915 0.891 0.871
0.749 0.683 0.637
0.4 0.5 0.6
0.852 0.832 0.813
0.7 0.8 0.9
Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
p-EBS-
-Na
r
+
0.932 0.918 0.906
0.773 0.723 0.688
0.600 0.568 0.539
0.893 0.880 0.866
0.793 0.772 0.754
0.513 0.488 0.466
1.0 1.2 1.4
0.737 0.709 0.687
1.6 1.8 2.0
m
-K
p-EBS-
p-EBS-
-CS
p-EBB-
7
9
Y
9
Y
0.929 0.915 0.902
0.769 0.717 0.682
0.916 0.888 0.864
0.782 0.683 0.634
0.904 0.864 0.834
0.734 0.652 0.595
0.659 0.634 0.611
0.885 0.862 0.839
0.650 0.617 0.587
0.841 0.817 0.792
0.593 0.557 0,524
0.804 0.777 0.751
0.548 0,509 0.475
0.852 0.838 0.827
0.590 0.569 0.550
0.819 0.795 0.772
0.560 0.534 0.508
0.767 0.741 0.715
0.494 0.466 0.440
0.725 0.700 0.675
0.444 0.417 0.392
0.446 0.412 0.385
0.808 0.781 0.757
0.531 0.498 0.469
0.751 0.712 0.676
0.485 0.445 0.409
0.689 0.642 0.604
0.416 0.373 0.338
0.650 0.603 0.568
0.369 0.329 0.298
0.672 0.665 0.660
0.363 0.347 0.333
0.738 0.722 0.711
0.445 0.424 0.407
0.640 0.606 0.584
0.377 0.348 0.326
0.567 0.538 0.514
0.309 0.284 0.264
0.538 0.511 0.488
0.272 0.250 0.232
2.5 3.0 3.5
0.661 0.682 0.706
0.309 0.297 0.290
0.705 0.713 0.737
0.379 0.362 0.355
0.554 0.536 0.538
0.288 0.260 0.242
0.476 0.455 0.440
0.227 0.201 0.182
0,454 0.435 0.425
0.199 0.176 0.160
4.0 4.5 5.0
0.735 0.773 0.822
0.288 0.290 0.298
0.768 0.802 0.837
0.355 0.357 0.363
0.548 0.563 0.582
0.230 0.222 0.215
0.429 0.421 0.418
0.167 0.154 0.145
0.420 0.423 0.428
0.147 0.138 0.130
5.5 6.0 7.0
0.870 0.917 1.009
0.308 0.320 0.349
0.874
0.372
0.433 0.438 0.448
0.124 0.119 0.110
8.0 9.0 10.0
1.100
0.385
0.462 0.469 0.474
0.104 0.098 0.093
,. Computed from gravimetric isopiestic vapor pressure comparison data supplied by Professor 0. D. Bonner, private communication. 2/3/2.303 employed above in fixing the osmotic and activity coefficients at 0.1 m. Values of dB/dT of 0.00338, 0.00138, 0.00175, 0.00323, and 0.00473 were employed for the acid and the lithium, sodium, potassium, and cesium salts, respectively. The r $ ~values in Tahle JV are believed to be reliable to 10 cal mole-’ or to &2%, whichever is the larger. Initial and final concentrations in moles per kilogram of water are indicated as mi and mf,respectivels, and Q is the heat absorbed in calories per mole of solute on diluting from mi to mf. Graphically smoothed r $ ~ values for interpolated molalities, M , and calculated relative partial molal heat contents, ,TI and 1,of solvent and solute, respectively, are given in Table V. The calculations of 1,and 1 2 employed the smoothed C#L values and the defining equations for these quantities.18 Heats of solution for the crystalline compounds are summarized in Table VI, where Q is the observed heat,
*
The Journal of Physical Chemistry
mt is the concentration of the final solution, and AH,’ is the “heat of solution to infinite dilution” obtained by correcting Q as in Table IV. The dissolution of the alkali metal p-ethylbenzenesulfonates appears to be more exothermic than for any other salts of these cations thus far measured. Interestingly, the difference in AH,’ values between the lithium and cesium pethylbenzenesulfonates was smaller than for any other of the alkali metal salts. The concentration dependence of the r$L values is shown in Figure 2, wherein the unique thermal behavior of aqueous ethylbenzenesulfonate solutions becomes apparent. An evolution of heat occurred on dilution from initial concentrations of 1 m and less with all salts. Further, aplot of r$Lagainst \&revealed that the (18) H. S. Harned and B. B. Owen. “The Phvsical Chemistrv of Electrolytic Solutions,” 3rd ed, Reinhold Pubiishing Corp., New York, N. Y . , 1958, p 176.
THERMODYNAMIC PROPERTIES OF AQUEOUSSOLUTIONS OF p-ETHYLBENZENESULFONIC ACID
Table IV:
Experimental Heats of Dilution of the pEthylbeneenesulfonates a t 25” mi
H pEBS
Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
3883
N a gEBS
Cs p-EBS
4%
Q
- 192
0.0929 0.182 0.451 0.837 1.797 3.190 4.300 4.860 6.340 6.890 7.870 13.22
0.0411 0.0418 0.0406 0.0393 0.0409 0.0426 0.0411 0.0399 0.0422 0.0423 0.0413 0.0427
0.0566 0.206 0.478 0.967 1.457 1.87 2.15 2.60 3.04 3.31
0.0413 0.0436 0.0413 0,0413 0.0425 0.0413 0.0413 0.0413 0,0425 0.0425
- 126 - 265
0.0918 0.192 0.477 0.681 0.902 1.46 1.986 2.60 3.16 3.96 4.95 6.10
0.0409 0.0417 0.0417 0.0416 0.0405 0.0415 0.0422 0.0412 0.0423 0.0426 0,0423 0.0419
- 99
-338 - 583 - 848 1060 - 1122 - 1201 - 1255 - 1351 - 1384 - 1498 1867
-
-
-413 - 554 - 573 -511 -430 -311 - 235 - 181
- 153 -216 -263 -268 - 197 - 59 25 218 324 479 704
dL
209 355 599 864 1076 1139 1218 1271 1368 1401 1515 1884 144 284 43 1 572 591 529 448 329 253 198 115 169 232 279 283 213 75 -9 -202 -308 -463 - 688
mi
Li pEBS
K p-EBS
Gf
0.0577 0.0935 0.201 0.449 0.494 0.950 1.016 1.509 2.003 2.53 3.28 4.39 5.24 6.39 8.00 8.57
0.0413 0.0413 0.0425 0.0400 0.0425 0.0413 0.0436 0.0480 0.0425 0.0447 0.0425 0.0436 0.0425 0.0425 0.0436 0.0443
0.0528 0.1369 0.334 0.553 0.573 0.919 1.055 1.429 1.909 2.019 2.628 2.89 3.402 4.078 4.26
0.0413 0.0417 0.0426 0.0413 0.0501 0.0408 0.0400 0.0423 0.0591 0.0426 0.0421 0.0423 0.0430 0.0648 0.0438
Q
- 123 - 182 - 306 - 546 -556 -911 - 943 - 1092 - 1147 - 1186 - 1226 - 1271 - 1325 - 1397 - 1542 - 1594
-82 - 188
-274
-382 - 376 -488 -481
-450 -318 -334 190 - 106 -8 142 130
-
9L
141 200 324 563 574 929 962 1113 1165 1205 1244 1290 1343 1415 1561 1613 97 205 29 1 399 396 505 497 467 340 351 207 123 25 - 118 - 112
Discussion
salt. Moreover, the measurements at 0.1 m show that the osmotic coefficient for the acid is also smaller than for the potassium salt. This behavior suggests that a slight association of hydrogen ion must occur. Ion association may be significant with the cesium salt, as indicated by the relatively small osmotic coefficients it shows in dilute solutions. The magnitude of the “unlike ion interaction parameter,” @ of eq 3, has been suggested12 as an approximate measure of association; for @ Wa+ > K+ > CS+, as with inorganic anions. Friedman2' has proposed that in the concentration range (i.e.?1-3 M ) where overlap is the main contribution to the value of 4~ that the overlap and hence C$L will be approximately linear in concentration (cf. Figure 2 ) . Comparisons with Heats and Standard Free Energies of Cation Exchange. The osmotic coefficient and heat of dilution values measured in this research will now be applied to determine the adequacy of the analogy between cross-linked organic ion exchangers and concentrated aqueous electrolyte solutions. This test will be performed by computing the standard free energies, AGO, and enthalpies, AH", for a hypothetical ion-exchange reaction between alkali metal cations, M1and AI2, or hydrogen ion, where X signifies the p-ethylbenzenesulfonate anion, when the products and reactants are in their standard states.
M1X(mi)
+ Mz+(m = 0)
AH0
nimm,)
+ &il+(m = 0)
&+(m = 0 )
+ X - ( m = 0)
(B)
and (b) the concentration of AI2+ and X - initially a t infinite dilution to a final concentration, mf
Aiz+(m = 0)
+ X-(m
Vr
A(AGD) = AGex" -
JVi
rdVe
(6)
The AGD values required by eq 6 and the values of the integral JVy7rdV,
were computed following the
method previously described." Values of A(AGD)and A ~ Lcomputed , with the data in Tables IT and IF', respectively, for values of mi and mf corresponding to the water contents of the pure cationic forms of the cross-linked ion exchangers in their respective standard states, are compared in Table VI1 with the values of AGex" - SndV, and AH,,"derived from equilibrium distribution and heat measurements,28 respectively, on the same cation exchangers. Comparisons unfortunately could not be made with exchangers of greater than nominal 8% DVB cross linking because of the limited solubility of sodium p-ethylbenzenesulfonate. However, the agreement between A ~ and L AH,," for the 2, 4,and 8% DVB exchangers appears satisfactory excepting with the potassium-sodium ion-exchange reaction where A@Lwas sig-
(A)
Reaction A may be regarded as the sum of two partial processes: (a) the dilution of MIX to infinite dilution from an initial concentration of mi
MIX(mi)
AGD(mi) - A G D ( ~=~ )
Table VII: Comparison of Standard Free Energies, AGE,", and Enthalpies, AHEx",of Cation Exchange with Free Energy and Heat of Dilution Differences for Aqueous Solutions of the Salts of pEthylbenzenesulfonate (kcal mole-')" Croas linking
mi
my
2 4 8
1.06 2.4 4.6
1.95 2.9 5.4
0.46 0.86 1.18
2 4 8
1.6 (2.8) 5.1
2 4 8 2 4 8
-
-A&''
SndV.
-A(AGD)
0.42 0.86 1.30
0.05 0.14 0.23
-0.56 -0.18 0.00
1.95 2.9 5.4
Na +/Li + 0.65 0.61 1.08 0.95 1.46 1.41
0.05 0.20 0.32
0.06 0.14 0.31
1.95 2.9 5.4
2.0 3.2 6.6
0.29 0.41 0.55
0.16 0.20 0.34
0.17 0.18 0.19
0.14 0.15 0.17
1.95 2.9 5.4
2.9 (4.3) 7.0
Cs +/Na 0.56 0.61 0.62 0.65 0.77 0.76
0.21 0.24 0.26
0.07 0.14 0.275
--Hexo
- A ~ L
Na +/H Exchange +
= 0)
E M2X(mf)
(C)
The heat evolved in reaction B will be AHD(mi) = -4L(mi), that in (C) will be -AHD = C$L(mf),and for reaction A, AH" = @~(rnr)- 4 ~ ( m i = ) A ~ L . To the extent that p-ethylbenzenesulfonic acid and its alkali metal salts are "model" compounds for the corresponding cation forms of cross-linked polystyrenesulfonate type cation exchangers, AH" may be compared with the standard heat of cation exchange, AH,,"
K +/Na +
+
Similarly, the standard free energy of cation exchange, AG,,", for the cross-linked exchanger, corrected for the decrease in the free energy of its molecular network, JrdV,, accompanying the standard-state reaction, may be compared with the difference in the ) , the apparent molal free energy of dilution, A ( A G ~ of "model" compound solutions The Journal of Ph~sicalChemistry
a
Values for mi, mt, -AH,.',
and -AG.,"
from ref 28.
(27) Y. C. Wu and H. L. Friedman, J. Phys. Chem., 70, 166 (1966). (28) G . E. Boyd, F. Vaslow, and S. Lindenbaum, ibid., 68, 690 (1964).
THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS OF ~-ETHYLBENZENESULFONIC ACID
nevertheless is believed to be consistent with the hypothesis that the gel solutions of cross-linked polystyrenesulfonate cation exchangers are analogous to concentrated aqueous electrolyte mixtures. Interestingly, this analogy appears to be valid at lower cross linkages in cation than in anion1’ exchangers. Presumably the alkali metal “counterions” are distributed in a much more diffuse double layer surrounding the negatively charged cation-exchange polymer chains and the counterion atmospheres about the chains overlap sufficiently for the “homogeneous gel solution” model to become a good approximation.
Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date: November 1, 1967 | doi: 10.1021/j100871a024
nificantly smaller than AH,”. Because of the unknown contribution of the enthalpy of swelling, AHonetwork,to AH,” a quantitative agreement cannot be expected. The concordancebetween A ~ and L AH,” obtained with the alkali metal p-ethylbenzenesulfonates, however, is demonstrably much better than that obtained with the chlorides. The correspondence between the corrected standardfreeenergyof exchange, AG,,” - JrdVe, and the dilution free-energy difference, A(AGD) , is satisfactory except with the ion-exchange reaction involving hydrogen ion for reasons not immediately evident. The majority of the thermodynamic data (Table VII)
3887
Volume 71,Number 18 November 1967
