AMMONIUM-HYDROGEN . 4 m THALLOUS-HYDROGEN EXCHAKGE
Sept., 1959
1117
THE EFFECT OF TEMPERATURE ON ION EXCHANGE EQUILIBRIA. 11. THE AMMONIUM-HYDROGEN AND THALLOUS-HYDROGEN EXCHANGES BY 0. D. BONNER AND ROBERT R. P R U E T T ' ~ ~ Department of Chemistry, University of South Carolina, Colz~itabia,South Carolina Received January 80, 1960
Ion-exchange reactions between ammonium and hydrogen and between thallous and hydrogen ion on Dowex-50 resinR of 16% DVB content have been studied over the temperature range 0 to 97.5" while maintaining a constant solut,ion ionic strength of approximately 0.1 M . The equilibrium constant and the standard free energy, enthalpy and entropy changes have been calculated for each exchange at each temperature. The differential free energy, enthalpy and entropy of exchange for each system is found to vary considerably with resin composition. One possible explanation of this variation is the assumption that the ion exchange resin in the hydrogen form is an acid which is similar in strength but probably slightly weaker than nitric acid.
The ion-exchange process involving the univalent ions A+, B + and a cation-exchange resin may be represented by the metathetical equation
+
A + (soln. phase) B+ (resin phase) = A + (resin phase) B+ (soln. phase) (1)
+
The equilibrium quotient calculated from the concentrations of the ions iiz the two phases will be dependent not only upon the ions involved in the exchange, the type of exchanger used and the temperature a t which the experiment is carried out, but also upon the composition of the phases a t equilibrium. The equilibrium constant may be calculated if the exchange is accomplished in aqueous solutions of infinite dilution from the relationship3t4 where K is the thermodynamic equilibrium constant and IC is the equilibrium quotient a t the resin composition XB+. A correction for solution phase activity coefficients should be made when solutions of finite concentration are used. It is not always possible to make this correction for equilibria a t elevated temperatures as the activity coefficient data are not available. If the solutions are relatively dilute ( p = 0.1 M ) , the correction should be small, however, since it involves a ratio of activity coefficients. The standard free energy change for the above reaction is AFo = -RT I n K . The standard enthalpy and entropy changes AHo and ASo may be determined from measurements of the change of the equilibrium constant with temperature. These thermodynamic functions have been reported5 for the exchange of sodium ion and hydrogen ion and for cupric ion and hydrogen ion on 16% DVB Dowex 50. I n this work the ammonium -hydrogen and thallous-hydrogen exchanges on the same resin were studied. Experimental
changes. The methods of equilibration and temperature control were the same as those for the cupric-hydrogen ex~ h a n g e . ~The concentration of each ion in each phase was determined experimentally for each of the exchange reactions as follows: Hydrogen ion-concentrations of hydrogen ion were determined volumetrically by titration with standard alkali; ammonium ion-an excess of formaldehyde was added to the solution containing ammonium ion and the liberated hydrogen ion was titrated with standard alkali; thallous ion-thallous ion concentrations were determined volumetrically by titration with standard potassium bromate solution in the presence of hydrochloric acid, methyl orange serving as an indicator.
Discussion and Results The ion exchange process as represented by equation 1 is in reality the sum of three processes. Ion A+ is transferred from the dilute aqueous solution to the concentrated resin phase, ion Bf is transferred from the concentrated resin phase to the dilute aqueous solution, and in the process some water is also usually transferred from one phase to the other as the water content of the fully swollen resin phase is not the same in all ionic forms. If one, however, considers the differential process in which one mole of ion A+ is exchanged for one mole of ion B+, the quantities of solution phase and resin phase being so great that there is no resultant change in composition of either phase, then there is no transfer of water from one phase to the other. This process is of further interest in that one may observe the effect of the resin composition on the free energy enthalpy and entropy changes accompanying the exchange reaction., If one chooses a t each temperature the standard state for the aqueous phase to be the usual hypothetical one molal solution, and for the resin phase, the resin having the desired ionic composition at equilibrium, one may then calculate for a resin of composition XB+,for the differential exchange of ions A+ and B+ a t temperature T, the thermodynamic quantities AF* = -2.3003 RT log k k AH* -2.303B d log-
Nitric acid, ammonium nitrate and thallous nitrate solutions of an ionic strength of 0.1 m were used for these ex(1) These results were developed under a project sponsored by the United States Atomic Energy Commission. (2) Part of t,he work described herein was included in a thesis submitted by Robert R. Pruett to the Universii.y of South Carolina in partial fulfillment of the requirements for the degree of Master of Science. (3) E. Hogfeldt, E. Ekedahl and L. G. Siilen, Acta Chem. S c a d . ,
4. 1471 11950). . . (4) 0.D. Bonner, W. J. Argersinger and A. W. Davidson, J . A m . Chem. Soc., '74, 1044 (1952). (5) 0. D. Bonner and L. L.Smith, THISJOURNAL, 61, 1614 (1967).
~
d(l/T)
(3) (4)
and AS* =
AH*
- AF*
(5)
These quantities are related to the corresponding quantities for the exchange represented by equation 1 by the equations
1418
0. D. BONNER AND ROBERT R. PRUETT
VOl. 63
3 -
2.60
3.00 3.40 3.80 1/T x 10'. Fig. 3. -Temperature dependence of equilibrium constants: A, thallous-hydrogen exchange B, ammoniumhydrogen exchange. 20 40 60 80 100 Mole yo ammonium resin. Fig. 1. -Ammonium-hydrogen exchange equilibrium data: A, 0'; B, 25'; C, 50'; D, 77"; E, 97.5". 0
k = 1
(XH+)resin
(m"4+)
1800
*\
soln 1400
a ,
'
1.4
'
'
b
1000
5 I
i
w 1.2
600
1.0
200 I
0.0 1 0
I
I
I
I
1
20 40 60 80 100 Mole % thallous resin. Fig. 2. -Thallous-hydrogen exchange equilibrium data: A, 0"; B, 25'; C, 50'; D, 77'; E, 97.5'. k = (XTL+) resin (mH+)soln (XE+) resin (WLTI+)soln
1
I
I
20 40 60 80 100 Mole % ammonium resin. Fig. 4.-Free energy and enthalpy changes for the ammonium-hydrogen exchange: A, AH*, 0'; B, AH*, 25'; C, AH*, 50'; D,AH*, 77'. E, AH*d 97.5'. F, AF* 0 ' ; G, AF*, 25'; H, AF*, 50"; f, AF*, 77 ; J, Ab*, 97.5":
AMMONIUM-HYDROGEN A N D THALLOUS-HYDROGEN EXCHANGE
Sept., 1959
1410
3200
Equilibrium data for the ammonium-hydrogen and thallous-hydrogen systems as a function of temperature are presented in Figs. 1 and 2. Both systems exhibit large variations of k with both temperature and resin composition. I n the case of the thallous-hydrogen exchange, k decreases by a factor of four for large hydrogen loadings between 0 and 97.5' and by a factor of two for large thallous loadings over this temperature range. The values of the differential free energy, enthalpy and entropy for these systems (Figs. 4-6) also vary considerably with temperature and resin composition. In both systems the values of these functions become less negative with increasing temperature and decreasing hydrogen ion content of the resin. The values of AS* for the thallous-hydrogen system actually become positive a t high temperatures and high thallous loading. The decrease in the selectivity coefficient with low hydrogen content may be explained by the assumption that all exchange sites are not the same with each ion occupying the sites preferred by it until these sites are used up. This assumption, which would be equally true for an exchange between any pair of ions, is valid if, for example, the sulfonated bridges (DVB rings) have properties different from those of the sulfonated polystyrene rings or if localized concentration differences exist in the resin because of statistical variations in the cros~linkage.~-~ Since the variation of k with resin loading is greater for exchanges which involve hydrogen ion, it is possible that an additional assumption, that the ion-exchange resin in the hydrogen form is an acid similar in strength but perhaps slightly weaker than nitric acid,*.*Omay be
,,.2400
9I 8
5 lGOO 1
800 I
O C .
0
35 50 77 97.5
KgA4
AFO, cal.
2.58 2.13 1.87 1.66 1.54
-511 -4449 -402 -353 -319
AHo, cal.
ASO,
-1259 -1091 -1016 995 - 912
-2.73 -2.15 -1.90 -1.72 -1.60
-
e.u.
TABLE TI THALLOUS-HYDROGEN EXCHANGE DATA ON 16% DVB DOWEX50 Temp., "C.
0 25 50 77 97.5
KT:
24.2 15.7 11.8
8.95 7.89
AFO, cal.
AHO, cal.
-1726 -1636 -1586 -1528 -1504
-3107 -2416 -2287 -2090 -1898
ASO, e.u.
-5.04 -2.62 -2.17 -1.60 -1.06
F.Walton, ibid., 47, 371 (1943). (7) I. H. Spinner, J. A. Ciric and W. F. Graydon, Cunud. J . Chem., (6) H.
Sa, 143 (1954). ( 8 ) D. Reichenberg and D. 8. McCauley, J . Chem. Soc.. 2741 (1955). (9) G. E. Myers and G. E. Boyd, THIS JOURNAL, 60, 321 (1956).
(10) The activity coefficients of solutions of nitric and p-toluenasulfonic acids tend t o support this view. R. A. Robinson and R. H. Stokes, Trans. Faraday Soc., 46, 612 (1949); 0. D. Bonner, G. D.
I
I
20 40 60 80 100 Mole % thallous resin. Fig. 5.-Free energy and enthalpy changes for the thallous-hydrogen exchangz: A, A H * , 0'; B, AH*, 25'; C, A H * , 50,"; D, AH*, 77 ; E, AH*, 97.5'; F, AF*, 0".I G,;AF*, 25 ; H, AF*, 50'; I, AF*, 77'; J, AF*, 97.5". 1
I
I
I
F
5.0
4.c
3.s
TABLEI AMMONIUM-HYDROGEN EXCHANGE DATA ON 16% DVB DOWEX50 Temp.,
I
0
L 2.0 d
I 1 .o
0.0
- 1.0 I
I
1
I
J
Mole yo ammonium or thallous resin. Fig. 6. -Entropy changes for the ammonium-hydrogen and thallous-h drogen exchanges: A, 0", NH4-H; B 25' "4-H; 50°, NH4-H; D, 77", "4-H; E, 97.5"; Nbr-H; F, O', T1-H. G, 25O, T1-H; H, 50", TI-H; I, 77", TI-H; J, 97.5", kl-H.
6,
Easterling, D. L. West and V. F. Holland, J . Am. Chem. ~ o c . ,77,242 (1955).
1420
0. D. BONNER A N D ROBERT R. PRUETT
desirable. Calculations indicate an ionization constant of the order of magnitude of five to ten. When the resin is predominantly in the salt form, the percentage of hydrogen existing in the undissociated form would be greater than when the resin is predominantly in the acid form, thus leading to smaller values of AF* for lower hydrogen loadings. This second assumption would also explain the decrease in AF* a t constant resin composition with increasing temperature as most ionization constants decrease with increasing temperature.l 1 The negative values of AH* are to be expected for these exchange reactions since the hydrogen ion is being diluted while the ammonium or thallous ion is being concentrated. One finds upon calculation of the heats of dilution for the nitrates,12 that the dilution of nitric acid is an exothermic process while the dilution of the nitrate salts with the exception of lithium is an endothermic process. On the basis of the second assumption the smaller (11) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Reinhold Publ. Corp., New York, N. Y., 1958, p. 755. (12) F. R. Bichowsky and F. D. Rossini, “The Thermochemistry of Chemical Substances,” Reinhold Publ. Corp., New York, N . Y., 1936, pp. 33, 34, 134, 142, 156, 166, 167, 169, 170.
Vol. 08
negative values of AH* a t low hydrogen loadings and high temperatures may be attributed to the absorption of energy for the ionization of some of the hydrogen associated with the resin when the exchange occurs. The values of AFO, AH0 and AS0 for the over-all ion-exchange process as represented by equation 1 have been calculated (Tables I and 11) using equations 6-8. These functions for both exchange systems have the same arithmetic sign but are larger in magnitude than the corresponding functions for the sodium-hydrogen exchange.6 Values of AF and AH may be calculated for the dilution of solutions of ammonium nitrate and nitric acid approximating the concentration of ammonium or hydrogen ion in the resin phase to a concentration of 0.1 M . Although they are not so large in absolute magnitude, the differences between the free energy of dilution and enthalpy of dilution of ammonium nitrate and nitric acid have the same arithmetic sign as the values of AFO and AH” for the ammonium-hydrogen exchange. This gives some justification to the consideration of the ion-exchange process as being essentially a concentration of one ion with the simultaneous dilution of the second ion.
THE EFFECT OF TEMPERATURE ON ION-EXCHANGE EQUILIBRIA. 111. EXCHANGES INVOLVING SOME DIVALENT IONS BY
0. D. BONNER A N D ROBERT R.
PRUETT’*2i3
Department of Chemistry, University of South Carolina, Columbia, S. C . Received January 30, 1969
Ion-exchange equilibria in seven systems involv.ing divalent ions have been investigated over the temperature range 0 to 97.5” using sulfonic acid type (Dowex-50) resins. I n all exchanges between two divalent ions, the equilibrium constant decreases with increasing temperature, with a resulting negative value for AHO. This is apparently characteristic of exchanges between ions of the same valence t y e since for all exchanges between two univalent ions negative AH0 values have also been observed. With the exception o r t h e cupric-magnesium system, the values of ASo for all exchanges between two divalent ions are positive. For the magnesium-hydrogen exchanges AH0 and AS0 are positive. The algebraic signs of these functions are identical with those of the cupric-hydrogen system already reported.
One divalent ion, the cupric ion, was included in the first paper4 of this series reporting preliminary investigation of the temperature dependence of ion-exchange equilibria. It was noted that the equilibrium constant for the sodium-hydrogen system (an exchange between two ions of the same valence) decreased with increasing temperature, while the equilibrium constant for the cuprichydrogen system increased with increasing temperature. No exchange reactions between two divalent ions were included in this earlier investigation. (1) These results were developed under a project sponsored by the United States Atomic Energy Commission. (2) Part of the work described herein was included in a thesis suhmitted by Robert R. Pruett to the University of South Carolina in partial fulfillment of the requirements for the degree of Master of Science. (3) The authors are indebted to Mr. L. A. Kitching, a Summer Research Associate supported by a grant from the National Science Foundation, for assistance with some of the analytioal results reported herein. (4) 0. D. Bonner and L. L. Smith, THISJOURNAL, 61, 1614 (1857),
Experimental The variation of the equilibrium quotient with temperature and resin composition of five additional ion-exchange systems involving divalent ions has been investigated. In two of these systems the per cent. divinylbeneene, or crosslinkage, of the resin has also been included as a variable. The method of attainment of equilibrium, temperature control and separation of resin and aqueous phases has been reported previously.‘ The concentrations of both ions in both the resin and aqueous phases were determined experimentally as described below. (a) Cupric-Zinc Exchange-The total concentration of cupric plus zinc ion was determined6 by compleximetric titration with a standard solution of the disodium salt of ethyenediaminetetraacetic acid (EDTA), PANE serving as an indicator. Cupric ion was then determined by the customary iodometric titration and zinc ion was calculated by difference. (b) Cupric-Magnesium and Calcium-Cupric Exchanged -In both of these exchanges cupric ion was determined compleximetrically by titration with EDTA, in a solution acidified with acetic acid t o a pH of 5, PAN serving as an (5) H. Flaschka and H. Abdine, Chemist AnaEyst, 46, 58 (1956). (6) PAN ie the abbreviation given the oompound l-(%pyridylazo)-2-naphthol.
I
