2220
L. LEIFER,A. W. DAVIDSON AND W. J. ARGERSINGER, JR.
Vol. 65
THE EFFECT OF IONIC STRENGTH ON EQUILIBRIUM IN SILVER-HYDROGEN ION EXCHANGE’ BY LESLIELEIFER,ARTHURW. DAVIDSON AND WILLIAM J. ARGERSINGER, JR. Chemical Laboratory of The University of Kansas, Lawrence, Kan. Received J u l y 18, 1961
From‘data on exchange equilibrium at 25’ between Dowex 50 of 10.5% divinylbenzene content and aqueous silver nitratenitric acid solutions at ionic strengths of 0.1, 0.3 and 1.0 molal, values were determined for the selectivity coefficients K,.for silver-hydrogen over a wide range of resin compositions. For the two higher concentrations, the presence of a sharp mmimum in the value of K , in resins of low silver content was confirmed. From the K , values and previously determined Ag+-H + activity coefficient ratios in the aqueous solution, values were calculated for the thermodynamic equilibrium constant K for the silver-hydrogen exchange. Extrapolation of these values t o zero ionic strength gives the figure 10.9 as the best value aa yet available for this constant, and one which shows good consistency with previously determined constants for resins of lower and higher divinylbenzene content, a8 well as with the best previously determined constants for sodiumhydrogen and silver-hydrogen exchange on the same resin.
Introduction Detailed studies have been reported previously for silver-hydrogen exchange on Dowex 50 of 10.5% divinylbenzene content with dilute solutions (0.02 and 0.1 molal)2 and with solutions of 1 molal total ionic ~ t r e n g t h . ~Despite the use of widely different methods of analysis and the overall 50-fold variation in ionic strength, the values determined in these two investigations for the selectivity coefficients K, (defined by the equation
in which m represents molality in the aqueous solution and N mole fraction in the resin) are in fair agreement over a wide range of resin compositions. Hogfeldt, Ekedahl and Sill&, however, reported a minimum value for the selectivity coefficient a t N A g Res = 0.15, whereas the data from our Laboratory did not extend to N A R~~ ~ values lower than 0.18. Studies have been reported also for the same exchange, a t 0.1 molal ionic strength, on similar resins of 8 and 16% divinylbenxene content;4 here a minimum in the selectivity coefficientresin composition curve was found for the latter resin only, a t N A g Res = 0.25. Since the mean activity coefficient ratios 7”oa/ in mixed aqueous solutions of ionic strengths from 0.1 to 1.0 molal are known for the entire range of compositions,6values can be found readily for the revised selectivity coefficientsK,, defined by the equation
and from these values, by a process of graphical i n t e g r a t i ~ n , ~the , ~ value of the thermodynamic equilibrium constant K, defined by the equation (1) From part of a thesis submitted by Leslie Leifer in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The University of Kansas, 1959. (2) E. Hiigfeldt, E. Ekedahl and L. G. Sill&, Acta Chem. Scarrd., 4, 1491 (1950). (3) 0.D. Banner, W. J. Argersinger, Jr., and A. W. Davidson, J. Am. Clrem. SOC.,74, 1044 (1952). (4) 0.D. Bonner and V. Rhett, J. Phys. Chem., 57, 254 (1953). (5) 0.D. Bonner, A. W. Davidson and W. J. Argersinger, Jr., J. Am. Chem. Soc., 74, 1047 (1952). (6) W.J. Argersinger, Jr., A. W. Davidson and 0. D. Banner, T7ans. Kansas Acad. Sci.. 63,404(1950). (7) E. Ekedahl, E. Hbgfeldt and I.. G. SillBn. Acta Chem. Scand., 4, 556 (1950).
K
=
K.
f
(fa
f
s Res)
- aE%Ag Res aAg%lRes
can be determined. The Swedish workers, on the assumption of unit activity coefficient ratio in dilute aqueous solutions, calculated from their data a value of 9.8 for K , whereas the early data from this Laboratory yielded a K value of 13.7. The purpose of the investigation here reported was threefold: (1) to determine whether or not the sharp increase in silver-hydrogen selectivity coefficient previously observed in resins of low silver content could be confirmed; (2) to observe the variation with ionic strength of values obtained for the thermodynamic equilibrium constant K for the silver-hydrogen exchange; (3) to compare the best K value obtainable directly from silverhydrogen exchange data with the value calculated (from the constants previously found in this Laboratory for sodium-hydrogen* and silver-sodium9 exchanges on the same resin) by means of the simple relationship KEAg = KHNaKNsAg
where in each case K y X represents the thermodynamic equilibrium constant for the reaction X++YRes =Y++XRes
Experimental Methods The resin used throughout was taken from a single large sample of Dowex 50 of 10.5% divinylbenzene content. It had been “recycled” three times between the hydrogen and sodium forms, a treatment which tends to minimize variation in capacity and selectivity. Visual inspection of the resin particles showed them to be of uniform color, and they were limited to a uniform narrow size range by the use of standard sieves. In most of the exchange experiments, the initial resin was pure hydrogen resin, obtained by repeated circulation of 20% hydrochloric acid through the sodium resin, followed by thorough washing with distilled water and partial drying in air a t room temperature. Since i t had been observed that extensive air drying tends to bring about fracture of the resin particles, with appreciable alteration of their exchange capacity, resin samples to be used for exchange always were left in a moist, tacky state. The equivalent weight of the hydrogen resin was determined in the following manner. Three weighed samples of the air dried material were subjected to exhaustive exchange with sodium chloride solution and the eluted acid was titrated with sodium hydroxide solution. A fourth weighed sample of the same resin was completely dried (8) A.
W. Davidson and
W. J. Srgersinger, Jr., Ann. lV. Y . Acad
Sci., 57,105 (1953).
(9) G. E. Wilson, A. W. Davidson and W. 3. Argersinger. Jr., J. Am. Chem. Soc.. 76,3824 (1954).
EFFECT OF IONIC STRENGTH ON SILVER-HYDROGEN IONEXCHANGE
Dec., 1961
by being heated to constant weight in an oven a t 115’ and its water content thus determined. The equivalent weight, calculated on the basis of the dry resin, was found to be 199.2 i 0.5. Samples of from 4 to 10 g. of hydrogen resin were agitated at 25” for suitable periods (varying from 2 to 36 hrs.), in blackened ground-glass stoppered flasks with 100- to 350-ml. samples of mixed silver nitrate-nitric acid solutions of various compositions a t fixed ionic strengths of 1.0, 0.3 and 0.1 molal. I n general, duplicate runs were not made a t a single solution composition, but rather the compositions were varied ialightly to give separate individual points on the exchange curve. Thus the general smoothness of the curve, rather than agreement of different runs for a single point, gives an indication of the reliability of the measurements. After equilibration the resin was allowed to settle and the equilibrium solution was pipetted off. The residue was placed in a large buchner funnel to which suction was applied, and washed by flooding with distilled water until the washings no longer gave a test for silver ion; this washing procedure usually was completed in 10-15 seconds. Since analyses for silver and hydrogen could be carried out on the same sample of equilibrium resin, the degree of dryness of the resin was not critical; hence the resin samples to be analyzed were merely superficially dried by pressure between pads of filter paper. The density of each equilibrium solution was determined by means of a pycnometer, and samples were analyzed for acidity by titration with standard sodium hydroxide solution and for silver content by one of the following methods. For solutions 0.01 to 0.1 molal in silver nitrate, titration with standard potassium iodide solution in the presence of ceric ammonium sulfatelo proved to be satisfactory. At concentrations between O.OOO1 and 0.01 molal, silver was determined by electronietric titration with standard potassium iodide solution; many of the results at these lower concentrations were checked by means of electrodeposition of silver from ammloniacal solution on a platinum gauze cathode. Weighed samples of the equilibrium resin were subjected to exhaustive exchange with concentrated sodium nitrate solution until free (of silver ion or, in the case of resin of low silver content, until the pH of the effluent solution was the same as that of the eluent. The eluate then was analyzed for acidity and for tjilver ion as already described. From two to five analyses were made on each solution and resin sample, and selectivity coejficients were calculated from the mean of the results.
Results I n Fig. 1, values of the logarithm of K,, the revised selectivity coefficient, calculated from our exchange data and the known HN03/AgN03 activity coefficient ratios, are plotted against the degree of exchange or mole fraction of silver resin, NAg Rea. From these plots were determined by graphical integration the activity coefficients of the resin components a t selected compositions, as shown in Table I, and also values for K , the thermodynamic equilibrium constant. TABLE I ACTIVITY COEFFLCENTS OF RESINCOMPONENTS Ionic strength
NAEFC-
0 .2
.4 .6 .8
I .o
M-
-0.1 fAs Rea
JH Rea
-0.3
M-
-1.0
M--
/AIR-
fHRea
/&Rea
/HRes
.”
11.00
..
1.13 1.09 1.05 1.02 1.00
l.00 l.02 1 .05 1 .15
1.16 1.10 1.05 1.02 1.00
K
.. =
11.7
1.00 0.96 0.98 1.03 1.11
..
K = 12.3
..
1.00 1.01 1.05 1.14 1.32
1.31 1.21 1.11
1.05 1.00
K
..
=
13.3
(10) A. Bloom and PJ. M. McNab, Ind. Eng. Chem., Anal. Ed., 8?167
(1936).
0.0
02
04
06
2221
08
IO
NAG R E S I N . Fig. 1.-Silver-hydrogen exchange at several ionic strengths: (A) 0.1 molal; horizontally half-filled circles; subtract 0.1 from ordinate scale. (B) 0.3 molal, open circles; (C) 1.0 molal, vertically half-filled circles, data from present work; filled circles, data from ref. 3.
Discussion I n most ion-exchange equilibria, the revised selectivity coefficients K , yx tend toward unity with increase in N , ; in other words, the resin shows increasing selectivity for the “preferred” ion with increasing content of the other i0n.l’ I n this respect the course of the selectivity curve for the silver-hydrogen exchange must be regarded as “abnormal,” since throughout a t least a large fraction of the composition range K a ~ Aincreases g with increasing N A R~ ~ ~It . may be noted, however, that the results obtained for 0.3 and 1.0 molal solutions in the present study again exhibit the sharp increase in K, ~ * g w i t hdecreasing N A R ~ ~ for ~ resins of low silver content, that first was observed in the earliest investigation of this exchange sysand later also for a more highly cross-linked resins4 For 0.1 molal solutions, however, our data (curve A in Fig. 1) show no such minimum, a t least down to an N A R~~ ~ value as low as 0.057. It is, of course, conceivable that a minimum might occur a t a still lower silver content, but investi(11) J. 4 . Etchener, Physical Chemistry of Ion-Exchange Resins, in J. O’M. Bockris, “Modern Aspects of Electrochemistry,” No. 2 Scademic Press, Ino., New York, 1954, p. 119.
,
2222
J. J. EGAN
gation of this region would necessitate accurate determination of silver ion at concentrations so low as to be inaccessible to the usual methods of chemical analysis. The variation in the calculated values of the thermodynamic equilibrium constant K with ionic strength remains to be considered. First, there is a possibility of the incidence of error in the determination of resin composition in consequence of exchange during the washing of the equilibrium resin. The very short duration of the washing procedure (10-15 sec.), however, argues against sufficiently extensive exchange to alter significantly the equilibrium resin composition. The procedure described removes adsorbed, invaded, and superficial electrolyte, but leaves essentially unchanged the composition of the equilibrium resin itself, in terms of which the process equilibria have been formulated. The major source of the variation of calculated values of K with ionic strength is no doubt the fact that, in our formulation of the exchange reaction, we have neglected both the transfer of water between solution and resin and changes in the amount of adsorbed electrolyte. It has been shown* that in the case of sodium-hydrogen exchange consideration of the first of these factors alone sufficed to bring the K values for various ionic strengths into satisfactory agreement. A further modification of the equilibrium equation to include changes in adsorbed electrolyte also has been disc u s ~ e d . ~The ~ ~ application '~ to the silver-hydrogen
Vol. 65
exchange of these more sophisticated treatments, however, would require much additional data, as yet unavailable, with regard not only to water and electrolyte uptake by the equilibrium resin, but also to water activity in the equilibrium solution. Since all of the disturbing effects diminish with increasing dilution, the best presently available value of the equilibrium constant is that obtained by extrapolation of the observed values to infinite dilution. When our values of K are plotted against the square root of the ionic strength an almost straight line is obtained, which yields by extrapolation a limiting value, KO, of 10.9. It is of interest to compare this value of KO with those obtained from two other sources. Linear interpolation of the values obtained by Bonner and Rhett4 for resins of 8 and 16% divinylbenzene content with 0.1 molal solutions gives for 10.5% divinylbenaenes the figure 9.05,which, corrected for the activity coefficient ratio, becomes 10.2. On the other hand, the product of the limiting value of K N ~6.54,9 ~ ~ , and that of K H ~1.6411, ~ , is 10.7. In view of the wide diversity of the experimental sources from which they are calculated, the approximate concordance of these three KO values appears to be not without significance. Acknowledgment.-This work was supported in part by contract DA-23-072-ORD-222 with the Office of Ordnance Research. (12) G. L. Gaines, Jr., and €1. C. Thomas, J . Chem. Phys., 21, 714 (1Y53).
(13) E. W. Baumann a n d W. J. Argersinger, Jr., J . A m . Chem. Soc.,
78, 1130 (1956).
A POLAROGRAPHIC STUDY OF EXCESS LEAD DISSOLVED I N MOLTEN LEAD CHLORIDE BYJ. J. EGAN] Max-Planck-Institul fur physikalische Chemie, Gottingen, Germany Received J u l y 15, 1061
The constitution of a solution of excess lead in molten lead chloride equilibrated with liquid Au-Ph alloys a t 518' was studied with the help of a polarographic technique. Limiting currents for the oxidation of subhalide a t a platinum microelectrode w anode were obtained and used w a measure of the concentration of dissolved excess lead, which was found to be proportional to the activity of lead. It is concluded that excess lead dissolves in the melt as Pbz++ions.
Introduction When lead is brought in contact with molten lead chloride it has been found2 that a small amount of the lead dissolves in the chloride. This is a general phenomenon that occurs in many metal-metal halide systems. The form in which the excess metal exists in the salt has been the subject of experimentation and speculation for many years. In the Cd-CdClz system, for example, both freezing point depression3 and magnetic susceptibility4 measurements have indi(1) Brookhaven National Laboratory, Upton, L. I., New York,
U. S. A. (2) J. D. Corbett a n d S. von Winbush, J . A m . Chem. Soc.. T I , 3964 (1955). (3) K. Crjothoim. F. Gronvold a n d J. Krogh-Moe, %bid., 77, 5824 (1955). (4) J. Farquharaon and E. Ileymann, Trans. Faraday Soc., 31, 1004 (1935).
cated that Cd dissolves in the melt as Cdz++ ions, although later analysis6 using revised heat of fusion data shows the necessity of postulating more complex species. The dissolution of excess lead in molten lead chloride may be assumed to be due (1) to the formation of monovalent lead ions P b $. P b + + = 2Pb+
( 1)
or (2) to the formation of Pbz++ ions analogous to the species Hgz++ prevailing in a solution of mercurous nitrate Pb
+ Pb++ = Pbp++
(2)
Since the solubility of excess lead in molten lead chloride is as low as 6 X mole % a t 500" according to Corbett and von Winbush,2 the ac( 5 ) L. E. Topel and A. S . Landis, J . Am. Chem. Soc., 82, 6291 (1960).
