254 OSCAR D. BONNXI~ AND VICKXES RHETT Vol. 57

ship holds only for adsorbed liquids having similar dipole moments and polarizabilities, considerable information on adhesion mechanisms can be gained from this approach. Obviously more data are needed to test its validity. It is conceivable, also, that the placement of the lines in Fig. 6 may be related to the concentration of polar sites on the solid surfaces, since the line for tin oxide with a higher concentration of ionic sites favorable to adsorption lies above that for untreated tin.

The lowering of the free surface energy (7,)

by a film adsorbed on the surface of a solid is the basis for the calculation of a fundamental quantity, the work of adhesion (WA). The values for W A given in Table I1 were calculated by the method of Jura and hark in^.^ Approximately four times as much work must be expended to separate liquid water from the surface of these solids as is needed to separate liquid heptane. The work required to separate water from these surfaces is about 2.5 times that necessary for the separation of propyl acetate or propyl alcohol.

EQUILIBRIUM STUDIES OF THE SILVER-SODIUM-HYDROGEN SYSTEM ON DOWEX 50

BY OSCAR D. BONNER AND VICKERS RHETT~ lhpartinent of Chemistry of the University of South Carolina, Columbia, S. C.

Received July d l , 1968

Equilibrium studies of the silver-hydrogen, silver-sodium and sodium-hydrogen exchanges on two samples of Dowex 50 have been made while maintaining a constant ionic strength of approximately 0.1 M . Comparison of these exchanges with another series of sodium-hydrogen exchanges, which have already been reported, shows a definite relationship between the selectivity of the resin and the maximum water uptake. The selectivity values and the selectivity-loading curves are dis- cussed in the light of present theories.

Introduction It is known that when an ion exchange reaction

occurs, selectivity is shown in nearly all instances. This is demonstrated by the fact that for a reaction such as

A + + BR~B = B+ + A R ~ ~ the mass action equilibrium quotient is usually different from unity. It is also recognized that this equilibrium quotient is not constant for an ex- change betnfeen two given ions but is a function of several variables, not all of which may be Some of the known variables are the capacity of the resin, the percentage divinyl benzene cross-linkage in the resin (as demonstrated by the maximum water uptake of the resin) and the percentage of each ion associated with the resin (ie., loading).

There are no exact cation exchange equilibria data in the literature for a thoroughly charactekized resin. . Most of the.earlier work.was of an explora- tory nature only. Recent investigators of ion ex- change equilibria have reported only the equilib- rium data and not the characteristics of the r e ~ i i i . ~ ~ ~ Theoretical interpretation of the ion exchange process and quantitative predictions of ion exchange selectivity have thus been very difficult.

Experimental These data, which will be presented, represent six series

of exchange reactions between three pairs of ions on two different resin samples. Equilibrium data on one resin sample (nominal 16% divinyl benzene) were obtained at Oak Ridge

(1) Part of the work described herein was included in a thesis sub- mitted by Vickers Rhett t o the University of South Carolina in partial fulfillment of the requirements for the degree of Master of Science.

(2) G . E. Boyd, Ann. Reu. PILUS. Chem., 11, 309 (1951). (3) E. Hogfeldt, E. Ekedahl and L. G. Sillen, Acta Chem. Scand.,

4, 1471 (1950). (4) 0. D. Boiiner, W. J. Argcrsinyer a i d A. W . Davidson, J. Am.

C‘hsm. Soc., 14, 1044 (1952).

National Laboratory and on the second sample (nominal 8% divinyl benzene) at the University of South Carolina.

Preparation of Resin Samples.-For the study of each exchange reaction two “pure” resins were prepared, one containing each of the cations involved in the exchange. The hydrogen form was prepared by passing 6 N hydro- chloric acid through a column of the commercial product until the effluent gave no further flame test for sodium ion. For the preparation of pure silver resin, hydro en resin was placed in a column and silver nitrate passed %rough until the pH of the effluent showed no more than a negligible de- crease from that of the influent. When radioactive meth- ods of analysis were to be used a trace of AgllO isotope was added to the influent silver solution. A sample of the in- fluent was retained in order to determine the activity per milliequivalent of silver ion. The pure sodium resin was obtained similarly by passing a solution of sodium chloride or sodium nitrate through a column containing pure hydro- gen resin. When radioactive methods of analysis were to be used a trace of Na2‘ isotope was added to the influent solution.

General Method.-In each exchange experiment, a weighed sample of the resin to be studied, of known moisture content, was placed in a ground glass stoppered flask in con- tact with an aqueous solution of the appropriate salts of the cations involved at a constant total ionic strength of 0.1 M . Equilibrium was hastened by agitation and was reached, in every case, withip two hours. The temperature was main- tained a t 25 i 1 .

Equilibrium Solution.-The concentration of each cation in the aqueous solution at equilibrium was determined by means of direct analysis; hydrogen ion by titration with standard sodium hydroxide solution; silver ion by poten- tiometric titration with standard potassium iodide solution or by measurement of radioactivity; sodium ion by means of measurements with a Beckman DU flame photometer or radioactivity measurements when NaZ4 isotope was used as a tracer. When sodium ion concentration was determined by means of the flame photometer, the test solution was closely bracket,ed with two solutions of known sodium ion content.

Equilibrium Resin.-The washed equilibrium resin was analyzed for each cation by means of complete exchange of both for a third ion which would not interfere in the deter- mination. For example, nitric acid solutions were used to displace silver and sodium ions from the cquilibrium resin in the silver-sodium exchange experiments. The resulting solution was then analyzed as before. When radiochemical

Feb., 1953 EQUILIBRIUM Sl 'UDIES OF THE SILVER-SODLUM-HYU~~OGEN SYS'l'gM ON DOWEX 50 255

methods of analysis were used, however, i t was not neces- sary to remove the silver or sodium ion from the equilibrium resin. Material balances showed a check within 0.3% in every instance where radiochemical methods were used.

Accuracy of the Analytical Methods.-The accuracy of the titrations of silver and hydrogen ion IS believed to be of the order of 0.1% and that of the other analytical determinations approximately 0.5%.

Discussion and Results The experimental data for these exchanges are

presented in Figs. 1-3. It was determined, by an experimental method described previously, that the maximum water uptake of the nominal 16%

0

25.0

20.0

15.0

4 10.0

5.0

20 40 60 80 100 Mole per cent. sodium resin

Fig. 1.-Sodium-hydrogen exchange. MH+ %NaRa . A' = __ MNA+ % &ea

0 20 40 60 80 100 Mole per cent. silver resin

Fig. 2.-Silver-hydrogen exchange.

45

36

27

d 18

9

0 Mole per cent silver resin

Fig. 3.-Silver-sodium exchange.

DVB resin in the hydrogen form was 103 g. per equivalent while that of the nominal 8% DVB resin in the same form was 200 g. per equivalent. It was also determined for t<he 8% DVB resin that the maximum water uptake was 182 g. per equivalent for the sodium form and 115 g. per equivalent for the silver form. The exchange capacity of both resins was 5.10 millieauivalents per gram in the dry hydrogen form.

These results may be compared with those pre- sented previously.4 It is now possible to report that these Drevious results were obtained qi th a resin (approx. 12% DVB) for which the maximum water uptake was 142 g. per equivalent in the hy- drogen form, 120 g. per equivalent in the sodium form and 86 g. per equivalent in the silver form.

By a comparison of the equilibrium results of the three series of exchanges on the three resin samples, i t is noted that there is a regular variation of K with loading for each resin sample and also a regular variation of K, for any one exchange a t constant loading, with the maximum water uptake of the resin. For the silver-sodium and silver-hydrogen exchanges K a t any loading decreases with in- creasing water uptake. For the sodium-hydrogen exchange however there is an inversion a t a loading of approximately 75%. It should also be noted that for two of the resin samples K becomes less than unity a t high sodium loading.' Thus, hy- drogen ion is actually preferred to sodium in these instances, giving a reversal in the selectivity of the resin.

This latter phenomenon possesses a special significance, in that i t would appear to negate the conclusion that the value of IC is due principally to an osmotic pressure effect caused by a difference in hydrated ionic volumes.s This conclusion is made to appear even more doubtful when one considers the slope of the silver-hydrogen curves between loadings of 10 and 100% silver ion. As (5) H. P. Gregor, J . Am. Chenz. Soc., 73, 642 (1051).

256 OSCAR D. BONNER AND VICKERS RHETT VOl . 57

hydrated silver ion is the smaller ion the slope of the curve should be negative instead of positive.

3.0

2.0

d

1 .o

100 125 150 175 200 Max. water uptake of hydrogen resin (G./eq.).

Fig. 4.-Variation of equilibrium quotient with water uptake a t various loadings.

These data should also furnish a test for the theory8p4 that the true thermodynamic equilibrium constant may be calculated from the equation

log K. = L ' l o g k dN

k being the equilibrium quotient corrected for solu- tion activity coefficients. Since these exchanges were accomplished in solutions of. ionic strength of approsimately 0.1 M , the activity coefficient ratio should be near unity and is taken as such. The

results obtained by performing the above integra- tion are presented in Table I.

TABLE I TABLE OF EQU~LIBRIUM CONSTANTS

Resin Equilibrium sample Exchange constant

8% DVB Na-H 1.49 Ag-H 5.84 Ag-Na 3.89 Ag-Na 3.92"

16% DVl3 Na-H 1.74 Ag-H 16.1 Ag-Na 10.2, Ag-Na 9.3"

a Calculated from ratio of silver-hydrogen and sodium- hydrogen exchanges.

The observed constant for the silver-sodium exchange with the higher cross-linked resin is seen to be slightly greater than the calculated value. This is probably to be expectJed as the average water content of the resin is lower for this exchange than for those exchanges when hydrogen ion is present, and this would tend to increase the selec- tivity of the resin. For the lower cross-linked resin, where the osmotic pressure effect is less important, the calculated and observed values for the silver- sodium exchange are in substantial agreement,

It may be further noted that if the maxinium water uptake of a Dowes 50 resin is known, it should be possible to calculate an equilibrium-loading curve since the capacity of these resins is relatively constant. As an example, in Fig. 4, data are pre- sented showing K for the sodium-hydrogen es- change as a function of maximum water uptake in the hydrogen form, for various percentages of sodium ion loading. The exchanges with 12% DVB resin were carried out a t 0.3 M ionic strength. However, activity coefficients in the aqueous phase have been taken into consideration. Similar families of curves may be drawn for the other exchanges.

Acknowledgment.-It is a pleasure to acknowl- edge the valuable assistance of Dr. G. E. Boyd in that portion of the work which was performed at Oak Ridge National Laboratories. The remainder of this work was made possible by a grant from the Research Corporation.