NOTES
350
therefore
(4) where
H
=
-46
(5)‘
Since p does not appear explicitly, only tables of H us. dmax/drni,, = R have been calculated. The method of solution was in principle somewhat similar to a graphical method due to Lord Kelvin7 except for several important modifications. Assume X r / b and Y,/b to be known. Trial values of X,+,/b and Y,+l/b (X’{+Iand Y’t+l)can be found by
by a grant. Dr. R. S. Hansen contributed helpful discussion during the course of the work. Indiana University supplied time on their IBM 709 for an independent recalculation which confirmed the G-1.5 calculation. (7) W. Thomson, Nature, 34, 290 (1886).
Interaction of Alkali Metal Cations with Silica Gel1 by H. Ti Tien Department of Chemistry, Northeastern University, Boston, Massachusetts (Received September 24,1964)
where S/b is the independent variable and A@ = AS/R,. A trial value of Rr+l/b,R’i+l/b, can be calculated from
_b
~
b
A corrected (unprimed) value of l/(Rt/b) is obtained from
and from this corrected (unprimed) values of Xf+l/band Y,+Jb can be readily calculated by repeating the entire calculation once using the corrected value of R,/b. Convergence was good enough so that increments of 0.01 could be used for AS/b. Furthermore, this method is well adapted for an electronic computer. The above procedure was programmed in machine language on a Bendix G-15 computer and solutions obtained for -0.35 < p < -0.60 in steps of 0.001. From these, tables of X,,, and Xminus. p were obtained by second-order interpolation using Bessel’s formula. Consistency was checked by noting the constancy of higher order differences. From these tables R and H us. p were in turn calculated. Again consistency was checked from higher order differences. A table of H us. R was next obtained by linear interpolation and is to be published separately.
Acknowledgments. The author is grateful to the Petroleum Research Fund, which supported this work T h e Journal of P h y W Chembtrg
The equilibrium selectivity order of an ion-exchanging system for the alkali metal ions is usually either that of the Hofmeister series2 or the sequence which follows the crystal radii.3z4 In cases in which these series are not observed, there are two theories which have been advanced recently explaining their exi~tence.5-~Maatman, et al., reported equilibrium exchange studies between alkali metal cations (Li, K, Xa) and silica gel.* They found that the lithium ion is less preferred than either Ka+ or K+, whereas no difference in selectivity coefficients was observed between Na+ and K+. They estimate the pK value of the silanol group of silica gel to be about 6-8. Further, Maatman, et al., compare the environment of the oxygen atoms of -0SiO- and OH- groups in aqueous solution. From their results they conclude that the reactions of these groups with the metal ions are similar. Previously, Dalton, McClanahan, and Maa tmang measured the equilibrium ~~
(1) The experimental work was done a t Department of Basic Research, Eastern Pennsylvania Psychiatric Institute, Philadelphia, Pa., while the author was on the staff, 1957-1963. (2) 0. D. Bonner, J . Phys. Chem., 59, 719 (1955). (3) H.P. Gregor, M. J. Hamilton, R. J. Oaa. and F. Bernstein, ibid., 60,266 (1956). (4) C. E. Marshall and G. Garcia, ibid., 63, 1663 (1959). (5) (a) D. 0. Rudin and G. Eisenman, Abstr. Commun. e l s t Congr. Physiol., Buenos Aires, 237 (1959); (b) G. Mattock, “ p H Measurement and Titration,” Macmillan Co., New York, N. Y., 1961, pp. 130-134. (6) G. N. Ling, J . Gen. Physiol., 43, 149 (1960). (7) H.T.Tien, J. Phys. Chem., 68, 1021 (1964). (8) D. L. Dugger, J. H. Stanton, B. N. Irby, B. L. McConnell, W. W. Cummings, and R. U‘.Maatman, ibid., 68,757 (1964). (9) R. R. Dalton, J. L. McClanahan, and R. W. Maatman, J . Colloid Sci., 17, 207 (1962).
NOTES
35 1
pH values of solutions containing silica gel and various alkali cations. The sequence of increasing pH value was found to be Li < S a < Cs < K. Earlier, we also carried out exchange studies on silica gel. The results for the five alkali metal ions are presented here. Although Maatman, et al., found no difference in selectivity coefficients between sodium and potassium ions, t>heirreported value for lithium ion is in fair agreement with our data. Our interest in performing the exchange reactions between the alkali cations and silica gel was directed toward establishing the equilibrium selectivity sequence. The purpose of this note, in addition to presenting complete selectivity coefficient values, is to make a few observations in view of available data.
Experimental Chemicals. Davison silica, gel under the designation Code-40 (6-12 mesh) was used. The gel as received was conditioned by ,alternating treatment with 1 N NaOH and 1 N HC1. At the end of the third cycle, the gel was washed with distilled and deionized water, converted into the sodium form, and dried in air. The other chemicals used were of reagent grade as reported earlier.7 Procedure. The exchange was carried out a t pH 6.7 by contacting the gel in the sodium form with 0.1 N chloride solutions of various alkali metals a t 25". Four sets of solutions were used with various cation (Li, K, Rb, Cs) to sodium ion ratios of 1: 9, 3 : 7 , 5 : 5, 7 : 3, and 9: 1. The equilibrium selectivity values were determined with the aid of radioactive Na22as the tracer. Other experimental details and the evaluation of selectivity coefficients were essentially the same as described previ~usly.~
Table I : Equilibrium Selectivity Coefficients a t pH 6.7 Cation
KNS~
Li Na K+ Rb CS
0.65
+ +"
+
+
1.oo
1.8 2.4 3.2
Reference cation.
Results and Discussion Table I presents equlllbrlum selectlvity coefficients for the five alkali metal lons. The reference cation used in all cases was Xa+.
The cation exchange reaction in the present case may be represented as
C+
+ NaR = CR + N a +
(1)
where R denotes the exchange site (;.e., -OSiO-) of silica gel and C + and Na + are the exchanging cations. The equilibrium selectivity coefficient is defined in the usual manner and is given by
The terms in brackets are equilibrium concentrations: Since the log-log plots of [CR]/ [NaR] us. [Na+]/ [C+] give straight lines with slope equal to unity in all cases studied, the interpretation of data is greatly simplified. The linear plots imply that the equilibrium selectivity coefficients, KN;, obtained in the present investigation are not affected by the composition in the gel phase. Further, the activity coefficient ratios, both in the aqueous phase and the gel phase, may be taken to be equal to unity. Therefore, as a first approximation a t least, the K may be assumed to be the true thermodynamic equilibrium constant. From the results given in Table I, the order of affinity of the silica gel for alkali metal ions is Cs > R b > K > Na > Li, which is the familiar Hofmeister series. The fact that we were able to measure appreciable differences among the five alkali metal ions, in contrast to the study reported by Maatman, et al., indicates that a higher order of resolution is possible using tracer technique. Maatman, el al., report the AF" (in kcal.) as follows: the AF" for Li+ is 10.1; the AF" values for Na+ and K + are the same, being 9.6 in both cases. Since the free energy and the equilibrium constant are related by the familiar equation, AF" = -RT In K,.and the equilibrium constants are logarithmically additive, the difference between any pair therefore is easily calculated. The free energy difference between Li+ and Na+ (or K+) is 0.5 kcal. as given by llaatman, et al. Hence, the equilibrium selectivity coefficient, KN~"',is about 0.43, which is in fair agreement with the value obtained in the present study. However, the sequence Li > Na > Cs > K reported earlier by Dalton, et aLJ9 based on equilibrium pH measurements is in apparent contradiction with the recent work of Maatman, et al.,a and our finding reported here. If the pK value 6-8 of the silanol group of silica gel is accepted as estimated by Maatman, et al., the interpretation based on the ion-exchange mechanism seems to be a dubious one. This may be seen from the following considerations. The pK value of an acid may be interpreted as a measure of electric field strength of the anion. The higher Volume 69, Number I
January 1985
352
the p K value the greater is the electric field intensity, which in turn should have a greater tendency to accept protons from neighboring water molecules (or free H + ) . This phenomenon would cause the so-called “localized hydrolysis” as proposed by Robinson and Harned. According to the Robinson-Harned theory, the intensity of the field around the cation, interacting with an anion through oriented water molecules, should increase in the order Li > Na > K > Rb > Cs. In terms of equilibrium selectivity coefficient sequence, it follows that an ion-exchange system having weak acidic groups such as carboxylic resins (e.g., IRC-50) should give the same order just mentioned. This has been shown to be in accord with experimental r e s u l t ~ . ~ , ~ J To explain the apparent contradiction in the observed orders noted earlier and in the present finding, the following interpretation is offered. The silica gel used, according to the manufacturer’s data, indicates that more than 50% of the surface area is associated with pores having radii between 10 and 30 A. If we view the interaction of alkali metal cations with silica gel as a case of physical sorption, then the observed Hofmeister series may be explained on the basis of the hydrated radius of cations. Thus since the hydrated radius of lithium ion is the largest, it would have the least opportunity to interact with the gel surface. The lithium ion therefore would be the least preferred. This is essentially the interpretation given by Dalton, et aL9 In regard to the exchange reaction as represented by eq. 1 and 2, the applicability to a physical sorption is not entirely surprising, since ion-exchange reactions
The SOUTM~ of P h u s b l Ghembtrg
NOTES
can be treated as special cases of physical sorption, which may be represented by the empirical Freundlich adsorption isotherm, y = axn (ie., y = [CR]/[n‘aR], z = [C+]/[Na+],and a = K N a C ) . The constant n is equal to unity in eq. 2. The exchange sites of silica gel, instead of being identified as -SiO- groups, may be described simply as the “active” sites available for physical sorption. The order Li > S a > Cs > K observed by Dalton, et ~ l . a, t~ high electrolyte concentrations and pH values is also explainable from the above considerations. The silica gel is apparently capable of both exchange reaction and physical sorption depending on the experimental conditions. From eq. 1 it can be seen that a t high electrolyte concentrations and pH values the ion-exchange reaction is favored, which gives the order of increasing affinity from Li+ to Cs+. On the other hand, the pore sizes of the gel will effectively exclude the larger ions, in which case a reversal of selectivity order is to be expected. Therefore, depending on experimental conditions, these two contrasting factors ( i e . , the exchange reaction and physical exclusion) may result in “unexpected” sequences of preference, such as the one noted by Dalton. et al.
Acknowledgment. The author wishes to express his appreciation to Dr. D. 0. Rudin, Department of Basic Research, Eastern Pennsylvania Psychiatric Institute, Philadelphia, Pa., for many stimulating discussions during his stay at the Institute. (10) R. A. Robinson and H. 9. Harned, Chem. Rev., 28, 419 (1941). (11) H. T. Tien, J . Phys. Chem., 67, 532 (1963).
