Sept., 1963
EXCHANGE SORPTION IN
THE
SYSTEMS Na-Cs-Ba MONTMORILLONITE
52 kcal. mole-’. This range is a little larger than might be expected because the energy difference between 1 einstein of 350 mp radiation and 1 einstein of 300 mp radiation is 13 kcal. mole-I. (iii) From their studies on the photolysis of methyl ketene, Kistiakowsky and Mahan4 showed that only “hot” ethylidene biradicals undergo internal disproportionation to form ethylene. The equivalent situation exists in our system in that I11 is formed less readily than I1 from IV. Of course, the detailed mechanisms of hydrogen migration and concbmitant double bond formation must differ somewhat in the two reactions. (iv) Because of the undoubtedly low value of‘ E,, the activation energy of reaction 1, for any reasonable value of e* the lifetime of IV* will not be much greater than a vibration frequency. This picture of a shortlived biradical may be an oversimplification. If the carbons associated with the lone electrons are sp3 hybridized then the free electrons are in orbitals pointing away from each other and there may well be a small energy barrier to the formation of the strained C-C bridgehead bond in 11. Thus, a t very low temperatures one might be able to detect IV. However, if the carbons are sp2 hybridized, as in the case of a methyl radical, then the electrons would be in p-orbitals perpendicular to the ring and we should expect interaction under all conditions. The use of the term biradical would then be incorrect in the strict sense. The reaction might better be regarded as molecular with the concerted elimination of nitrogen and formation of the
1781
C-C bridgehead bond to fok-m 11, or migration of hydrogen to form 111. Because of the nitrogen these transition states will differ somewhat from that for the reaction I1 & 111. (v) The absence of reaction with oxygen other than as an inert gas indicates the absence of a triplet biradical. It is known for example that 0 2 reacts rapidly with triplet methylene13 but not with singlet methylene . (vi) The reaction with nitric oxide is often regarded as a test for free radicals. However, in this system nitric oxide may be reacting with 11* and III* directly rather than with the biradical intermediate IV*. We hope that experiments with mixed added gases and metallic mirrors will answer some of these problems. (vii) Quantum yield measurements, in terms of consumption of I, in isooctane solution gave the value 1.0 f 0.10 (for both 313 and 334 mp radiation). Thus, the primary step is unexceptional with no complications: from internal or external quenching or from fluorescence.l5 Acknowledgment.-It is a pleasure to acknowledge helpful discussions with Dr. G. B. Kistiakowsky (Harvard University) and Dr. M. Rosenblum (Brandeis University). The azo compound was prepared by Dr. R. Zand in work done under N.S.F. Grant G-14049, Department of Chemistry, Brandeis University. (13) H. M. Frey, J . Am. Chem Soc., 82, 5947 (1960). (14) A. W. Strachan and W.A. Noyes, Jr., ibid., 76,3258 (1954). (15) The absence of fluorescence was confirmed by Mr. K. Norland of Brandeis who kindly ran the fluorescence spectrum,
ADSORPTION STUDIES ON CLAY MINERALS. 17111. A COXSISTENCY TEST OF EXCHANGE SORPTION IN THE SYSTEMS SODIUM-CESIUM-BARIUM MONTMORILLONITE1 BY RUSSELLJ. LEWISAND HENRYC. THOMAS Department of Chemistry, University of North Carolina, Chapel Hill,N . C. Received January 25, 1563
-
Standard free energies of exchange from solutions of the chlorides a t 0.04 N on a purified montmorillonite clay Na, -2152 cal./mole; Ba 2Na, -496 cal./mole; have been determined for the three reactions: Cs 2Cs -+ Ba, -3677 cal./mole. These satisfy the requirement of additivity. Activity coefficients as functions of surface composition are given.
Studies of the ion-exchange behavior of siliceous minerals have in rnost cases been confined to single pairs of ions so that tests of the additivity of the standard free energies of the reactions have not often been made. Such additivity is a minimum requirement of consistency in this work. It has, for example, been demonstrated conclusively for Li-Na-K exchanges in sodalite.2 In the only case involving clay minerals of which the writers are aware3 the result was not entirely convincing. Such a consistency test is particularly desirable in work with the clays, where the definition of the extent of the surface region under study, as determined by the nature of the experiment, can give different results with different ions. Thus the ion-exchange (1) We are indebted t o the International Atomic Energy Agenoy for a grant which made this work possible. 12) R. M. Barrer a n d J. D. Falconer, Proc. Rou. SOC.(London), A236, 234 (1956). (3) C.N. Merriam, Jr., a n d H. C. Thomas, J . Chem. Phys., 24, 995 (1956).
-+
“capacity” of a clay mineral as determined by a chromatographic elution depends directly on the method used for the determination of the free volume of the column. Results differing by as much as 5% in the capacity are obtained when comparing a free volume determined by weight with that determined by isotopic anion elution in the case of montmorillonite in contact with sodium chloride solution. In this case the anion is definitely repelled from the clay surface. Such effects if undetected might produce serious discrepancies in thermodynamic calculations. The effect is very small or absent in the presence of kesium and barium. We report here examinations of the equilibria of the three pairs of Na+, Cs+, Ba++ on a purified wontmorillonite which satisfy the consistency test. The clay used in this work mas the Reference Clay Mineral KO. 23 of the American Petroleum Institute, from Chambers, Arizona. I n unpurified form this material
RUSSELLJ. LEWISAND HENRY c. THOMAS
1782 I
I
0
0.2
0.4
0.8
0.6
Fig. 1.-Stoichiometric equilibrium coefficients on montmorillonite a t 30’: 0, Cs+ NaM e Na+ CsM, In Kc’ us. (CS); A, Ba++ 2iYaM 2Ka+ BaM, In K,’ us. (Ba); 0,2Cs+ BaM2 e B a + + 2Csh1, In R,‘ us. (Cs).
+
+
+
+
+
+
has been studied rather extensively; it was thought that a comparison of the behavior of a purified specimen with that of the natural clay might prove informative. This material has been shown to exhibit little or none of the complicated effects known as “ion fixation,” a t least under the conditions of our experiments. We are thus dealing with nearly as simple a clay system as is possible. Experimental After crushing and standing for a day under distilled water, the clay was dibpersed by adding sodium hexametaphosphate to a concentration of 0.1%. While there may be some danger of contamination in the use of these phosphate mspensions, i t was found that clays so prepared sorbed less phosphate than could be detected by the molybdate test applied to solutions obtained by leaching the clays with 0.02 HC1. With an ordinary centrifuge, material of equivalent spherical diameter (e.s.d.) less than 0.5 p was separated as a suspension. This material was passed through a Sharples “Supercentrifuge” so as to obtain a separation a t 0.1 p e.s.d. The subpensions which contained particles of larger diameter were diluted and again centrifuged to remove the fines. Both the effluent and the deposit on the centrifuge liner indicated that the clay contained only small amounts of the smaller particles. The clay, now nearly in the size range 0.1-0.5 p e.s.d., was divided into two parts and each dispersed in 181. of water. Hydrochloric acid was added to pH 5-6, then enough NaCl to flocculate the clay. The final salt concentration was about 0.05 N . The clay was again supercentrifuged, removed from the liner, and dispersed in a minimum of distilled water. A few drops of toluene was added to each container to prevent microbial growth. Equilibrium measurements were made as follows. The clay suspension was pipetted into pure filter paper pulp. After drying for 2-4 hr. a t 110” the clay-pulp dispersion was ground and mixed. For a typicai measurement weighed portions of this material were used to prepare each of six small columns. These were merely small glass test tubes, with a hole in the bottom, of such a diameter as to fit snugly into a plastic tube, which in turn fit closely within the well of a scintillator. The tubes were filled from bottom to top as follows: glass wool, pure paper pulp, clay-pulp dispersion, glass wool. The standard of radioactivity was contained in a similar tube (with no hole), the tube being filled, sometimes with the aid of paper pulp, to the same height as the columns with which it was to be compared. All measurements depend on direct comparison of column with appropriate standard in the well of the scintillator. Before equilibration with the solutions of interest the columns were treated with an amount of 1 N NaCl equivalent to 200-300
Vol. 67
times the capacity of the clay contained. Of the six columns prepared for a single determination, in two-ion cases, three carried tracers for one ion and three for the other. The total ion content of the tube was taken as the sun1 of the uptakes of the separate ions. I n the present case this procedure is safe; the capacity of the Chambers montmorillonite has been repeatedly shown to be independent of composition €or any of the ions with which we are here concerned. The method does require that the preparation of the columns be reproducible. To test this eleven columns were brought to equilibrium with 0.04 N NaC1 carrying Na-22 as tracer, each containing the same weight of a clay-pulp dispersion. By subtracting the content of the free volume (as determined by weight) the sodium uptake of the clay surface region was found. The series of eleven determinations gave 0.1050 f 0.0035 mequiv. for uptake and maximum deviation. The columns were brought to equilibrium at 30.0 & 0.1” with the solution under study. (Infrequent temperature excursions of 1’ were notired; the effect of temperature on these equilibria is such that these were insignificant.) The tracers for the ions were Na-22, Cs-134, and Ba-133. All solutions were a t a total concentration of 0.04 N . At lower concentrations with pure NaCl solutions losses of clay from the columns occurred. Sorption by the paper pulp in these columns was measured and found to be less than 1%of the sorption by the clay; any effect due to the pulp has been disregarded. In the near trace regions for one or the other of the ions, where equilibrium is but slowly reached, checks were made by repeated counts of the column as more and more solution passed through it. Information so obtained enabled a proper adjustment of elution volumes throughout the range of composition.
Results and Discussion I n Fig. 1 the results of the measurements in the twoion cases are shown as logarithms of the stoichiometric equilibrium quotients for the reactions as indicated, parentheses around a symbol being used to denote the equivalent fraction of that ion on the surface. In the computation of the equilibrium quotients small discrepancies in the data are greatly magnified, particularly near the ends of the isotherms. Examination of the data makes it evident that we cannot suppose our values of In K,’ to be more reliable than to 10.2. I n computing the standard free energies we have deliberately neglected what may well be real small variations in In K,’. The curves for these quantities in Fig. 1 show the character of the smoothing introduced. I n all cases we have assumed that the analog of Henry’s lam is obeyed in the trace region and have extrapolated the curves to definite intercepts. That this is justifiable has been demonstrated in a considerable variety of cases for low concentrations of the more strongly sorbed ion. At the other extreme of the isotherm competition between the weakly held metal ion and the hydrogen ion may become of significance. Uncertainties in the free energies due to these extrapolations are, however, small. We illustrate the calculation of the standard free energy and of the surface region activity coefficients in the Na-Ba case, writing the thermodynamic equilibrium constant as
so defining the quantity K , and the observed quotient K,’. The ratio of the solution phase activity coef~ B ~ , determinate. ficients, Y N ~ ~ is~ thermodynamically The activity coefficients for the surface region, the f’s, refer to combinations of the ions with a mass of exchanger of definite composition; they are not individual ion activity coefficients. These surface region activity
EXCHANGE SORPTION IN THE SYSTEMS Na-Cs-Ba MONTMORILLOXITE
Sept., 1963
coefficients are defined in terms of equivalent fractions,
--L
+1
e.g. =
P'Ba
f RT 1n (Ba)fBa
in such a manner that they become unity for the monoion surface. The choice of the equivalent fraction as the composition variable is a natural one for mixed valence cases and, in fact, can be seen to lead to the simplest forms for the activity coefficients for an idealized surface. If such a surface consists of a rigid array of charged sites and if the enth,alpy of exchange is zero regardless of composition, the configurational entropy then determines the free energy; K, is constant; and the activity coefficients defined for equivalent fractions have their corresponding simple forms. (The simplicity is lost for a mole fraction definition. In both cases the activity coefficients are individually dependent on compo~ition.~)If, now, we neglect the small variation in the activity of the water in passing from 0.04 N NaCl to 0.04 N BaCl2, the Gibbs-Duhem equation together with the above relations enable the calculation of the surface activity coefficients and hence of In K InfNa2 = (Ba)(l $- ln K O )In f~~= - (Na) (1 -I- In K,)
Jo(Ba)
ln K , X d(Ba)
+ LBa)In K OX d(Ba) 1
and la K = --I
+ lIno K, X d(Ba) 1
The computations for the three cases have been carried out. We have consistently neglected the solution phase activity coefficients and so have identified K , and Kc' for the following reasons. For the Cs-Na case the quantities cancel to high approximation. In the mixed charge cases the errors due to this neglect may amount to as much as 0.25 in In K. I n the consistency test, however, these errors tend to cancel and cannot significantly affect the final result. On converting to energy units we find for the standard free energy increments of the three reactions the values shown in Table I, Combining the results for the first two reactions gives (4) The situation is entirely analogous in the case of liquid mixtures of molecules of unequal size. See, for example, G. N. Lewis and M. Randall, "Thermodynamics," McGraw-Hill Book Co., Inc., New York, N. Y . , 1961, p. 287 ff., where the argument can be transcribed immediately for the present case by noting that the ratio of the molal volumes of the pure liquids corresponds t o the charge ratio of the exchengingions.
-1 -2
. . . /" --. .-- i_ _ I
I
I
..- ...- ...- ...-
0pclga
1783
I
I
I
I
- .. . . -
I
-__
,/
-
A
-3
2
-
-I-1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
3
k
0
-11
0 1
0
2' I
0.2
0.4
Y
0.8
0.6
Fig. 2 . S u r f a c e phase activity coefficientson montmorillonite a t 30': A 1,2, lnfBa, In fcS2 us. (Cs); B 1,2, In fx8, In fcS us. (Cs); C 1,2, lnfNa2, InfBsvs. (Ba).
TABLE I STANDARD FREEENERGIES FOR EXCHANGES ON MONTMORILLONITE AT 30" -AFo = 2152 cal. Cs+ NaM Na* CsM, Ba*+ 2NaM 2Na+ BaM2, -AFo = 496 cal.
++ + + 2Cs+ + BaMz%Ba++ + 2CsM,
-AFa
=
3677 cal.
the predicted value for the third, -AFo = 3808 cal. The discrepancy of 131 cal. is rather less than might reasonably have been expected. The marked decrease in selectivity -for - cmium at high cesium loading is apparent both with sodium and with barium. In the competitions between barium and sodium, loading the surface with the selectively held ion produces a similar but much smaller effect. This effect is reflected in the behavior of excess free energies of the nonpreferred ion on the clay surface as is seen in Fig. 2, where the logarithms of the activity coefficients are depicted as functions of surface composition. It would be of interest to extend the measurements to other temperatures to enable an examination of the relative contributions of the exchange enthalpies and exchange entropies. The apparently near approach to ideal behavior in both the Cs-Na and Cs-Ba cases may well be fortuitous.
