STANLEY BUKATA AND JACOBA. MAR~NSKY
994
Ion Exchange in Concentrated Electrolyte Solutions. 111.
Zeolite Systems with Salts of Group I and I1 Metals
by Stanley Bukata112and Jacob A. Marinsky3 The Department of Chemistry, State University of New York at Buffalo,Buffalo, New Yorll (Received June 18, 1963)
The selectivity coefficients for the ion exchange of cesium with sodium A-zeolite, cesium and sodium with potassium h-zeolite, and sodium and barium with calcium A-zeolite have been determined in dilute and concentrated solutions. The exchanging ions were a t radioactive tracer level concentrations so that the fraction of the exchanged ion of the zeolite was essentially unity in both the resin and external liquid phases. Quantitative treatment of the observed data was accomplished by assuming that the zeolite phase may be treated as a highly concentrated electrolyte solution having only one diffusible ion and as a cross-linked network which exerts a pressure on the internal solution phase. The special properties of the zeolite, rigidity and resistance of electrolyte incursion, facilitate the treatment and permit the accurate prediction of selectivity a t any external electrolyte concentration of two mobile counter ions a t micro- and macroconcentration levels, respectively, on the basis of ‘one selectivity measurement if the thermodynamic properties of the mixed electrolyte in the aqueous phase are known. Conversely, in the absence of such thermodynamic data, activity coefficients of the trace component can be computed from the experimentally determined selectivity coefficients.
Introduction The ion-exchange behavior of natural and synthetic zeolites has been rather extensively investigated for many years, the bulk of the work having been done in dilute electrolyte solutions.* Recently, Platek and Marinsky6 reported work in concentrated solutions with the lithium form of the synthetic A-type zeolite6 whose structure is well-characterized.’ They suggested that this zeolite may be considered to be a highly “cross-linked” exchanger and that a relationship of the type suggested by Gregors and Glueckaufg for organic resins may also apply for this exchanger; namely In
aj
=
In dj
a +Vj RT
(1)
where aj and Vj represent the activity and partial molar volume of component j, T is the difference in osmotic pressure between the interior of the zeolite and The Journal of Physical Chemistry
the external solution, and the bar placed above the symbol is used to differentiate the resin phase froin the aqueous phase. Equation 2a then governs the cxchange process for uni-univalent exchange in 1: 1 electrolyte solutions with the A-zeolite in the N +form and the exchange carried out in solutions of NX MX.’O
+
(1) Union Carbide Doctoral Fellow, 1961-1962. (2) This paper is based on a dissertation submitted by S. Bukata in partial fulfillment of the requirements for the degree of Doctor of
Philosophy. (3) Correspondence to be addressed to this author. (4) F. Helfferich. “Ion Exchange,” McGraw-Hill Book Co., Inc., New York, N. Y., 1962, Chapter 5, particularly pp. 183-193. (5) W. A. Platek and J. A. Marinsky, J . Phys. Chem., 65, 2118 (1961). (6) R. M. Barrer and E. A. D. White, J. Chem. Soc., 1561 (1952). (7) D. W. Breck, et al., J . A m . Chem. SOC.,7 8 , 5963, 5972 (1956). (8) H. P. Gregor, ibid., 7 0 , 1923 (1948); 73, 642 (1951). (9) E. Glueckauf, Proc. Roy. SOC.(London), A214, 207 (1952). (10) G. E. Boyd and B. A. Soldano, 2.Elektrochem., 57, 162 (1953).
IONEXCHANGE: IN CONCENTRATED ELECTROLYTE SOLUTIONB
4 hl YhMX 1 n T - 21nYiNX
YN
(24
+
For the univalent-divalent (KX MXJ and divalent-divalen t (SX2 MXZ)systems, also studied in this research program, the working equations are
+
In
(mN +) z(mM+ t) (?nN +> '(fill
+
+)
=
In K
=
In
(4M +) (-7x+I +
p 2
and
+
3 In ' E z ~ ( v M Y+NX2
+ +
- vN++)/RT (2c)
where K is the experimentally determined selectivity coefficient, m is the molal concentration of the species, -7 is the activity coefficient of the ion in the zeolite phase, and y*, is the mean molal activity coefficient of the electrolyte in the external solution phase. It was the objective of the first phase of this research to demonstrate the applicability of the above model for the anatysis of the ion-exchange behavior of the A zeolite. Its special properties of rigidity and high resistance to electrolyte intrusion, because of the high negative charge due to the ring of oxygen atoms in the faces and corners of the cubic unit cell and the small opening available to the exchanging io~is,'mere expected to facilitate evaluation of the terms on the right-hand side of eq. 2a to provide a quantitative prediction of K with varying ionic strength in uni-univalent electrolyte systems containing one macro- and one microelectrolyte component whose activity behavior in the presence of the bulk electrolyte was calculable. Once the va,lue of this model was demonstrated i t was the objective of the second phase of this research to employ the model further to estimate activity coefficients of trace components, not otherwise obtainable, in bulk electrolyte from a series of selectivity measurements made as a function of the Concentration. In order to obtain the first objective with organic exchangers it has been necessary to limit investigation to dilute solutions where electrolyte invasion is not a complicating factor. Weakly cross-linked exchangers, to represent the unrestrained macromolecule, are then needed to permit estimate of the ~ M / ? N and T / R T ( P M- PN)ternis to be employed in eq. 2 for the cross-linked systems.8-11 Platek and MarinskyKhave
995
pointed out that for zeolites the methods used for organic exchangers are not applicable since the zeolite cannot be made in an "uncross-linked" form. It was believed, however, assuming the applicability of the model to the A-zeolite, that the special properties of framework inflexibility and resistance of electrolyte intrusion, even at high external electrolyte concentra,tion, eliminated the need for this type of approach for the attainment of our objective. In the first phase of the program the exchanging ion N was kept a t radioactive tracer level concentrations in solutions of h/lX (0.1 m and greater). Thus the ion fraction of M was essentially unity in both the zeolite and external solution phases. According to our model, the zeolite is rigid, its composition in these studies is essentially constant, and In ? M / ~ N is constant. If the model is correct this term should be available from a single measurement of K a t any external electrolyte concentration and, using this value, K should be calculable at any other concentration with eq. 2a. To demonstrate this result the value of n was obtained ajs a function of electrolyte concentration from eq. 1 by assigning a value to the water activity (also COMstant on the basis of our model) in the zeolite phase. It was assumed for these computations, also, that the partial molar volume of solvent and ions were constant. The mean activity coeEcient ratio of micro- and inacrocomponent in the mixed electrolyte systems were calculated. I n the second phase of this study, the zeolite parameters, In y ~ + + / ( j h +and ) ~ In T ~ + + / j k +were + determined from the experimental selectivity coefficients a t low concentrations of MX2. It was assumed that, at these dilutions, the effect of the MXL on the mean molal activity coefficients of the microcomponent would not be noticeable within the error limits of the experimental measurement. The published y*-value for the pure electrolyte a t the ionic strength of the experiment was used. The selectivity coefficient values that were measured a t the higher concentrations of MX2 were then employed in eq. 2b and 2c to calculate the mean activity coefficient of the microcomponent a t the higher concentrations. Since XX2 or S X was present in ver,y low concentrations the activity coefficients for MX2 are identical with those for the pure electrolyte and the literature values were employed for the computation in every case.
Experimental Materials. The sodium A-zeolite was kindly sup(11) B. A. Soldano, et al., J . A m . Chem. floc., 7 7 , 1331, 1334, 1336 (1955).
Volume 68, Number 6
May, IO64
STANLEY BUKATA AR'D JACOB A. MARINSKY
996
plied by the Linde Company. Its preparation for use in equilibration experiments included a sedimentation technique which was repeated five times to remove amorphous silica and alumina adhering to the commercial product. About 50 g. of zeolite were slurried with 500 ml. of a 0.1 M KaC1 solution in a 500-ml. graduated cylinder. The zeolite crystals were allowed to settle for about 30 min. The fine material remaining in suspension was discarded by decantation. The residual zeolite was filtered, washed with deionized water, dried a t 80' to remove surface moisture, and stored over a saturated ammonium chloride solution to maintain a constant water content. Subsequent preparation of the potassium A-zeolite, based on the reactions
+ Agf = AgZ + Ns+ AgZ + K + + 2CNSKZ + Ag(CNS)zNaZ
=
consisted of the following operations. Thirty grams of hydrated sodium A-zeolite were converted to the silver form by equilibration with 500 ml. of a 0.3 M silver nitrate solution for 1 hr. in the dark. The mixture was filtered and the solid product was washed and again equilibrated for 1 hr. with 500 ml. of 0.3 M silver nitrate solution. This procedure was repeated two more times. The zeolite was separated by filtration and washed with deionized water and then was added to 300 ml. of a saturated potassium thiocyanate solution and stirred for 0.5 hr. The solid after filtration was added to 150 ml. of a saturated potassium thiocyanate solution and equilibrated for 1 hr. After another equilibration the product was filtered, washed, dried a t 80', and stored over a saturated ammonium chloride solution. Conversion to the calcium A-zeolite was accomplished as follows. About 100 g. of hydrated sodium A-zeolite were equilibrated with 500 ml. of a 2 M calcium nitrate solution for 2 hr. The zeolite was filtered and again equilibrated with 500 ml. of 2 M calcium nitrate solution for 2 hr. The procedure was repeated five more times. The final product was washed with deionized water, dried a t 80" to remove surface moisture, and stored over a saturated amnionium chloride solution to maintain a constant water content. The final product contained about O . O l ~ osodium as ascertained by flame photometry. The y-emitting, radioactive nuclides, 2.3-year Cs134 and 12.8-day Ba14040-hr. La140, were purchased from the Radioisotopes Division of the Oak Ridge National Laboratories. Carrier-free 2.6-year Ka22 was obtained from the Yuclear Science and Engineering Corporation. Analytical grade reagents were from The .Journal of Physical Chemistry
J. T. Baker Co. and were used without further purification. Equilibration Procedure. The hydrated zeolite was equilibrated a t the ambient temperature, 24 =t 3", with a solution containing MX or MXZin macroscopic quantities and NX or NXz in radioactive tracer quantities. For an experiment, zeolite was accurately weighed into a 2-ounce capacity polyethylene bottle. Plastic equipment was used since glass was found to adsorb appreciable quantities of the radioactive Cs tracer. The weight of the zeolite was varied with the concentration of the external solution to keep the uptake of the tracer a t about 25-75y0 of the initial amount. About 0.1 g. was used with the 0.1 m solutions and 2 to 3 g. was used a t 6 m. About 15 ml. of the equilibrating solutions of (MX NX) was added and its weight determined. The mixture was shaken from 24-48 hr. on a shaking machine a t a speed sufficient to keep the zeolite from settling. After equilibration, the mixture was transferred to e 15-ml. conical polypropylene centrifuge tube which was stoppered and centrifuged for 0.5 hr. Two ml. of the supernatant liquid were pipetted (polyethylene pipet) into a 16 X 105 mm. lusteroid test tube. The weight of the liquid transferred was determined. The activity of the samples and standards were measured in a 1.25 X 2 in. well-type sodium iodide, thallium-activated, 7-ray scintillation crystal detector. In the case of the Ca-Ba exchange the liquid was separated from the equilibrated mixture and was
+
0
I 0.2
I 0.4
I
0.6 p / p o (relative humidity).
I
0.8
Figure 1. Water sorption isotherm of sodium A-zeolite.
I
1.0
IONEXCHANGE IN CONCENTRATED ELECTROLYTE SOLUTIONS
allowed to stand for 14 days to ensure restoration of transient equilibrium between the 12.8-day Ba140 parent and its 40-hr. La140daughter prior to measurement of the y-activity in the sample. Evaluation of Zeolite Parameters. The osmotic pressure term, T , was evaluated by use of eq. 1 assuming a, =. 0.16 and is constant. In Fig. 1, the water adsorption isotherm (25") is given for sodium A-zeolite.12 There is little change in the amount of water taken up per gram of zeolite as the value of p/po (=a,) varies from unity to a value of about 0.16. A sharp decrease in water content of the zeolite occur8 below 0.16. Similar behavior is observed for other zeolites. This result is considered to indicate that at a, = 0.16 the activity of water inside and outside of the zeolite is equivalent. When the external water activity is greater than 0.16 the internal water activity remains about constant and to a first approximation is equal to 0.16. At lower a, values the n-term is believed to disappear (a, = a,). A value of 18 ml. was used for the partial molar volume of water. Values published for the partial molal volumes of the ions a t infinite dilutionlS were used. Another approximation, constancy of partial molar volumes, was employed as a simplification. The values of yrt, the activity coefficients in mixed electrolyte solutions, were computed for the uniunivalent systems. Since NX is present in trace quantities the activity coefficients for R2X are identical with those for pure MX solutions and are found in the literature. l 4 The activity coefficients for trace N X in the presence of MX were calculated by use of the Harned-Cooke14 equation in the form
where Y ~ ( N X ) is the activity coefficient of a trace of N X in the presence of MX a t molality m, YNX(O) is the activity coefficient of pure NX a t molality m, and a: and p are experimentally determined parameters. The In T;M/-& term is evaluated, as previously mentioned, by using the above parameters in eq. 2a after a single measurement of K a t any concentration value. In the case of the univalent-divalent and divalent-divalent systems K was measured a t 0.127 and 0.094 m Ca(NO&, respectively. The effect of the Ca(N03)2 on the mean activity coefficient of the trace ion, Na+ or Ba++, was neglected. The In ~ C ~ / ( - Y Nand ~ ) ~In Y C ~ / ~ parameters ;B~ obtained in this manner were used in eq. 2b and 2c to calculate the activity coefficients of the trace electrolyte NaN03 or Ba(V03)2 as a function of the change in K with Ca(NO& concentration.
997
Constancy of TM/TN is to be expected in all the systems since electrostatic interactions are essentially unchanged. The zeolite is rigid and electrolyte incursion is essentially absent. It was experimentally determined that the Na A-zeolite is not noticeably invaded by KaC1 under the conditions employed in this work. It was assumed that no incursion occurs in any of the other systems studied since the bromides, nitrates, and acetates that were also used are larger than the chloride ion.
Results I n Table I, selectivity coefficients for the system, NaA-NaC1-CsCl, are given. Using the experimental value of K a t 2.255 m NaCl (K,) the In Y N ~ + / ~ C ~ + term was calculated to be 3.390. The values of Ke were obtained from eq. 2a using this number. The y*-values were obtained froni the data of Robin~on.'~ Modified selectivity coefficients, Ke', are also given in the table for comparison
(4)
Table I : Selectivity Data for the System NaA-NaC1-CsC1
a
2a.
External NaCl molality
Kea
KCb
Keto
0.053 0.106 0.537 1.085 2.255 3.383 4.510 6.068
2.77 2.78 2.56 2.22 1.85 1.61 1.37 1.18
2.81 2.83 2.55 2.31 1.85 1.52 1.32 1.09
2.86 2.86 2.78 2.58 2.47 2.44 2.31 2.32
K,
=
experimental selectivity.
'K,
=
calculated from eq.
K,' = calculated from eq. 4.
In Tables I1 and I11 the data for the systems NaAXaBr-CsBr and NaA-Ka acetate-& acetate alae similarly presented. The values of K , as a function of == molality were calculated again using In ?;xa+/ yea+ 3.390. In the absence of imbibement and significant expansion or contraction of the zeolite matrix, this zeolite parameter for the Na-Cs exchange should be (12) Permission to use these data was kindly granted by D. W. Breck. (13) P. Mukerjee, J . Phys. Chem., 65, 740 (1961). (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions." 2nd Ed., Butterworth Scientific Publications, London, 1959. (15) R. A. Robinson, J . A m . Chem. SOC.,74, 6035 (1952).
Volume 68, A'umber 6 May, 1964
998
STANLEY BUKATA AND JACOB A. h/IARINSKY
constant regardless of the anionic form of the salts in the external solution. The r&-values for NaBr and CsBr were calculated using eq. 3. The unavailability of any interaction coefficients for this system, however, necessitated re-employment of the a- and @-termsthat were used for the NaC1-CsC1 system16 as the most reasonable approximation. The activity coefficients up to 3.5 m were taken from Robinson and Stokes.14 Beyond 3.5 m the values are from Landolt-Bornsteinla since Robinson and Stokes do not report any values above 3.5 m. There is disagreement between the two sources below 3.5 m and we believe the data of Robinson and Stokes to be more valid on the basis of the good correlation that is obtained between K , and K , in the lower concentration range. The values a t 5.503 and 7.903 m are used only to demonstrate the prediction of the trend of selectivity by this approach.
Table I1 : Selectivity Data for System NaA-NaBr-CsBr External NaBr molality
K,
0.080
2.86 2.48 2.26 1.84 1.14 0.72 0.47
0.401 0.810 1.660 3,490 5.503 7.903
KO
2.84 2.54 2.25 1.69 1.08 0.60 0.32
where 4~ = osmotic coefficient of CsAc a t molality m, +C = osmotic coefficient of NaAc a t molality m, and CYB = interaction coefficient. I n Tables IV and V selectivity data for the system KA-KCI-CsCl and KA-KC1-NaCl are given. The values of In YK+/YN+ = 2.340 and 0.1793 were .determined from K , a t 2.090 and 1.831 m KC1, respectively. The y*-values and interaction parainetcrs were obtained from the data of R o b i n ~ o n . ’ ~ ~ ”
Table I V : Selectivity Data for the Systems KA-KCl-CsC1 External KC1 molality
0 0 0 1
049 098 499 000 2 090 3 220 4 414
K,
2 2 2 2 2 2 2
92 77 67 58 48 45 45
KO
2 2 2 2 2 2 2
80 80 72 66 48 39 36
Ke ‘
3 2 2 2 2 2 2
00 83 76 74
78 82 90
KB ’
2.94 2.71 2.64 2.53 2.06 2.25 1.92
Table 111: Selectivity Data for System NaA-NaAc-CsAc External
Table V : Selectivity Data for the System KA-KC1-NaCl External KC1 molality
Ke
KO
Ke ’
0.1089 0.4394 0.8905 1 ,8308 2.8291 3.8851
3.42 3.52 3.49 3.59 3.75 3.80
3.41 3.48 3.51 3.59
3.40 3.45 3.39 3.42 3.49 3.46
3.69 3.77
NaAo
molality
K,
KO
Ke ‘
0.186 0,470 0.959 2.001 2.558 3,554
3.06 3.20 3.35 3.73 3.89 4.31
3.09 3.15 3.31 3.70 3.89 4.36
3.02 3.15 3.23 3.52 3.63 3.92
In the YaA-XaAc-CsAc system the trend in activity coefficients of the acetates are opposite to those of the chlorides and bromides and study of the selectivity of this system was expected to be a useful test of the approach that has been employed herein. Unfortunately there are no published a-values for this system as well. The interaction parameters needed to be approximated by using the relation14 +B
- q k = 2.303ma~
T h e Journal of Physical Chemistry
(5)
Tables VI and VI1 contain known aqueous phase activity coefficient data for the heterovalent systems. Tables VI11 and IX present the experimental selectivity coefficient values together with the estimated values of (1) the ?r-term and (2) the activity coefficient of the trace component a t the various experimental concentrations of Ca(N03)2. Also included in Table VI11 are interaction coefficients (al2),estimated for the Na-Ca systems studied, from the experimentally determined selectivity COefficients. The presumption for evaluation of 0112 is that the Harned rule’* is valid for this system. (16) Landolt-Bornstein, “Physikalisch-Chemischen Tabellen,” 5 Auflage, Vol. 2, part 2, Verlag von Julius Springer, 1931, p. 1125. (17) R. A. Robinson, T r a n s . Faraday SOC.,49, 1147 (1953).
IONEXCHANGE IN CONCENTRATED ELECTROLYTE SOLIJTIONS
-
-Aq Table VI : Activity Coefficients in the Aqueous Phase
'+--,
for the System CaZ-Ca( for CaZ-Ca(N03)2-N~NTn NO3)2-NaNO3(trace)-H20 Ca(NOa)z molality
Ca(N0a)z
NaNOs
0 127 0 256 0 517
0 0 0 0 0 0
1 055 2 218 5 036
aw
Yl(Q)
Yl(0)
0 0 0 0 0 0
486 410 363 338 353 513
0 0 0 0 0 0
740 680 614 543 468 386
~~~
994 989 997 959 890 709
~~~
Table VI1 : Activity Coefficients in the Aqueous Phase for the System CaZ-Ca( NOa)'-Ba( N03)2(trace)-HzO Ce(N0a)z molality
0 0 0 0 1 3
Ca(N0a)z
NaNOs aw
"fl(0)
0 490 0 434 0 381
0941 1900 381 773 599 469
0 432 0 348 0 266
0 0 0 0 0 0
0 344 0 339 0 406
996 991 983 966 924 809
999
has been employed to describe the selectivity behavior of organic exchangers has been shown to be applicable to the A-zeolite. The special properties of the zeolite permit the accurate prediction of selectivity at any external electrolyte concentration of two mobile counter ions a t micro- and macroconcentrations levels, respectively, on the basis of one selectivity measurement if the thermodynamic properties of the mixed electrolyte in 1,he aqueous phase is known. The factors that, contribute importantly to the ionexchange beha,vior of the A-type zeolite in dilute electrolyte mixtures are apparent from examination of Table X presented below. The value of the ?rAV/RT terms in the dilute solution region and the corresponding ratio of the activity coefficient of the ions in the zeolite phase are given in Table X together with the selectivity coefficients that were evaluated for the several systems studied. The activity coefficient ratio of the salts in the external dilute solutions is close to unity so that the t,hird term of eq. 2 becomes of minor importance in this region.
Table X : Zeolite Parameters Table VI11 : Selectivity Data for the
System
System CaZ-Ca( N03)2--NaN03( trace)-HzO Ca(N0s)z molality
7.59 X 7.54 X 6.34 X 5.26 X 3.37 X 1.59 X
0.127 0.256 0.517 1.055 2.218 5.036
~~~~~
&CP
IO' 10' 10' 10' 10' 10'
nAV/RT
yi(o)
YW)
an
-1.491 -1.487 -1.477 -1.458 -1.401 -1.215
0.740 0.680 0.614 0.543 0.468 0.386
0.740 0.668 0.583 0.524 0.478 0.501
+0.03 +0.04 +0.015 -0.004 -0.022
...
~
Table IX : Selectivity Data for the System CaZ-Ca( N03)z-Ba(N03)2(trace)-HzO Ca(N0a)z molality
Kexp
0 0941 0 1900 0 381 0 773 1 599 3 469
2 14 2 01 2 02 0 97 0 63 0 35
*AV/RT
-0 -0 -0 -0 -0 -0
548 547 544 539 526 485
Yl(0)
Yl(0)
0 432 0 348 0 266
0 0 0 0 0 0
432 374 329 232 198 191
Discussion The excellent agreement of K , and K , in each of the uni-univalent systems over the total concentration range that was studied indicates attainment of the first objective of this investigation. The model that
NaZ-NaCl-CsC1 NaZ-NaBr-CsBr NaZ-YaAc-CsAc KZ-KC1-NaCl KZ-KC1-CsCl
K,
nAV/RT
-2 -2 -2 +1 -1
299 299 293 036 261
2 2 3 3 2
77 86 06 42 92
In K ,
In W / Y N
1 0819 1 0508 1 1184 1 2296 1 0716
3 390 3 390 3 390 0 1793 2 3405
-
The nA/VRT values are large and thus cannot be neglected in considering selectivity. For all the systems except the KZ-KC1-NaC1 system the values are negative. Only in this system does the nAV/RT term become the major term. In the other systems the aAV/RT and the resin activity coefficient ratio are of the same order of magnitude with the activity coefficient ratio predominating. One cannot generalize as to which term predominates. The third term in eq. 2 is of minor importance in dilute solution (0.1 m or less) but in concentrated solutions it becomes quite important. Figure 2 shows its effect. The ?rAV/RT term is such to increase the selectivity coefficient slightly with increasing concentration. However, the selectivity coefficients decrease with increasing concentration for the systems NaZNaC1-CsC1 and NaZ-XaBr-CsBr showing the pronounced effect that the external solution has. The selectivity coefficient increases with concentration for the NaAc-CsAc system due to the nA/RT term and Volume 68, Number 6 May, 1964.
STANLEY BUKATA AND JACOBA. MARINSKY
1000
KC1-CsC1 system assuming no 0-term. These are compared to the values obtained by Robinson18 using the isopiestic method. The agreement is good.
Table XI : Interaction Coefficient Calculations
P a
I
1
,
1
2
3
Figure 2 .
H20:
L1,
X
I
I
,
I
4 5 6 7 NaX external molality.
I
8
Selectivity data for systems NaZ-XaX-CsX(ltrace)= Ac-; A, X = Br-; 0, X = C1-.
the term involving activity coefficients in the external solution. The selectivity coefficients for the systems in Fig. 2 approach each other 3.0 a t infinite dilution as they should since the exchanging ions are the same and the zeolite is at a constant mole fraction, X N s + = 1. The good agreement found by use of this model for the zeolite also suggests that one might use experimentally determined selectivity coefficients to obtain Harned interaction coefficients in mixed electrolyte solutions. Table XI contains interaction coefficients calculated from experimental K values. for the IC?-
The Journal of Physical Chemistry
KC1
- a12
molality
calcd.
- 01120
1.00 2.09 3.22 4.41
0.014 0.009 0.006 0.004
0.019 0.009
0.004 0.004
Values from ref. 18.
This result indicates the potential utility of the model for estimating the activity coefficients of trace components in the presence of bulk electrolyte, our second objective. In fact when we examine the results given in Tables VI11 and IX we note that the derived observations are indeed reasonable. The calculated a12values for NaKOa are of the order of magnitude observed for other systems. They change sign. This behavior is observed in other systems when the yl(0) of one electrolyte is higher than the other electrolyte and with increasing concentration becomes lower as is the case in the Ca(N03)2-NaS03 system. The yl(0) of Ca(NO3)2 is higher than that of Ba(NO& and interactions would be such as to make yo(1) of Ba(SO3)2 higher than yl(o). Such a trend is observed.
Acknowledgment. Financial support through Contract No. AT(30-1)-2269 with the U . s. Atomic Energy Commission is gratefully acknowledged. (18) R. A. Robinson, J . Phys. Chem., 6 5 , 662 (1961)
