J. Chem. Soc., Faraday Trans. I, 1988, 84(3), 687-702 Multicomponent Ion Exchange in Zeolites Part 3.-Equilibrium Properties of the Sodium/Potassium/Cadmium-Zeolite X System Kevin R. Franklin? and Rodney P. Townsend*$ Department of Chemistry, The City University, Northampton Square, London ECl V OHB A study is reported on the ternary exchange equilibrium involving the cations sodium, potassium and cadmium in zeolite X. This system is an apt one on which to test recently developed prediction procedures since it is possible, in principle, to convert zeolite X to the 100%-exchanged homoionic forms of each of these three cations, thus avoiding the normalisation problems reported previously (K. R. Franklin and R. P. Townsend, J. Chem. Soc., Faraday Trans. I, 1985,81,3127; K. R.Franklin and R. P. Townsend, J. Chem. Soc., Furaday Trans. 1, 1985, 81, 1071). In addition, cadmium salts in solution show markedly non-ideal behaviour even in dilute solution, and therefore the procedures developed for allowing for this non-ideality can be tested adequately. Data are given not only for the ternary system but also for the three conjugate binaries, for which the thermodynamic closure rule ('triangle rule') is shown to hold. In general, successful prediction of exchange equilibria for different external solution concentrations is shown to be possible, although systematic errors develop at the highest concentration examined. In parts 1 and 2 of this series, ' 7 the equilibrium ion-exchange properties of the sodium/ calcium/magnesium-zeolite A system were discussed.Models, based on rigorous thermodynamic treatment^,^*^ were described, which enabled the prediction of both binary and ternary ion-exchange selectivities as a function of the total external solution concentration, These models were then used to predict experimental selectivity data for the Na/Ca/Mg-A system. In this paper, these studies are extended to exchange equilibria involving the ions sodium, potassium and cadmium in zeolite X. In contrast to the commercially important Na/Ca/Mg-A exchange, the Na/K/Cd-X system has less immediate practical importance, but from the viewpoint of testing theoretical predictive models it has significant advantages over the former. First, careful prior studies have shown, within the limitations of experimental uncertainty, that all three of the conjugate binary exchange systems (viz.Na/K-X, Na/ Cd-X and K/Cd-X) hold two important properties in common. These are that exchange of one ion for another can proceed to 100°/~ of the exchange capacity of zeolite X, and that the exchanges are thermodynamically reversible. 5-9 For the Na/Ca/Mg-A system, neither the Na/Mg-A nor the Ca/Mg-A conjugate binary exchanges showed 100% replacement of the former ion by the latter,' and there were, in addition, doubts as to the reversibility of the Ca/Mg-A system.' As a result, complications arose when attempts were made to test the predictive models.2 Secondly, it is appropriate to test the thermodynamic model^^.^ with systems t Present address : Chemistry Department, Edinburgh University, West Mains Road, Edinburgh EH9 355.1 Present address : Unilever Research, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW. 687688 Ion-exchange Equilibrium Properties of Zeolites involving the cadmium ion, because solutions of cadmium salts show markedly non- ideal behaviour even in quite dilute aqueous solution due to ion-pairing.*-1° Since it is a basic tenet of those predictive models which are based on thermodynamic theory that solution-phase non-ideality is often the significant factor in determining selectivity changes as a function of ionic it is therefore logical to test these models with systems where marked non-ideality is expected to be manifest. The results of these tests are reported in this paper. Experiment a1 Materials Zeolite X was purchased from BDH as a fine powder, and was supplied in the sodium form.All other chemicals were AnalaR grade, and were used without further purification. Preparation of Maximally Exchanged Zeolites Although the zeolite had been supplied in the sodium form, previous experience had shown that a substantial deficiency in sodium was often present in commercial samples of zeolite X. Thus the zeolite was first exchanged several times with solutions of sodium nitrate (1 mol dm-3) in order to obtain as far as possible the homoionic sodium form of the zeolite. The zeolite was then washed briefly with water and dried at 80 “C. Finally, and before chemical analysis or use, the zeolite was equilibrated with water vapour over saturated aqueous sodium chloride in a desiccator at room temperature.Maximally exchanged samples of potassium X and cadmium X were prepared by exhaustively exchanging 20g aliquots of sodium-exchanged X with 400 cm3 portions of normalt solutions of either potassium nitrate or cadmium nitrate. The exchanges were carried out at room temperature over one day, and up to 50 one-day exchanges were used. Following the final exchanges, the zeolites were washed, dried and equilibrated over water vapour in the same manner as for the sodium form of the zeolite. Throughout these procedures, great care was taken to monitor the levels of hydronium exchange which may have occurred during the preparation of the different exchanged forms. Other studies have shown that the levels of hydronium exchange attained in aluminium-containing zeolites are critically dependent on the zeolitic framework charge,12 and on the amount of acid gases dissolved in s01ution.l~ For these reasons, extensive washing of the samples under conditions open to the atmosphere was avoided, and strict pH control of the wash water was observed.These matters, and the appropriate procedures, are all discussed in detail elsewhere. l3 Levels of hydronium exchange were determined by inference from comprehensive chemical analyses of the materials, and in appropriate cases, by complete chemical analyses of both exchanging phases (viz. zeolite and external solution) followed by mass balances. Chemical Analyses For the isotherms, both exchanging phases were analysed for all exchanging ions each time in order to construct each isotherm point.In addition, the aluminium content of the zeolite sample was analysed in some cases as a further check. t Throughout this paper, the term ‘equivalent ’ refers to one mole of unit negative or positive charges, and the term ‘normal’ refers to the concentration in solution of species in equivalents. Thus the normality of a solution with respect to ionic species i is z,ci, where zi is the valency and ci is the molarity (mol dm-s) of i in solution.K. R. Franklin and R. P . Townsend 689 For the zeolite phase, silica, alumina and water contents were determined by gravimetric methods previously described.'* The sodium, potassium and cadmium contents were determined after the zeolite had been dissolved in 30 YO nitric acid. Sodium and potassium were determined by standard methods using flame photometry, while cadmium was analysed by atomic absorption spectroscopy using an air-acetylene flame.No interferences were encountered during these analyses. For the solution phase, sodium and potassium were again determined using flame photometry. For concentrations greater than mol dm-3 a titrimetric method was employed to analyse for cadmium, using EDTAf at pH 5.15 At lower levels, cadmium concentrations were determined using an EG and G model 264 polarograph, operating in the differential pulse anodic stripping mode.16 Construction of Ion-exchange Isotherms The experimental approach was similar to that used for the construction of isotherms for the Na/Ca/Mg-A system.' All of the isotherms were constructed at a total normality of 0.1 equiv.dm-3 using a seven day exchange time, and at a temperature of 298 K. The starting material employed for both the binary and ternary exchange studies was Na-X except for the construction of the binary Cd/K-X isotherm, where the starting material was K-X. Isotherm points were obtained by contacting 0.2g aliquots of the zeolite with 50 cm3 portions of solution containing the nitrate salts of either both (binary studies) or all three (ternary studies) metal ions. To obtain high loadings of the ingoing cation(s), it was found to be necessary to use larger volumes of solution, or in some cases, even multiple exchanges. After equilibration, the two phases were separated by centrifugation, and the zeolite phase was washed carefully with water.Finally both phases were analysed for all exchanging ions. Thermodynamic reversibility of exchange was tested for the binary isotherms using the 'wet method ' described previous1y.l' For reasons given elsewhere, and concerned with the number of degrees of freedom possessed by a ternary exchange system,18 there is no simple experimental method of testing for reversibility in a ternary exchange situation. Thus overall reversibility of the ternary exchange isotherm was taken as proved if all three conjugate binary systems had been shown to be reversible within the limits of experimental error.18 All the isotherm data were plotted in terms of equivalent fractions, which were defined for the binary and ternary exchange systems, respectively, as follows. For the binary isotherms, the equivalent fraction of (say) ion A in the zeolite phase (1) is defined as whereas the corresponding function for the solution phase is (2) E A = 'A mA/(zA mA + 'I3 EA = 'A ',/('A 'A+', and z,, z , are the valencies of the exchanging ions A": and BZi.Similarly, the functions mA, mB and c,, C, are, respectively, the molalities (mol kg-l yf zeolit?) and molar concentrations in solution (mol dm-3) of the exchanging ions A'A and B'B. For the ternary isotherm, the equivalent fractions are E A = 'A mA/(zNa mNa + 'K mK + 'Cd %dl EA = 'A 'A/(',, 'Na + 'K cK + 'Cd 'Cd). (3) and (4) It should be noted that the definitions of equivalent fraction in the zeolite phase given in eqn (2) and (4) are normalised functions, i.e. they have been adjusted for any t Ethylenediamine tetra-acetic acid.690 Ion-exchange Equilibrium Properties of Zeolites Table 1.Analysis of the sodium potassium and cadmium forms of zeolite X Na-X (Yo w/w) K-X (% w/w) Cd-X (% w/w) SiO, Na,O CdO totals Si :A1 Zcation :A1 4 0 3 H2O K2O 36.71 24.70 23.60 14.76 0.00 0.00 99.77 1.261 0.983 35.23 23.54 20.18 0.29 20.54 0.00 99.78 1.270 0.963 30.31 20.25 23.12 0.24 0.00 24.10 98.02 1.270 0.965 hydronium exchange which may have occurred. The effect of hydronium exchange on equilibrium selectivities is discussed elsewhere. ‘ 9 12, 13, l9 In the present study, levels of hydronium exchange up to ca. 12% were encountered at low ECd values, but the extent of hydronium exchange decreased as Ecd increased. Results and Discussion Maximally Exchanged Zeolites The results of the chemical analyses of the three maximally exchanged forms of X are given in table 1.Unit cell compositions, derived from the data in table 1, are as follows : Na-X Na83.5 [&O]i.4 [A102184.9 [si021~07.i [H201228.4 K-X K79.9 Nai.5 [H3Oh.i [A102184.6 [sio21i07.4 [H201202.2 Cd-X : Cd40.0 Na1.6 [H3OI3.o [A O2184.6 [si021i07.4 [H20127~.5- The levels of hydronium exchange are included in the unit cell compositions. Because of the experimental precautions alluded to above (in the experimental section), these levels are not high, despite the large number of exchanges which were undertaken. In the case of the cadmium sample, the total percentage (table 1) is rather low: subsequent experiencel39 l9 has shown that aluminium and especially silicon may have been somewhat underestimated here, which means that the hydronium content of the Cd-X sample was probably slightly higher than indicated.Binary Exchange Isotherms In fig. 1-3 are given, respectively, the binary ion-exchange isotherms for the K/Na, Cd/Na and Cd/K exchange reactions in X. All three isotherms were found, within the limits of experimental uncertainty, to be reversible. In all three cases, complete replacement of the original ion by the entering one seemed to be possible, although removal of the last traces of sodium from X by either potassium or cadmium is difficult (see fig. 1 and 2, and also the discussion above regarding table 1). The potassium/sodium isotherm (fig. 1) is sigmoidal in shape, with the zeolite showing a slight preference for potassium at low loadings of this ion, and the converse preference at high loadings.Comparisons with previous studies5* 7* show very good agreement regarding the general shape. Using the procedures of Glueckauf,20v 21 a standard freeK . R. Franklin and R. P . Townsend 69 1 1 0.8 0.6 EK 0.4 0.2 Fig. 1. K/Na-X exchange isotherm obtained at 298 K and at total normality 0.1 equiv. dm-3: 0, forward points; x , reverse points. 0.2 0.4 - 0.6 0.8 1 Ecd Fig. 2. Cd/Na-X exchange isotherm obtained at 298 K and at total normality 0.1 equiv. dm-3: 0, forward points; x , reverse points. energy of exchange of 0.48 kJ equiv.-l was obtained. This value agrees well with the values previously given by Sherry5 and by Townsend et al.' (0.59 and 0.40 kJ equiv.-' respectively), but not with those of Barrer et a1.' (-0.84 kJ equiv.-l), or Ames22 ( - 0.80 kJ equiv?).A complete understanding of these discrepancies is not completely clear; however, AmesZ2 did use a pelleted sample of zeolite X, and also an external692 Ion-exchange Equilibrium Properties of Zeolites 0.2 -I 0.2 0.4 - 0.6 0.8 1 0 Em Fig. 3. Cd/K-X exchange isotherm obtained at 298 K and at total normality 0.1 equiv. dm-s: 0, forward points; x , reverse points. 14 2 - 0 0.2 0.4 - 0.6 0.8 1 EM Fig. 4. Corrected selectivity quotient plots for the K/Na, Cd/Na and Cd/K binary exchanges: A, K/Na: M = K; 0, Cd/Na: M = Cd; I, Cd/K: M = Cd. solution concentration of 1 mol dm-3. The effects that any binder may have had on the equilibrium, and the possibility of salt imbibition at such a high solution c~ncentration,~~ must both be considered in this case.The very marked preference which zeolite X displays for cadmium over either sodium or potassium is seen clearly in fig. 2 and 3. The experimental selectivity for cadmium appears to be normally higher using the sodium form of X rather than the potassium form (cf. fig. 2 and 3), and the very high negative values of the calculated standard free energies of exchange reflect the very high preference for cadmium (values of AG* were -4.92 and -5.30 kJ equiv.-' for the Cd/Na and Cd/K exchanges, respectively).K. R. Franklin and R. P. Townsend 693 However, the overall affinities (reflected in the standard free energy values) show an affinity of K-X for cadmium which is marginally higher than that shown by Na-X, in apparent contradiction to the isotherm data.There is, however, no contradiction. Fig. 4 shows plots of the logarithm of the Gaines and Thomas21 corrected selectivity quotient KG, where and K, is the mass-action quotient for the exchange reaction: The function r is the correction for non-ideality in the aqueous solution phase: its evaluation is discussed in detail el~ewhere.~ The r correction is of similar magnitude for both the Cd/Na and Cd/K exchanges, so fig. 4 reflects well the selectivities of the Na-X and K-X samples for cadmium over all compositions of the exchanger. It is seen that although the preference of Na-X for cadmium is greater than that of K-X in the region E,, = 0.5-0.9, for values of E,, < 0.5 the converse is true.Owing to the very low values of ECd in this region (fig. 2 and 3) this cannot be seen from simple inspection of the is0 t herms. Previous equilibrium studies of the Cd/Na-X system have been r e p ~ r t e d , ~ - ~ * and recently, very detailed examinations have ruled out the possibility of significant degrees of over-exchange of cadmium occurring, either through precipitation of basic salts on the external surfaces of the zeolite crystallites8-'' or through the exchange of complexed species into the zeolite.' It seems therefore that one can view the apparent reversibilities of the Cd/Na-X and Cd/K-X systems (fig. 2 and 3) as genuine, and therefore these data may be used with confidence in conjunction with thermodynamic procedures in order to predict selectivities (see below).Gal and Radovanov' obtained a value of AG* = -4.2 kJ equiv.-' for the Cd/Na exchange in X, a value close to those found by Fletcher and Townsend for the same exchange reaction using different co-anions in solution (-4.26, -4.24 and -4.48 kJ equiv.-').' The value obtained here (- 4.92 kJ equiv.-l) is slightly higher: this undoubtedly reflects a lesser degree of extrapolation to low Ec, values in this present study compared to earlier ones [cf. fig. 2, 3 and 4 with data given in ref. (6) and (S)]. Finally, reversibility of exchange can be confirmed using the ' triangle rule ',18 which (providing the standard states are consistent8) has been applied successfully bef0re.l'~~~ For the three conjugate binary exchanges described here, the triangle rule states that On inserting the values obtained experimentally for AG*, eqn (7) becomes 0.48 + 4.92 - 5.30 = 0.10 kJ equiv.-l, a result in good agreement with theory, and one which confirms that the application of thermodynamic procedures to the binary exchange data is justified.The Na/K/Cd-X Ternary Isotherm 113 sets of analyses of equilibrium compositions of the crystal phase and of the corresponding solution phase were carried out in order to construct the Na/K/Cd-X ternary isotherm. The resulting data points are shown in fig. 5 (a) and (b) for the solution and zeolite phases, respectively. It is apparent that a comprehensive coverage of the possible range of solution and zeolite phase compositions was achieved. Fig. 6 shows the resulting ternary isotherm, with the data represented by a diagram on which the solution- phase composition coordinates have been distorted with respect to the crystal phase,'.l8 so that each solution datum point lies directly on top of the corresponding datum point for the zeolite phase. The distorted plot was in part constructed by eye since the694 Ion-exchange Equilibrium Properties of Zeolites K Cd Na K Cd Fig. 5. Experimental points obtained for the construction of the Na/K/Cd-X ternary isotherm, measured at 298 K and at a total solution normality of 0.1 equiv. dm-3: (a) solution phase; (b) zeolite phase. Correspondingly numbered points on the two diagrams provide examples of tie-lines between the two diagrams.K. R. Franklin and R. P . Townsend 695 Na K Cd Fig. 6. Ternary exchange isotherm for the Na/K/Cd-X system, with the data depicted using distorted 10% grid lines to represent the solution phase (see text).mathematical procedure previously described" for the construction of such diagrams was found to fail for systems such as this, where very high selectivities occur. The selectivity which zeolite X displays for each ion separately in the presence of the other two is seen more clearly by displaying individually the appropriate subsets of those grid lines which together comprise the ternary diagram in fig. 6. The three subsets are shown in fig. 7. Thus fig. 7 (a) shows the selectivity pattern for sodium; moving along the edge corresponding to the binary potassium/sodium exchange reaction, the sigmoidal isotherm plot of fig. 1 can be traced, and the spacing of the grid lines indicates a lack of any strong preference for either ion on the part of the zeolite.In contrast, as the cadmium content of the zeolite is increased, the grid lines giving the equilibrium concentrations of sodium in solution converge strongly, emphasising the strong preference which X shows for cadmium over sodium. Fairly similar behaviour is seen in fig. 7(b), while fig. 7 ( c ) emphasises further this high and general selectivity for cadmium. As explained elsewhere," l8 these selectivity trends can be quantified using pseudo- binary' separation factors of the form where the subscripts A and B refer to any two of the three ions involved in the ternary exchange. Logarithmic plots of &&, gdi: and :&, corresponding to the data given in fig.6 and 7, are given in fig. 8.696 lon- exchange Equilibrium Properties of ZeolitesK. R. Franklin and R. P . Townsend 697 0 I698 Ion-exchange Equilibrium Properties of Zeolites Table 2. Coefficients of best-fitting polynomials of binary exchange data [after eqn (9)] coefficients of for n = system ion A 0 1 2 3 4 5 K/Na-X K 1.273 0.092 -19.04 33.74 -18.01 - Cd/Na-X Cd 9.360 -20.34 55.49 154.6 229.5 -119.9 Cd/K-X Cd 12.64 -16.07 -5.586 12.27 -2.681 - Table 3. Binary exchange predictions for the Cd/Na-X system total E C d normality lequiv. dm-3 ECd (observed) (predicted) 0.400 0.170 0.769 0.764 0.400 0.456 0.874 0.861 0.400 0.669 0.933 0.902 0.025 2.4 x 0.059 0.086 0.025 0.087 0.832 0.874 0.025 0.235 0.904 0.91 1 Table 4.Binary exchange predictions for the Cd/K-X system total E C d normality /equiv. dm-3 ECd (observed) (predicted) 0.400 0.032 0.523 0.524 0.400 0.181 0.657 0.634 0.400 0.485 0.840 0.806 0.400 0.671 0.742 0.73 1 0.025 4.1 x 10-5 0.328 0.333 0.025 0.145 0.735 0.773 0.025 0.3 15 0.835 0.838 Prediction of Exchange Selectivities The theory and procedures employed in the prediction of both binary and ternary exchange equilibria have been described in detail previously2 for the Na/Ca/Mg-A system. An iteration method was employed for all predictions, and for reasons explained before,2 the preferred procedure was to predict crystal-phase compositions from a chosen initial solution composition. Considering the binary exchange systems first, the predictions were undertaken using as base data the experimental isotherms measured at a total normality of 0.1 equiv.dm-3 (fig. 1-3). The base data were expressed as a series of polynomials, which expressed the dependence of the logarithm of the corrected selectivity quotient KG on the crystal-phase composition : ln K, = a ~ A + ~ E ~ + ~ ~ A . . + vg. (9) For the K/Na-X and Cd/Na-X exchanges, a fourth-order fit was found to beK. R. Franklin and R. P. Townsend 699 Table 5. Coefficients of best-fitting polynomials of ternary exchange data [after eqn (1 l)] coefficients (ai) of PNa for i = ~~ dependent 0 1 2 3 4 5 variable Ink,,,, -22.68 235.2 - 1165 2694 - 2797 1072 In kK/Cd - 33.95 9.063 1.45 1 39.69 -31.95 - coefficients (83) ofEjcd for j = dependent variable 1 2 3 4 5 13.79 55.21 - 152.9 155.9 - -5.194 206.4 -289.3 119.3 52.38 - satisfactory, while for the Cd/Na-X system, a fifth-order polynomial was the preferred choice.The coefficients of the polynomials used are given in table 2. As before,2 predictions were then made at total solution concentrations of 0.025 and 0.4 equiv. dm-3. Examples of some of these predictions for the Cd/Na-X and Cd/K-X exchanges are given in tables 3 and 4, and it is seen that good agreement was obtained between predicted and experimental values in most cases. These results conform with previous experience on similars or different2* la binary systems. Considering next the ternary Na/K/Cd-X system, problems arose in making the starting point of each iteration the zeolite phase composition which is in equilibrium with the chosen solution composition on the experimental isotherm (fig.6). For many solution compositions, the very high selectivity for cadmium made it impossible to read off accurately the corresponding crystal-phase compositions from the isotherm, because of the problems involved in accurately fitting such isotherms with a polynomial that covered the whole composition range. The problem was overcome by using subsets of polynomials to fit the experimental isotherm data (fig. 6 and 7). Each subset fitted only a small part of the whole isotherm, but the set overall fitted the whole composition range. Each subset comprised polynomials of the form where i = Na, K or Cd, and tl(i)-tn(i) are appropriate polynomial coefficients. pseudo-binary corrected selectivity quotients2.Next, using these equations, surface polynomials expressing the dependence of on composition were constructed : n m InkclA = C u i e + C PI,!.?; i - 0 I- 1 where k,,, may be either of two pseudo-binary quotients kKiNa or kK/Cd defined, respectively, ad8 kK/Na = (EK ‘NalENa rK/Na (12) and kK/Cd = (g ‘CdlECd ‘K2) rK/Cd (13) where rK/Na and I‘K/Cd are corrections for non-ideality in the solution phase.2*9*18 The coefficients of the best-fitting polynomials are given in table 5 . As before2 the best fits were defined for N sets of data using a sum of residuals R: (kC/A(predicted) /kC/A(rneasured))l (N-P-Q-1)700 Ion-exchange Equilibrium Properties of Zeolites Na K Cd Fig. 9. Experimental and predicted zeolite phase compositions for the Na/K/Cd-X system at 0.4 equiv.dm-a: A, solution composition at 0.1 equiv. dmV3; 0, predicted zeolite composition at 0.4 equiv. dm+; 0, experimental zeolite composition at 0.4 equiv. dm-3; W, zeolite composition at 0.1 equiv. dm+. where P and Q are the orders of the polynomial with respect to EA and EB, respectively. Care has to be taken2 in making the criterion for best fit a minimum value of R as a function of P and Q; however, contrary to the Na/Ca/Mg-A system1* high orders were required for adequate predictions because of the high selectivity of X for cadmium (table 5 ) . Using the procedures described elsewhere2 ternary equilibrium compositions were predicted for total solution concentrations of 0.025 and 0.4 equiv. dmb3, respectively. Examples are shown in fig. 9 and 10.The starting point for each prediction was a set of equilibrium compositions for each phase as determined by experiment at a total solution normality of 0.1 equiv. dm-3. Then, for the chosen solution composition, values of rK/Na and r K / C d were calculated at this composition at either 0.4 (fig. 9) or 0.025 equiv. dm-3 (fig. lo). An iteration procedure (described elsewhere2) was then applied to predict the corresponding crystal-phase composition at the chosen final solution normality. Finally, the accuracy with which the crystal-phase compositions had been predicted was tested by determining experimentally the actual final zeolite composition. All these data points are shown on fig. 9 and 10 for every prediction test. In most cases, reasonably good agreement was obtained between theory and experiment.It is, however, noteworthy that predictions seem to contain within themselves an element of systematic error. Thus if one examines first the binary predictions (tables 3 and 4), it is clearly seen that predictions at 0.4equiv. dm-3 show generally lower &,values than those observed experimentally (fig. 9), whereas the converse trend is seen at a solution concentration of 0.025 equiv. dm-3. For the ternary systems, the extra degree of compositional freedom introduced into each phase leads toK. R. Franklin and R. P . Townsend 70 1 Na K Cd Fig. 10. Experimental and predicted zeolite phase compositions for the Na/K/Cd-X system at 0.025 equiv. dm-3: A, solution composition at 0.1 equiv. dm-3; 0, predicted zeolite composition at 0.025 equiv.dm-3; 0, experimental zeolite composition at 0.025 equiv. dm-3; m, zeolite composition at 0.1 equiv dm-3. a concomitant increase in experimental error which masks to some extent these trends; nevertheless they can still be discerned (fig. 9 and 10). A possible explanation for these trends may lie in the partial failure of a basic tenet on which these prediction procedures depend, viz. that the ratio of magnitudes of activity coefficients in the zeolite phase should not vary significantly with changes in concentration in the external solution phase.2.11 If the ratio should vary, this results in the value of the corrected selectivity coefficients changing with solution concentration for a given crystal-phase composition." Causes of such variations may be changes in the intracrystalline content and activity of guest molecules such as water ;ll another possibility which is pertinent to the system considered here is the known tendency of cadmium to associate with anionic species to form complexes which may be positive, neutral or even negatively ~harged.~ This tendency is not pronounced when (as here) nitrate is the co-anion, and for the solution phase, the effects of any such association are allowed for adequately in terms of the magnitudes of rKINa and I'KICd.Also, Cd(NO,)+ species are not expected to be included within the zeolite channels or cages to any significant degree due to Donnan exclusion ;' however, neutral Cd(NO,),, the quantity of which will be greater in more concentrated solutions, could be imbibed, and within the crystal these species would certainly affect the magnitudes of the corrected selectivity coefficients.Overall, deviations between prediction and theory are small in the Na/K/ Cd-X system, but exchanges where the corrected selectivity coefficients vary markedly with solution concentration have been found, and these are discussed in part 4 of this series.702 Ion-exchange Equilibrium Properties of Zeolites Finally, while considering the accuracy of these predictive methods, it is worth comparing the procedure employed here and also in part 2 of this series2 with that used earlier. Here, values of crystal-phase compositions have been predicted from an initial solution value. In an earlier study, also on the Na/Cd-X system, the opposing approach of predicting Ecd was used which is much more time-consuming2 in terms of computing time, because r has to be recalculated for each iteration step.A comparison of data in table 3 with earlier results8 shows that both procedures give similar deviations. Irrespective of which procedure is used, errors tend to increase as ECd tends to zero. This is of course a consequence of the very high selectivity which X displays for cadmium over the alkali-metal ion ; errors incurred in analysis are exacerbated when calculating the corrected selectivity coefficients. K. R. F. gratefully acknowledges an S.E.R.C. CASE award with Unilever Research. References 1 K. R. Franklin and R. P. Townsend, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 1071. 2 K. R. Franklin and R. P. Townsend, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 3127. 3 P. Fletcher and R. P. Townsend, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 965. 4 P. Fletcher and R. P. Townsend, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 2077. 5 H. S. Sherry, J. Phys. Chem., 1966, 70, 1158. 6 I. J. Gal and P. Radovanov, J. Chem. Soc., Faraday Trans. I , 1975, 71, 1671. 7 R. M. Barrer, L. V. C. Rees and M. Shamsuzzoha, J. Inorg. Nucl. Chem., 1966, 28, 629. 8 R. P. Townsend, P. Fletcher and M. Loizidou, Proc. 6th Int. ConJ Zeolites, Reno, Nevada, 1983 9 P. Fletcher and R. P. Townsend, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 1731. (Butterworths, London, 1984), p. 110. 10 M. Loizidou and R. P. Townsend, J. Chem. Soc., Dalton Trans., 1987, 191 1. 1 1 R. M. Barrer and J. Klinowski, J. Chem. Soc., Faradzy Trans. 1, 1974,70, 2080. 12 R. P. Townsend, K. R. Franklin and J. F. OConnor A h . Sci. Technol., 1984, 1, 269. 13 R. Hart and R. P. Townsend, paper in preparation. 14 R. M. Barrer and R. P. Townsend, J. Chem. Soc., Faraday Trans. 1, 1976, 72, 661. 15 A. Vogel, A Textbook of Quantitative Inorganic Analysis (Ldngmans, London, 1978), p. 324. 16 J. F. OConnor, Ph.D. Thesis (The City University, London, 1988). 17 P. Fletcher and R. P. Townsend, J. Chem. Soc., Faraday Trans. 1, 1981, 77, 497. 18 P. Fletcher, K. R. Franklin and R. P. Townsend, Philos. Trans. R. Soc. London, Ser. A, 312, 141 (see 19 C. J. Adams, K. R. Franklin, R. P. Townsend and S. J. Whelan, in New Developments in Zeolite 20 E. Glueckauf, Nature (London), 1949, 163, 414. 21 G. L. Gaines and H. C. Thomas, J. Chem. Phys., 1953, 21, 714. 22 L. L. Ames, Am. Mineral., 1964, 49, 127. 23 R. M. Barrer and A. J. Walker, Trans. Faraday Soc., 1964, 60, 171. 24 T. C. Golden and R. G. Jenkins, J. Chem. Eng. Data, 1981, 26, 366. especially pp. 150 and 160). Science and Technology, Proc. 7th Int. Con$ Zeolites, Tokyo, 1986. Paper 612 100 ; Received 29th October, I986