Mechanism of ion exchange in zirconium phosphates. 31. Thermodynamics of alkali metal ion exchange on amorphous zirconium phosphate

Abstract

greatly different from the dimerization constant. Both models, therefore, yield essentially the same result. However, the two-constant attenuated model definitely does not fit the A 0 data.In general, it can be said that the isodesmic model describes the A 0 data excellently, whereas it describes the associative behavior of T H and MB only fairly well. The two-constant models fit the data of these two dyes somewhat better than the isodesmic model, yielding association constants of different magnitude than the latter model. The data are not accurate enough or available over a wide enough range of concentration to distinguish between the models for MB and TH. The clear-cut interpretation of the A 0 data is probably the result of its greater solubility, making possible the acquisition of data over a much greater concentration range than that of the other dyes.The question of whether nonideality effects have been properly accounted for should be considered. The nonideality of a charged molecule may be thought as being made up of two parts: that due to charge and that due to excluded volume. The former type of nonideality is accounted for in the denominator of eq 1-111. The use of TEA, in causing this term to approach 1, makes the molecule more ideal by reducing the charge nonideality. The excluded volume contribution to nonideality is small for these molecules because of the limited size of the stacks (the largest weight average degree of polymerization found was -13). In turn, the effect of the virial coefficient on the observed molecular weight must also be small, especially at the low dye concentrations here employed. Finally, it should be pointed out that the equilibrium constants obtained must be the thermodynamic equilibrium constants. In 1968 Braswellg showed that for such systems, even if the activity coefficient for each species differs from one, if the Debye-Huckel limiting law is valid, then yz = yI2 and y3 = yI3, etc., so that the ratios of the activity coefficients that appear in the equilibrium equation are always equal to unity.The observed values of the association constants may be compared with those found by previous investigators. First, however, it must be realized that the intrinsic association constants (site basis) used here are one-fourth the value of the usual dimerization constant because of the four ways that two monomers can combine. Therefore, the values reported in Table I1 must be increased by a factor of 4 in order to be comparable with those found by other authors. Our values for A 0 (36 X lo3 and 9.6 X lo3 at 5 and 30 "C, respectively) are lower than those of Zanker?' which were 60 X lo3 at 6 "C and 15 X lo3 at 36 "C. The value we found for MB at 30 "C in TEA (3.2 X lo3 for isodesmic or 6.7 X lo3 or 5.0 X lo3 for the two-constant models) differs considerably from that found by us in H209(2.0 X lo3 a t 30 "C) or dilute NaCP5 (2.4 X lo3 a t 30 "C).However, when one looks at the wide range of values reported (see Tables I and I1 in ref 36) by various investigators and realizes the varie...

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