Abstract
A statistical thermodynamic treatment has been successfully applied to several uni-univalent and uni-bivalent anion exchange reactions, with, in the latter case, an empirical correction factor to allow for the effects of non-uniformity of cross-linking in the exchanger. From the plots of ln K[c] against the equivalent fraction exchanged values of o, the interaction energy associated with placing two B[z-] ions on adjacent sites, and K[T], the thermodynamic equilibrium constant and hence the standard free energy of exchange, DeltaG°, have been calculated. The standard enthalpies of exchange have been obtained both by an accurate calorimetric method and by application of the van't Hoff isochore. The good agreement shown between these two methods provides additional support for the theoretical approach. For some uni-univalent reactions, where data was available, linear correlations have been obtained between DeltaG°, the standard free energy of exchange, and S[ho], the partial molar entropy of hydration and, to a lesser extent, DeltaG°, the free energy of hydration of the ions. The selectivities for several univalent organic acid anions have been explained on the basis of interactions between the carbon chains and the external and exchanger aqueous phases and for some bivalent organic acid anions partly on the basis of the differences in charge separation. The interaction energy, o, is independent of temperature, but is dependent on external electrolyte concentration. It is also related to the water content of the exchanger and, more particularly, to the ratio of the water content divided by the crystal radius of the ion concerned. A method for predicting values of o and DeltaG° has been introduced and found to be useful in assessing the accuracy of the results obtained. The effect of changes in cross-linking on the foregoing phenomena has also been studied.