Prediction and Interpretation of Selectivity

The prediction of selectivity for a given ion over another even in qualitative terms, let alone quantitatively, ultimately requires an understanding of the ion exchange phenomenon in terms of the fundamental properties of the system components. No single characteristic can account for observed results, and studies to date amply demonstrate that many system properties affect selectivity behaviour in ways that have assisted our understanding of the mechanism involved. 

One of the earliest, and reasonably successful, approaches to quantitatively predicting selectivity behaviour was through the thermodynamic treatment of ion exchange systems as a Gibbs-Donnan membrane equilibrium. Such a description is given by equation 5.29 which for the sake of simplicity is shown in terms of single ion activity coefficients  

A rigorous thermodynamic expression would be required to consider terms for the equilibrium transport of water (solvent) and nonexchange electrolyte but these contributions are often ignored for exchange at low total external ionic strength. 

All subsequent models for selectivity behaviour are, in some way or other, disguised in equation 5.29 the reason for this being that deviations from theoretical ideal behaviour as expressed through the values of resin phase activity coefficients, or by the interaction energetics required by a mechanistic model, are equivalent statements. In other words, the fundamental causal factors which determine selectivity plus any inadequacies in our understanding are all reflected in the adopted model whether thermodynamic or molecular. 

If the conventional standard and reference states for dilute electrolyte solutions are adopted the pressure-volume term is usually neglected for simple non-hydrated ions, and further assuming the activity coefficient ratio in the external solution to equal unity, equation 5.29 becomes  

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