Ion Pair Association Constants and Solvent Composition

Abstract

THE variation of ion-pair association constants, K_A, with change in solvent is generally summarized as a plot of log K_A against the reciprocal of the solvent permittivity, ε, thereby testing the success of theoretical treatments of ion association¹. Generally, agreement between theory and experiment is qualitative rather than quantitative. For example², in a plot of this sort for lithium iodide in mixtures of dioxan and water, the curve has two essentially linear portions covering the range 44.47 ⩾ ε > 19.13 (that is, 10² Δε⁻¹ = 2.9787) and 12.03 ⩾ ε > 4.00 (that is, 10²Δε⁻¹=17.6874). Even in the event of the plot being a straight line, the molecular significance of the trends in association constant with bulk permittivity are not obvious. For this reason, other correlations must be sought. One such possibility is the relation between log K_A and the mean molecular weight of the solvent. For relations of this sort, comparison between the properties of solutes in various solvents is facilitated by converting derived parameters, for example, association constants expressed in molarities, K_A(C), to corresponding thermodynamic parameters using mole fraction concentration units², such as K_A(x) (assuming densities at 80, 87, 91 and 95 wt per cent dioxan in water are equal). Thus this removes the cratic contributions leaving the required unitary quantities³. In Fig. 1 comparison is made between plots of log K_A against both ε⁻¹ and the mean molecular weight, M̄, for lithium iodide in dioxan–water mixtures at 25° C. The correlation with solvent molecular weight is at least as good as that with permittivity and is perhaps preferable since the permittivity is also some function of solvent composition. Correlation between a derived quantity, for example K_A, with a continuum function begs the question of how the latter is related to solvent composition.