Solubility parameters and the distribution of ions to nonaqueous solvents

Provided a singly charged, spherically symmetrical ion has a radius greater than ca. 0.2 nm, its distribution to a nonaqueous solvent from water can be accounted for by assigning to it a Hildebrand solubility parameter estimated for an uncharged atom or molecule, regardless of the model assumed for the Gibbs energy of charging the ion - that of Born, Abraham, and Liszi (J. Chem. Soc., Faraday Trans. 1 1978, 74, 1604, 2858) or Abe (J. Phys. Chem. 1986, 90, 713) - in the nonaqueous phase. For smaller ions, however, no choice of solubility parameter or ion size can alone account for their extractability. The extensive data available for the Gibbs energy of transfer of monovalent ions from water to a variety of solvents can be accounted for by assigning to the ion, in addition to a plausible solubility parameter, an effective radius r_s = (r³_i + Δr³_s)^1/3, wherein r_i is the radius of the ion and Δr_s is an adjustable distance characteristic of the solvent. Separate sets of Δr_s values are needed for cations and anions. While the alternative models for charging the ion all give acceptable fits to the data, the shell model of Abraham and Liszi was selected as the most appropriate. The distance Δr_s can be predicted for cations from the molar volume of the solvent and its hydrogen-bond acceptance index β. For anions, Δr_s can be predicted from the molar volume and the hydrogen-bond donation index α. On the basis of these correlations, expressions are derived for predicting the extractability of a singly charged, approximately spherical ion and its activity coefficient in the nonaqueous phase.