The Thermodynamics of Ion Association in Solution. I. An Extension of the Denison-Ramsey Equations

The Dension-Ramsey treatment of ion-pair formation has been extended, taking into account in the potential energy term the various possible interactions between ions and their induced dipoles. In addition, orientation entropy effects have been included. Internuclear distances calculated in this way from published ion-pair constants are smaller than those calculated by the Denison-Ramsey or the Bjerrum equation and were only slightly larger (∼15%) than the crystallographic radii. Further extension to include higher ionic aggregates was made and the result applied to ion triplet and quadrupole formation. In these ion aggregates the calculated internuclear distances between ions are nearly the same as in ion pairs, in contradistinction to results obtained using earlier treatments. In solvents of dielectric constant less than 7 (benzene, dioxane, anisole, chlorobenzene, and tetrahydrofuran) quaternary ammonium salts do not appear to form solvent-separated ionic aggregates.