Three Empirical Correlations Connecting Gaseous Cluster Energies and Solvation Energies of Alkali Metal and Halide Ions

Abstract

This paper gives two empirical correlations of formation Gibbs energies of gaseous clusters ΔG^f_n as function of number of solvent molecules attached to the ion, n, and one correlation connecting the ΔG^f_n for each individual cluster with the total ΔG^o_hydr value. The experimental ratios of ΔG^f₂/ΔG^f₁ and ΔG^f₃/ΔG^f₁ for both alkali metal and halide ions are on average equal to 0.75 and 0.5, respectively. ΔG^f_n values for n ≥ 4 are correlated with n as ΔG^f_n = [a/(n - 1)] ΔG^f₁ + b ΔG^f₁. For all available data on cluster energies and each individual cluster, the ΔG^f_n's are straight-line functions of ΔG^o_hydr. This well corresponds to another empirical rule stating that the Gibbs energies of transfer of ions between two solvents are often as well straight-line functions of ΔG^o_hydr [J. Rais and T. Okada, J. Phys. Chem. A, 2000, 104, 7314]. Tentative models of the found behavior are proposed. A full data set of the gaseous cluster energies of formation based on inclusion of new, usually not used entries from the literature is provided.