Thermochemically Consistent Free Energies of Hydration for Di- and Trivalent Metal Ions

This paper uses the relationship between the standard half reduction potential, the third ionization potential, and the free energies of hydration (ΔG_hyd) of M²⁺ and M³⁺ ions to calculate new values of ΔG_hyd for M²⁺ and M³⁺ ions. The numbers are “thermochemically consistent”, i.e. all numbers agree with the applied thermochemical cycle. This enables the tabulation of many ΔG_hyd derived mainly from the data compiled by Marcus, but consistent with ΔG_hyd(H⁺) = 1100 kJ/mol and SHE = 4.44 V. The accuracy of the new values of ΔG_hyd(M³⁺) is by definition similar to the accuracy of the experimental hydration energy of the ΔG_hyd(M²⁺) used for calculation, and vice versa, i.e. the new data have the same accuracy or higher than previously reported. As a result, the literature values for Cr³⁺ and Au³⁺, and Pd²⁺ are substantially revised. The approach also allows the calculation of new ΔGhyd for metal ions such as Mn³⁺, Ti²⁺, Ag³⁺, Ni³⁺, Cu³⁺, Au²⁺, and the theoretically interesting but experimentally inaccessible +2 ions of lanthanides. The new numbers enable a discussion of the previously unreported trend in ΔG_hyd(M³⁺) for the 3d metal ions, which relates to the ligand field stabilization energies and effective nuclear charge as for the M²⁺ ions. The new tabulated values should be accurate with the applied assumptions to within 10 kJ/mol and may be of value for other thermochemical calculations, for interpretation of the aqueous trend chemistry of the metal ions, and as benchmarks for theoretical chemistry.