Directly Relating Reduction Energies of Gaseous Eu(H2O)n3+, n = 55−140, to Aqueous Solution: The Absolute SHE Potential and Real Proton Solvation Energy

In solution, half-cell potentials are measured relative to other half-cells resulting in a ladder of thermodynamic values that is anchored to the standard hydrogen electrode (SHE), which is assigned an arbitrary value of exactly 0 V. A new method for measuring the absolute SHE potential is introduced in which reduction energies of Eu(H(2)O)(n)(3+), from n = 55 to 140, are extrapolated as a function of the geometric dependence of the cluster reduction energy to infinite size. These measurements make it possible to directly relate absolute reduction energies of these gaseous nanodrops containing Eu(3+) to the absolute reduction enthalpy of this ion in bulk solution. From this value, an absolute SHE potential of +4.11 V and a real proton solvation energy of -269.0 kcal/mol are obtained. The infrared photodissociation spectrum of Eu(H(2)O)(119-124)(3+) indicates that the structure of the surface of the nanodrops is similar to that at the bulk air-water interface and that the hydrogen bonding of interior water molecules is similar to that in aqueous solution. These results suggest that the environment of Eu(3+) in these nanodrops and the surface potential of the nandrops are comparable to those of the condensed phase. This method for obtaining absolute potentials of redox couples has the advantage that no explicit solvation model is required, which eliminates uncertainties associated with these models, making this method potentially more accurate than previous methods.