Directly Relating Gas-Phase Cluster Measurements to Solution-Phase Hydrolysis, the Absolute Standard Hydrogen Electrode Potential, and the Absolute Proton Solvation Energy

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Abstract

Hydrated ion nanocalorimetry is used to measure reduction energies and H atom affinities of gaseous hydrated ions by determining the energy deposited into these nanodrops from the number of water molecules lost upon reduction by thermally generated electrons (see figure).

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Solution-phase, half-cell potentials are measured relative to other half-cell potentials, resulting in a thermochemical ladder that is anchored to the standard hydrogen electrode (SHE), which is assigned an arbitrary value of 0 V. A new method for measuring the absolute SHE potential is demonstrated in which gaseous nanodrops containing divalent alkaline-earth or transition-metal ions are reduced by thermally generated electrons. Energies for the reactions 1) M(H2O)242+(g)+e(g)→M(H2O)24+(g) and 2) M(H2O)242+(g)+e(g)→MOH(H2O)23+(g)+H(g) and the hydrogen atom affinities of MOH(H2O)23+(g) are obtained from the number of water molecules lost through each pathway. From these measurements on clusters containing nine different metal ions and known thermochemical values that include solution hydrolysis energies, an average absolute SHE potential of +4.29 V vs. e(g) (standard deviation of 0.02 V) and a real proton solvation free energy of −265 kcal mol−1 are obtained. With this method, the absolute SHE potential can be obtained from a one-electron reduction of nanodrops containing divalent ions that are not observed to undergo one-electron reduction in aqueous solution.

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