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

Abstract

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-(H 2 O) 24 +H(g) and the hydrogen atom affinities of MOH(H 2 O) 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 oneelectron reduction of nanodrops containing divalent ions that are not observed to undergo oneelectron reduction in aqueous solution.

Measuring the extent and width of internal energy deposition in ion activation using nanocalorimetry

“…Mn is the only divalent metal ion that dissociates by both pathways with 32 water molecules (Figure 1a), although both pathways are observed for all the transition-metal ions with 24 water molecules [27].…”

“…H atom loss upon EC can potentially occur via several different mechanisms [26,27]. Reduction of hydronium ion, formed transiently or facilitated by the incoming electron, would result in formation of H 3 O, which is nominally stable in isolation [34] and should readily dissociate via H atom loss under these conditions.…”

“…Using different nanocalorimetry based methods, three values for the absolute standard hydrogen electrode (SHE) potential that all agree within 5% of each other (ϩ4.05, ϩ4.11, and ϩ4.21 V) were obtained [22,25,27]. These values can also be used to establish the absolute solvation free-energy and enthalpy of the proton [25,27]. A single half-cell potential of a redox couple has not previously been measured directly in solution, and both the SHE potential and the solvation free-energy and enthalpy of the proton are conventionally assigned an arbitrary value of zero and other thermochemical values are reported relative to these standards.…”

“…Ions that dissociate via sequential fragmentation and that have known threshold dissociation energies and similar dissociation entropies have also been used [18 -20]. From the abundance of the product ions, information about both the average energy and the width of the energy deposition can be inferred.An alternative approach to measuring internal energy deposition uses nanometer-sized hydrated ions as "nanocalorimeters," to precisely measure the amount of energy that is deposited into these ions upon activation [21][22][23][24][25][26][27][28][29][30]. When these ions are activated, they sequentially lose water molecules.…”

“…This method has been used to measure the internal energy deposited with ECD of a diprotonated peptide [29], and has also been used to obtain absolute reduction energies of hydrated ions that can be related to solution-phase reduction potentials [22,25,27]. Using different nanocalorimetry based methods, three values for the absolute standard hydrogen electrode (SHE) potential that all agree within 5% of each other (ϩ4.05, ϩ4.11, and ϩ4.21 V) were obtained [22,25,27]. These values can also be used to establish the absolute solvation free-energy and enthalpy of the proton [25,27].…”