Directly Relating Reduction Energies of Gaseous Eu(H₂O)_n³⁺, n = 55−140, to Aqueous Solution: The Absolute SHE Potential and Real Proton Solvation Energy

Abstract

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.

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

“…Broad distributions of M 2ϩ (H 2 O) n and M 3ϩ (H 2 O) n can be formed via nanoelectrospray ionization and trapped in the ion cell where they are thermalized to the temperature of the copper jacket surrounding the ion cell (133 K) [25,31]. Individual clusters are isolated using SWIFT waveforms and are irradiated with thermally generated electrons for electron capture (EC) experiments.…”

“…Under the conditions of these experiments (Ͻ10 Ϫ8 Torr), collisional and radiative cooling should be minimal [21][22][23]. Clusters with fewer than 55 water molecules dissociate faster than the timescale of the experiment so kinetic shift effects are negligible [25]. Because experimentally measured sequential water molecule binding energies have not been obtained for the clusters formed in these experiments, E 0 values are obtained from a discrete implementation of the Thomson liquid drop model (TLDM) [38].…”

“…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].…”