Directly relating reduction energies of gaseous Eu(H2O)n(3+), 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.

Figure 1

Nanoelectrospray mass spectra of Eu(H₂O)_n³⁺ and EuOH(H₂O)_m²⁺ optimized for (a) larger and (b) smaller cluster sizes, and (c) electron capture mass spectrum of Eu(H₂O)₅₅³⁺ resulting in the loss of 16–19 water molecules from the reduced precursor as a result of electron capture dissociation (ECD) and blackbody infrared radiative dissociation (BIRD). Up to two water molecules are lost from Eu(H₂O)₅₅³⁺ and EuOH(H₂O)₃₃²⁺ as a result of BIRD. The theoretical isotope distribution of Eu(H₂O)₅₅³⁺ is inset (left) in (c). The peak at m/z = 381 contains a ~24% contribution from Eu(H₂O)₅₅³⁺ from and ~76% contribution EuOH(H₂O)₃₃²⁺. Asterisks mark peaks corresponding to H(H₂O)₂₁⁺ (m/z = 379), H(H₂O)₂₀⁺ (m/z = 361), Eu(OH)₂(H₂O)⁺ (m/z = 367), and instrumental noise (m/z = 411).

Figure 2

The average number of water molecules lost from reduced Eu(H₂O)_n³⁺ as a result of electron capture as a function of the precursor cluster size, n.

Figure 3

The average number of water molecules lost from Eu(H₂O)₁₁₀³⁺ as a result of electron capture as a function of the reaction delay time between the end of electron capture and start of ion excitation and detection. The solid line is a linear regression best-fit line to the data from 0.250 to 1.50 s, and the dashed line is a guide for the eye.

Figure 4

Modeled cluster effective temperatures (left axis, closed symbols) for Eu(H₂O)_n–x²⁺ and the calculated sequential energy removed by the xth water molecule (right axis, open symbols) for Eu(H₂O)_n³⁺, n = 55 (diamonds) and n = 140 (circles), activated by electron capture. The energy removed by each lost water molecule is obtained from the water molecule binding energy and the average energy partitioned into the translational and rotational modes of the products upon the loss of each water molecule. The dashed line indicates the temperature of the equilibrated ion cell and average temperature of the precursor ions prior to electron capture (133 K).

Figure 5

The negative of the measured Eu(H₂O)_n³⁺ cluster recombination enthalpies vs n^−1/3. The solid line is a linear regression best-fit line, and the dashed line is a best-fit line using a slope (18.76 eV) calculated using the Born solvation model. The y-axis intercept of the former line corresponds to the absolute solution-phase reduction enthalpy of the Eu^3+/2+ half-cell (−3.03 ± 0.06 eV). The precursor cluster sizes, n, for each measurement are indicated on the top horizontal axis.

Figure 6

Ensemble infrared photodissociation spectrum of Eu(H₂O)_n³⁺, n = 119–124, at 133 K. The photodissociation intensity is obtained from the average number of water molecules lost due to absorption of infrared radiation from a wavelength tunable OPO/OPA laser system corrected for absorption of blackbody infrared photons and laser power.

Scheme 1