Question #44251

The standard reduction potential ($E^\circ_{\ce{M^{2+}/M}}$) of 3d transition metals is dictated by the Born-Haber cycle. While the radial probability distribution (RDF) of 3d orbitals contracts across the series (increasing $Z_{eff}$ and ionization energies), \ce{Ni} exhibits an anomalously less negative $E^\circ$ than expected from its high ionization energy, primarily due to its exceptional hydration thermodynamics driven by high Crystal Field Stabilization Energy (CFSE).

Consider the oxidation half-cell reaction relative to the Standard Hydrogen Electrode (SHE) at $300\text{ K}$: $\ce{Ni(s) + 2H+(aq) -> Ni^{2+}(aq) + H2(g)}$

Given the following thermodynamic data at $300\text{ K}$: $\bullet$ $E^\circ_{\ce{Ni^{2+}/Ni}} = -0.25\text{ V}$ $\bullet$ Enthalpy of sublimation of \ce{Ni(s)}, $\Delta_{sub}H^\circ = 430\text{ kJ/mol}$ $\bullet$ Sum of first and second ionization enthalpies of \ce{Ni}, $IE_1 + IE_2 = 2490\text{ kJ/mol}$ $\bullet$ Absolute enthalpy of oxidation for SHE ($\ce{H2(g) -> 2H+(aq) + 2e-}$), $\Delta H^\circ_{ox}(\text{SHE}) = 876.65\text{ kJ/mol}$ $\bullet$ Standard entropy change for the full cell reaction, $\Delta S^\circ_{rxn} = -28\text{ J K}^{-1}\text{ mol}^{-1}$ $\bullet$ Faraday's constant, $F = 96500\text{ C mol}^{-1}$

Calculate the standard hydration enthalpy ($\Delta_{hyd}H^\circ$) of \ce{Ni^{2+}(aq)}.