Question #44219

For a transition metal $M$ which forms a $3d^8$ $M^{2+}$ ion, the following thermodynamic parameters are given at $300 \text{ K}$:

$\bullet$ Enthalpy of atomization, $\Delta H_{at} = 430 \text{ kJ mol}^{-1}$ $\bullet$ Sum of first and second ionization enthalpies, $IE_1 + IE_2 = 2490 \text{ kJ mol}^{-1}$ $\bullet$ Isotropic (spherical) hydration enthalpy of $M^{2+}(g)$, $\Delta H_{hyd, iso} = -1980 \text{ kJ mol}^{-1}$ $\bullet$ Crystal field splitting energy ($\Delta_o$) for the octahedral aquo complex $[M(H_2O)_6]^{2+}$ is $100 \text{ kJ mol}^{-1}$ $\bullet$ Standard entropy change for the half-reaction $M(s) \rightarrow M^{2+}(aq) + 2e^-$, $\Delta S^\circ = +100 \text{ J K}^{-1} \text{ mol}^{-1}$ $\bullet$ Absolute standard Gibbs free energy of oxidation for $H_2(g) \rightarrow 2H^+(aq) + 2e^-$ is $+838.25 \text{ kJ mol}^{-1}$

Calculate the standard reduction potential $E^\circ_{M^{2+}/M}$ at $300 \text{ K}$. (Given: $F = 96500 \text{ C mol}^{-1}$)