Question #45035

Consider the oxidation of a divalent metal complex \ce{[M(en)3]^{2+}} by \ce{Ce^{4+}} in an aqueous medium: $\ce{[M(en)3]^{2+}(aq) + Ce^{4+}(aq) <=> [M(en)3]^{3+}(aq) + Ce^{3+}(aq)}$ At $298 \text{ K}$, the standard cell potential for this reaction is $E^\circ = -0.050 \text{ V}$. The standard entropy change for the oxidation of the corresponding aqua complex: $\ce{[M(H2O)6]^{2+}(aq) + Ce^{4+}(aq) <=> [M(H2O)6]^{3+}(aq) + Ce^{3+}(aq)}$ is $\Delta S^\circ_1 = -23.5 \text{ J K}^{-1} \text{ mol}^{-1}$. The standard entropies of formation (ligand substitution) for the ethylenediamine (en) complexes from their aqua counterparts are: $\ce{[M(H2O)6]^{3+}(aq) + 3en(aq) <=> [M(en)3]^{3+}(aq) + 6H2O(l)} \quad \Delta S^\circ_2 = +180.0 \text{ J K}^{-1} \text{ mol}^{-1}$ $\ce{[M(H2O)6]^{2+}(aq) + 3en(aq) <=> [M(en)3]^{2+}(aq) + 6H2O(l)} \quad \Delta S^\circ_3 = +60.0 \text{ J K}^{-1} \text{ mol}^{-1}$ Assuming $\Delta H^\circ$ and $\Delta S^\circ$ are independent of temperature, at what temperature will the oxidation of \ce{[M(en)3]^{2+}} by \ce{Ce^{4+}} become thermodynamically spontaneous under standard conditions? (Given: $1 \text{ F} = 96500 \text{ C mol}^{-1}$)