Question #44900

An electrochemical cell operates at $1000\text{ K}$ in an inert molten fluorocarbon solvent. The cathode compartment contains a mixture of solid $\ce{MF_4}$ and $\ce{MF_3}$, while the anode is a standard fluorine gas electrode ($\frac{1}{2} \ce{F2(g)} + e^- \rightarrow \ce{F^- (melt)}$, $E^\circ = 0.00\text{ V}$). \ \ Given the following standard thermodynamic data at $1000\text{ K}$:\ $\bullet$ $\Delta G^\circ_{\text{sublimation}}(M) = 500\text{ kJ/mol}$\ $\bullet$ $\sum_{i=1}^{3} IE_i(M) = 4000\text{ kJ/mol}$\ $\bullet$ $IE_4(M) = 4767\text{ kJ/mol}$\ $\bullet$ $\Delta G^\circ_{\text{dissociation}}(\ce{F2}) = 160\text{ kJ/mol}$\ $\bullet$ $\Delta G^\circ_{\text{electron affinity}}(\ce{F}) = -340\text{ kJ/mol}$\ $\bullet$ $\Delta G^\circ_{\text{lattice}}(\ce{MF_3}) = -5500\text{ kJ/mol}$\ $\bullet$ $\Delta G^\circ_{\text{lattice}}(\ce{MF_4}) = -10200\text{ kJ/mol}$\ $\bullet$ $\Delta G^\circ_{\text{solvation}}(\ce{F^-}, \text{melt}) = -400\text{ kJ/mol}$\ \ Calculate the standard reduction potential ($E^\circ$) for the half-cell reaction: \ $\ce{MF_4(s) + e^- -> MF_3(s) + F^- (melt)}$\ \ (Assume Faraday's constant $F = 96500\text{ C/mol}$)