Question #44771

A novel Direct Methanol Fuel Cell (DMFC) operates at 298 K using a cathodic half-cell where \ce{MnO4^{-}(aq)} is reduced. Due to the specific electrocatalyst and a buffered local cathode pH of 4.0, the reduction strictly yields \ce{MnO2(s)} as the only manganese product. The anode oxidizes \ce{CH3OH(aq)} to \ce{CO2(g)}.

Given standard reduction potentials at 298 K: $E^\circ(\ce{MnO4^{-}}/\ce{Mn^{2+}}) = 1.51 \text{ V}$ $E^\circ(\ce{MnO2}/\ce{Mn^{2+}}) = 1.21 \text{ V}$ $E^\circ(\ce{CO2}/\ce{CH3OH}) = 0.01 \text{ V}$

The cell operates with $[\ce{MnO4^{-}}] = 0.1 \text{ M}$, $[\ce{CH3OH}] = 0.1 \text{ M}$, and $P_{\ce{CO2}} = 1 \text{ bar}$. The overall enthalpy change ($\Delta H$) for the balanced cell reaction (per mole of \ce{CH3OH} consumed) is $-1150.76 \text{ kJ/mol}$.

Assuming $\frac{2.303 RT}{F} = 0.06 \text{ V}$ and Faraday's constant $F = 96500 \text{ C/mol}$, what is the operating thermodynamic efficiency ($\eta = \frac{\Delta G}{\Delta H}$) of this fuel cell?