Question #45020

A hydrogen-oxygen fuel cell operates at $300 \text{ K}$ with non-standard partial pressures: $P_{\ce{H2}} = 10 \text{ bar}$ and $P_{\ce{O2}} = 100 \text{ bar}$. The standard enthalpy of formation of liquid water is $\Delta H^\circ_f(\ce{H2O}, l) = -300 \text{ kJ mol}^{-1}$. The absolute molar entropies at $300 \text{ K}$ are $S^\circ(\ce{H2}, g) = 150 \text{ J K}^{-1}\text{mol}^{-1}$, $S^\circ(\ce{O2}, g) = 300 \text{ J K}^{-1}\text{mol}^{-1}$, and $S^\circ(\ce{H2O}, l) = 60 \text{ J K}^{-1}\text{mol}^{-1}$.

Assume Faraday's constant $F = 100,000 \text{ C mol}^{-1}$ and the Nernst factor $\frac{2.303 RT}{F} = 0.06 \text{ V}$ at $300 \text{ K}$.

Determine the operating cell potential ($E_{\text{cell}}$) and the thermodynamic efficiency ($\eta = \frac{\Delta G_{\text{operating}}}{\Delta H^\circ} \times 100$) of the fuel cell under these conditions.