Question #44773

A \ce{H2-O2} fuel cell operates using an aqueous \ce{KOH} electrolyte. Due to continuous operation and solvent evaporation, the boiling point of the electrolyte solution is elevated by $0.0104 \text{ K}$. Assume the density of the dilute solution is $1.0 \text{ kg L}^{-1}$ (molarity $\approx$ molality). The standard reversible potential of the cell is $E^\circ = 1.23 \text{ V}$. The cell operates at a constant current of $I = 46 \text{ mA}$ and has a cell constant $G^* = 0.01 \text{ cm}^{-1}$. The molar conductivity of the \ce{KOH} solution follows the Debye-Hückel-Onsager equation: $\Lambda_m = \Lambda_m^\circ - B\sqrt{C}$. Given: $K_b(\ce{H2O}) = 0.52 \text{ K kg mol}^{-1}$, $\Lambda_m^\circ = 250 \text{ S cm}^2 \text{ mol}^{-1}$, $B = 500 \text{ S cm}^2 \text{ mol}^{-3/2} \text{ L}^{1/2}$. Assuming activation and concentration overpotentials are negligible, what is the operational voltage ($V_{cell}$) of the fuel cell at this state?