In a standard fuel cell operating at , the standard Gibbs free energy of formation for is . Calculat — Electrochemistry Chemistry Question
Question
In a standard $H_2-O_2$ fuel cell operating at $298\text{ K}$, the standard Gibbs free energy of formation for $H_2O(l)$ is $-237.2\text{ kJ mol}^{-1}$. Calculate the theoretical standard electromotive force ($E^\circ_{cell}$) of this fuel cell in Volts. (Use $1\text{ F} = 96500\text{ C mol}^{-1}$)
💡 Solution & Explanation
The overall reaction in the $H_2-O_2$ fuel cell is $H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)$. For this reaction, $2$ moles of electrons are transferred per mole of water formed ($n=2$). The standard Gibbs free energy change $\Delta G^\circ = -237.2\text{ kJ mol}^{-1} = -237200\text{ J mol}^{-1}$. Using the relation $\Delta G^\circ = -nFE^\circ_{cell}$, we have $-237200 = -2 \times 96500 \times E^\circ_{cell}$. Solving for $E^\circ_{cell}$ yields $237200 / 193000 \approx 1.229\text{ V}$, which rounds to $1.23\text{ V}$.