The standard free energy change () for the cell reaction is at . Given that , calculate the exact st — Electrochemistry Chemistry Question
Question
The standard free energy change ($\Delta rG^\circ$) for the cell reaction $2Fe(s) + O_2(g) + 4H^+(aq) \rightarrow 2Fe^{2+}(aq) + 2H_2O(l)$ is $-644.62\text{ kJ mol}^{-1}$ at $298\text{ K}$. Given that $F = 96500\text{ C mol}^{-1}$, calculate the exact standard cell potential ($E^\circ_{cell}$) for this reaction in Volts.
💡 Solution & Explanation
The reaction involves the oxidation of two Iron atoms ($Fe \rightarrow Fe^{2+} + 2e^-$), transferring $2 \times 2 = 4$ moles of electrons. Simultaneously, one $O_2$ molecule is reduced, gaining 4 electrons. Thus, $n = 4$. Using the fundamental relation $\Delta G^\circ = -nFE^\circ_{cell}$, we plug in the values: $-644.62 \times 10^3\text{ J mol}^{-1} = -4 \times 96500 \times E^\circ_{cell}$. Solving for $E^\circ_{cell}$ gives $\frac{644620}{386000} \approx 1.67\text{ V}$.