Based on Latimer principles, if the standard reduction potential for is and the standard reduction p — Electrochemistry Chemistry Question
Question
Based on Latimer principles, if the standard reduction potential for $Cu^{2+} + e^- \rightarrow Cu^+$ is $+0.15\text{ V}$ and the standard reduction potential for $Cu^+ + e^- \rightarrow Cu$ is $+0.50\text{ V}$, calculate the standard reduction potential (in Volts) for the direct $2$ -electron reduction $Cu^{2+} + 2e^- \rightarrow Cu$.
💡 Solution & Explanation
Standard electrode potentials ($E^\circ$) are intensive properties and cannot be added directly. Instead, the standard Gibbs free energy changes ($\Delta G^\circ$) must be used. $\Delta G^\circ_1 = -1F(0.15)$ and $\Delta G^\circ_2 = -1F(0.50)$. For the overall $2e^-$ reduction, $\Delta G^\circ_3 = \Delta G^\circ_1 + \Delta G^\circ_2 = -0.15F - 0.50F = -0.65F$. Setting $\Delta G^\circ_3 = -nFE^\circ_3 = -2FE^\circ_3$, we find $-2FE^\circ_3 = -0.65F$, resulting in $E^\circ_3 = 0.65 / 2 = 0.325\text{ V}$.