An electrolyte concentration cell is constructed using two identical solid cobalt electrodes: . What — Electrochemistry Chemistry Question
Question
An electrolyte concentration cell is constructed using two identical solid cobalt electrodes: $Co(s) \| Co^{2+}(0.001\text{ M}) \|\| Co^{2+}(0.1\text{ M}) \| Co(s)$. What is the cell potential ($E_{cell}$) at temperature $T$ expressed algebraically in terms of $R$, $T$, and $F$?
💡 Solution & Explanation
For an electrolyte concentration cell composed of identical electrodes, the standard potential $E^\circ_{cell} = 0$. The overall cell reaction involves oxidation in the dilute half-cell and reduction in the concentrated half-cell. The Nernst equation is $E_{cell} = 0 - \frac{RT}{nF} \ln \frac{[Co^{2+}]_{anode}}{[Co^{2+}]_{cathode}}$. For Cobalt, $n = 2$. $E_{cell} = -\frac{RT}{2F} \ln \frac{0.001}{0.1} = -\frac{RT}{2F} \ln(10^{-2}) = -\frac{RT}{2F} (-2 \ln 10) = +\frac{RT}{F} \ln 10$. Equivalently, this can be mathematically manipulated to $-\frac{RT}{F} \ln(0.1)$, as $\ln(10) = -\ln(0.1)$.