The measured electromotive force (EMF) of the standard cell at is . Using the Nernst equation, compu — Electrochemistry Chemistry Question
Question
The measured electromotive force (EMF) of the standard cell $Zn(s) \| Zn^{2+}(0.01\text{ M}) \|\| Fe^{2+}(0.001\text{ M}) \| Fe(s)$ at $298\text{ K}$ is $0.2905\text{ V}$. Using the Nernst equation, compute the theoretical standard cell potential ($E^\circ_{cell}$) in Volts. (Use $\frac{2.303RT}{F} = 0.0591\text{ V}$)
💡 Solution & Explanation
The overall cell reaction involves the $2e^-$ oxidation of $Zn$ and the $2e^-$ reduction of $Fe^{2+}$, meaning $n = 2$. The Nernst equation states $E = E^\circ - \frac{0.0591}{n} \log \frac{[Zn^{2+}]}{[Fe^{2+}]}$. Substituting the known values: $0.2905 = E^\circ_{cell} - \frac{0.0591}{2} \log \frac{0.01}{0.001} \implies 0.2905 = E^\circ_{cell} - 0.02955 \log 10 \implies 0.2905 = E^\circ_{cell} - 0.02955$. Rearranging to solve for standard potential gives $E^\circ_{cell} = 0.2905 + 0.02955 \approx 0.32\text{ V}$.