Consider the plot of the reduction potential (y-axis) versus (x-axis) for the half-cell reaction at — Electrochemistry Chemistry Question
Question
Consider the plot of the reduction potential $E_{red}$ (y-axis) versus $\log_{10}[Cu^{2+}]$ (x-axis) for the half-cell reaction $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$ at $298\text{ K}$. The generated graph is a straight line. What is the expected mathematical slope of this line? (Use $\frac{2.303RT}{F} = 0.0591\text{ V}$)
💡 Solution & Explanation
According to the Nernst equation for the reduction half-reaction: $E_{red} = E^\circ - \frac{0.0591}{n} \log \frac{1}{[Cu^{2+}]}$. Rearranging gives $E_{red} = E^\circ + \frac{0.0591}{2} \log[Cu^{2+}]$. Comparing this to the equation of a straight line $y = mx + c$, the slope $m$ is $+0.0591 / 2 = 0.0295\text{ V}$.