A specialized concentration cell is constructed as . The measured EMF of this cell at is exactly . I — Electrochemistry Chemistry Question
Question
A specialized concentration cell is constructed as $M(s) \| M^{2+}(C_1) \|\| M^{2+}(C_2) \| M(s)$. The measured EMF of this cell at $298\text{ K}$ is exactly $0.059\text{ V}$. If the cathode compartment contains a standard $0.1\text{ M}$ aqueous solution of $M^{2+}$, what is the required molarity ($C_1$) of the $M^{2+}$ solution located in the anode compartment? (Take $\frac{2.303RT}{F} = 0.059\text{ V}$)
💡 Solution & Explanation
For a concentration cell built from identical electrodes, standard potential $E^\circ_{cell} = 0$. The Nernst equation reduces to $E_{cell} = -\frac{0.059}{n} \log \frac{[M^{2+}]_{anode}}{[M^{2+}]_{cathode}}$. Given $n = 2$, we have $0.059 = -\frac{0.059}{2} \log \frac{C_1}{0.1}$. Simplifying, $1 = -0.5 \log \frac{C_1}{0.1} \implies \log \frac{C_1}{0.1} = -2$. Taking the antilog yields $\frac{C_1}{0.1} = 10^{-2} = 0.01$. Thus, $C_1 = 0.1 \times 0.01 = 0.001\text{ M}$.