Electro Chemistry Part 3

Concept:This is a concentration cell where both electrodes are made of the same metal $M$, but the electrolyte concentrations ($c_1$ and $c_2$) are different. The cell potential depends on the concentration gradient.Explanation:The cell reaction involves transfer of $M^+$ from higher concentration to lower concentration.At the anode, oxidation occurs: $M \rightarrow M^+ + e^-$.At the cathode, reduction occurs: $M^+ + e^- \rightarrow M$.For a positive cell potential ($E_{\text{cell}} > 0$), the spontaneous direction is from higher to lower concentration.If $c_1$ is at the anode, the reaction is $M^+(c_2) \rightarrow M^+(c_1)$.Using the Nernst equation: $$E_{\text{cell}} = -0.059 \log \frac{c_1}{c_2}$$For $E_{\text{cell}} > 0$, $\frac{c_1}{c_2} < 1 \Rightarrow c_1 < c_2$.If $c_1$ is at the cathode, the reaction is $M^+(c_1) \rightarrow M^+(c_2)$.Then: $$E_{\text{cell}} = -0.059 \log \frac{c_2}{c_1} > 0$$This requires $\frac{c_2}{c_1} < 1 \Rightarrow c_2 < c_1$, i.e., $c_1 > c_2$.Thus, a positive cell potential is obtained when $c_1$ is at the cathode and $c_1 > c_2$.Answer:Option B: If $c_1$ is present at cathode, then $c_1 > c_2$.