Question

Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming $M^+$ ($M \to M^+ + e^-$). The cation $M^+$ is present in two different concentrations $c_1$ and $c_2$ as shown above. Which of the following statement is correct for generating a positive cell potential?

• A. If $c_1$ is present at anode, then $c_1>c_2$.
• B. If $c_1$ is present at cathode, then $c_1>c_2$.
• C. If $c_1$ is present at anode, then $c_1 = c_2$.
• D. If $c_1$ is present at cathode, then $c_1<c_2$.

Hint:

For a concentration cell to produce positive potential, the concentration at the cathode must be higher than the concentration at the anode.

Answer 1

The Correct Option is D

The given cell is a concentration cell of the type: \[ M \,|\, M^+(c_1) \,||\, M^+(c_2) \,|\, M \] For a concentration cell, the electrode with lower ion concentration acts as the cathode, while the electrode with higher ion concentration acts as the anode. The cell potential is given by: \[ E_{\text{cell}} = \frac{RT}{F} \ln \left( \frac{[M^+]_{\text{anode}}} {[M^+]_{\text{cathode}}} \right) \] For $E_{\text{cell}}>0$: \[ [M^+]_{\text{anode}}>[M^+]_{\text{cathode}} \] Therefore, if $c_1$ is present at the cathode, it must be less than $c_2$. \[ c_1<c_2 \] \[ \therefore \text{The correct condition is option (D).} \]