Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming $$M^{+}(M\rightarrow M^{+}+e^{-})$$. 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?

The given cell is a metal/metal-ion concentration cell: the same metal $$M(s)$$ is present at both electrodes, but the molar concentration of the cation $$M^{+}$$ differs.

Overall cell reaction (at 298 K):
Anode (oxidation)   $$M(s) \rightarrow M^{+}(c_{\text{anode}})+e^{-}$$
Cathode (reduction) $$M^{+}(c_{\text{cathode}})+e^{-}\rightarrow M(s)$$

Using the Nernst equation for a concentration cell with $$n=1$$ transferred electron, the cell potential is

$$E_{\text{cell}} = \frac{0.0591}{1}\,\log\left(\frac{c_{\text{cathode}}}{c_{\text{anode}}}\right)$$

For the cell potential to be positive we must have

$$\log\left(\frac{c_{\text{cathode}}}{c_{\text{anode}}}\right) \gt 0 \quad\Longrightarrow\quad c_{\text{cathode}} \gt c_{\text{anode}}$$

Now compare the four statements provided:

Case 1: Option A — “If $$c_1$$ is present at anode, then $$c_1=c_2$$.”
If the two concentrations are equal, $$c_{\text{cathode}}=c_{\text{anode}}$$, so $$E_{\text{cell}}=0$$, not positive. Hence wrong.

Case 2: Option B — “If $$c_1$$ is present at cathode, then $$c_1 \gt c_2$$.”
Here $$c_{\text{cathode}}=c_1$$ and $$c_{\text{anode}}=c_2$$. The requirement for a positive potential is exactly $$c_1 \gt c_2$$, so this statement is correct.

Case 3: Option C — “If $$c_1$$ is present at cathode, then $$c_1 \lt c_2$$.”
This yields $$c_{\text{cathode}} \lt c_{\text{anode}}$$, giving a negative $$E_{\text{cell}}$$, so it is incorrect.

Case 4: Option D — “If $$c_1$$ is present at anode, then $$c_1 \gt c_2$$.”
That would imply $$c_{\text{anode}} \gt c_{\text{cathode}}$$, again producing a negative cell potential; therefore wrong.

Hence, the only correct statement that guarantees a positive cell potential is:

Option B which is: If $$c_1$$ is present at cathode, then $$c_1 \gt c_2$$.