The standard reduction potential for $Fe^{2+}$|Fe and $Sn^{2+}$|Sn electrodes are -0.44 V and -0.14 V respectively for the cell reaction. $Fe^{2+}+Sn\rightarrow Fe+Sn^{2+}$ the standard emf is:

Question

Accepted Answer

To determine the standard electromotive force (emf) for the given cell reaction, we need to calculate the difference in standard reduction potentials between the two half-reactions involved in the cell.

The cell reaction given is:
$$ \text{Fe}^{2+} + \text{Sn} \rightarrow \text{Fe} + \text{Sn}^{2+} $$

The standard reduction potentials are provided as:
- $ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} $ with $ E^\circ = -0.44 \, \text{V} $
- $ \text{Sn}^{2+} + 2e^- \rightarrow \text{Sn} $ with $ E^\circ = -0.14 \, \text{V} $

For the cell reaction, we need to consider the oxidation and reduction processes:
- The oxidation half-reaction is: $ \text{Sn} \rightarrow \text{Sn}^{2+} + 2e^- $
- The reduction half-reaction is: $ \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} $

The standard emf ($ E^\circ_{\text{cell}} $) of the cell is calculated using the formula:
$$ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} $$

Substituting the given values:
$$ E^\circ_{\text{cell}} = (-0.44 \, \text{V}) - (-0.14 \, \text{V}) $$
$$ E^\circ_{\text{cell}} = -0.44 \, \text{V} + 0.14 \, \text{V} $$
$$ E^\circ_{\text{cell}} = -0.30 \, \text{V} $$

Thus, the standard emf for the cell reaction is $-0.30 \, \text{V}$, which corresponds to Option 2.

**Explanation for Other Options:**

1. **Option 1 (0.30 V):** This option is incorrect because it suggests a positive emf, which would imply that the cell reaction is spontaneous under standard conditions. However, the calculated emf is negative, indicating a non-spontaneous reaction.

3. **Option 3 (0.58 V):** This option is incorrect because it does not match the calculated emf value. The calculation clearly shows that the emf is $-0.30 \, \text{V}$, not $0.58 \, \text{V}$.

4. **Option 4 (-0.58 V):** This option is incorrect because it overestimates the magnitude of the negative emf. The correct calculation yields $-0.30 \, \text{V}$, not $-0.58 \, \text{V}$.

In conclusion, the correct answer is Option 2, $-0.30 \, \text{V}$, as it accurately reflects the calculated standard emf for the given cell reaction.