`E_(Mn^(3+)//Mn^(2+))^@`is highly positive than that of `E_(Cr^(3+)//Cr^(2+))^@orE_(Fe^(3+)//Fe^(2+))^@` because

Options

A. `Mn^(2+)(d^5)` can be easily oxidised to `Mn^(3+)(d^4)` due to low ionisation enthalpy
B. third ionisation enthalpy of Mn is much larger due to stable half filled `d^5` electronic configuration of `Mn^(2+)`
C. `Mn^(3+)` is more stable than `Mn^(2+)` due to higher oxidation state
D. second ioonisation enthalpy of Mn is higher than third ionisation enthalpy.

Answer

To solve the question regarding the standard electrode potential \( E^\circ \) of the Mn\(^{3+}\)/Mn\(^{2+}\) couple being highly positive compared to the Cr\(^{3+}\)/Cr\(^{2+}\) and Fe\(^{3+}\)/Fe\(^{2+}\) couples, we will analyze the electronic configurations and stability of the ions involved.

### Step-by-Step Solution:

1. **Identify the Electronic Configurations**:
- For Mn\(^{3+}\): The electronic configuration is [Ar] 3d\(^4\).
- For Mn\(^{2+}\): The electronic configuration is [Ar] 3d\(^5\).
- For Cr\(^{3+}\): The electronic configuration is [Ar] 3d\(^3\).
- For Cr\(^{2+}\): The electronic configuration is [Ar] 3d\(^4\).
- For Fe\(^{3+}\): The electronic configuration is [Ar] 3d\(^5\).
- For Fe\(^{2+}\): The electronic configuration is [Ar] 3d\(^6\).

2. **Analyze Stability**:
- Mn\(^{2+}\) has a half-filled d-subshell (3d\(^{5}\)), which is particularly stable due to exchange energy and symmetry.
- Mn\(^{3+}\) (3d\(^{4}\)) is less stable compared to Mn\(^{2+}\) because it does not have a half-filled configuration.
- In the case of chromium, Cr\(^{2+}\) (3d\(^{4}\)) is more stable than Cr\(^{3+}\) (3d\(^{3}\)), but the difference in stability is not as significant as in the case of manganese.
- For iron, Fe\(^{3+}\) (3d\(^{5}\)) is stable due to half-filled configuration, while Fe\(^{2+}\) (3d\(^{6}\)) is less stable.

3. **Standard Electrode Potential**:
- The standard electrode potential \( E^\circ \) for the Mn\(^{3+}\)/Mn\(^{2+}\) couple is highly positive (approximately +1.57 V) because the conversion from Mn\(^{3+}\) to Mn\(^{2+}\) involves a transition from a less stable state to a more stable state (half-filled d-subshell).
- The \( E^\circ \) for Cr\(^{3+}\)/Cr\(^{2+}\) is positive but not as high as that of manganese because the stability difference is less pronounced.
- For Fe\(^{3+}\)/Fe\(^{2+}\), the potential is negative because it involves going from a stable state (Fe\(^{3+}\)) to a less stable state (Fe\(^{2+}\)), which is not favorable.

4. **Conclusion**:
- Therefore, the reason \( E^\circ \) for Mn\(^{3+}\)/Mn\(^{2+}\) is highly positive compared to the other couples is due to the significant stability of the Mn\(^{2+}\) ion with its half-filled d-subshell configuration, making the reduction process favorable.

### Final Answer:
The standard electrode potential \( E^\circ \) for the Mn\(^{3+}\)/Mn\(^{2+}\) couple is highly positive compared to that of Cr\(^{3+}\)/Cr\(^{2+}\) or Fe\(^{3+}\)/Fe\(^{2+}\) because Mn\(^{2+}\) has a stable half-filled d-subshell configuration (3d\(^{5}\)), making the reduction of Mn\(^{3+}\) to Mn\(^{2+}\) highly favorable.