Explain why `E^(@)` for `Mn^(3+)//Mn^(2+)` couple is more positive than that for `Fe^(3+)//Fe^(2+)`(At. Nos. Mn=25,Fe=26)?

Answer

To explain why the standard electrode potential (E°) for the Mn³⁺/Mn²⁺ couple is more positive than that for the Fe³⁺/Fe²⁺ couple, we can follow these steps:

### Step 1: Write the electronic configurations
- For Mn³⁺: The atomic number of manganese (Mn) is 25. The electronic configuration of Mn is [Ar] 3d⁵ 4s². When it loses three electrons to form Mn³⁺, it loses the two 4s electrons and one 3d electron, resulting in:
\[ \text{Mn}^{3+} : [Ar] 3d^4 \]

- For Mn²⁺: When Mn loses two electrons to form Mn²⁺, it loses the two 4s electrons, resulting in:
\[ \text{Mn}^{2+} : [Ar] 3d^5 \]

- For Fe³⁺: The atomic number of iron (Fe) is 26. The electronic configuration of Fe is [Ar] 3d⁶ 4s². When it loses three electrons to form Fe³⁺, it loses the two 4s electrons and one 3d electron, resulting in:
\[ \text{Fe}^{3+} : [Ar] 3d^5 \]

- For Fe²⁺: When Fe loses two electrons to form Fe²⁺, it loses the two 4s electrons, resulting in:
\[ \text{Fe}^{2+} : [Ar] 3d^6 \]

### Step 2: Analyze the stability of the configurations
- The configuration of Mn²⁺ (3d⁵) is particularly stable because it is half-filled. Half-filled d-orbitals provide extra stability due to exchange energy and symmetry.

- In contrast, the configuration of Fe²⁺ (3d⁶) is not as stable as Mn²⁺ since it is not half-filled and has more electrons in the d-orbitals, leading to increased electron-electron repulsion.

### Step 3: Compare the reduction potentials
- The reduction potential (E°) for the Mn³⁺/Mn²⁺ couple is more positive than that for the Fe³⁺/Fe²⁺ couple due to the stability of the resulting ions after reduction:
- Mn³⁺ is more eager to gain an electron to become Mn²⁺ because it achieves a stable half-filled configuration (3d⁵).
- Fe³⁺, on the other hand, is already in a more stable state (3d⁵) and does not have the same driving force to gain an electron to become Fe²⁺ (3d⁶).

### Step 4: Conclusion
- The more positive E° value for the Mn³⁺/Mn²⁺ couple indicates a stronger tendency to be reduced compared to the Fe³⁺/Fe²⁺ couple. This is primarily due to the stability of the half-filled d-orbital configuration in Mn²⁺, which makes the reduction of Mn³⁺ to Mn²⁺ more favorable.

### Final Answer
Thus, the standard electrode potential \( E^\circ \) for the Mn³⁺/Mn²⁺ couple is more positive than that for the Fe³⁺/Fe²⁺ couple because Mn²⁺ has a stable half-filled d-orbital configuration, while Fe²⁺ does not have the same stability.

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