`E^(Theta)` value for the couple `Cr^(3+)//Cr^(2+)` and `Mn^(3+)//Mn^(2+)` are `-0.41 and +1.51` volts respectively. Considering these
value select the correct option from the following statements.

Options

A. `Cr^(2+)`act as a reducing agent and `Mn^(3+)` act as an oxidising
agent in their aqueous solutions.
B. `Cr^(2+)` (aq) is more stable than `Cr^(3+)` (aq).
C. `Mn^(3+)`(aq) is more stable than `Mn^(2+)` (aq).
D. None of these

Explanation

To solve the problem regarding the standard electrode potentials of the couples \( \text{Cr}^{3+}/\text{Cr}^{2+} \) and \( \text{Mn}^{3+}/\text{Mn}^{2+} \), we will analyze the given values and determine the reducing and oxidizing agents based on these potentials.

### Step-by-Step Solution:

1. **Identify the Standard Electrode Potentials**:
- For the couple \( \text{Cr}^{3+}/\text{Cr}^{2+} \), the standard electrode potential \( E^\circ = -0.41 \, \text{V} \).
- For the couple \( \text{Mn}^{3+}/\text{Mn}^{2+} \), the standard electrode potential \( E^\circ = +1.51 \, \text{V} \).

2. **Determine the Nature of Each Ion**:
- A negative \( E^\circ \) value indicates that the reaction is less favorable for reduction, suggesting that \( \text{Cr}^{2+} \) can easily lose an electron to become \( \text{Cr}^{3+} \). Thus, \( \text{Cr}^{2+} \) acts as a strong reducing agent.
- A positive \( E^\circ \) value indicates that the reaction is favorable for reduction, suggesting that \( \text{Mn}^{3+} \) can easily gain an electron to become \( \text{Mn}^{2+} \). Thus, \( \text{Mn}^{3+} \) acts as an oxidizing agent.

3. **Analyze Electron Configurations**:
- The electron configuration of \( \text{Cr}^{2+} \) is \( [Ar] 3d^4 \). When it loses an electron to become \( \text{Cr}^{3+} \), it reaches a more stable configuration of \( [Ar] 3d^3 \), which is a half-filled T2G level.
- The electron configuration of \( \text{Mn}^{3+} \) is also \( [Ar] 3d^4 \). When it gains an electron to become \( \text{Mn}^{2+} \), it reaches a stable configuration of \( [Ar] 3d^5 \), which is exactly half-filled.

4. **Conclusion**:
- Based on the analysis, \( \text{Cr}^{2+} \) is a strong reducing agent because it can easily oxidize to \( \text{Cr}^{3+} \).
- \( \text{Mn}^{3+} \) is a strong oxidizing agent because it can easily reduce to \( \text{Mn}^{2+} \).

5. **Select the Correct Option**:
- The correct statement is: \( \text{Cr}^{2+} \) acts as a reducing agent and \( \text{Mn}^{3+} \) acts as an oxidizing agent.

### Final Answer:
**Cr²⁺ acts as a reducing agent and Mn³⁺ acts as an oxidizing agent.**