`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, we need to analyze the given standard reduction potentials and the stability of the oxidation states of chromium and manganese. The values provided are:

- \( E^\Theta \) for the couple \( \text{Cr}^{3+} // \text{Cr}^{2+} = -0.41 \, \text{V} \)
- \( E^\Theta \) for the couple \( \text{Mn}^{3+} // \text{Mn}^{2+} = +1.51 \, \text{V} \)

### Step 1: Analyze the Standard Reduction Potentials
The standard reduction potential indicates the tendency of a species to gain electrons and be reduced. A higher (more positive) value indicates a stronger oxidizing agent.

- For \( \text{Cr}^{3+} // \text{Cr}^{2+} \): \( E^\Theta = -0.41 \, \text{V} \) suggests that \( \text{Cr}^{3+} \) is less likely to be reduced to \( \text{Cr}^{2+} \).
- For \( \text{Mn}^{3+} // \text{Mn}^{2+} \): \( E^\Theta = +1.51 \, \text{V} \) indicates that \( \text{Mn}^{3+} \) is a strong oxidizing agent and readily accepts electrons to be reduced to \( \text{Mn}^{2+} \).

### Step 2: Determine the Stability of Oxidation States
- **Chromium**: The electronic configuration for \( \text{Cr}^{3+} \) is \( [Ar] 3d^3 \) and for \( \text{Cr}^{2+} \) is \( [Ar] 3d^4 \). The \( 3d^3 \) configuration is relatively stable due to half-filled \( t_{2g} \) orbitals.
- **Manganese**: The electronic configuration for \( \text{Mn}^{3+} \) is \( [Ar] 3d^4 \) and for \( \text{Mn}^{2+} \) is \( [Ar] 3d^5 \). The \( 3d^5 \) configuration is half-filled and thus more stable.

### Step 3: Identify the Reducing and Oxidizing Agents
- **Chromium**: Since \( E^\Theta \) for \( \text{Cr}^{3+} \) is negative, it is more stable in the \( +3 \) oxidation state. Therefore, \( \text{Cr}^{2+} \) can act as a reducing agent, oxidizing itself to \( \text{Cr}^{3+} \).
- **Manganese**: With a positive \( E^\Theta \), \( \text{Mn}^{3+} \) is more stable and acts as an oxidizing agent, while \( \text{Mn}^{2+} \) is less stable in comparison.

### Conclusion: Select the Correct Statement
Based on the analysis:
1. **Correct Statement**: \( \text{Cr}^{2+} \) is used as a reducing agent, and \( \text{Mn}^{3+} \) is used as an oxidizing agent.
2. **Incorrect Statements**: \( \text{Cr}^{2+} \) is more stable than \( \text{Cr}^{3+} \) (false), and \( \text{Mn}^{3+} \) is more stable than \( \text{Mn}^{2+} \) (false).

### Final Answer
The correct option is that \( \text{Cr}^{2+} \) acts as a reducing agent and \( \text{Mn}^{3+} \) acts as an oxidizing agent.

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