In acidic medium, `KMnO_4` oxidises `FeSO_4` solution. Which of the following statements is correct?

Options

A. 10 mL of 1 N `kMnO_4` solution oxidises 10 mL of 5 N `FeSO_4` solution.
B. 10 mL of 1 M `KMnO_4` solution oxidises 10 mL of 5 M `FeSO_4` solution.
C. 10 mL of 1 M `KMnO_4` solution oxidises 10 mL of 1 M `FeSO_4` solution.
D. 10 mL of 1 N `KMnO_4` solution oxidises 10 mL of 0.1 M `FeSO_4` solution.

Explanation

To solve the problem, we need to analyze the oxidation-reduction reaction between KMnO4 and FeSO4 in an acidic medium. Here are the steps to determine which statement is correct:

### Step 1: Understand the Reaction
In acidic medium, KMnO4 acts as an oxidizing agent and FeSO4 acts as a reducing agent. The balanced reaction can be represented as:
\[ \text{KMnO}_4 + \text{FeSO}_4 \rightarrow \text{Mn}^{2+} + \text{Fe}^{3+} \]

### Step 2: Determine Oxidation States
- In KMnO4, the oxidation state of Mn is +7.
- In FeSO4, the oxidation state of Fe is +2.
- In the products, Mn is reduced to +2 and Fe is oxidized to +3.

### Step 3: Calculate Change in Oxidation States
- For Mn: Change from +7 to +2 (a change of 5).
- For Fe: Change from +2 to +3 (a change of 1).

### Step 4: Determine n-Factors
- The n-factor for KMnO4 is 5 (since Mn changes from +7 to +2).
- The n-factor for FeSO4 is 1 (since Fe changes from +2 to +3).

### Step 5: Apply the Concept of Gram Equivalents
In a redox reaction, the gram equivalents of the oxidizing agent (KMnO4) and the reducing agent (FeSO4) must be equal:
\[ n_1 \cdot V_1 = n_2 \cdot V_2 \]
Where:
- \( n_1 \) = n-factor of KMnO4 = 5
- \( n_2 \) = n-factor of FeSO4 = 1
- \( V_1 \) and \( V_2 \) are the volumes of KMnO4 and FeSO4 solutions, respectively.

### Step 6: Analyze Each Option
1. **Option 1:** 10 ml of 1N KMnO4 oxidizes 10 ml of 5N FeSO4.
- \( N_1 \cdot V_1 = 1 \cdot 10 = 10 \)
- \( N_2 \cdot V_2 = 5 \cdot 10 = 50 \)
- Not equal, **incorrect**.

2. **Option 2:** 10 ml of 1M KMnO4 oxidizes 10 ml of 5M FeSO4.
- \( N_1 = n_1 \cdot M_1 = 5 \cdot 1 = 5 \)
- \( N_2 = n_2 \cdot M_2 = 1 \cdot 5 = 5 \)
- \( N_1 \cdot V_1 = 5 \cdot 10 = 50 \)
- \( N_2 \cdot V_2 = 5 \cdot 10 = 50 \)
- Equal, **correct**.

3. **Option 3:** 10 ml of 1M KMnO4 oxidizes 10 ml of 1M FeSO4.
- \( N_1 = 5 \) and \( N_2 = 1 \)
- \( N_1 \cdot V_1 = 5 \cdot 10 = 50 \)
- \( N_2 \cdot V_2 = 1 \cdot 10 = 10 \)
- Not equal, **incorrect**.

4. **Option 4:** 10 ml of 1M KMnO4 oxidizes 10 ml of 0.1M FeSO4.
- \( N_1 = 5 \) and \( N_2 = 0.1 \)
- \( N_1 \cdot V_1 = 5 \cdot 10 = 50 \)
- \( N_2 \cdot V_2 = 0.1 \cdot 10 = 1 \)
- Not equal, **incorrect**.

### Conclusion
The correct statement is **Option 2**: 10 ml of 1M KMnO4 oxidizes 10 ml of 5M FeSO4.

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