What volume of 0.1M `H_(2)O_(2)` solution will be required to completely reduce 1 litre of 0.1 M `KMnO_(4)` in acidic medium?

Options

A. 2500ml
B. 500ml
C. 1000ml
D. 1200ml

Answer

To solve the problem of how much volume of 0.1M \( H_2O_2 \) solution is required to completely reduce 1 liter of 0.1M \( KMnO_4 \) in acidic medium, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**:
In acidic medium, \( KMnO_4 \) acts as an oxidizing agent and \( H_2O_2 \) acts as a reducing agent. We need to find out how many equivalents of \( H_2O_2 \) are required to reduce the \( KMnO_4 \).

2. **Calculate the Equivalents of \( KMnO_4 \)**:
The concentration of \( KMnO_4 \) is 0.1 M and the volume is 1 L.
\[ \text{Equivalents of } KMnO_4 = \text{Molarity} \times \text{Volume} = 0.1 \, \text{mol/L} \times 1 \, \text{L} = 0.1 \, \text{mol} \]
In acidic medium, the n-factor of \( KMnO_4 \) is 5 (since it can gain 5 electrons). Therefore, the number of equivalents of \( KMnO_4 \) is:
\[ \text{Equivalents of } KMnO_4 = 0.1 \, \text{mol} \times 5 = 0.5 \, \text{equivalents} \]

3. **Determine the Equivalents of \( H_2O_2 \)**:
The n-factor of \( H_2O_2 \) is 2 (since it can lose 2 electrons). Let \( V \) be the volume of \( H_2O_2 \) solution required. The number of equivalents of \( H_2O_2 \) can be expressed as:
\[ \text{Equivalents of } H_2O_2 = \text{Molarity} \times \text{Volume} = 0.1 \, \text{mol/L} \times V \, \text{L} \]
The number of equivalents of \( H_2O_2 \) is:
\[ \text{Equivalents of } H_2O_2 = 0.1 \times V \times 2 \]

4. **Set the Equivalents Equal**:
Since the equivalents of \( H_2O_2 \) must equal the equivalents of \( KMnO_4 \):
\[ 0.1 \times V \times 2 = 0.5 \]

5. **Solve for \( V \)**:
Rearranging the equation gives:
\[ V = \frac{0.5}{0.1 \times 2} = \frac{0.5}{0.2} = 2.5 \, \text{L} \]

6. **Convert to Milliliters**:
Since the question asks for the volume in milliliters, we convert liters to milliliters:
\[ V = 2.5 \, \text{L} \times 1000 \, \text{mL/L} = 2500 \, \text{mL} \]

### Final Answer:
The volume of 0.1M \( H_2O_2 \) solution required to completely reduce 1 liter of 0.1M \( KMnO_4 \) in acidic medium is **2500 mL**.