A 20 ml solution containing 0.2 g impure `H_(2)O_(2)` reacts completely with 0.316 g of `KMnO_(4)` in acidic medium. What would be volume strength of `H_(2)O_(2)` solution? [Given: Molar mass of `H_(2)O_(2)=34` & `KMnO_(4)= 158` g/mol]

Explanation

To solve the problem, we need to determine the volume strength of the impure hydrogen peroxide (H₂O₂) solution based on its reaction with potassium permanganate (KMnO₄) in acidic medium.

### Step-by-Step Solution:

1. **Determine the number of equivalents of KMnO₄:**
- Given mass of KMnO₄ = 0.316 g
- Molar mass of KMnO₄ = 158 g/mol
- n-factor of KMnO₄ in acidic medium = 5 (since it reduces from +7 to +2)
- Calculate the equivalent weight of KMnO₄:
\[ \text{Equivalent weight of KMnO₄} = \frac{\text{Molar mass}}{\text{n-factor}} = \frac{158}{5} = 31.6 \text{ g/equiv} \]
- Calculate the number of equivalents of KMnO₄:
\[ \text{Equivalents of KMnO₄} = \frac{\text{Mass}}{\text{Equivalent weight}} = \frac{0.316}{31.6} = 0.01 \text{ equiv} \]

2. **Set up the equivalence relation for H₂O₂:**
- The reaction between H₂O₂ and KMnO₄ shows that the equivalents of H₂O₂ will equal the equivalents of KMnO₄:
\[ \text{Equivalents of H₂O₂} = \text{Equivalents of KMnO₄} = 0.01 \text{ equiv} \]

3. **Calculate the equivalent weight of H₂O₂:**
- Molar mass of H₂O₂ = 34 g/mol
- n-factor of H₂O₂ = 2 (since it can donate 2 electrons)
- Calculate the equivalent weight of H₂O₂:
\[ \text{Equivalent weight of H₂O₂} = \frac{\text{Molar mass}}{\text{n-factor}} = \frac{34}{2} = 17 \text{ g/equiv} \]

4. **Calculate the mass of H₂O₂ in the solution:**
- Using the number of equivalents of H₂O₂:
\[ \text{Mass of H₂O₂} = \text{Equivalents} \times \text{Equivalent weight} = 0.01 \times 17 = 0.17 \text{ g} \]

5. **Calculate the normality of the H₂O₂ solution:**
- Volume of the solution = 20 mL = 0.020 L
- Normality (N) is calculated as:
\[ N = \frac{\text{Mass of H₂O₂}}{\text{Equivalent weight of H₂O₂} \times \text{Volume in L}} = \frac{0.17}{17 \times 0.020} = 0.5 \text{ N} \]

6. **Calculate the volume strength of H₂O₂:**
- Volume strength is given by:
\[ \text{Volume strength} = \text{Normality} \times 5.6 = 0.5 \times 5.6 = 2.8 \]

### Final Answer:
The volume strength of the H₂O₂ solution is **2.8**.