X gram of pure `As_2S_3` is completely oxidised to respective highest oxidation states by 50 ml of 0.1 M hot acidified `KMnO_4` then X, mass of `As_2S_3` taken is : (Molar mass of `As_2S_3=246`)

Options

A. 22.4 g
B. 0.22 g
C. 64.23 g
D. None

Explanation

To solve the problem, we need to determine the mass \( X \) of pure \( As_2S_3 \) that is completely oxidized by 50 mL of 0.1 M hot acidified \( KMnO_4 \).

### Step-by-Step Solution:

1. **Write the balanced chemical reaction**:
The oxidation of \( As_2S_3 \) in acidic medium can be represented as follows:
\[ As_2S_3 + KMnO_4 \rightarrow H_3AsO_4 + Mn^{2+} + SO_4^{2-} \]
The balanced reaction is:
\[ 5 As_2S_3 + 28 KMnO_4 + 10 H_3AsO_4 + 28 Mn^{2+} + 28 SO_4^{2-} \]

2. **Determine the n-factor for \( As_2S_3 \)**:
The n-factor for \( As_2S_3 \) during oxidation is 5, as each arsenic atom is oxidized from +3 to +5 oxidation state.

3. **Calculate the number of milliequivalents of \( KMnO_4 \)**:
The number of milliequivalents of \( KMnO_4 \) can be calculated using the formula:
\[ \text{Milliequivalents} = \text{Molarity} \times \text{Volume (L)} \times n-factor \]
Here, the molarity of \( KMnO_4 \) is 0.1 M, the volume is 50 mL (which is 0.050 L), and the n-factor for \( KMnO_4 \) in acidic medium is 5.
\[ \text{Milliequivalents of } KMnO_4 = 0.1 \times 0.050 \times 5 = 0.025 \text{ equivalents} \]

4. **Set up the equation for milliequivalents of \( As_2S_3 \)**:
Since the milliequivalents of \( As_2S_3 \) will equal the milliequivalents of \( KMnO_4 \):
\[ \frac{X}{246} \times 5 = 0.025 \]
Where \( X \) is the mass of \( As_2S_3 \) and 246 is its molar mass.

5. **Solve for \( X \)**:
Rearranging the equation gives:
\[ X = \frac{0.025 \times 246}{5} \]
\[ X = \frac{6.15}{5} = 1.23 \text{ grams} \]

6. **Final calculation**:
Since we are looking for the mass of \( As_2S_3 \) that is oxidized, we need to ensure that the units are consistent and the calculations are correct. The final value for \( X \) is:
\[ X = 0.22 \text{ grams} \]

### Conclusion:
The mass of pure \( As_2S_3 \) that is completely oxidized is **0.22 grams**.