The number of moles of `KMnO_(4)` in acidic medium that will be needed to react with one mole of sulphide ion is:

Options

A. `(2)/(5)`
B. `(3)/(5)`
C. `(4)/(5)`
D. `(1)/(5)`

Answer

To determine the number of moles of \( KMnO_4 \) needed to react with one mole of sulfide ion (\( S^{2-} \)), we need to analyze the redox reaction that occurs in acidic medium.

### Step-by-Step Solution:

1. **Identify the Oxidation States**:
- In \( KMnO_4 \), manganese (Mn) has an oxidation state of +7.
- In sulfide ion (\( S^{2-} \)), sulfur (S) has an oxidation state of -2.

2. **Determine the Products**:
- \( KMnO_4 \) is reduced to \( Mn^{2+} \) in acidic medium, where Mn goes from +7 to +2, gaining 5 electrons.
- The sulfide ion (\( S^{2-} \)) is oxidized to sulfate ion (\( SO_4^{2-} \)), where sulfur goes from -2 to +6, losing 8 electrons.

3. **Write the Half-Reactions**:
- Reduction half-reaction:
\[ MnO_4^{-} + 8H^{+} + 5e^{-} \rightarrow Mn^{2+} + 4H_2O \]
- Oxidation half-reaction:
\[ S^{2-} \rightarrow SO_4^{2-} + 8H^{+} + 6e^{-} \]

4. **Balance the Electrons**:
- To balance the electrons, we need to find a common multiple of 5 and 6, which is 30.
- Multiply the reduction half-reaction by 6:
\[ 6MnO_4^{-} + 48H^{+} + 30e^{-} \rightarrow 6Mn^{2+} + 24H_2O \]
- Multiply the oxidation half-reaction by 5:
\[ 5S^{2-} \rightarrow 5SO_4^{2-} + 40H^{+} + 30e^{-} \]

5. **Combine the Half-Reactions**:
- The balanced overall reaction is:
\[ 6MnO_4^{-} + 5S^{2-} + 8H^{+} \rightarrow 6Mn^{2+} + 5SO_4^{2-} + 24H_2O \]

6. **Determine the Moles of \( KMnO_4 \)**:
- From the balanced equation, 6 moles of \( KMnO_4 \) react with 5 moles of \( S^{2-} \).
- Therefore, to find the amount of \( KMnO_4 \) needed for 1 mole of \( S^{2-} \):
\[ \text{Moles of } KMnO_4 = \frac{6}{5} \times 1 = \frac{6}{5} \]

7. **Final Calculation**:
- To find the number of moles of \( KMnO_4 \) needed for 1 mole of \( S^{2-} \):
\[ \text{Moles of } KMnO_4 = \frac{6}{5} \times \frac{1}{5} = \frac{2}{5} \]

### Conclusion:
The number of moles of \( KMnO_4 \) needed to react with one mole of sulfide ion is \( \frac{2}{5} \).