Which of the following is correct representation of reaction of acidified permanganate solution with sulphur dioxide?

Options

A. `2MnO_(4)^(-)+5SO_(2)+2H_(2)Orarr5SO_(4)^(2-)+2Mn^(2+)+4H^(+)`
B. `MnO_(4)^(-)+SO_(2)+2H_(2)OrarrS+Mn^(2+)+4H^(+)`
C. `2MnO_(4)^(-)+5SO_(2)+2H_(2)Orarr4SO_(3)^(2-)+S+2Mn^(2+)+4H^(+)`
D. `3MnO_(4)^(-)+2SO_(2)+2H_(2)Orarr2S+3Mn^(2+)+4H^(+)`

Explanation

To determine the correct representation of the reaction between acidified permanganate solution and sulfur dioxide, we need to follow these steps:

### Step 1: Identify the Oxidation States
1. **Calculate the oxidation state of manganese in permanganate ion (MnO4⁻)**:
- Let the oxidation state of Mn be \( x \).
- The oxidation state of oxygen is \(-2\).
- The equation becomes:
\[ x + 4(-2) = -1 \implies x - 8 = -1 \implies x = +7 \]
- Thus, Mn in MnO4⁻ has an oxidation state of +7.

2. **Calculate the oxidation state of sulfur in sulfur dioxide (SO2)**:
- Let the oxidation state of sulfur be \( y \).
- The equation becomes:
\[ y + 2(-2) = 0 \implies y - 4 = 0 \implies y = +4 \]
- Thus, sulfur in SO2 has an oxidation state of +4.

### Step 2: Determine the Reaction
3. **Identify the change in oxidation states**:
- Mn is reduced from +7 in MnO4⁻ to +2 in Mn²⁺.
- Sulfur is oxidized from +4 in SO2 to +6 in sulfate ion (SO4²⁻).

### Step 3: Write the Half-Reactions
4. **Write the half-reaction for the reduction of permanganate**:
- The half-reaction for MnO4⁻ to Mn²⁺ in acidic medium is:
\[ \text{MnO}_4^- + 8\text{H}^+ + 5\text{e}^- \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} \]

5. **Write the half-reaction for the oxidation of sulfur dioxide**:
- The half-reaction for SO2 to SO4²⁻ is:
\[ \text{SO}_2 + 2\text{H}_2\text{O} \rightarrow \text{SO}_4^{2-} + 4\text{H}^+ + 2\text{e}^- \]

### Step 4: Balance the Overall Reaction
6. **Combine the half-reactions**:
- To balance the electrons, multiply the sulfur dioxide half-reaction by 5:
\[ 5\text{SO}_2 + 10\text{H}_2\text{O} \rightarrow 5\text{SO}_4^{2-} + 20\text{H}^+ + 10\text{e}^- \]
- Now add the two half-reactions:
\[ 2\text{MnO}_4^- + 16\text{H}^+ + 10\text{e}^- + 5\text{SO}_2 + 10\text{H}_2\text{O} \rightarrow 2\text{Mn}^{2+} + 8\text{H}_2\text{O} + 5\text{SO}_4^{2-} + 20\text{H}^+ + 10\text{e}^- \]

7. **Simplify the equation**:
- Cancel out the electrons and simplify:
\[ 2\text{MnO}_4^- + 5\text{SO}_2 + 2\text{H}_2\text{O} \rightarrow 2\text{Mn}^{2+} + 5\text{SO}_4^{2-} + 4\text{H}^+ \]

### Conclusion
The balanced equation for the reaction of acidified permanganate solution with sulfur dioxide is:
\[ \boxed{2\text{MnO}_4^- + 5\text{SO}_2 + 2\text{H}_2\text{O} \rightarrow 2\text{Mn}^{2+} + 5\text{SO}_4^{2-} + 4\text{H}^+} \]