Which of the following reactions are disproportionation reactions?
`(A)" " Cu^(+)rarrCu^(2+)+Cu`
`(B)" "3 MnO_(4)^(2-)+4H^(+)rarr2MnO_(4)^(-)+MnO_(2)+2H_(2)O`
`(C )" "2KMnO_(4)rarrK_(2)MnO_(4)+MnO_(2)+O_(2)`
`(D)" "2MnO_(4)^(-)+3Mn^(2+)+2H_(2)O rarr5MnO_(2)+4H^(+)`

Options

A. I,II
B. I,II,III
C. II,III,IV
D. I,IV

Explanation

To determine which of the given reactions are disproportionation reactions, we need to identify whether any element in each reaction undergoes both oxidation and reduction simultaneously. A disproportionation reaction is characterized by a single species being oxidized and reduced in the same reaction.

### Step-by-Step Solution:

1. **Analyze Reaction A:**
\[ \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \]
- Oxidation states:
- Cu in Cu⁺: +1
- Cu in Cu²⁺: +2 (oxidation)
- Cu in Cu: 0 (reduction)
- Here, Cu⁺ is oxidized to Cu²⁺ and reduced to Cu.
- **Conclusion:** This is a disproportionation reaction.

2. **Analyze Reaction B:**
\[ 3 \text{MnO}_4^{2-} + 4 \text{H}^+ \rightarrow 2 \text{MnO}_4^{-} + \text{MnO}_2 + 2 \text{H}_2\text{O} \]
- Oxidation states:
- Mn in MnO₄²⁻: +6
- Mn in MnO₄⁻: +7 (oxidation)
- Mn in MnO₂: +4 (reduction)
- Here, Mn in MnO₄²⁻ is oxidized to MnO₄⁻ and reduced to MnO₂.
- **Conclusion:** This is a disproportionation reaction.

3. **Analyze Reaction C:**
\[ 2 \text{KMnO}_4 \rightarrow \text{K}_2\text{MnO}_4 + \text{MnO}_2 + \text{O}_2 \]
- Oxidation states:
- Mn in KMnO₄: +7
- Mn in K₂MnO₄: +6 (reduction)
- Mn in MnO₂: +4 (reduction)
- Here, both Mn species are reduced, and there is no oxidation occurring.
- **Conclusion:** This is not a disproportionation reaction.

4. **Analyze Reaction D:**
\[ 2 \text{MnO}_4^{-} + 3 \text{Mn}^{2+} + 2 \text{H}_2\text{O} \rightarrow 5 \text{MnO}_2 + 4 \text{H}^+ \]
- Oxidation states:
- Mn in MnO₄⁻: +7
- Mn in Mn²⁺: +2 (oxidation)
- Mn in MnO₂: +4 (reduction)
- Here, Mn in MnO₄⁻ is reduced to MnO₂, and Mn²⁺ is oxidized to MnO₂.
- **Conclusion:** This is not a disproportionation reaction.

### Final Conclusion:
The disproportionation reactions from the options provided are:
- **Option A:** Cu⁺ → Cu²⁺ + Cu
- **Option B:** 3 MnO₄²⁻ + 4 H⁺ → 2 MnO₄⁻ + MnO₂ + 2 H₂O