Which of the following reactions are disproportionation reaction?
A. `2Cu^(+) to Cu^(2+) + Cu`
B. `3MnO_(4)^(2-) + 4H^(+) to 2MnO_(4)^(-) + MnO_(2) + 2H_(2)O`
C. `2KMnO_(4) overset(Delta) to K_(2)MnO_(4) + MnO_(2) + O_(2)`
C. `2KMnO_(4) overset(Delta) to K_(2)MnO_(4) + MnO_(2) + O_(2)`
D. `2MnO_(4)^(-) + 3Mn^(2+) + 2H_(2)O to 5MnO_(2) + 4H^(oplus)`
Select the correct option from the following:

Options

A. A and B only
B. A, B and C only
C. A, C and D
D. A and D only

Explanation

To determine which of the given reactions are disproportionation reactions, we need to analyze each reaction to see if a single element undergoes both oxidation and reduction. A disproportionation reaction is characterized by one species being simultaneously oxidized and reduced.

### Step-by-Step Solution:

1. **Analyze Reaction A:**
\[ 2Cu^+ \rightarrow Cu^{2+} + Cu \]
- **Oxidation States:**
- \(Cu^+\) has an oxidation state of +1.
- \(Cu^{2+}\) has an oxidation state of +2.
- \(Cu\) (elemental form) has an oxidation state of 0.
- **Changes:**
- \(Cu^+\) to \(Cu^{2+}\): Oxidation (loss of 1 electron).
- \(Cu^+\) to \(Cu\): Reduction (gain of 1 electron).
- **Conclusion:** This is a disproportionation reaction.

2. **Analyze Reaction B:**
\[ 3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^{-} + MnO_2 + 2H_2O \]
- **Oxidation States:**
- For \(MnO_4^{2-}\): \(Mn\) is +6.
- For \(MnO_4^{-}\): \(Mn\) is +7.
- For \(MnO_2\): \(Mn\) is +4.
- **Changes:**
- \(Mn\) changes from +6 to +7 (oxidation).
- \(Mn\) changes from +6 to +4 (reduction).
- **Conclusion:** This is a disproportionation reaction.

3. **Analyze Reaction C:**
\[ 2KMnO_4 \overset{\Delta}{\rightarrow} K_2MnO_4 + MnO_2 + O_2 \]
- **Oxidation States:**
- For \(KMnO_4\): \(Mn\) is +7.
- For \(K_2MnO_4\): \(Mn\) is +6.
- For \(MnO_2\): \(Mn\) is +4.
- **Changes:**
- \(Mn\) changes from +7 to +6 (reduction).
- \(Mn\) changes from +7 to +4 (reduction).
- **Conclusion:** This is **not** a disproportionation reaction since both changes are reductions.

4. **Analyze Reaction D:**
\[ 2MnO_4^{-} + 3Mn^{2+} + 2H_2O \rightarrow 5MnO_2 + 4H^{+} \]
- **Oxidation States:**
- For \(MnO_4^{-}\): \(Mn\) is +7.
- For \(Mn^{2+}\): \(Mn\) is +2.
- For \(MnO_2\): \(Mn\) is +4.
- **Changes:**
- \(Mn\) changes from +7 to +4 (reduction).
- \(Mn\) changes from +2 to +4 (oxidation).
- **Conclusion:** This is **not** a disproportionation reaction since different manganese species are involved.

### Final Conclusion:
The disproportionation reactions are found in options A and B.

### Correct Option:
**A and B are disproportionation reactions.**

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