Which of the following reactions are disproportionation reactions ?
`(i) Cu^(+) to Cu^(2+) + Cu `
`(ii) 3MnO_4^(2-) + 4H^(+ ) to 2MnO_4^(-) + MnO_2 + 2H_2O`
` (iii) 2KMnO_4 to K_2 MnO_4 + MnO_2 + O_2`
` (iv) 2MnO_4^(-) + 3Mn^(2+) + 2H_2O to 5MnO_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 analyze each reaction to see if a single element undergoes both oxidation and reduction. A disproportionation reaction is characterized by the same element being oxidized and reduced simultaneously.

### Step-by-Step Solution:

**Step 1: Analyze Reaction (i)**
**Reaction:** \( \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \)

- In this reaction, copper is oxidized from \( \text{Cu}^+ \) to \( \text{Cu}^{2+} \) (loss of one electron).
- Simultaneously, \( \text{Cu}^+ \) is reduced to \( \text{Cu} \) (gain of one electron).
- Since the same element (Cu) is undergoing both oxidation and reduction, this is a disproportionation reaction.

**Step 2: Analyze Reaction (ii)**
**Reaction:** \( 3\text{MnO}_4^{2-} + 4\text{H}^+ \rightarrow 2\text{MnO}_4^{-} + \text{MnO}_2 + 2\text{H}_2\text{O} \)

- In this reaction, manganese in \( \text{MnO}_4^{2-} \) has an oxidation state of +4, while in \( \text{MnO}_4^{-} \) it is +7, and in \( \text{MnO}_2 \) it is +4.
- Here, manganese is oxidized from +4 to +7 and reduced from +4 to +6.
- Since the same element (Mn) is undergoing both oxidation and reduction, this is also a disproportionation reaction.

**Step 3: Analyze Reaction (iii)**
**Reaction:** \( 2\text{KMnO}_4 \rightarrow \text{K}_2\text{MnO}_4 + \text{MnO}_2 + \text{O}_2 \)

- In this reaction, manganese in \( \text{KMnO}_4 \) is in the +7 oxidation state, while in \( \text{K}_2\text{MnO}_4 \) it is +6 and in \( \text{MnO}_2 \) it is +4.
- However, there is no simultaneous oxidation and reduction of the same manganese atom; it is only being reduced.
- Therefore, this is **not** a disproportionation reaction.

**Step 4: Analyze Reaction (iv)**
**Reaction:** \( 2\text{MnO}_4^{-} + 3\text{Mn}^{2+} + 2\text{H}_2\text{O} \rightarrow 5\text{MnO}_2 + 4\text{H}^+ \)

- In this reaction, manganese in \( \text{MnO}_4^{-} \) is +7, while in \( \text{MnO}_2 \) it is +4, and \( \text{Mn}^{2+} \) is +2.
- Here, some manganese is being oxidized and some reduced, but not the same manganese atom.
- Thus, this is also **not** a disproportionation reaction.

### Conclusion:
The disproportionation reactions from the given options are:
- (i) \( \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \)
- (ii) \( 3\text{MnO}_4^{2-} + 4\text{H}^+ \rightarrow 2\text{MnO}_4^{-} + \text{MnO}_2 + 2\text{H}_2\text{O} \)