To determine which of the given reactions are disproportionation reactions, we first need to understand the concept of a disproportionation reaction. A disproportionation reaction is a specific type of redox reaction in which a single substance is simultaneously oxidized and reduced, forming two different products.
Now, let's analyze each given reaction:
-
Reaction (a): \(2Cu^{+} \rightarrow Cu^{2+} + Cu^{0}\)
- The copper ion \(Cu^+\) is both oxidized and reduced in this reaction.
- Oxidation: \(Cu^+ \rightarrow Cu^{2+} + e^-\)
- Reduction: \(Cu^+ + e^- \rightarrow Cu^0\)
- Result: This is a disproportionation reaction.
-
Reaction (b): \(3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O\)
- Manganese in \(MnO_4^{2-}\) is both oxidized and reduced.
- Oxidation: \(MnO_4^{2-} \rightarrow MnO_4^-\)
- Reduction: \(MnO_4^{2-} \rightarrow MnO_2\)
- Result: This is a disproportionation reaction.
-
Reaction (c): \(2KMnO_4 \frac{\Delta}{\rightarrow} K_2MnO_4 + MnO_2 + O_2\)
- This reaction does not feature manganese being both oxidized and reduced.
- Result: This is not a disproportionation reaction.
-
Reaction (d): \(2MnO_4^- + 3Mn^{2+} + 2H_2O \rightarrow 5MnO_2 + 4H^+\)
- Manganese is not simultaneously oxidized and reduced in this reaction.
- Result: This is not a disproportionation reaction.
From the analysis above, reactions (a) and (b) show characteristics of disproportionation reactions where the same element undergoes both oxidation and reduction. Therefore, the correct option is:
(a) and (b) only