The given reaction is the disproportionation of the manganate ion (\( \text{MnO}_4^{2-} \)) in acidic medium (\( \text{H}^+ \)). In a disproportionation reaction, a single substance is simultaneously reduced and oxidized to form two different products.
Let's analyze the reaction:
- For the manganate ion (\( \text{MnO}_4^{2-} \)), manganese is in the +6 oxidation state.
- During the reaction, this can be both reduced to a lower oxidation state and oxidized to a higher oxidation state. Possible products could be:
- Manganese(IV) oxide (\( \text{MnO}_2 \)) where manganese is in the +4 oxidation state - this represents reduction.
- Permanganate ion (\( \text{MnO}_4^- \)) where manganese is in the +7 oxidation state - this represents oxidation.
- Given these possible products, we can conclude that the manganate ion disproportionates into \( \text{MnO}_2 \) and \( \text{MnO}_4^- \).
Therefore, the correct option is \(({MnO2,\ MnO4^-})\).
Let's reason why the other options are incorrect:
- \(({MnO,\ MnO2})\) - In this pair, MnO corresponds to Mn in +2 oxidation state which usually does not form in such reactions.
- \(({MnO2,\ MnO})\) - Again, MnO represents an uncommon and unlikely state for manganese in this context.
- \(({MnO4^-,\ MnO})\) - The permanganate ion is correctly there, but MnO is not typically formed in these disproportionation reactions.
Tip: In an acidic disproportionation reaction involving manganese, always check the standard oxidation states that can feasibly be generated from the intermediate state of Mn(+6).