Which type of reaction `MnO_(4)^(2-)`show with acid , dilute -alkali or water.

Answer

To determine the type of reaction that \( \text{MnO}_4^{2-} \) undergoes with acid, dilute alkali, or water, we can analyze each condition step by step.

### Step 1: Reaction with Acid
When \( \text{MnO}_4^{2-} \) is added to an acidic solution, it undergoes a disproportionation reaction. This means that the same species is both oxidized and reduced.

**Reaction:**
\[ \text{MnO}_4^{2-} + 2 \text{H}^+ \rightarrow \text{MnO}_4^{-} + \text{MnO}_2 + \text{H}_2O \]

**Oxidation States:**
- In \( \text{MnO}_4^{2-} \), manganese is in the +6 oxidation state.
- In \( \text{MnO}_4^{-} \), manganese is in the +7 oxidation state.
- In \( \text{MnO}_2 \), manganese is in the +4 oxidation state.

### Step 2: Balancing the Reaction in Acidic Medium
To balance the reaction, we need to ensure that the number of atoms and charges are equal on both sides.

1. **Electrons:**
- \( \text{MnO}_4^{2-} \) gains 2 electrons to become \( \text{MnO}_4^{-} \).
- \( \text{MnO}_4^{2-} \) loses 1 electron to become \( \text{MnO}_2 \).

2. **Balancing the Reaction:**
- Multiply the \( \text{MnO}_4^{2-} \) by 2 to balance the electrons:
\[ 2 \text{MnO}_4^{2-} + 4 \text{H}^+ \rightarrow 2 \text{MnO}_4^{-} + 2 \text{MnO}_2 + 2 \text{H}_2O \]

### Step 3: Reaction with Water
In a neutral solution (water), \( \text{MnO}_4^{2-} \) also undergoes a disproportionation reaction.

**Reaction:**
\[ \text{MnO}_4^{2-} + 2 \text{H}_2O \rightarrow \text{MnO}_4^{-} + \text{MnO}_2 + 4 \text{OH}^- \]

### Step 4: Balancing the Reaction in Neutral Medium
1. **Electrons:**
- Similar to the acidic medium, the manganese in \( \text{MnO}_4^{2-} \) transitions to both +4 and +7 oxidation states.

2. **Balancing the Reaction:**
- To balance the reaction:
\[ 3 \text{MnO}_4^{2-} + 2 \text{H}_2O \rightarrow 2 \text{MnO}_4^{-} + 4 \text{OH}^- \]

### Step 5: Reaction with Dilute Alkali
In dilute alkaline conditions, \( \text{MnO}_4^{2-} \) is stable and does not undergo any significant reaction. Therefore, no reaction occurs.

### Summary of Reactions:
- **With Acid:** Disproportionation to \( \text{MnO}_4^{-} \) and \( \text{MnO}_2 \).
- **With Water:** Disproportionation to \( \text{MnO}_4^{-} \) and \( \text{MnO}_2 \).
- **With Dilute Alkali:** No reaction.