State the conditions under which the following preparations are carried out. Give the necessary equations which need not be balanced. Potassium permanganate from manganese dioxide.

Explanation

To prepare potassium permanganate (KMnO4) from manganese dioxide (MnO2), the following steps outline the conditions and necessary equations involved in the process:

### Step 1: Fusion of Manganese Dioxide with Potassium Hydroxide
**Conditions:**
- Heat the mixture of manganese dioxide (MnO2) and potassium hydroxide (KOH) in the presence of an oxidizing agent (such as oxygen, O2).

**Equation:**
\[ \text{MnO}_2 + 4 \text{KOH} + \text{O}_2 \rightarrow 2 \text{K}_2\text{MnO}_4 + 2 \text{H}_2\text{O} \]
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