Balance the following equations :
(i) `KMnO_(4) + H_(2)SO_(4) + H_(2)O_(2) to K_(2)SO_(4) + MnSO_(4) + H_(2)O + O_(2)`
(ii) `KMnO_(4) + KCl + H_(2)SO_(4) to MnSO_(4) + K_(2)SO_(4) + H_(2)O + Cl_(2)`
(iii) `MnO_(2) + H_(2)O_(2) to MnO_(4)^(-) + MnO_(4)^(-) + H_(2)O` (Basic medium)

Explanation

To balance the given equations, we will follow systematic steps for each reaction. Let's break down the balancing process for each of the three reactions provided.

### (i) Balancing the equation:
**Unbalanced Reaction:**
\[ \text{KMnO}_4 + \text{H}_2\text{SO}_4 + \text{H}_2\text{O}_2 \rightarrow \text{K}_2\text{SO}_4 + \text{MnSO}_4 + \text{H}_2\text{O} + \text{O}_2 \]

**Step 1: Balance Potassium (K)**
- There are 2 K on the right side in \( \text{K}_2\text{SO}_4 \).
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