`H_(2) O_(2)` solution `(20 mL)` reacts quantitatively with a solution of `KMnO_(4) (20 mL)` acidified with dilute `H_(2) SO_(4)`. The same volume of the `KMnO_(4)` solution is just decolourised by `10 mL` of `MnSO_(4)` in neutral medium. simulataneously forming a dark brown precipitate of hydrated `MnO_(2)`. The brown precipitate is dissolved in `10 mL` of `0.2 M` sodium oxalate under boiling condition in the presence of dilute `H_(2) SO_(4)`. Write the balanced equations involved in the reactions and calculate the molarity of `H_(2) O_(2)` solution.

Explanation

To solve the problem, we need to write the balanced equations for the reactions and then calculate the molarity of the hydrogen peroxide (H₂O₂) solution.

### Step 1: Write the balanced equation for the reaction of H₂O₂ with KMnO₄ in acidic medium.

The reaction between hydrogen peroxide and potassium permanganate in an acidic medium can be represented as follows:

\[ 2 \text{KMnO}_4 + 3 \text{H}_2\text{SO}_4 + 5 \text{H}_2\text{O}_2 \rightarrow \text{K}_2\text{SO}_4 + 2 \text{MnSO}_4 + 8 \text{H}_2\text{O} \]

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