The `Mn_3O_4` formed on strong heating of a sample of `MnSO_4 . 4H_2O` was dissolved in 100 cm of 0.1 N `FeSO_4` containing dilute `H_2SO_4` . The resulting solution reacted completely with `50 cm^3` of `KMnO_4` solution. `25 cm^3` of this `KMnO_4` solution required `30 cm^3` of 0.1 N `FeSO_4`solution for complete reaction. Calculate the amount of `MnSO_4 . 4H_2O` in the sample.

Explanation

To solve the problem step by step, we need to follow the reactions and stoichiometry involved in the process.

### Step 1: Understanding the Reaction
When `MnSO4.4H2O` is heated, it decomposes to form `Mn3O4`. The balanced equation for this reaction is:
\[ 3 \text{MnSO}_4 \cdot 4 \text{H}_2\text{O} \rightarrow \text{Mn}_3\text{O}_4 + 3 \text{SO}_2 + 4 \text{H}_2\text{O} \]

### Step 2: Determine the Moles of KMnO4
From the problem, we know that `25 cm³` of the `KMnO4` solution reacts with `30 cm³` of `0.1 N FeSO4`.
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