A sample of hydrazine sulphate `(N_(2)H_(6)SO_(4))` was dissolved in `100 mL` water. `10 mL` of this solution was reacted with excess of `FeCl_(3)` solution and warmed to complete the reaction. Ferrous ions formed were estimated and it required `20 mL` of `M//50 KMnO_(4)` solutions. Estimate the amount of hudrazine sulphate in one litre of solution.
Given `4Fe^(3+)+N_(2)H_(4)rarrN_(2)+4Fe^(2+)+4H^(+)`
`MnO_(4)^(-)+5Fe^(2+)+8H^(+)rarrMn^(2+)+5Fe^(3+)+4H_(2)O`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Reaction
The given reactions are:
1. \( 4Fe^{3+} + N_2H_4 \rightarrow N_2 + 4Fe^{2+} + 4H^+ \)
2. \( MnO_4^- + 5Fe^{2+} + 8H^+ \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O \)

From these reactions, we can see that 1 mole of hydrazine (\(N_2H_4\)) reacts with 4 moles of \(Fe^{3+}\) ions, and 1 mole of \(MnO_4^-\) reacts with 5 moles of \(Fe^{2+}\).
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