`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

`2KMnO_(4)+3H_(2)SO_(4)+5H_(2)O_(2)toK_(2)SO_(4)+2MnSO_(4)+8H_(2)O`
`2KMnO_(4)+3MnSO_(4)+2H_(2)Oto5MnO_(2)+2H_(2)SO_(4)+K_(2)SO_(4)`
`MnO_(2)+Na_(2)C_(2)O_(4)+2H_(2)SO_(4)toMnSO_(4)+Na_(2)SO_(4)+2H_(2)O+2CO_(2)`
millimoles of `Na_(2)C_(2)O_(4)=10xx0.2=2`
`m" Eq of "Na_(2)C_(2)O_(4)=4`
`m" Eq of "MnO_(2)=4`
`m" Eq of "KKMnO_(4)=4`
`m" Eq of "H_(2)O_(2)=4`
millimoles of `H_(2)O_(2)=2`
millimoles of `H_(2)O_(2)=` Molarity`xxV_(mL)`
or `2=` molarity `xx20`
or molarity `=0.1`