Hydrogen peroxide solution `(20 mL)` reacts quantitatively with a solution of `KMnO_(4) (20 mL)` acidified with dilute of `H_(2)SO_(4)`. The same volume of the `KMnO_(4)` solution is just decolourised by `10 mL` of `MnSO_(4)` in neutral medium simultaneously 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)`.

Explanation

`(i) underset(1 " mole")underset(ppt.)(MnO_(2))+underset(1 " mole")(Na_(2)C_(2)O_(4))+2H_(2)SO_(4) to MnSO_(4)+Na_(2)SO_(4)+2CO_(2)+2H_(2)O`
`mM " of " MnO_(2)=mM " of" Na_(2)C_(2)O_(4)=10xx0.2=2`
(ii) `underset(2 " mole")(2KMnO_(4))+3MnSO_(4)+2H_(2)Oto underset(5 "mole")underset(ppt.)(5MnO_(2))+K_(2)SO_(4)+2H_(2)O`
mM of `KMnO_(4)=mM " of" MnO_(2)xx(2)/(5)=2xx(2)/(5)=(4)/(5)`
`(iii) underset(2 " mole")(2KMnO_(4))+3H_(2)SO_(4)+underset(5 " mole")(5H_(2)O_(2)) to K_(2)SO_(4)+2MnSO_(4)+8H_(2)O+5O_(2)`
`therefore mM " of " H_(2)O_(2)=mM " of " KMnO_(4)xx(5)/(2)=(4)/(5)xx(5)/(2)=2`
`therefore M xx20=2`
or `M_(H_(2)O_(2))=(2)/(20)=0.1M`