One of the methods of preparation of per disulphuric acid, `H_(2)S_(2)O_(8)`, involve electrolytic oxidation of `H_(2)SO_(4)` at anode `(2H_(2)SO_(4)toH_(2)S_(2)O_(8)+2H^(+)+2e^(-))` with oxygen ad hydrogen as by-products in such an electrolysis, 9.722 L of `H_(2)` and `2.35L` of `O_(2)` were generated at STP. What is the weighht of `H_(2)S_(2)O_(8)` formed?

Answer

`43.45g`

Explanation

In beginning :
At anode:
`2H_(2)SO_(4) rarr H_(2)S_(2)O_(8) +2H^(4) + 2e^(-)`
At anode:
`2H_(2)O +2e^(-) rarr H_(2) +2OH^(-)`
After some time:
At anode:
`2H_(2)O rarr 4H^(+) +O_(2) +4e^(-)`
At anode:
`2H_(2) +2e^(-) rarr H_(2) +2OH^(-)`
moles of `O_(2)` evolved `=(2.35)/(22.4)`
during this time moles of `H_(2)` evolved `=(2xx 2.35)/(22.4)`
volume of `H_(2)` evolved with `O_(2) =(2 xx 2.35)/(22.4) xx 22.4 = 4.7 L`
volume of `H_(2)` evolved with `H_(2)S_(2)O_(8) = 9.722 - 4.7 = 5.022 L`
moles of `H_(2)` evolved `=(5.022)/(22.4)`
moles of `H_(2)S_(2)O_(8)` formed `=(5.022)/(22.4)`
wt. of `H_(2)S_(2)O_(8)` formed
`=(5.022)/(22.4) xx 194 = 43.45 g`