Marshall's acid `(H_(2)S_(2)O_(8))` or peroxodisulphuric acid is prepared by the electrolytic oxidation of mmol`H_(2)SO_(4)` as `:`
`2H_(2)SO_(4) rarr H_(2)S_(2)O_(8)+2H^(o+)+2e^(-)`
`O_(2)(g)` and `H_(2)(g)` are obtained as byproducts. In such electrolysis `4.48L` of `H_(2)(g)` and `1.12L` or `O_(2)(g)` were produced at `STP`. The weight of `H_(2)S_(2)O_(8)` formed is
`a. 9.7g" "b.19.4g" "c.14.5g" "d.29.1g`

Explanation

`b.` Refer Section `(point h)`.
Aqueous `underset((dil or conc))(H_(2)SO_(4)) overset(El ectrolysis)rarr2H^(o+)+SO_(4)^(2-)`
At anode, two reactions are competing `:`
`i. 2SO_(4)^(2-) rarr S_(2)O_(8)^(2-)+2e^(-)`
`ii. H_(2)O rarr (1)/(2)O_(2)+2H^(o+)+2e^(-)`
At cathode, only one reaction occurs `:`
`2H^(o+) (` from `H_(2)SO_(4)) +2e^(-) rarr H_(2)(g)`
Since one reaction at cathode and two reactions at anode are taking place, therefore, the equivalent of `H_(2)(g)` produced at cathode at cathode should be equal to the equibalent of `O_(2)(g)` produced `+` equivalent of `H_(2)S_(2)O_(8)` formed.
`:.` Equivalent of `H_(2)=`Equivalent of `O_(2)+` Equivalent of `H_(2)S_(2)O_(8)`
`(4.48)/(22.4//2)=(1.12)/(22.4//4)+(W_(H_(2)S_(2)O_(8)))/(194//2)`
`0.4=0.2+(W)/(97)`
`:. W_(H_(2)S_(2)O_(8)=19.4g`