`A` sample of fuming sulpheric acid containing `H_(2)SO_(4), SO_(3)` and `SO_(2)` weighing `1.00g` is found to require `23.47mL` of `1.00 M` alkali `(NaOH)` for neutralisation. `A` separate sample shows the presence of `1.50% SO_(2)`. Find the percentage of "free" `SO_(3),H_(2)SO_(4)` and "combined" `SO_(3)` in the sample.

Answer

`H_(2)SO_(4)=35.38%,"Free"SO_(3)=63.1%,"combined"SO_(3)=28.89%`

Explanation

`{:(H_(2)SO_(4)rarra),(SO_(3)" "rarrb),(SO_(2)" "rarrc):}}" "a+b+c=1g`
`SO_(2)rarr1.5%`
so, `C=0.015 g rarr SO_(2)`
`a+b = 0.985 g`
`H_(2)SO_(4)+2NaOHrarrNa_(2)SO_(4)`
`(a)/(98)`
`SO_(2)+2NaOHrarrNa_(2)SO_(4)+H_(2)O`
`(b)/(80)`
`SO_(2)+2NaOHrarrNa_(2)SO_(3)+H_(2)O`
`(0.015)/(64)`
`((a)/(98)+(b)/(80)+(0.015)/(64))=23.47xx10^(-3)`
`0.0102a+0.0125b+0.00234=0.011735`
`a+1.225 b =1.1275`
`a+b=0.985`
`0.225b=0.1425`
`b=0.633grarrSO_(3)`
`a=0.35MgrarrH_(2)SO_(4)`
combined `SO_(3)=(0.3514)/(98)xx80=0.2868g`