Question

Calculate `pH_(1),[HS^(-)],[S^(2-)],[Cl^(-)]` in a solution which is `0.1M` in `HCl& 0.1M in H_(2)S`.Given that `K_(a_(1))(H_(2)S)=10^(-7),K_(a_(2))(H_(2)S)=10^(-14)`.Also calculate degree of dissociation of `H_(2)S` &`HS^(-)` in solution.

Answer 1

`underset(0.1M)(HCl)+underset(0.1M)(H_(2)S)`
`,.pH=1` (most of `[H^(+)]`comes form `HCl`&`[Cl^(-)]=0.1M`
`{:(,H_(2)hArr,H^(+),+,HS^(-)),(t=0,C_(1),0,,0):}`
at eq.`:.C_(1)-C_(1)alpha_(1)0.1+C_(1)a_(2) C_(1)alpha_(1)`
`(~~0.1)`
`K_(a_(1))=(C_(1)alpha_(1)alpha_(2)xx0.1)/(C_(1)alpha_(2)(1-alpha_(2)))`
degree of dissociation of `H_(2)S=alpha_(1)=(10^(-7))/(10^(-1))=10^(-6)`
`{:(,HS^(-)hArr,S^(2-),+H^(+)),(at eq.,C_(1)alpha_(1)(1-alpha_(2)),C_(1)alpha_(1)alpha_(2),~~0.1):}`
`10^(-14)=(C_(1)alpha_(1)a_(2)xx0.1)/(C_(1)alpha_(1)(1-alpha_(2)))`
rArr degree of dissocation of `HS^(-)`=alpha_(2)=10^(-13)`
`[S^(2-)]=C_(1)alpha_(1)alpha_(2)=10^(-1)xx10^(-6)xx10^(-13)=10^(-20)M`
`[HS^(-)]~~C_(1)alpha_(1)=10^(-1)xx10^(-6)=10^(-7)M`.