An aqueous solution contains `0.10 M H_(2)S` and 0.20 M HCl. If the equilibrium constants for the formation of `HS^(–)` from `H_(2)S` is `1.0xx10^(–7)` and that of `S^(2-)` from `HS^(–)` ions is `1.2xx10^(–13)` then the concentration of `S^(2-)` ions in aqueous solution is

Options

A. `6xx10^(-21)`
B. `5xx10^(-19)`
C. `5xx10^(-8)`
D. `3xx10^(-20)`

Answer

D

Explanation

`HCl to underset((0.2+x+y))(H^(+))+underset(0.2)(Cl^(-))`
`underset(0.1-x)(H_(2)S)hArrunderset((0.2+x+y))(H^(+))+underset((x-y))(HS^(-))` : `K_(a_(1))=10^(-7)`
`underset((x-y))(HS^(-))hArrunderset((0.2+x+y))(H^(+))+underset((y))(S^(2-))` : `K_(a_(2))=1.2xx10^(-13)`
`[H^(+)]=(0.2+x+y)M=0.2M`
`K_(a_(1))=([H^(+)][HS^(-)])/([H_(2)S])=(0.2xx[HS^(-)])/(0.1-x)=(0.2[HS^(-1)])/(0.1)`
(x=negligible)
`[HS^(-)]=(K_(a_(1))xx0.1)/(0.2)=(1)/(2)xx10^(-7)`
`K_(a_(2))=([H^(+)][S^(2-)])/([HS^(-)])=([0.2M][S^(2-)])/((1)/(2)xx10^(-7))`
`[S^(2-)]=(K_(a_(2))xx(1)/(2)xx10^(-7))/(0.2)=(1.2xx10^(-13)xx(1)/(2)xx10^(-7))/(0.2)`
`=3.0xx10^(-20)M`