`H_(2)S` is bubbled into a `0.2M NaCN` solution which is `0.02M` each in `Ag(CN)_(2)^(Theta)` and `(Cd(CN)_(4)^(2-)`. If `K_(sp)` of `Ag_(2)S` and `CdS` are `10^(-50)` and `7.1 xx 10^(-28)` and `K` instability for `[Ag(CN)_(2)^(Theta)]` and `[Cd(CN)^(2-)underset(4)']` are `1.0 xx 10^(-20)` and `7.8 xx 10^(-18)`, which sulphide will precipitate first?

Explanation

`{:(,H_(2)ShArr,2H^(o+)+,S^(2-),),(NaCNrarr,Na^(o+)+,CN^(Theta),,),(0.1,0,0,,),(0,0.2,0.2,,):}`
Also `Ag(CN)_(2)^(Theta) hArr Ag^(o+) + 2CN^(Theta)`
`K = ([Ag^(o+)][CN^(Theta)])/([Ag(CN)_(2)]) = ([Ag^(o+)](0.2)^(2))/(0.02) = 1.0 xx 10^(-20)`
`[Ag^(o+)] = 5xx 10^(-21)M`
For `Cd(CN)_(4)^(2-) hArr Cd^(2+) + 4CN^(Theta)`
`K = ([Cd^(2+)][CN^(Theta)]^(4))/([Cd(CN)_(4)]^(2-))`
`7.3 xx 10^(-18) = ([Cd^(2+)]xx(0.2)^(4))/(0.02)`
`[Cd^(2)] = 9.75 xx 10^(-17)`
Now, `[Ag^(o+)]^(2) xx [S^(2-)] = 1.0 xx 10^(-50)`
`:. [S^(2-)]` needed to precipitate `Ag_(2)S`
`= (1.0 xx 10^(-50))/((5xx10^(-21))^(2)) = 4 xx 10^(-10)M`
`[S^(2-)]` needed to precipitate `CdS`
`=(7.1 xx 10^(-28))/(9.75 xx 10^(-17)) = 7.28 xx 10^(-21)M`
Therefore, `CdS` will be precipitated first.