The `K_(sp)` of `Ag_(2)CrO_(4)` is `1.1xx10^(-12)` at `298K`. The solubility (in mol/L) of `Ag_(2)CrO_(4)` in a `0.1 M AgNO_(3)` solution is

Options

A. `1.1 xx 10^(-11)`
B. `1.1 xx 10^(-10)`
C. `1.1 xx 10^(-12)`
D. `1.1 xx 10^(-9)`

Answer

B

Explanation

`Ag_(2)CrO_(4)(s) overset((aq))(hArr) 2Ag^(+) (aq)+CrO_(4)^(2-)(aq)`
`AgNO_(3)(s)overset((aq))(to)underset(0.1M)(Ag^(+))(aq)+underset(0.1M)(NO_(3)^(-)(aq))`
`[CrO_(4)^(2-)] =S,[Ag^(+)]=(2S +0.1]=0.1 M`
`[Ag^(+)]` being very very small can be negilected as compared to 0.1 M
`K_(sp) =[Ag^(+)]^(2)[CrO_(4)^(2-)]`
`[CrO_(4)^(2-)] =(K_(sp))/[Ag^(+)]^(2) =(1.1xx 10^(-12))/((0.1)^(2))`
`=1.1 xx 10^(-10) M`
`[S] =1.1xx 10^(-10) "mol " L^(-1)`