`K_(sp) of Ag_2CrO_4` is `1.1 times 10^-12`. What is solubility of `Ag_2CrO_4` in 0.1 M `K_2CrO_4`.

Explanation

`Ag_2CrO_4 leftrightarrow 2Ag^+ +CrO_4^(2-)`
x 2x x
x is the solubility of `Ag_2CrO_4` in 0.1 M `K_2CrO_4`
`K_2CrO_4 leftrightarrow 2K^+ + CrO_4^(2-)`
0.1 M 0.2 M 0.1 M
`[Ag^+]=2x`
`[CrO_4^(2-)]=(x+0.1) approx 0.1 therefore x lt lt 0.1`
`K_(sp)=[Ag^+]^2 [CrO_4^(2-)]`
`1.1 times 10^-12=(2x)^2 (0.1)`
`1.1 times 10^-12=0.4x^2`
`x^2=(1.1 times10^-12)/0.4`
`x=sqrt((1.1 times10^-12)/0.4)`
`x=sqrt(2.75 times10^-12)`
`x=1.65 times 10^-6 M`