What is `[Ag^(+)]` in a solution made by dissolving both `Ag_(2)CrO_(4)` and `Ag_(2)C_(2)O_(4)` until saturation is reached with respect to both salt ?
`[K_(sp) = (Ag_(2)C_(2)O_(4)) = 2 xx 10^(-11), K_(sp) (Ag_(2)CrO_(4)) = 2 xx 10^(-12)]`

Options

A. `2.80 xx 10^(-4)`
B. `7.6 xx 10^(-5)`
C. `6.63 xx 10^(-6)`
D. `3.52 xx 10^(-4)`

Answer

D

Explanation

`Ag_(2)CrO_(4)(s) hArr underset(2x+2y)((2Ag)^(+)(aq.)) + underset(x)(CrO_(4)^(2-)(aq.))`
`Ag_(2)C_(2)underset(2y+2x)(O_(4)(s))hArr2Ag^(+)underset(y)((aq.))+C_(2)O_(4)^(2-)(aq.)`
`(K_(sp_(1)))/(K_(sp_(1))) = x/y = (2xx10^(-12))/(2 xx 10^(-11)) rArr = 0.1 `
`2 xx 10^(-11) = (2 x + 2y)^(2).y`
`2 xx 10^(-11) = 4.84y^(3)`
`y = 1.6 xx 10^(-4)`
`:. x = 0.16 xx 10^(-4)`
Total `[Ag^(+)] = 2 x + 2y`
`= (2 xx 0.16 + 2 xx 1.6) xx 10^(-4) = 3.52 xx 10^(-4)`