If `K_(sp)` of `Ag_(2)CO_(3)` is `8xx10^(-12)` the molar solubility of `Ag_(2)CO_(3)` in `0.1 M AgNO_(3)` is

Options

A. `1.1xx10^(-11)`
B. `1.1xx10^(-10)M`
C. `1.1xx10^(-12)`
D. `1.1xx10^(-9)`

Answer

B

Explanation

Plan in presence of common ion (in this case `Ag^(+) ion )` solubility of sparingly soluble salt is decreased.
Let solubility of `Ag_(2)CrO_(4)` in presence of 0.1M
`AgNO_(3) = x`
`Ag_(2)CrO_(4) rarr 2 Ag^(+) + CrO_(4)^(2-)`
`AgNO_(3) rarr Ag^(+) + NO_(3)^(-)`
`Total [Ag^(+)] = (2x + 0.1 M) approx 0.1M`
As x <<< 0.1 M
`[CrO_(4)^(2-)] = xM`
Thus, `[Ag^(+)]^(2)[CrO_(4)^(2-)] = K_(sp)`
`(0.1)^(2)(x) = 1.1 xx 10^(-12)`
`:' x = 1.1 xx 10^(-10)M`