At `20^(@)C`, the `Ag^(+)` ion concentration in a saturated solution `Ag_(2)CrO_(4)` is `1.5 x10^(-4)` mol `//` litre. At `20^(@)C`, the solubility product of `Ag_(2)CrO_(4)` would be

Options

A. `3.3750 xx 10^(-12)`
B. `1.6875 xx 10^(-10)`
C. `1.6875 xx 10^(-12)`
D. `1.6875 xx 10^(-11)`

Answer

C

Explanation

`{:(AgCrO_(4),hArr,2Ag^(+),+,CrO_(4)^(-)),(,,(2S)^(2),S):}`
`K_(sp) = 4S^(3)` given `2S = 1.5 xx 10^(-4)`
`:. K_(sp) = (2S)^(2) xx S`
`= (1.5 xx 10^(-4))^(2) xx ((1.5 xx 10^(-4))/(2)) = 1.6875 xx 10^(-12)`