The volume of water needed to prepare a satured solution of `Ag^(o+)` having maximum `[Ag^(o+)]` ion by selecting one out of three slats form:
`AgC1(K_(sp) = 2.0 xx 10^(-10)), AgBr (K_(sp) = 5 xx 10^(-13))`, and `Ag_(2)CrO_(4)(K_(sp) = 2.4 xx 10^(-12))`. whcih compound should be used to have maximum `[Ag^(o+)]`?

Options

A. `AgC1`
B. `AgBr`
C. `Ag_(2)CrO_(4)`
D. Any one of them

Answer

C

Explanation

`S_(AgC1) = sqrt(K_(sp)) = (2 xx 10^(-10))^(1//2)`
`= 1.414 xx 10^(-5)M`
`S_(AgBr) = sqrt(K_(sp)) = (5 xx 10^(-13))^(1//2)`
`(50 xx 10^(-14))^(1//2) = 7.071 xx 10^(-7)M`
`S_(Ag_(2)CrO_(4)) = ((K_(sp))/(4))^(1//3) =((2.4 xx 10^(-12))/(4))^(1//3)`
` = (0.6)^(1//3) xx10^(-4)`
` = (6)^(1//3) xx ((1)/(10))^(1//3) xx 10^(-4)`
` = 1.817 xx (1)/(2.154) xx 10^(-4)`
` = 0.8 xx 10^(-4) = 8 xx 10^(-5)M`
Solubility of `Ag_(2)CrO_(4)` is maximum.
Note: Don't solve the exact value, taken an approximate of cube root of `10^(-12)` to get the approximate answer.
So solubility is maximum in `Ag_(2)CrO_(4)`.