Solubility of `AgI` in `0.05M BaI_(2)` solution is `10^(-15)M`. The solubility of `AgI` in water is

Options

A. `25 xx 10^(-7)`
B. `10^(-7)M`
C. `5 xx 10^(-8)`
D. `10^(-8)M`.

Answer

D

Explanation

`AgI hArr underset(x)Ag^(o+)+underset(x)I^(Theta)]K_(sp) = [Ag^(o+)] [I^(Theta)]`
`:. [I^(Theta)] = (x + 0.1)`
`{:(BaI_(2)hArr,Ba^(2+),+,2I^(Theta),),(0.005M,0,,0,),(0,0.05M,,2xx0.05=0.1M,):}`
`:. [I^(Theta)] = (x + 0.1)`
`K_(sp) = [Ag^(o+)] [I^(Theta)] = x (x + 0.1)`
`=x^(2) + 0.1 ~~ 0.1 x` (neglecting `x^(2))`
`= 0.1 xx 10^(-15) = 10^(-16)`
Solubility of `AgI` in pure water.
`= sqrt(K_(sp)) = sqrt(10^(-16)) = 10^(-8)M`.