The precipitate of `Ag_(2)CrO_(4) (K_(sp) = 9 xx 1^(-12))` is obtained when equal volumes of the following are mixed

Options

A. `10^(-4)M Ag^(+) + 10^(-4) M CrO_(4)^(2-)`
B. `10^(-2)M Ag^(+) + 10^(-3) M`
C. `10^(-5)M Ag^(+)+ 10^(-3) M`
D. `10^(-4)M Ag^(+) + 10^(-5) M`

Answer

2

Explanation

Precipitation occurs when the ionic product exceeds `K_("sp")` value. When equal volumes of two solutions are mixed,
the concentration of each is reduced to half. Therefore,
In first case,
Ionic product, I.P. ` = (1/2 xx 10^(-4))^(2) (1/2 xx 10^(-4)) = 1/8 xx 10^(-12) = 1.25 xx 10^(-13)`
As, I.P. `lt K_("sp")`
No precipitation occurs.
In second case,
I.P.` = (1/2 xx 10^(-2))^(2)(1/2 xx 10^(-3)) = 1/8 xx 10^(-7) = 1.25 xx10^(-8)`
As, I.P. `gt K_("sp")`
Precipitation occurs.
In third case,
I.P. ` = (1/2 xx 10^(-5))^(2)(1/2 xx 10^(-3)) = 1/8 xx 10^(-13) = 1.25 xx 10^(-14)`
As, I.P. `lt K_("sp")`
No precipitation occurs.
In fourth case,
I.P. ` = (1/2 xx 10^(-4))^(2) (1/2 xx 10^(-5)) = 1/8 xx 10^(-13) = 1.25 xx 10^(-14)`
As, I.P. `lt K_("sp")`
No precipitation occurs.