In 1L saturated solution of `AgCI[K_(SP)(AgCI)= 1.6xx10^(-10)], 0.1` mole of CuCI `[K_(SP)(CuCI)=1.0xx10^(-6)]` is added. The resulrant concentration of `Ag^(+)` in the solution is `1.6xx10^(-x)`. The value of `"x"` is:

Explanation

`AgCI hArr underset(S')(Ag^(o+))+ underset((S"+x))(CI^(Theta))(K_(sp)=1.6 xx 10^(-10))`
`CuCI hArr underset(x)(Cu^(o+)) + underset((x+S'))(CI^(Theta)) (K_(sp) = 1 xx 10^(-6))`
`:. S'(S' +x) = 1.6 xx 10^(-10)`
`x(x+S') = 10^(-6)`
`(S')/(x) = 1.6 xx 10^(-4)`
`:. S' = (1.6 xx 10^(-4))x. rArr x(x+1.6 xx 10^(-4)x) = 10^(-6)`
`rArr x = 10^(-3)`
`:.S' = 1.6 xx 10^(-7) = 1.6 xx 10^(-x)` (The value of `x = 7)`
Alternative method:
`CI^(Theta)` will befrom `CuCI` (Since `CuCI` is more soluble than `AgCI` as it is evident form their `K_(sp)` value)
`K_(sp) = [Cu^(o+)] [CI^(Theta)] = 10^(-6) = x xx x rArr x = 10^(-3)`
Since `AgCI` is sparingly soluble.
`K_(sp) of AgCI = [Ag^(o+)] (10^(-3))`
`.16 xx 10^(-10) = [Ag^(o+)] (10^(-3))`
`:.[Ag^(o+)] = 1.6 xx 10^(-7) = 1.6 xx 10^(-x)` (the value of `x =7)`