What would be the solubility of AgCl in 0.1 M NaCl solution ? `(K_(sp)" for AgCl"=1.2xx10^(-10))`

Options

A. 0.1 M
B. `1.2xx10^(-6)M`
C. `1.2xx10^(-9)M`
D. `1.2xx10^(-10)M`

Answer

C

Explanation

Let the solubility of `AgCl = x mol L^(-1)`
`[Ag^(+)]=x M, [Cl^(-)]=(0.1+x)M`
`K_(sp)=[Ag^(+)][Cl^(-)]`
`1.2xx10^(-11)=(x)(0.1+x)`
`therefore 1.2xx10^(-10)=0.1 x +x^(2)`
(`x^(2)` is negligible because x is small)
`0.1x = 1.2xx10^(-10)`
or `x=1.2xx10^(-9)`