Question

In $1L$ saturated solution of $AgCl\left[K_{sp}\right(AgCl)=1.6\times {10}^{-10}]$, $0.1mol$ of $CuCl\left[K_{sp}\right(CuCl)=1\times {10}^{-6}]$ is added. The resultant concentration of ${Ag}^{+}$ in the solution is $1.6\times {10}^{-x}$. The value of $x$ is:

Answer 1

$AgCl\rightleftharpoons A{g}^{+}C{l}^{-}$

$CuCL\rightleftharpoons C{u}^{+}+C{l}^{-}$

Net $\left[C{l}^{-}\right]$ in solution $x+y$

$K_{(}SP)AgCl=1.6\ast {10}^{-}10=[A{g}^{+}\left]\right[C{l}^{-}]=x(x+y)$

$x(x+y)=1.6\ast {10}^{-}10$

$S_{(}SP)AgCl=1.6\ast {10}^{-}10=[A{g}^{+}\left]C{l}^{-}\right]=x(x+y)$

From (i) and (ii)

$\frac{x}{y}=1.6\ast {10}^{-}4\to y=\frac{x}{1.6\ast {10}^{-}4}$

Substituting for $y$ in Equation 1

$x(x+\frac{x}{1.6\ast {10}^{-}10})=1.6\ast {10}^{-}10$

$X^2=(1.6{)}^2\ast {10}^{-}14$

$x=1.6\ast {10}^{-}7$

The resultant concentration of $A{g}^{+}$ in the solution $=1.6\ast {10}^{-}7$.