Question

In 1 L saturated solution of $AgCl\left[K_{sp}\right(AgCl)=1.6\times {10}^{-10}],$ 0.1 mole of $CuCl[K_{p\left(CuCl\right)}=1.0\times {10}^{-6}]$ is added. The resultant concentration of $A{g}^{+}$ in the solution is $1.6\times {10}^{-x}.$ The value of 'x' is ___

Answer 1

Ans: 7
It is a case of simultaneous solubility of salts with a common ion. Here, solubility product of CuCl is much greater than that of AgCl, it can be assumed that $C{l}^{-}$ in solution comes mainly from CuCl.
$\left[C{l}^{-}\right]=\sqrt{K_{sp}\left(CuCl\right)}={10}^{-3}M$
Now, for $AgCl,K_{sp}=1.6\times {10}^{-10}=\left[A{g}^{+}\right]\left[C{l}^{-}\right]$
$=\left[A{g}^{+}\right]\times {10}^{-3}$
$\Rightarrow \left[A{g}^{+}\right]=1.6\times {10}^{-7}$
Hence, $x=7$