Question

In $1L$ saturated solution of $AgCl\left[K_{sp}(AgCl)1.6\times 10^{10}\right],0.1$ mole of $CuCl\left[K_{sp}(CuCl)1.0\times 10^6\right]$ is added. The resultant concentration of $Ag$ in the solution is $1.6\times 10^x$. The value of ${}^{\prime }{x}^{\prime }$ is

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer: (C)

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 $CuCl$.
$\Rightarrow \left[C{l}^{-}\right]=\sqrt{K_{sp}(CuCl)}=10^{-3}M$
Now for $AgCl:K_{sp}=1.6\times 10^{-10}$
$=\left[A{g}^{+}\right]\left[C{l}^{-}\right]$
$=\left[A{g}^{+}\right]\times 10^{-3}$
$1.6\times 10^{-7}$
$\Rightarrow \left[A{g}^{+}\right]=1.6\times 10^{-7}$