Question

In $1 \,L$ saturated solution of $AgCl \left[K_{ sp }( AgCl ) 1.6\times 10^{10}\right], 0.1$ mole of $CuCl \left[K_{ sp }( CuCl ) 1.0\times10^6\right]$ 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 $Cl ^{-}$in solution comes mainly from $CuCl$.
$\Rightarrow \left[ Cl ^{-}\right]=\sqrt{K_{ sp }( CuCl )}=10^{-3} M$
Now for $AgCl : K_{ sp }=1.6 \times 10^{-10}$
$=\left[ Ag ^{+}\right]\left[ Cl ^{-}\right] $
$=\left[ Ag ^{+}\right] \times 10^{-3} $
$1.6 \times 10^{-7}$
$\Rightarrow \left[ Ag ^{+}\right]=1.6 \times 10^{-7}$