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In $1 L$ saturated solution of $AgCl \left[ K _{ sp }( AgCl )=1.6 \times 10^{-10}\right]$, $0.1$ mol 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 " $x$ " is
$7$
$8$
$9$
$2$
Solution
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 .
$\left[ Cl ^{-}\right]=\sqrt{ K _{ sp }( CuCl )}=10^{-3} M$
Now, for $AgCl , K _{ sp }=1.6 \times 10^{-10}=\left[ Ag ^{+}\right]\left[ Cl ^{-}\right]$
$=\left[ Ag ^{+}\right] \times 10^{-3}$
$\Rightarrow \quad\left[ Ag ^{+}\right]=1.6 \times 10^{-7}$
$\text { Hence, } x=7$
