Question

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

Answer 1

$K_{sp}\left(AgCl\right)=1.6\times {10}^{10}$

moles $AgC{l}_{\left(s\right)}\rightleftharpoons A{g}_{\left(aq\right)}^{+}+C{l}_{\left(aq\right)}^{-}$

At $Eq{b}^m$ - $s$ $s$

After adding $CuCl$ $s^{\prime }$ $s^{\prime }+C$ $CuCl\left(0.1moles\right)⟶C$

$K_{sp}=\left[s\right]\left[s^{\prime }\right]=s^2$

$\Rightarrow K_{sp}=\left[s^{\prime }\right][s^{\prime }+C]$

as $s^{\prime }<<C$ thus

$\Rightarrow K_{sp}=s^{\prime }.C$

$\Rightarrow 1.6\times {10}^{10}=0.1\times s^{\prime }$

or $s^{\prime }=\frac{1.6\times {10}^{10}}{0.1}=1.6\times {10}^{11}$

So, the concentration of $\left[A{g}^{+}\right]$ is $s^{\prime }=1.6\times {10}^{11}$

$\Rightarrow x=-11$