Chemistry - Ionic Equilibrium Question with Solution | TestHub

$\begin{array}{ccccc}{\text{Ag}}_2{\text{CrO}}_4\left(\mathrm{s}\right)& \rightleftharpoons & 2{\text{Ag}}^{+}\left(\mathrm{aq}\right)& +& {\text{CrO}}_4^{2-}\\ & & \left(2\text{S}\right) \text{molar}& & \left(\text{S}\right) \text{molar}\end{array}$
$\begin{array}{ccccc}{\text{AgNO}}_3\left(\mathrm{aq}\right)& ⟶& {\text{Ag}}^{+}\left(\mathrm{aq}\right)& +& {\text{NO}}_3^{-}\left(\mathrm{aq}\right)\\ & & \left(0\text{.}1\right) \text{molar}& & \left(0\text{.}1\right) \text{molar}\end{array}$
$\left[{\mathrm{Ag}}^{+}\right]=\left(2\mathrm{S}+0.1\right) \mathrm{molar}$
$\left[{\text{CrO}}_4^{2-}\right]=\left(\mathrm{S}\right)\text{ molar}$
Here, $\mathrm{S}$ is the solubility of ${\mathrm{Ag}}_2{\mathrm{CrO}}_4$ in aqueous  ${\mathrm{AgNO}}_3$.

$\Rightarrow$${\left[{\text{Ag}}^{+}\right]}^{\mathrm{2 }}\left[{\text{CrO}}_4^{2-}\right]={\left(2\text{S}+0\text{.}1\right)}^2\left(\text{S}\right)=1\text{.}1\times 10^{-12}$
                      $\text{S}\ll 0\text{.}1$
$\Rightarrow$${\left(0.1\right)}^2\left(\mathrm{S}\right)=1.1\times 10^{-12}=10^{-2}\times \mathrm{S}$

$\mathrm{S}=1.1\times 10^{-10}\mathrm{M}$