Solubility of a sparingly soluble salt XB₂ in water is x. What will be its solubility in a solution of YB having concentration of 0.001 M?

Let solubility of XB₂ in a 0.001 M solution of YB be S

 S<<x

common ion effect.

${\mathrm{XB}}_2\left(\mathrm{s}\right)\rightleftharpoons \underset{\mathrm{S}}{{\mathrm{XB}}_2(\mathrm{aq}})\to \underset{\mathrm{S}}{{\mathrm{X}}^{+2}(\mathrm{aq}})+\underset{{10}^{-3} +2\mathrm{S}}{2{\mathrm{B}}^{-}\left(\mathrm{aq}\right)}$

$\mathrm{YB}\to \underset{{10}^{-3}}{{\mathrm{Y}}^{+}\left(\mathrm{aq}\right)}+\underset{{10}^{-3}}{{\mathrm{B}}^{-}\left(\mathrm{aq}\right)}$

$$\begin{gathered} {\mathrm{K}}_{\mathrm{sp}}=\mathrm{x}\times (2\mathrm{x}{)}^2=\left[{\mathrm{X}}^{+2}\right]\times {\left[{\mathrm{B}}^{-}\right]}^2 \\ \Rightarrow 4{\mathrm{x}}^3=\mathrm{S}\times {\left(2\mathrm{S}+{10}^{-3}\right)}^2 \\ \Rightarrow 4{\mathrm{x}}^3\cong \mathrm{S}\times {\left({10}^{-3}\right)}^2 \\ \Rightarrow 4{\mathrm{x}}^3=\mathrm{S}\times {10}^{-6} \\ \Rightarrow \mathrm{S}=4\times {\mathrm{x}}^3\times {10}^6 \end{gathered}$$