Chemistry - Ionic Equilibrium Question with Solution | TestHub

Concept of common $-\mathrm{i}\mathrm{o}\mathrm{n}$ will be applicable for $\mathrm{O}{\mathrm{H}}^{-}$ group.

$\text{Al}{\left(\text{OH}\right)}_3\rightleftharpoons \underset{\text{S }}{\text{A}{\text{l}}^{\text{3+}}}+\underset{\left(3s+0.2\right)}{3\left(\text{O}{\text{H}}^{-}\right)}$

$\mathrm{K}\mathrm{s}\mathrm{p}$ for $\mathrm{A}\mathrm{l}{\left(\mathrm{O}\mathrm{H}\right)}_3=2.4\times {10}^{-24}=\mathrm{s}{\left(3\mathrm{s}+0.2\right)}^3$

Looking at $\mathrm{K}\mathrm{s}\mathrm{p},$ it is clear that $\mathrm{s}$ will be much lesser than $0.2.$

Or, $\mathrm{s}\ll 0.2$

$\mathrm{s}\times {\left(0.2\right)}^3=2.4\times {10}^{-24}\Rightarrow \mathrm{s}=2.4\times {10}^{-24}/0.008$
or, $\mathrm{s}=3\times {10}^{-22}$