Chemistry - Ionic Equilibrium Question with Solution | TestHub

Total dissolved Pb: $S=\left[{\mathrm{Pb}}^{2+}\right]+\left[\mathrm{Pb}(\mathrm{OH}{)}_3^{-}\right]=\frac{K_{sp}}{{\left[{\mathrm{OH}}^{-}\right]}^2}+K_c\left[{\mathrm{OH}}^{-}\right]$.

For minimum $S$: $\frac{\mathrm{d}S}{\mathrm{d}\left[{\mathrm{OH}}^{-}\right]}=-\frac{2K_{sp}}{{\left[{\mathrm{OH}}^{-}\right]}^3}+K_c=0$.

${\left[{\mathrm{OH}}^{-}\right]}^3=\frac{2K_{sp}}{K_c}$, so $\left[{\mathrm{OH}}^{-}\right]=\sqrt[3]{2K_{sp}/K_c}$.

Answer: (B).