Slaked lime \(\left[\mathrm{Ca}(\mathrm{OH})_{2}ight]\) is used to soften hard water by removing calcium ions from hard water through the reaction

\[\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \longrightarrow{ }_{2 \mathrm{CaCO}_{3}(s)}+2 \mathrm{H}_{2} \mathrm{O}(l)\]

Although \(\mathrm{CaCO}_{3}(s)\) is considered insoluble, some of it does dissolve in aqueous solutions. Calculate the molar solubility of \(\mathrm{CaCO}_{3}\) in water \(\left(K_{\mathrm{sp}}=8.7 \times 10^{-9}ight)\).