Slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2}\), is used to soften hard water by
removing calcium ions from hard water through the reaction
\(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{Ca}^{2+}(a q)+2
\mathrm{HCO}_{3}^{-}(a q) \rightarrow\)
\(2 \mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\)
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 \(\left(K_{\text {sp }}=8.7 \times
10^{-9}\right)\).