Notes on Carbon Dioxide and Calcium Carbonate Chemistry

Carbon Dioxide Reaction with Hydroxide Ions

The balanced chemical equation for the reaction between carbon dioxide gas and hydroxide ions:
CO2(g) + 2OH^-(aq) \rightarrow CO3^{2-}(aq) + H_2O(l)

When CO2(g) is bubbled into a saturated solution of Ca(OH)2, a cloudy precipitate of CaCO_3(s) forms.
At 25^\circ C, the solubility-product constant, K{sp}, of CaCO3(s) is 3.4 \times 10^{-9}. (Note the temperature dependence of K_{sp}).

Net ionic equation for the precipitation of CaCO3(s) from the solution: Ca^{2+}(aq) + CO3^{2-}(aq) \rightarrow CaCO_3(s)

Calculation of [CO3^{2-}] in the saturated solution of Ca(OH)2 just before CaCO_3(s) begins to precipitate:
The K{sp} expression for calcium carbonate (CaCO3) is given by: K{sp} = [Ca^{2+}][CO3^{2-}]
In a saturated solution of Ca(OH)_2, the concentration of Ca^{2+} ions can be determined.
Just before precipitation, the ion product is equal to the K_{sp}.
We are asked to find the concentration of carbonate ions [CO3^{2-}] just before the calcium carbonate CaCO3(s) begins to precipitate.
Given that K_{sp} = 3.4 \times 10^{-9}, and we need to consider the calcium ion concentration [Ca^{2+}] in the saturated calcium hydroxide solution.