What happens when carbon dioxide gas is passed through lime water and why does it is disappear when excess carbon dioxide

When carbon dioxide gas is passed through lime water, it turns milky or turbid due to the formation of calcium carbonate which is insoluble in water. Following is the chemical equation for the reaction

Ca(OH)2 + CO2 → CaCO3 + H2O

However, when excess of carbon dioxide is passed through the solution, the turbidity disappears and a clear solution is obtained due to the formation of calcium bicarbonate, which is soluble in water. Following is the chemical equation for the reaction

CaCO3 + H2O + CO2 → Ca(HCO3)2