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When carbon dioxide is passes into lime water (a solution of calcium hydroxide) an insoluble precipitate of calcium carbonate is produced this is composed of tiny particles that cause the milkiness.

Ca(OH)2 +CO2 -> CaCO3 +H2O

When excess carbon dioxide is passed in this produces some carbonic acid, H2CO3 that reacts with the calcium carbonate to produce soluble calcium hydrogen carbonate, (calcium bicarbonate).

CO2 +H2O -> H2CO3

H2CO3 + CaCO3 -> Ca(HCO3)2

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