Lime water is used for the detection of Carbon dioxide.
Lime water is basically a calcium compound called calcium hydroxide with molecular formula Ca(OH)2. When Carbon dioxide is pass through it, it turns milky due to the formation of calcium carbonate.
The balanced equation for the reaction is as follow :-
CO2 + Ca (OH)2 → CaCO3 + H2O
This CaCO3 is white precipitate which make the solution milky or cloudy.