You can identify carbon dioxide by bubbling it through limewater; if carbon dioxide is present, the limewater will turn milky.
This change occurs due to a chemical reaction. Limewater is a solution of calcium hydroxide (Ca(OH)₂). When carbon dioxide (CO₂) is bubbled through it, the following reaction takes place:
Ca(OH)₂(aq) + CO₂(g) → CaCO₃(s) + H₂O(l)
The reaction produces calcium carbonate (CaCO₃), which is an insoluble solid. This solid precipitates out of the solution in the form of tiny particles, causing the limewater to appear milky or cloudy. If you continue to bubble CO₂ through the solution, the milky solution will eventually become clear again as the calcium carbonate reacts further to form soluble calcium bicarbonate.
Therefore, the milkiness of limewater is a characteristic and easily observable indicator of the presence of carbon dioxide.