When carbon dioxide ($CO_2$) is mixed with limewater ($Ca(OH)_2$), they react to form a milky white precipitate of calcium carbonate ($CaCO_3$). This reaction is used as a test for carbon dioxide.

Here's how the reaction occurs:

1. Limewater is a clear, colorless solution of calcium hydroxide ($Ca(OH)_2$) in water.

2. Carbon dioxide is a colorless, odorless gas.

3. When carbon dioxide is bubbled through limewater, it dissolves in the water and reacts with the calcium hydroxide to form calcium carbonate and water:

$CO_2(g) + Ca(OH)_2(aq) \rightarrow CaCO_3(s) + H_2O(l)$

4. Calcium carbonate is a white, insoluble solid, which appears as a milky white precipitate in the solution. This makes the limewater turn cloudy.

The reaction is reversible:

If you continue bubbling carbon dioxide through the limewater, the milky white precipitate will eventually dissolve. This is because the excess carbon dioxide will react with the calcium carbonate to form calcium bicarbonate ($Ca(HCO_3)_2$), which is soluble in water:

$CaCO_3(s) + CO_2(g) + H_2O(l) \rightarrow Ca(HCO_3)_2(aq)$

In summary:

* Carbon dioxide reacting with limewater results in the formation of a milky white precipitate of calcium carbonate, which is a characteristic indication of the presence of carbon dioxide.

* The reaction is reversible, and excess carbon dioxide can dissolve the precipitate.