How is \[C{{O}_{2}}\] gas tested in the laboratory?

Hint: The chemical used for testing carbon dioxide in the laboratory is an aqueous solution of a hydroxide of an alkaline earth metal. Sometimes carbon dioxide (\[C{{O}_{2}}\]) can also be tested by using a flame. The formation of insoluble white precipitate indicates the presence of carbon dioxide.

Complete step by step answer:
There are two tests for the detection of carbon dioxide.
Firstly, \[C{{O}_{2}}\] will extinguish a flame, though, as any oxygen free gas will also turn off a flame, this is a poor test and may possibly result in misidentification.
The best way of testing Carbon dioxide is to bubble it through “lime water”.

\[Ca{{(OH)}_{2}}_{(aq)}+C{{O}_{2}}_{(g)}\to CaC{{O}_{3}}_{(s)}+{{H}_{2}}{{O}_{(l)}}\]
(Lime water)

In the above reaction carbon dioxide reacts with calcium hydroxide and forms calcium carbonate and water.
After passing \[C{{O}_{2}}\]through lime water it turns into milky. Lime water turns milky as the \[Ca{{(OH)}_{2}}\](Calcium hydroxide) reacts with \[C{{O}_{2}}\]to form \[CaC{{O}_{3}}\](Calcium Carbonate) which is insoluble in water and thus forms a milky white precipitate.

Additional Information:
Let us see the ways to prepare \[C{{O}_{2}}\].
Prepare a small amount of hydrochloric acid (\[HCl\]), of 2 M concentration and add few granules of \[CaC{{O}_{3}}\]in to a test tube and close it by bung (a small rubber cork).

\[CaC{{O}_{3(s)}}+2HC{{l}_{(aq)}}\to CaC{{l}_{2(aq)}}+{{H}_{2}}{{O}_{(l)}}+C{{O}_{2(g)}}\]

In the above reaction calcium carbonate reacts with hydrochloric acid and forms calcium chloride, water and carbon dioxide as a gas.
Now we can use the formed \[C{{O}_{2}}\]for testing purposes.

Note: Don't be confused between Calcium Hydroxide with Calcium oxide. Both are not the same. Calcium oxide has the chemical formula CaO while calcium hydroxide has the chemical formula \[Ca{{(OH)}_{2}}\].