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Write an equation for the reaction which takes place when gas X reacts with lime water to form white precipitate Y.

Answer
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Hint:As it's given that the gas X reacts with lime water and we know that limewater is the common name for a dilute aqueous solution of calcium hydroxide. Calcium hydroxide has the formula $Ca{\left( {OH} \right)_2}$ .

Complete answer:
Given in the question is a gas X reacts with lime water and forms a compound Y.
Carbon dioxide \[\left( {C{O_2}} \right)\] gas reacts with lime water which is a solution of calcium hydroxide having formula $Ca{\left( {OH} \right)_2}$ , and forms a white precipitate which appears milky because of calcium carbonate, \[CaC{O_3}\] . Adding more carbon dioxide results in the precipitate dissolving to form a colourless solution of calcium hydrogen carbonate.
So here,
Compound ‘X’ is carbon dioxide gas $ \to C{O_2}$
Compound ‘Y’ is calcium carbonate $ \to CaC{O_3}$
The chemical equation for the reaction which take place
\[Ca{\left( {OH} \right)_{2(s)}} + C{O_{2(g)}} \to CaC{O_{3(s)}} + {H_2}{O_{\left( l \right)}}\]
Hence, Calcium Carbonate is formed.
The compound Y called calcium carbonate is the active ingredient in agricultural lime and is created when calcium ions in hard water react with carbonate ions to create lime scale.

Note:
This is used as a test for carbon dioxide \[\left( {C{O_2}} \right)\] . When carbon dioxide is bubbled through limewater the lime water changes from colourless to milky. Calcium carbonate is medicinally used as a calcium supplement or as an antacid, but excessive consumption can be hazardous and cause poor digestion. It is the common substance that is found in the rocks as the minerals calcite and aragonite (most notably as limestone, which is a type of sedimentary rock consisting mainly of calcite) and is the main component of pearls and the shells of marine organisms, snails, and eggs.