What happens when Carbon dioxide is passed through lime water for a short time?

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Solution

The chemical formula of lime water: $Ca {(OH)}_{2}$
When we pass carbon dioxide through lime water for a short duration, a white calcium carbonate precipitate forms and it turns into lime water milky.
Chemical reaction can be written as:
$\underset{(Calcium hydroxide)}{Ca {(OH)}_{2}} + \underset{(Carbon dioxide)}{{CO}_{2}} \to \underset{(Calcium carbonate)}{{CaCO}_{3}} + \underset{(Water)}{H_{2} O}$

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What happens when carbon dioxide gas is passed through lime water for a sufficient time?

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