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Chemical $A$ is used for water softening to remove temporary hardness, $A$ reacts with $N{a_2}C{O_3}$ to generate caustic soda. When $C{O_2}$ is bubbled through $A$, it turns cloudy. What is the chemical formula of $A$ ?
A. $CaC{O_3}$
B. $CaO$
C. $Ca{(OH)_2}$
D. $Ca{(HC{O_3})_2}$

Answer
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Hint: It is an inorganic compound which is also known as slaked lime. It is a colorless crystal that appears like white powder. It forms when calcium oxide is mixed with water. It is also known as hydrated lime or quicklime or caustic lime. Lime water is the saturated solution of the given chemical $A$.

Complete answer:
The chemical $A$ is calcium hydroxide having chemical formula as $Ca{(OH)_2}$. It is used for water softening to remove the temporary hardness of water.
When calcium hydroxide is reacted with sodium carbonate the formation of caustic soda takes place the following reaction occur as:
$Ca{(OH)_2} + N{a_2}C{O_3} \to CaC{O_3} \downarrow + NaOH$
When calcium hydroxide is treated with carbon dioxide gas then it forms calcium carbonate. And the solution turns into a milky appearance. The following reaction shown as:
$Ca{(OH)_2} + C{O_2} \to CaC{O_3} \downarrow + {H_2}O$

So, option (C) is correct.

Note:
Soap does not form lather with hard water. This hardness of water is due to the presence of bicarbonates and sulphates of metals that are calcium and magnesium. The temporary hardness is a type of water hardness which is caused by the presence of dissolved bicarbonate of calcium and magnesium. These metal cations make the water hard. There are many ways that are used for the softening of water. Softening of water is the process of removing water hardness. One of the ways of water softening is done with lime. In this process, calcium hydroxide is used to soften water by removing the metal ions. As hydrated lime is mixed with the water to raise its $pH$ level and then the ions get precipitated that causes water hardness. The lime softening process has many benefits as in the reduction of dissolved minerals in the water and the reduction of heavy metals and other elements.