Chemical A is used for water softening to remove temporary hardness. A reacts with sodium carbonate to generate caustic soda. When CO₂ is bubbled through a solution of A, it turns cloudy. What is the chemical formula of A

Presence of the calcium bicarbonates and magnesium bicarbonates in water causes temporary hardness. This can be removed by treating water with $\mathrm{Ca}(\mathrm{OH}{)}_2$ as it forms insoluble precipitate which can be removed by filtration. Therefore, chemical A is identified as calcium hydroxide.

$\underset{\mathrm{Chemical} \mathrm{A}}{\mathrm{Ca}{\left(\mathrm{OH}\right)}_2}+\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}_2\to 2{\mathrm{CaCO}}_3\downarrow +2{\mathrm{H}}_2\mathrm{O}$

Calcium hydroxide reacts with sodium carbonate to forms caustic soda (sodium hydroxide).

$\underset{\mathrm{Chemical} \mathrm{A}}{\mathrm{Ca}{\left(\mathrm{OH}\right)}_2}+{\mathrm{Na}}_2{\mathrm{CO}}_3\to {\mathrm{CaCO}}_3\downarrow +2\mathrm{NaOH}$

It shows milky appearance when calcium hydroxide treated with carbon dioxide gas.
$\underset{\mathrm{Chemical} \mathrm{A}}{\mathrm{Ca}(\mathrm{OH}{)}_2}+{\mathrm{CO}}_2\to \underset{\mathrm{cloudy} \mathrm{appearance}}{{\mathrm{CaCO}}_3\downarrow }+{\mathrm{H}}_2\mathrm{O}$