When dil. HCl is added to sodium carbonate, a colourless gas is evolved which turns lime water milky. The milkiness of lime water is due to the formation of

The chemical reactions are given below.

${\text{Na}}_{\text{2}}{\text{CO}}_3+2\text{HC}l\to 2\text{NaC}l+{\text{H}}_{\text{2}}\text{O}+{\text{CO}}_2\uparrow$

${\text{CO}}_{\text{2}}+\text{Ca}{\left(\text{OH}\right)}_{\text{2}}\to \underset{\text{Milky\hspace{0.17em}white}}{{\text{CaCO}}_{\text{3}}}+{\text{H}}_{\text{2}}\text{O}$

Therefore, carbon dioxide gas is responsible to get a milkyness of lime water.