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

${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}\left(s\right)}+2\text{HC}{l}_{\left(aq\right)}\to 2\text{NaC}{l}_{\left(aq\right)}+{\text{H}}_{\text{2}}{\text{O}}_{\left(l\right)}+{\text{CO}}_{2\left(g\right)}\uparrow$

When this ${\text{CO}}_{\text{2}}$ is passed through lime water it turns milky white substance,

${\text{CO}}_{2\left(g\right)}\uparrow +\text{Ca}{\left(\text{OH}\right)}_{\text{2}\left(aq\right)}\to \underset{Milkywhite}{{\text{CaCO}}_{\text{3}}}\downarrow +{\text{H}}_{\text{2}}{\text{O}}_{\left(l\right)}$