(X=CACO3, Y=CA(OH)2, G=CL2, Z=CAOCL2) $1$. The gas evolved at the anode during the electrolysis of brine ($NaCl$ solution) is chlorine gas $(G = Cl_2)$.
$2$. When chlorine gas is passed over dry slaked lime $(Y = Ca(OH)_2)$,it produces bleaching powder $(Z = CaOCl_2)$,which is used for disinfecting drinking water.
$3$. The reaction is: $Ca(OH)_2 + Cl_2 \rightarrow CaOCl_2 + H_2O$.
$4$. Since $Y$ is calcium hydroxide,the metal carbonate $X$ is calcium carbonate $(CaCO_3)$.
$5$. When $CaCO_3$ reacts with an acid (e.g.,$HCl$),it releases $CO_2$ gas: $CaCO_3 + 2HCl \rightarrow CaCl_2 + H_2O + CO_2$.
$6$. When this $CO_2$ is passed through lime water $(Ca(OH)_2)$,it turns milky due to the formation of $CaCO_3$: $Ca(OH)_2 + CO_2 \rightarrow CaCO_3 + H_2O$.