In one of the industrial processes used for the manufacture of sodium hydroxide,a gas $X$ is formed as a by-product. The gas $X$ reacts with lime water to give a compound $Y$,which is used as a bleaching agent in the chemical industry. Identify $X$ and $Y$ and provide the chemical equations for the reactions involved.

(X=CL_2, Y=CAOCL_2) In the chlor-alkali process for the manufacture of sodium hydroxide,hydrogen gas and chlorine gas $(X)$ are formed as by-products.
When chlorine gas $(X)$ reacts with dry slaked lime (lime water),it forms calcium oxychloride (bleaching powder),which is compound $Y$.
The chemical reactions are as follows:
$2NaCl(aq) + 2H_2O(l) \rightarrow 2NaOH(aq) + Cl_2(g) + H_2(g)$
Here,$X = Cl_2$ (Chlorine gas).
$Ca(OH)_2(s) + Cl_2(g) \rightarrow CaOCl_2(s) + H_2O(l)$
Here,$Y = CaOCl_2$ (Calcium oxychloride or bleaching powder).