Chlor-alkali process is used for manufacturing sodium hydroxide which yields chlorine and hydrogen gases are formed as by-products.
2NaCl(aq) + 2H2O(l) →2NaOH(aq) + Cl2(g) +H2(g)
Chlorine gas on reaction with limewater produces bleaching powder. Bleaching powder is used as a bleaching agent in chemical industries.
Ca(OH)2(s) + Cl2(g) →CaOCl2(s) + H2O(l)
Therefore, X is chlorine gas, and Y is bleaching powder.