A gas X is produced as a by-product in one of the industrial procedures used to make sodium hydroxide. The compound Y, which is employed as a bleaching agent in the chemical industry, is produced when the gas X combines with lime water.

The compound X and Y could be?

The reaction of X with lime water occurs as follows:
 $C{l}_2+\mathit{CaC}{O}_3\to \mathit{CaOC}{l}_2+C{O}_2$

When sodium hydroxide is formed the gas X will react with lime water milky to give a bleaching agent $\mathit{CaOC}{l}_2$. So the gas X should be chlorine gas. Compound Y is calcium oxychloride ($\mathit{CaOC}{l}_2$), often known as bleaching powder and utilized as a bleaching agent in the chemical industry.

Hence, the compound X and Y are ${\mathit{Cl}}_2$ and $\mathit{CaOC}{l}_2$ respectively.