(i) Identification of X and Y:
Compound X is Gypsum (\( \text{CaSO}_4 \cdot 2\text{H}_2\text{O} \)), and compound Y is Plaster of Paris (\( \text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O} \)). Plaster of Paris loses water molecules upon heating to form Gypsum. Gypsum is used as a support for fractured bones.
(ii) Obtaining X from Y:
Gypsum (\( \text{CaSO}_4 \cdot 2\text{H}_2\text{O} \)) can be converted back to Plaster of Paris (\( \text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O} \)) by heating it at 373 K. This process removes some of the water molecules from Gypsum to form Plaster of Paris.