Equation of X with Carbon Dioxide
The equation of substance X with carbon dioxide can be represented as follows:
X + CO2 → H2O + Y

Obtaining Substance X
Substance X, commonly known as limewater or calcium hydroxide, can be obtained by adding calcium oxide (quicklime) to water. The chemical equation for this reaction is:

CaO + H2O → Ca(OH)2

Testing Carbon Dioxide with Substance X
When substance X (calcium hydroxide) is exposed to carbon dioxide, it reacts to form calcium carbonate (Y) and water. The equation for this reaction is:

Ca(OH)2 + CO2 → CaCO3 + H2O

This reaction is commonly used to test for the presence of carbon dioxide gas. The limewater solution turns cloudy or milky when carbon dioxide is bubbled through it, indicating the formation of calcium carbonate.

Explanation
Substance X, calcium hydroxide, is a white powder that is sparingly soluble in water. When calcium oxide (quicklime) is added to water, it undergoes a chemical reaction to form calcium hydroxide, which is a strong base. Calcium hydroxide is commonly used in agriculture, construction, and water treatment.

When carbon dioxide gas is bubbled through a limewater solution, it reacts with calcium hydroxide to form calcium carbonate and water. Calcium carbonate is a white solid that is insoluble in water. This reaction is used to test for the presence of carbon dioxide gas in a sample. The formation of calcium carbonate causes the limewater solution to turn cloudy or milky, indicating the presence of carbon dioxide. This reaction is also used in the production of chalk, limestone, and marble.

A. X- calcium hydroxide --- Ca[OH]2
Ca[OH]2 + CO2 ------>  CaCO3 + H2O
b. Calcium hydroxide is obtained by the reaction of calcium oxide with water.
    CaO + H2O -------> Ca[OH]2 + Heat