**Answer:**

**Introduction:**
Lime water is a solution of calcium hydroxide (Ca(OH)2) in water. When lime water is exposed to air, it turns milky due to the formation of a precipitate called calcium carbonate (CaCO3). This reaction occurs because air contains carbon dioxide (CO2) which reacts with calcium hydroxide to form calcium carbonate.

**Explanation:**
When lime water is exposed to air, the following reaction takes place:
Ca(OH)2 + CO2 → CaCO3 + H2O

**Carbon Dioxide (CO2):**
Carbon dioxide is a gas that is present in the air we breathe. It is produced by various natural processes such as respiration, decay of organic matter, and combustion. Carbon dioxide is also released during the fermentation process in drinks like beer and soda.

**Formation of Calcium Carbonate:**
When carbon dioxide from the air reacts with calcium hydroxide in lime water, it forms calcium carbonate, which is insoluble in water. As a result, the calcium carbonate precipitates out of the solution, giving it a milky appearance.

**Equation:**
Ca(OH)2 + CO2 → CaCO3 + H2O

**Significance of Lime Water Turning Milky:**
The milky appearance of lime water when exposed to air is an important indicator that carbon dioxide is present in the air. This property of lime water is used as a simple and inexpensive test for the presence of carbon dioxide gas.

**Carbon Dioxide Test:**
The test for carbon dioxide using lime water is commonly known as the "limewater test" or "carbon dioxide test." It is often used in science experiments and demonstrations to show the presence of carbon dioxide gas. When carbon dioxide is bubbled through lime water, it turns milky due to the formation of calcium carbonate.

**Conclusion:**
In conclusion, lime water turns milky when exposed to air because air contains carbon dioxide. The carbon dioxide reacts with calcium hydroxide in lime water to form calcium carbonate, which precipitates out of the solution. This property of lime water is used as a simple test to detect the presence of carbon dioxide gas.