why moist air is lighter than dry air?

Avogadro's law tells us that a given number of gas molecules (e.g., a mole) always occupies the same amount of space at a given temperature, regardless of the chemical composition of the gas. Thus, the density of any gas depends on the molecular mass of the gas molecules. Dry air is a mixture of 80% nitrogen molecules (N2 - molecular mass = 28) and 19% oxygen molecules (O2 - molecular mass = 32); it has an average molecular mass of 28.1g per mole.

The molecular mass of water (H2O) is 18. Thus, while liquid water is much more dense than air, gaseous water is less dense than dry air. Therefore, humid air, which contains a mixture of air and gaseous water, is lighter (less dense) than dry air.