Please see the work below.
Work Step by Step
We know that under the same conditions of temperature and pressure equal volumes of all gases contain an equal number of molecules.Dry air has $N_2$ with molar mass 28 and $O_2$ having a molar mass 32. When water with molar mass 18 is mixed with it, it replaces some of $O_2$ and $N_2$ which have a higher mass. Thus, for the same volume of air, moist air will weigh less than that of dry air. Since the moist air comes down from a rain cloud, dry air will rise creating low pressure and hence a low pressure shows an imminent rainfall.