Question

“Dry air” is defined as air with no water vapor, and the molecular weight of air, Mair = 28.97 kg/kmol, is for dry air (zero humidity). “Wet air” is typically defined as air with 100% humidity.

(a) Calculate the mol fraction of water vapor in wet air at STP conditions. Give your answer in units of PPM to three significant digits.

(b) Compare the molecular weight of dry air and wet air at STP conditions. Which air is heavier? Explain. Comment about how humid air feels compared to dry air. In particular, in the summer time most people say that high-humidity air feels “thicker” or “heavier” than low-humidity air at the same temperature. Does this feeling agree with your calculations?

Answer 1

(a) Dry air has a molar mass of 0.029 kg. It is denser than water vapour, which has a molar mass of 0.018 kg. Therefore, humid air is lighter than dry air.

If the total atmospheric pressure is P and the water vapour pressure is p, the partial pressure of the dry air component is P - p .

The weight ratio of the two components, water vapour and dry air is:

kg water vapour / kg dry air = 0.018 ×p / ( 0.029 ×(P - p ) ) = 0.62 ×p / (P - p )

At room temperature P - p is nearly equal to P, which at ground level is close to 100,000 Pa,

and at 100% humidity p = 1

so, approximately: kg water vapour / kg dry air = 0.62 ×10^-5

(b) The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear counter-intuitive. This occurs because the molar mass of water (18 g/mol) is less than the molar mass of dry air(around 29 g/mol). For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume (Avogadro's Law). So when water molecules (water vapor) are added to a given volume of air, the dry air molecules must decrease by the same number, to keep the pressure or temperature from increasing. Hence the mass per unit volume of the gas (its density) decreases.

in the summer time most people say that high-humidity air feels “thicker” or “heavier” than low-humidity air at the same temperature but this feeling does not agree with our calculations