How To Calculate Molar Mass Of Air

The molar mass of any solid, liquid, or gaseous substance is the number of grams of the substance in its molecular (molar) form that contains 6.0221367 X e^23 atoms of the substance (Avogadro's Number). This is because the mass of a substance is dependent on the molecular weight of the substance, which is determined by the number of protons and neutrons in the nucleus of the atom. Therefore the molar mass of a substance such as air is dependent on the sum of all the volume fractions of each molecular component times their individual molecular weights.

Step 1

Determine the major gaseous elements that comprise air and their average volumetric fractions comprising air (where air equals 1 volumetric unit). In order of greatest magnitude – Nitrogen comprises 78.09 percent of air, so its volumetric fraction is 0.7809. Oxygen comprises 20.95 percent of air, so its volumetric fraction is 0.2095. Argon comprises 0.933 percent or a fraction of 0.00933. Carbon dioxide comprises 0.03 percent, or a fraction of 0.0003. Following these major four are the remainder, each of which whose fraction is too small to affect the molar mass calculation: Neon 0.000018; helium 0.000005; krypton 0.000001, hydrogen 0.0000005, and xenon 0.09 X 10^-6.
(As a side note, most hydrogen in the world is combined with oxygen to form water).

Step 2

Multiply each fraction corresponding to a component times its molecular weight (remembering that molecules of nitrogen and oxygen both contain two atoms when in air, so their respective atomic weights of 14.007 and 16 must be multiplied by 2 to yield molecular weights of 28.014 and 32).

Nitrogen: 28.014 X 0.7809 = 21.876 Oxygen: 32 X 0.2095 = 6.704 Argon: 39.94 X 0.00933 = 0.3726 Carbon dioxide: 44.01 X 0.0003 = 0.013 Neon: 20.18 X 0.000018 = 3.6324 X 10^-4 Helium: 4.00 X 0.000005 = 2.0 X 10^-5 Krypton: 83.8 X 0.000001 = 8.38 X 10^-5 Hydrogen 2.02 X 0.0000005 = 1.01 X 10^-6 Xenon: 131.29 X 0.09 X 10^-6 = 1.18 X 10^-5

Step 3

Add all the molecular weight fractions to arrive at a molar mass of air of 28.9656. What this number means is that one mole or one molecular measure of air that contains 6.0221367 X e^23 molecules of gas weighs 28.9656 grams at standard atmospheric conditions of 60 degrees Fahrenheit and 14.696 pounds-per-square-inch absolute (psia). It would occupy 22.4 liters or 22.4/28.3168 liter/cubic foot = 0.7910 cubic feet.