How to Calculate the Molar Mass of Air

The molar mass of a hydrogen molecule (H₂) is the lowest among all compounds under normal conditions.

The weight of an atom or a molecule is too small to make any meaningful measurement, and hence, they are grouped together so that the numbers thus obtained can be used for practical calculations. When molecules are grouped together they form a mole.

Molar mass is the physical property of a substance and is denoted by 'M'. It can also be defined as the weight of a mole of a substance (in gm or kg), in which there are 6.022 × 1023 atoms of the substance. This value is known as the 'Avogadro's Number'.

According to the International System of Units (SI unit), the unit of molar mass is Kg/Kmol, which is usually expressed as g/mol. It allows comparison between the amount of a substance and its mass.

So how to calculate the molar mass of air, which is composed of various gases in different proportions? Air is a mixture, and the formula to obtain the average molar mass of a mixture is as given below,

M = ∑a_i × Y_i

Here,
M = Molar Mass
a_i = Fraction of the Constituent 'i'
Y_i = Molar Mass of the Constituent 'i'

Air contains about 0.7808 fractions (78.08%) of nitrogen, 0.2905 fractions (29.05% ) of oxygen, 0.00933 fractions (0.933%) of argon, and about 0.003 fractions (0.03%) of carbon dioxide. The rest of the elements have relatively small influence on the calculation of the molar mass.

These elements include 0.000018 fractions (0.0018%) of neon, 0.000005 fractions (0.0005%) of helium, 0.000001 fractions (0.0001%) of krypton, 0.0000005 fractions (0.00005%) of hydrogen, and 9 × 10^-8 fractions (9 × 10^-6%) of xenon.

The steps for the calculation of molar mass of an element have been given here.

• Nitrogen = 28 g/mol
• Oxygen = 32 g/mol
• Argon = 40 g/mol
• Carbon Dioxide = 44 g/mol
• Neon = 20 g/mol
• Helium = 4 g/mol
• Krypton = 83.8 g/mol
• Hydrogen = 2 g/mol
• Xenon = 131.29 g/mol

Replace the values for the fractions of constituents present in air along with their molar mass.

M =(0.7808 × 28) + (0.2095 × 32) + (0.00933 × 40) + (0.0003 × 44) + (0.000018 × 20) + (0.000005 × 4) +(0.000001 × 83.8) + (0.0000005 × 2.02) +(9 × 10-8 × 131.29)
= 21.86 + 6.704 + 0.373 + 0.013 + 0 + 0 + 0 + 0 + 0
= 28.96

Hence, the molar mass of dry air is 28.96 g/mol.

In English units, the standard unit of measurement of molecular mass of air is 'lbm/lbmol' (pound - mass/pound - mole). The actual value of molar mass of air remains the same as the fractions of its constituents which are taken into consideration for the calculations. Hence, the molar mass of air, in English units, is 28.96 lbm/lbmol.