# What is the molecular weight of air?

Aug 22, 2016

28.96 g / mol

#### Explanation:

This is a fun question.

According to table 5.1 on page 155 of Atmospheric Science: An Introductory Survey By John M. Wallace, Peter V. Hobbs (table can be seen here on Google Books) dry air is composed of:

Nitrogen: 78.084%
Oxygen: 20.946%
Argon: 0.934%
Carbon dioxide: 0.03%

If you add these up you get: 78.084 + 20.946 + 0.934 + 0.03 = 99.994% (the remaining material 100 - 99.994 = 0.006% consists of trace amounts of other gases)

These percentages are percentage volume and one mole of gas at stand temperature and pressure occupies 22.4 liters (but that is really irrelevant to this question as the volumes cancel).

The atomic / molecular weights are:

Nitrogen: 14.0067 x 2 = 28.0134 g/mol (remember it is ${N}_{2}$)
Oxygen: 15.9994 x 2 = 31.9988 g/mol (remember it is ${0}_{2}$)
Argon: 39.948 g/mol
Carbon dioxide: 44.01 g /mol

We know the percentage composition so we can use that to work out the weight of each component:

Nitrogen: (78.084 / 100) x 28.0134 = 21.8739 g/mol
Oxygen: (20.946 / 100) x 31.9988 = 6.7025 g/mol
Argon: (0.934 / 100) x 39.948 = 0.373 g/mol
Carbon dioxide: (0.03 / 100) x 44.01 = 0.013203 g/mol

If we add these up we get: 21.8739 + 6.7025 + 0.373 + 0.013203 = 28.96 g / mol.