Avogadro's number and the mass of an air molecule

Theory, modelling, guessing and experimenting are all intertwined. Each step progressing from one idea to the next. However, this is a very cleaned up view of the progress of science. Science is much messier than this and many ideas lead to dead ends and wrong predictions.

Knowing:

• The diameter of an air molecule, 4 x 10^-10m,
• The space occupied by a molecule in liquid, (d³= {4 x 10^-10}³= 64 x 10^-30m³),
• The change of volume from a liquid to gas

You can calculate how many molecules there are in a room, (4m x 3m x 3m = 24 m³) giving about 5 x 10²⁶ molecules.

This is in fact an estimate of the Avogadro number for a kilo-mole. A kilogram mole of any gas contains 6 x 10²⁶molecules. It occupies 22.4 m³at 0 °C, or about 24 m³at room temperature, and atmospheric pressure.

Mass of an air molecule

Number of molecules in a room 24 m³, N = 5 x 10²⁶

Mass of air molecules in a room 24 m³, M = Vp = 24 x 1.2 kg = 28.2 kg

Therefore, Mass of an air molecule = 28.2 / 5 x 10^-26 = 5.6 x 10^-26kg

When students know more about the structure of air (mainly nitrogen and oxygen) then the mass of their atoms can be estimated (they are fairly close in mass).

All this comes from imagining a theoretical picture, guided by the things we know about nature, such as Newton's Laws of Motion, and then making estimates and measurements.