The mole and the Avogadro constant

The unit for the amount of a substance is the mole. It is defined as the amount of a substance that contains the same number of particles (atoms or molecules) as the number of atoms in 12 g of the isotope carbon-12. This number is known as the Avogadro constant (N_A or L) and is 6.02 x 10²³ particles per mole.

The ratio of the mass of one mole of the substance to one twelfth of the mass of one mole of carbon-12 is called the relative molecular mass of the substance - it is 32 for oxygen, 2 for hydrogen and so on.

A knowledge of the Avogadro constant enables us to calculate the number of molecules in any mass of a substance and therefore to get an idea of the size of one molecule.
For example, a drop of water of volume 1.0 cm³ has a mass of 1 g. The relative molecular mass of water is 18, and therefore this drop of water must contain 6.02x10²³/18 = 3.34x10²² molecules.

Avogadro's constant is the number of particles in a mole of the substance. This number is always the same.
So in:
1 mole of hydrogen (2 g) there are 6.02x10²³ molecules (hydrogen exists as H₂)
1 mole of oxygen (32 g) there are 6.02x10²³ molecules (oxygen exists as O₂)
1 mole of copper (63 g) there are 6.02x10²³ atoms
1 mole of uranium 235 (235 g) there are 6.02x10²³ atoms

For example if we have 2 kg of uranium in a fuel rod we have 2000/235 = 8.51 moles and this contains 8.51x6.02x10²³ = 5.12x10²³ atoms and so 5.12x10²³ uranium nuclei.

The average volume of a water molecule must therefore be 2.99x10^{- 23} cm³, and if we assume the molecules to be spherical the diameter of a water molecule is about 2x10^-8 cm or 2x10^-10 m, a result confirmed by X-ray diffraction.