The mole - Higher

Introducing the mole, the unit of measurement for the number of particles in a substance

It is often useful in chemistry to know the number of atoms, ions or molecules involved in a chemical reaction. The mole is the unit for amount of substance. It is abbreviated to mol.

1 mol is the amount of substance that contains the same number of particles as there are atoms in 12.0 g of carbon-12.

Since atoms are so very small and have very little mass, the number of atoms in 12.0 g of carbon-12 is huge. It is equal to the Avogadro constant:

The Avogadro constant = 6.022 × 1023 atoms per mole.

Calculating the number of particles

The number of particles of a substance can be calculated using:

  • the Avogadro constant
  • the amount of substance in mole

number of particles = Avogadro constant × amount (mol)


Calculate the number of water molecules in 0.5 mol of water.

Number of water molecules = 6.022 × 1023 × 0.5

= 3.011 × 1023

It is important to be clear about the particles involved. For example, 3.011 × 1023 water molecules contain 9.033 × 1023 atoms. This is because a water molecule, H2O, contains three atoms.


Calculate the number of oxygen atoms in 0.5 mol of oxygen molecules, O2.

Number of atoms = 2 × 0.5 × 6.022 × 1023

= 6.022 × 1023

Masses of atoms

The Avogadro constant can be used to calculate the mass of an atom in grams:

\[mass\ of\ atom\ (g)\ =\ \frac{A_{r}\ of\ element}{Avogadro\ constant}\]


Calculate the mass of a magnesium atom.

(Relative atomic mass, Ar = 24.3)

\[mass\ of\ Mg\ atom\ =\ \frac{24.3}{6.022 × 10^{23}}\]

= 4.04 × 10-23 g

It is important to give the final answer to the lowest number of significant figures used in the calculation. In this example, this is the same number of significant figures as the Ar value.


Calculate the mass of a carbon atom. (Relative atomic mass, Ar = 12.0)

\[mass\ of\ C\ atom\ =\ \frac{12.0}{6.022 × 10^{23}}\]

= 1.99 × 10-23 g

Masses of molecules

The Avogadro constant can be used to calculate the mass of a molecule in grams:

\[mass~of~molecule~(g) = \frac{M_{r}~of~substance}{Avogadro~constant}\]


Calculate the mass of a bromine molecule. (Relative formula mass, Mr = 159.8)

\[mass\ of\ bromine\ molecule\ (g)\ = \frac{159.8}{6.022 × 10^{23}}\]

= 2.654 × 10-22 g

This answer is given to 4 significant figures because both numbers used in the calculation are given to 4 significant figures.


Calculate the mass of a water molecule. (Relative formula mass, Mr = 18.0)

\[mass\ of\ water\ molecule\ (g)\ = \frac{18.0}{6.022 × 10^{23}}\]

= 2.99 × 10-23g

One mole of any object contains the Avogadro number of that object, 6.022 × 1023.