# 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 , or involved in a chemical reaction. The 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 , the number of atoms in 12.0 g of carbon-12 is huge. It is equal to the :

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 amount of substance in mole

number of particles = Avogadro constant × amount (mol)

Example

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.

Question

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:

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

Example

Calculate the mass of a magnesium atom.

(, 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 used in the calculation. In this example, this is the same number of significant figures as the Ar value.

Question

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:

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

Example

Calculate the mass of a bromine molecule. (, 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.

Question

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.