# The mole - Higher

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

The actual of and are too small to be of practical use in calculations. Therefore a special quantity, called a , is used.

In terms of mass, a mole (mol) is the (Ar) of an in grams, or the (Mr) in grams if it's a . Examples for elements and compounds are given in the table below, along with its formula, relative formula mass (RFM) and the mass of 1 mole.

ExampleFormulaRFMMass of 1 mole
CalciumCa4040 g
OxygenO22 x 16 = 3232 g
Calcium carbonateCaCO340 + 12 + (3 × 16) = 100100 g

As the mole quantity is based on the relative masses of atoms, there is a relationship between a mole of a substance and the number of it contains. As atoms and molecules are so small the number in a mole is very large. This number is called the , and it is equal to: 602,000,000,000,000,000,000,000 (= 6.02 × 1023) formulae units.

$The~Avogadro~constant = 6.02~\times10^{23}$

The Avogadro constant is defined as: the number of carbon atoms in exactly 12 g of carbon-12, 12C.

One mole, 1 mol, of a substance is defined as: the Avogadro constant number of particles (which is 6.02 × 1023 atoms, molecules, or of that substance).

For example:

• the formula of methane is CH4
• the relative atomic mass (Ar) of C = 12
• the Ar of H = 1
• so the relative formula mass (Mr) of CH4 = 12 + (4 × 1) = 16
• so 1 mole of methane = 16 g of methane and contains 6.02 × 1023 molecules
• 16 g of methane = 6.02 × 1023 as there are 5 atoms in each formulae (molecule)
• 16 g of methane = 5 × 6.02 × 1023 = 3.01 × 1024 atoms

## Calculating the number of particles

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

• the Avogadro constant number (6.02 × 1023)
• the amount of substance in mole

Number of particles = 6.02 × 1023 × mol

### Example

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

Number of water molecules = 6.02 1023 × 0.5

= 3.01 × 1023

It is important to be clear about the particles involved. For example, 3.01 × 1023 water molecules contain 9.03 × 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 × 6.02 × 1023

= 6.02 × 1023