Moles and Avogadro's Constant

GCSE Chemistry · Quantitative Chemistry

What Is a Mole?

The mole is the unit used to count atoms, molecules and ions in chemistry. One mole of any substance contains exactly 6.022 × 10²³ particles. This number is called Avogadro's constant (symbol: Nₐ).

Why do we need moles? Atoms are far too small and numerous to count individually. One teaspoon of water contains roughly 1.7 × 10²⁵ molecules. The mole gives us a convenient way to count by weighing.

The Key Relationship: Moles, Mass and Mr

The number of moles of a substance is calculated from its mass and relative formula mass:

moles = mass (g) ÷ relative formula mass (Mr)

Or rearranged:

mass = moles × Mr
Mr = mass ÷ moles

You can use a formula triangle with mass at the top and moles and Mr at the bottom.

Relative Formula Mass (Mr)

The relative formula mass is the sum of the relative atomic masses of all atoms in the formula. Use the periodic table to find Ar values.

Examples:

H₂O: Mr = (2 × 1) + 16 = 18
CO₂: Mr = 12 + (2 × 16) = 44
CaCO₃: Mr = 40 + 12 + (3 × 16) = 100
Mg(OH)₂: Mr = 24 + 2 × (16 + 1) = 58
Ca(NO₃)₂: Mr = 40 + 2 × (14 + 48) = 164

Be careful with brackets — multiply everything inside by the subscript outside.

Worked Examples

Example 1: Finding Moles from Mass

How many moles in 11 g of carbon dioxide (CO₂)?

Mr of CO₂ = 44

Moles = 11 ÷ 44 = 0.25 mol

Example 2: Finding Mass from Moles

What is the mass of 0.5 mol of sodium hydroxide (NaOH)?

Mr of NaOH = 23 + 16 + 1 = 40

Mass = 0.5 × 40 = 20 g

Example 3: Finding Moles of a Specific Atom

How many moles of oxygen atoms are in 0.2 mol of calcium carbonate (CaCO₃)?

CaCO₃ contains 3 oxygen atoms per formula unit.

Moles of O = 0.2 × 3 = 0.6 mol

Using Moles with Equations

Balanced equations tell you the ratio of moles of reactants and products.

For example: 2Mg(s) + O₂(g) → 2MgO(s)

This tells us:

2 moles of magnesium react with 1 mole of oxygen
To produce 2 moles of magnesium oxide

Calculation Example

What mass of magnesium oxide is produced when 4.8 g of magnesium burns completely?

Step 1: Find moles of Mg

Moles = 4.8 ÷ 24 = 0.2 mol

Step 2: Use the equation ratio

2Mg → 2MgO, so ratio is 1:1

Moles of MgO = 0.2 mol

Step 3: Find mass of MgO

Mr of MgO = 24 + 16 = 40

Mass = 0.2 × 40 = 8.0 g

Number of Particles

To find the actual number of particles:

Number of particles = moles × 6.022 × 10²³

Example: How many molecules are in 9 g of water?

Moles = 9 ÷ 18 = 0.5 mol

Number of molecules = 0.5 × 6.022 × 10²³ = 3.011 × 10²³

Moles of Gases (Higher Tier)

At room temperature and pressure (RTP = 20°C, 1 atm), one mole of any gas occupies 24 dm³ (24000 cm³).

Moles of gas = volume (dm³) ÷ 24

Moles of gas = volume (cm³) ÷ 24000

Example: What volume does 0.1 mol of CO₂ occupy at RTP?

Volume = 0.1 × 24 = 2.4 dm³

Exam Tips

Always show your working in mole calculations — marks are awarded for method
Watch the units: g for mass, dm³ or cm³ for volume, mol for moles
Round your Mr to whole numbers from the periodic table unless told otherwise
Check your answer is sensible — if you get 0.001 mol of something that weighs 500 g, something has gone wrong
Learn the molar volume of a gas at RTP: 24 dm³/mol