The Mole and Avogadro's Constant [H]

This lesson covers the mole concept and Avogadro's constant as required by the AQA GCSE Chemistry specification (4.3.1). This is Higher Tier only content. The mole is the chemist's unit for counting particles — atoms, molecules, ions, or formula units. Understanding how to convert between moles, mass, and Mr is essential for all higher-level quantitative chemistry calculations.

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What Is a Mole?

A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. One mole of any substance contains exactly 6.02 x 10^23 particles. This number is called Avogadro's constant and is given the symbol NA.

Term	Symbol	Value
Mole	mol	The amount of substance that contains 6.02 x 10^23 particles
Avogadro's constant	NA	6.02 x 10^23 per mole

The mole allows chemists to count atoms and molecules by weighing them. Since individual atoms are far too small to count, the mole bridges the gap between the atomic scale and the laboratory scale.

Why 6.02 x 10^23?

This number was chosen so that one mole of carbon-12 atoms has a mass of exactly 12 g. This means:

• One mole of hydrogen atoms (Ar = 1) has a mass of 1 g
• One mole of oxygen atoms (Ar = 16) has a mass of 16 g
• One mole of carbon atoms (Ar = 12) has a mass of 12 g
• One mole of iron atoms (Ar = 56) has a mass of 56 g

Exam Tip: The value of Avogadro's constant (6.02 x 10^23) will always be given to you in the exam — you do not need to memorise it. However, you must be able to use it in calculations.

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The Mole and Relative Formula Mass

The mass of one mole of a substance (in grams) is numerically equal to its relative formula mass (Mr) or relative atomic mass (Ar). This mass is sometimes called the molar mass.

Substance	Formula	Mr	Mass of 1 mole
Water	H2O	18	18 g
Carbon dioxide	CO2	44	44 g
Sodium chloride	NaCl	58.5	58.5 g
Calcium carbonate	CaCO3	100	100 g
Sulfuric acid	H2SO4	98	98 g
Glucose	C6H12O6	180	180 g

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The Mole Triangle

The relationship between moles, mass, and Mr is given by the equation:

moles = mass (g) / Mr

This can be rearranged into three forms:

• moles = mass / Mr
• mass = moles x Mr
• Mr = mass / moles

graph TD
    A["Mole Calculations"] --> B["moles = mass / Mr"]
    A --> C["mass = moles x Mr"]
    A --> D["Mr = mass / moles"]
    B --> E["Use when you know mass and Mr"]
    C --> F["Use when you know moles and Mr"]
    D --> G["Use when you know mass and moles"]

    style A fill:#9b59b6,color:#fff
    style B fill:#3498db,color:#fff
    style C fill:#3498db,color:#fff
    style D fill:#3498db,color:#fff

Exam Tip: Draw a triangle with mass at the top, and moles and Mr at the bottom. Cover the quantity you want to find: if mass is covered, multiply moles by Mr; if moles is covered, divide mass by Mr; if Mr is covered, divide mass by moles. This works just like the speed-distance-time triangle.

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Worked Examples: Calculating Moles from Mass

Example 1: How many moles in 36 g of water (H2O)?

• Mr of H2O = (2 x 1) + 16 = 18
• moles = mass / Mr = 36 / 18
• moles = 2 mol

Example 2: How many moles in 11 g of carbon dioxide (CO2)?

• Mr of CO2 = 12 + (2 x 16) = 44
• moles = mass / Mr = 11 / 44
• moles = 0.25 mol

Example 3: How many moles in 4.9 g of sulfuric acid (H2SO4)?

• Mr of H2SO4 = (2 x 1) + 32 + (4 x 16) = 2 + 32 + 64 = 98
• moles = mass / Mr = 4.9 / 98
• moles = 0.05 mol

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Worked Examples: Calculating Mass from Moles

Example 4: What is the mass of 0.5 moles of sodium hydroxide (NaOH)?

• Mr of NaOH = 23 + 16 + 1 = 40
• mass = moles x Mr = 0.5 x 40
• mass = 20 g

Example 5: What is the mass of 3 moles of calcium carbonate (CaCO3)?

• Mr of CaCO3 = 40 + 12 + (3 x 16) = 100
• mass = moles x Mr = 3 x 100
• mass = 300 g

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Using Avogadro's Constant [H]

To calculate the number of particles in a given amount of substance:

Number of particles = moles x Avogadro's constant (NA)

Number of particles = moles x 6.02 x 10^23

Worked Example: How many molecules in 2 moles of water?

• Number of molecules = 2 x 6.02 x 10^23
• Number of molecules = 1.204 x 10^24

Worked Example: How many atoms in 0.1 mol of iron?

• Number of atoms = 0.1 x 6.02 x 10^23
• Number of atoms = 6.02 x 10^22

Worked Example: How many moles is 3.01 x 10^23 atoms of copper?

• moles = number of particles / NA
• moles = 3.01 x 10^23 / 6.02 x 10^23
• moles = 0.5 mol

Exam Tip: Be careful with the difference between atoms and molecules. One mole of water (H2O) contains 6.02 x 10^23 molecules, but it contains 3 x 6.02 x 10^23 = 1.806 x 10^24 atoms (because each molecule contains 3 atoms).

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Converting Between Mass and Number of Particles

To go from mass to number of particles (or vice versa), use moles as the intermediate step:

mass --> moles --> number of particles

Worked Example: How many molecules are in 9 g of water (H2O)?

Step 1: Calculate moles: moles = mass / Mr = 9 / 18 = 0.5 mol

Step 2: Calculate number of molecules: 0.5 x 6.02 x 10^23 = 3.01 x 10^23 molecules

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Practice Table