Count gas particles with the mole
Treat amount of substance as an SI base quantity and connect a mole to the Avogadro constant.
Section 15 · Ideal gases
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 15. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use pressure, volume, temperature in kelvins, energy and scientific notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the SI base unit for amount of substance?
What you will learn
- Use amount of substance as an SI base quantity measured in moles
- Relate one mole of particles to the Avogadro constant
- Convert between particle number N and amount n
The mole measures amount of substance
Amount of substance is an SI base quantity with the base unit mole, symbol mol. The amount n tells how many specified elementary entities are present; state whether the entities are molecules, atoms, ions or another particle type.
A mole is not a mass unit. A sample's mass also depends on the mass of each entity, whereas the amount in moles counts entities through the Avogadro constant.
Use the Avogadro constant to count entities
One mole contains a number of particles equal to the Avogadro constant, NA = 6.02 × 10²³ mol⁻¹. The particle count is N = nNA; rearranging gives n = N/NA.
Check that N is a number of the entity named in the question and that n is in mol. The subscript in NA distinguishes the Avogadro constant from particle number N.
Pause and explain
How many particles are in one mole?
Worked example
How many molecules are in 0.50 mol of a gas?
Show the worked solution
- Use N = nNA.
- N = 0.50 × 6.02 × 10²³.
- Give a particle count.
Answer N = 3.01 × 10²³ molecules.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate the number of molecules in 0.25 mol of a gas.
Give me a hint
Multiply the amount in moles by NA.
Compare my reasoning
- N = nNA.
- N = 0.25 × 6.02 × 10²³.
- State the number of molecules.
N = 1.505 × 10²³ molecules, about 1.51 × 10²³.
Look for these in your work
- Relation selected
- Amount multiplied
- Particles identified
A gas sample contains 1.204 × 10²⁴ molecules. Calculate its amount of substance.
Give me a hint
Divide particle number by Avogadro's constant.
Compare my reasoning
- n = N/NA.
- n = 1.204 × 10²⁴ / 6.02 × 10²³.
- Give mol.
n = 2.00 mol.
Look for these in your work
- Relation rearranged
- Powers of ten handled
- Mole unit stated
Two sealed containers each hold one mole of a different gas. Compare their particle counts without assuming their masses are equal.
Give me a hint
The mole counts specified entities; mass depends on what each particle is made of.
Compare my reasoning
- Each sample has n = 1 mol.
- Each therefore contains NA particles of its named gas.
- Their masses may differ because the particle species may have different masses.
Both contain 6.02 × 10²³ specified particles, even though their total masses need not match.
Look for these in your work
- Equal amount interpreted
- Avogadro count applied
- Mass distinguished from amount
Common mistakes
- Treating mol as a mass unit
- Using the reciprocal when calculating N from n
- Leaving unclear which particles are being counted
What can you explain now?
What is the SI base unit for amount of substance?
Compare with the explanation
The mole, mol
Amount of substance is measured in moles.
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Make it stick
How does the Avogadro constant connect amount in moles to a count of particles?
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