IB Physics SLTopic B.3 — The Behaviour of GasesPaper 1 & 2Mole · Avogadro Constant · Molar Mass~7 min read
The Mole & Amount of Substance
A single breath of air contains more molecules than there are stars in the observable universe — far too many to count one at a time. The mole is the unit physicists invented to make numbers like that manageable.
📘 What you need to know
The mole (mol) is one of the seven SI base units. It measures amount of substance, not mass.
One mole is defined as the amount of substance containing as many elementary entities as there are atoms in exactly 12 g of carbon-12.
That number is the Avogadro constant, NA = 6.02 × 10²³ mol⁻¹ — given in the data booklet, so it doesn’t need to be memorised.
Moles, particle count and the Avogadro constant are linked by n = N ÷ NA.
One mole of any element has a mass in grams equal to its relative atomic mass; for a compound, add up the relative atomic masses of every atom present.
What Is a Mole?
Think of the mole as a counting unit, the same way “a dozen” means 12 of something regardless of what that something is. A mole always means the same enormous number of particles — 6.02 × 10²³ of them — whether you’re counting atoms of helium, molecules of water, or grains of sand (though you’d need a very large container for that last one).
One mole of any substance — atoms, molecules, or ions — always contains the same number of particles: the Avogadro constant, N_A = 6.02 × 10²³ mol⁻¹.
Counting Particles — n = N ÷ NA
Once you know the Avogadro constant, you can convert freely between “how many particles” and “how many moles.”
Number of molesn = N ÷ NA
where n is the amount of substance (mol), N is the number of particles, and NA = 6.02 × 10²³ mol⁻¹ is the Avogadro constant. Rearranged, this also gives you the number of particles directly from a known number of moles: N = n × NA.
Molar Mass — From Atoms to Grams
The mole also bridges particle counts and something you can actually put on a balance: mass.
Molar massmr = m ÷ n
where mr is the molar mass (g mol⁻¹), m is the mass (g), and n is the amount of substance (mol). One mole of any element has a mass in grams equal to its relative atomic mass — helium’s relative atomic mass is 4, so one mole of helium has a mass of 4 g. For a compound, add up the relative atomic masses of every atom in the formula.
Water’s molar mass is built by adding up the relative atomic masses of every atom in H₂O: two hydrogens (1 each) plus one oxygen (16), giving 18 g mol⁻¹.
Quick recap: n = N ÷ N_A converts between moles and particle count. m_r = m ÷ n converts between moles and mass. For compounds, molar mass is the sum of the relative atomic masses of every atom present.
WE 1
A cylinder contains 80 moles of oxygen gas. Calculate the number of oxygen molecules in the cylinder.
Step 1 — Rearrange for NN = n × NAStep 2 — SubstituteN = 80 × (6.02 × 10²³)N ≈ 4.82 × 10²⁵ moleculesNote this counts molecules of O₂, not individual oxygen atoms.
WE 2
A sample contains 1.8 × 10²¹ atoms of neon gas, which has a molar mass of 20 g mol⁻¹. Calculate the total mass of neon in the sample.
Step 1 — Find the number of molesn = N ÷ N_A = (1.8 × 10²¹) ÷ (6.02 × 10²³)n ≈ 2.99 × 10⁻³ molStep 2 — Find the massm = m_r × n = 20 × (2.99 × 10⁻³)m ≈ 0.0598 gA small number of moles still corresponds to a real, measurable mass — this is the mole doing its job as a bridge unit.
💡 Top tips
Both NA and the ideal gas constant are given in the data booklet — you don’t need to memorise them, though knowing 6.02 × 10²³ by heart speeds things up.
Molar mass is in g mol⁻¹, so multiplying by moles gives a mass in grams, not kilograms — convert if a question needs kilograms.
For compounds, count every atom in the formula, not just one of each element — water has two hydrogens, not one.
⚠ Common mistakes
Treating “number of moles” and “number of particles” as the same thing — n and N are related by NA, but they are different quantities with different units.
Forgetting to convert between grams and kilograms when combining a molar-mass calculation with another equation that expects SI units.
Adding relative atomic masses incorrectly for a compound — double-check the subscripts in the formula before summing.
Up next: Gas Laws — where the mole becomes the “n” in pV = nRT, linking amount of substance directly to a gas’s pressure, volume and temperature.
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Book a free session and we’ll work through mole and molar mass calculations until they’re second nature.
