IB Physics HLThe Behaviour of GasesPaper 1 & 2The Mole~9 min read
The Mole & Amount of Substance
A tiny puff of gas holds so many particles that counting them one at a time is hopeless. So instead of counting, we bundle them — into a giant “chemist’s dozen” called the mole. Get comfortable with the mole and you can flip freely between mass, moles and number of particles. That’s the counting toolkit for the whole gas topic.
📘 What you need to know
The mole is the SI base unit for amount of substance (not mass)
One mole contains 6.02 × 1023 particles — the Avogadro constantNA
Number of particles: N = nNA (so n = N / NA)
One mole of an element has a mass in grams equal to its relative atomic mass (helium = 4 g)
For a compound, add up the atomic masses (water = 18 g per mole)
Molar mass links mass and moles: mr = m / n, in g mol−1
Because molar mass is in g mol−1, your masses come out in grams, not kilograms
What is a mole?
A “dozen” is just a handy word for 12 of something. The mole is the same idea, only enormously bigger: it’s a fixed number of particles, chosen so the numbers in chemistry and physics come out sensible. That number is the Avogadro constant:
Avogadro constantNA = 6.02 × 1023 mol−1
So one mole of anything — atoms, molecules, particles — is 6.02 × 1023 of them. (It’s officially defined as the number of atoms in exactly 12 g of carbon-12, but for calculations you just use the value above.) To get the total number of particles, multiply the moles by NA:
Number of particlesN = n × NA
where N is the number of particles, n is the number of moles (mol), and NA is the Avogadro constant. Turn it around and you can count moles from particles: n = N / NA.
WE 1
A container holds 0.50 mol of oxygen gas. How many oxygen molecules is that?
Step 1 — use N = n × NAN = 0.50 × (6.02×10²³)N = 3.0 × 10²³ moleculesHalf a mole, but still hundreds of billions of billions of molecules. That’s why we bundle!
Molar mass: turning moles into grams
Moles let us count particles — but in the lab we weigh things. The bridge between them is the molar mass: the mass of one mole. Handily, for an element it’s just the relative atomic mass in grams. Helium’s relative atomic mass is 4, so one mole of helium weighs 4 g.
For a compound, you simply add up the atomic masses of its atoms. Water, H2O, is two hydrogens (mass 1 each) plus one oxygen (mass 16):
Add up the relative atomic masses: 1 + 1 + 16 = 18. So one mole of water has a mass of 18 g, i.e. a molar mass of 18 g mol−1.
The molar mass ties mass and moles together with one neat equation:
Molar massmr = m / n
where mr is the molar mass (g mol−1), m is the mass (g), and n is the number of moles. Rearrange it however you need: m = mrn, or n = m / mr.
Joining it all up
Here’s the picture worth memorising. Moles sit in the middle, with molar mass on one side (to reach mass) and the Avogadro constant on the other (to reach number of particles). Multiply going one way, divide going back.
The conversion map. Multiply left-to-right (× mr, × NA); divide right-to-left. Moles are always the stepping stone in the middle.
WE 2
How many water molecules are there in 36 g of water? (Molar mass of water = 18 g mol−1.)
Step 1 — mass → moles: n = m / mrn = 36 ÷ 18 = 2.0 molStep 2 — moles → particles: N = n × NAN = 2.0 × (6.02×10²³)N = 1.2 × 10²⁴ moleculesStraight across the map: mass → moles → particles.
WE 3
A flask contains 3.01 × 1022 molecules of carbon dioxide, CO2, which has a molar mass of 44 g mol−1. Find the mass of gas.
Step 1 — particles → moles: n = N / NAn = (3.01×10²²) ÷ (6.02×10²³) = 0.050 molStep 2 — moles → mass: m = mr × nm = 44 × 0.050m = 2.2 gThe map in reverse: particles → moles → mass. And the answer is in grams, because mr was in g mol⁻¹.
Mass grams
÷ mr → ← × mr
Moles
× NA → ← ÷ NA
Particles
🛠️ Counting particles and mass
Find the molar mass — for a compound, add up the relative atomic masses.
Mass → moles: divide by the molar mass, n = m / mr.
Moles → particles: multiply by NA, N = nNA.
Going backwards? Just divide instead of multiply at each step.
Check units: molar mass in g mol−1 means masses land in grams.
💡 Top tips
Moles are the middle step — go mass → moles → particles, never mass → particles directly.
Multiply forwards, divide backwards on the conversion map.
Molar mass of a compound = sum of its atoms’ relative atomic masses.
NA is in the data booklet — no need to memorise it, though it speeds you up.
g mol−1 gives grams — convert to kg only if the question needs it.
⚠ Common mistakes
Confusing the number of moles with the number of particles — they differ by a factor of NA
Multiplying when you should divide (or vice versa) — check which way you’re crossing the map
Forgetting the mass comes out in grams, not kilograms
Forgetting to add up all the atoms for a compound’s molar mass
Treating the mole as a mass — it’s an amount (a count of particles)
Quick recap: A mole is 6.02 × 1023 particles (the Avogadro constant). Use N = nNA to swap between moles and particles, and the molar mass mr = m/n to swap between moles and mass. Moles are the stepping stone in the middle: multiply forwards, divide backwards.
You can now count the uncountable — sliding between grams, moles and particles at will. That’s the last piece of groundwork. Next we bring pressure, volume and temperature together in the Gas Laws (Boyle’s, Charles’s and the pressure law), where all this finally pays off.
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