IB Chemistry SL
Topic 1 — Counting Particles by Mass
Paper 1 & 2
Core idea
~8 min read
The Mole
Atoms are far too small and too numerous to count one by one, so chemists group them into a standard-sized package: the mole. Just like “a dozen” always means 12, “a mole” always means the same huge number of particles — and that lets us connect mass to the number of particles.
📘 What you need to know
- One mole is the amount of a substance containing as many particles as there are atoms in exactly 12.00 g of carbon-12.
- That number is the Avogadro constant (NA or L) = 6.02 × 1023 mol-1.
- It applies to atoms, molecules and ions alike.
- The mass of one mole (the molar mass) in grams equals the relative atomic or formula mass.
- Relative atomic mass (Ar) is the weighted average mass of an atom compared to 1/12 of a carbon-12 atom; relative formula mass (Mr) is the same idea for a compound.
What the mole is
The Avogadro constant is simply the number of particles in one mole — 6.02 × 1023. It’s defined so that one mole of a substance has a mass, in grams, equal to its relative mass.
- 6.02 × 1023 atoms of carbon-12 have a mass of exactly 12.00 g.
- One mole of water (H2O) has a mass of (2 × 1.01 + 16.00) = 18.02 g.
Think of the mole exactly like the word “dozen”. A dozen eggs is 12 eggs; a mole of atoms is 6.02 × 10²³ atoms. The only reason the number is so big is that atoms are unimaginably small.
Watch what you’re counting
A mole counts whatever particle you name — and that matters for molecules, because one molecule contains several atoms.
- A monatomic element like Na: 1 mole = 6.02 × 1023 atoms.
- A diatomic molecule like H2: 1 mole = 6.02 × 1023 molecules, but 2 × that many atoms = 1.204 × 1024 atoms.
- An ionic compound like NaCl: 1 mole = 6.02 × 1023 formula units, containing 1.204 × 1024 ions in total.
WORKED EXAMPLEFor 1 mole of each, give the number of atoms (or molecules/formula units) and the relative mass: (a) Na, (b) H2, (c) NaCl. Use Ar: Na = 22.99, H = 1.01, Cl = 35.45.
(a) Na (monatomic)
6.02 × 10²³ atoms; mass = 22.99 g.
(b) H₂ (diatomic)
6.02 × 10²³ molecules = 1.204 × 10²⁴ atoms; M_r = 2.02 g.
(c) NaCl (ionic)
6.02 × 10²³ formula units = 1.204 × 10²⁴ ions; M_r = 58.44 g.
Relative atomic and formula mass
Two “relative mass” terms come up constantly:
- Relative atomic mass (Ar) — the weighted average mass of an atom of an element, compared to 1/12 of a carbon-12 atom. It’s a ratio, so it has no units.
- Relative formula mass (Mr) — the same idea applied to a whole compound: just add up the Ar values of all the atoms in the formula.
🧪 Working out Mr
- List each element in the formula and how many atoms of it there are.
- Multiply each element’s Ar by its number of atoms.
- Add all the values together.
For example, K2CO3: (2 × 39.10) + 12.01 + (3 × 16.00) = 138.21. And Ca(OH)2: 40.08 + (2 × 16.00) + (2 × 1.01) = 74.10.
Note: “relative formula mass” is the term used for compounds containing ions (like K2CO3), but it’s calculated in exactly the same way as relative molecular mass.
💡 Exam tip
- Read carefully whether a question asks for atoms, molecules/formula units, or ions — for anything but a monatomic element these give different numbers.
- The Avogadro constant and Ar values are in the data booklet and periodic table — you don’t need to memorise them.
Up next: Molar Mass — using the mole to convert between mass, moles and number of particles with simple formula triangles.
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