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Lessons / Amount of substance / GCSE and A-level

How do you count atoms you can’t see?

The A-level picture: the SI definition, molar mass, and calculations from equations.

  1. A spoon of sugar12 g
  2. One sugar crystal0.5 mm
  3. One sugar molecule1 nm
  4. One carbon atom0.15 nm
n = m / M
What the simulation shows, in words

A calculator. Type a formula and a mass. A bar shows how the molar mass is shared between the elements, and the working shows Mr, the amount in moles and the number of particles. Switch between exam data-sheet values, rounded to one decimal place, and the full IUPAC 2024 values.

The definition, since 2019

The mole is one of the seven base units of the SI. Since 20 May 2019 it has been defined by fixing the Avogadro constant at exactly

NA = 6.022 140 76 × 1023 mol−1

so one mole is exactly that number of specified particles. Before 2019 the mole was defined as the number of atoms in exactly 12 g of carbon-12. The two definitions agree to better than a part in a billion, so for any calculation you will do, 12 g of carbon-12 still contains one mole of atoms.

Relative atomic mass, Ar, is the average mass of an atom of an element, taking account of its natural isotopes, compared with one twelfth of the mass of an atom of carbon-12. It has no units. Molar mass, M, is the mass per mole and has units of g mol⁻¹. They have the same number.

Why some Ar values look rounded

IUPAC’s Commission on Isotopic Abundances and Atomic Weights reviews these values every two years. For most elements the isotope mix is the same everywhere and Ar is known to five significant figures: sodium is 22.990. For some, the mix depends on where the sample came from. Lithium from different minerals differs enough that IUPAC gives only 6.94, and lead, whose isotopes come partly from radioactive decay, is 207.2. Elements with no stable isotopes, such as technetium, have no standard value at all.

Calculations from equations

Magnesium burns in oxygen: 2Mg + O₂ → 2MgO. What mass of magnesium oxide forms from 4.86 g of magnesium? (Ar: Mg 24.3, O 16.0)

  1. Moles of Mg = 4.86 ÷ 24.3 = 0.200 mol
  2. The ratio Mg : MgO is 2 : 2, so moles of MgO = 0.200 mol
  3. M of MgO = 24.3 + 16.0 = 40.3 g mol⁻¹, so mass = 0.200 × 40.3 = 8.06 g

The same three steps work with solutions, using n = c × V with V in dm³, and with gases, using pV = nRT with p in Pa, V in m³ and T in K.

Particles, carefully

Say what the particles are. One mole of oxygen gas is 6.02 × 10²³ O₂ molecules but 1.20 × 10²⁴ oxygen atoms. One mole of sodium chloride contains one mole of Na⁺ ions and one mole of Cl⁻ ions, so 1.20 × 10²⁴ ions in all. The calculator calls the particles of ionic compounds formula units, which is the correct term.

Safety

Magnesium burns with a very bright flame that can damage eyes. It appears here as a calculation only.