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How do you count atoms you can’t see?

The GCSE picture: the mole, relative formula mass and n = m ÷ Mr.

  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, or choose one, and a mass in grams. A bar shows how the mass of one mole of that substance is shared between its elements, for example 88.8% oxygen and 11.2% hydrogen for water. Below, the working is written out in three steps: the relative formula mass, the number of moles, and the number of particles.

A number too big to count

Atoms are far too small and far too many to count one by one. A teaspoon of water holds about 10²³ molecules. So chemists count them the way a bank counts coins: by weighing.

The counting unit is the mole. One mole of anything is 6.02 × 10²³ of it: atoms, molecules or ions. That number is the Avogadro constant. Count one a second and a mole would take about 19 million billion years, more than a million times the age of the Universe.

Why that number is so useful

The number was chosen so that one mole of a substance has a mass in grams equal to its relative formula mass, Mr.

  • Carbon has a relative atomic mass of 12, so one mole of carbon atoms has a mass of 12 g.
  • Water, H₂O, has Mr = 1 + 1 + 16 = 18, so one mole of water molecules has a mass of 18 g.

Different substances, different masses, but the same number of particles in each.

The one equation

number of moles = mass in g ÷ Mr

How many moles are in 9 g of water? Mr = 18, so 9 ÷ 18 = 0.5 mol. That is 0.5 × 6.02 × 10²³ = 3.01 × 10²³ molecules.

What is the mass of 2 moles of carbon dioxide? Mr of CO₂ = 12 + 16 + 16 = 44. Rearrange: mass = moles × Mr = 2 × 44 = 88 g.

Use the calculator to check your own working. Type any formula, including brackets such as Ca(OH)₂, and a mass.

Why chemists care

A balanced equation is a recipe written in moles. In 2H₂ + O₂ → 2H₂O, two molecules of hydrogen react with one of oxygen, so two moles of hydrogen react with one mole of oxygen. Moles turn that into masses you can weigh out, which is how chemists work out how much of each reactant to use and how much product to expect.

Safety

The calculator works out amounts on paper. It isn’t a guide to measuring out or mixing real chemicals.