Atoms are too small and too many to count one by one. The mole is a fixed number of particles, 6.022 × 10²³, chosen so that one mole of a substance has a mass in grams equal to its formula mass.
A balanced equation states numbers of particles. 2 H₂ + O₂ → 2 H₂O means two hydrogen molecules react with one oxygen molecule. To use this in a laboratory, you need to know how many molecules are in a sample.
Particles cannot be counted one by one. A single drop of water, about 0.05 mL, contains about 1.7 × 10²¹ molecules. What can be measured easily is mass. So chemistry needs a link between a measured mass and a number of particles. The mole is that link.
A dozen is 12 of anything. A mole is 6.02214076 × 10²³ of anything. This number is the Avogadro constant, written NA. Since 2019 it has been fixed exactly by definition. For calculations, 6.022 × 10²³ is used.
The number is very large compared with everyday counts. A mole of eggs would cover the whole surface of the Earth in a layer about 70 km deep. Because atoms are so small, a mole of atoms or molecules is a convenient laboratory amount. One mole of water has a mass of about 18 g.
Relative atomic masses are measured on a scale where an atom of carbon-12 has mass exactly 12. On this scale, hydrogen is about 1, oxygen about 16 and magnesium about 24.
The Avogadro constant was chosen so that one mole of atoms has a mass in grams equal to its relative atomic mass. (Since the 2019 definition, this is true to better than one part in a billion.) So 12 g of carbon-12 is one mole of carbon atoms, and 16 g of oxygen atoms is one mole.
This is what makes the mole useful: weighing a sample tells you how many particles it contains.
Carbon has relative atomic mass 12 and magnesium 24. You weigh out 12 g of carbon and 24 g of magnesium. How do the numbers of atoms compare?
They are equal: one mole of each, 6.022 × 10²³ atoms.
A magnesium atom has twice the mass of a carbon atom. So twice the mass of magnesium is needed to contain the same number of atoms. Equal numbers of moles always means equal numbers of particles, whatever the masses.
For a compound, add the relative atomic masses of all the atoms in its formula. This gives the relative molecular mass. That many grams is one mole of the compound.
H₂O: 2(1) + 16 = 18. So 18 g of water is one mole, 6.022 × 10²³ molecules. CO₂: 12 + 2(16) = 44. So one mole of carbon dioxide has a mass of 44 g.
The mass of one mole of a substance is its molar mass, M, in g/mol. Its numerical value equals the relative atomic or molecular mass.
Two conversion factors. Molar mass converts between mass and moles. The Avogadro constant converts between moles and number of particles.
How many molecules are in 9 g of water?
Mass to moles: the molar mass of water is 18 g/mol. n = 9 g ÷ 18 g/mol = 0.5 mol.
Moles to molecules: N = 0.5 mol × 6.022 × 10²³ mol⁻¹ = 3.011 × 10²³ molecules.
Nine grams of water, less than a tablespoon, contains about 3 × 10²³ molecules. The count came from one weighing and two multiplications.
1One mole of any substance contains ____ particles (the Avogadro constant, to 4 significant figures).
2Why does 12 g of carbon-12 contain one mole of atoms?
3The molar mass of water (H₂O) is…
4You weigh out 12 g of carbon (relative atomic mass 12) and 24 g of magnesium (24). The number of atoms is…
5How many moles are in 44 g of carbon dioxide (molar mass 44 g/mol)?
6To convert an amount in moles to a number of particles, you…
Next: working out a compound’s formula from its composition by mass.
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