Guide
Moles and Avogadro's Number Explained
The mole is the idea that makes quantitative chemistry possible, and it is also the one that trips up most beginners. Part of the trouble is the name: a mole is not a mass, not a volume and not a property of a substance. It is a count, in exactly the sense that a dozen is a count - just an enormously larger one, chosen to suit the scale of atoms.
This guide explains what the mole counts, where Avogadro's number comes from and why its definition changed in 2019, and how to move between grams, moles and particle counts without losing track of which one you are holding. The arithmetic is short; the care goes into naming exactly what you are counting.
The counting problem chemistry has
Chemical reactions happen particle by particle. One carbon atom combines with two oxygen atoms; one zinc atom displaces one copper ion. But no laboratory can count atoms directly, and no atom is heavy enough to weigh on its own - a single carbon atom has a mass of roughly 2 × 10⁻²³ g, which no balance will ever register.
The mole solves this by fixing a bundle size. Choose a number of particles so large that a mole of atoms weighs a convenient handful of grams, and you can weigh a sample and know how many particles it contains. That is the entire purpose of the mole: it lets a balance stand in for a counter.
What Avogadro's number is
Avogadro's number is 6.02214076 × 10²³, and the Avogadro constant is that value per mole. Since the SI redefinition that took effect in May 2019, the figure is exact by definition: one mole is defined as containing exactly 6.02214076 × 10²³ elementary entities, and that is the whole definition. It is a chosen number, in the same way that the metre is now fixed by a chosen value for the speed of light.
You will still meet the older definition - 'the number of atoms in exactly 12 grams of carbon-12' - in many textbooks, and it is worth knowing because it explains where the value came from. Before 2019 the mole was tied to that carbon-12 sample and Avogadro's number had to be measured, with a small experimental uncertainty attached. The relationship survives the change: 12 g of carbon-12 still contains one mole of atoms to far better precision than any calculation you will do. What changed is which statement is the definition and which is now a consequence of it.
Three quantities, two relationships
Almost every mole problem in an introductory course is built from just two equations. Mass and amount are linked by molar mass: amount in moles equals mass in grams divided by molar mass in grams per mole. Amount and particle count are linked by the Avogadro constant: number of particles equals moles multiplied by 6.022 × 10²³.
Sketching the chain from grams to moles to particles before you start is the single most useful habit here. Moles sit in the middle, so every conversion passes through them, and the direction of travel tells you whether to multiply or divide. If the answer comes out with the wrong order of magnitude, it is nearly always because a step went the wrong way.
A worked conversion
Take a typical question: how many molecules are there in 25.0 g of carbon dioxide?
- Find the molar mass of CO₂ from the periodic table: 12.011 + 2(15.999) = 44.009 g/mol.
- Convert mass to moles: 25.0 ÷ 44.009 = 0.568 mol.
- Convert moles to molecules: 0.568 × 6.022 × 10²³ = 3.42 × 10²³ molecules.
- Sanity-check the size. 25.0 g is a little over half of 44.009 g, so the answer should be a little over half of 6.022 × 10²³ - and 3.42 × 10²³ is.
- Run it backwards to confirm: 3.42 × 10²³ ÷ 6.022 × 10²³ = 0.568 mol, and 0.568 × 44.009 = 25.0 g.
Say exactly what you are counting
The mole counts whichever entity you name, and naming it loosely is the most common source of wrong answers. One mole of water is 6.022 × 10²³ water molecules - but every molecule contains three atoms, so the same 18.015 g sample holds 1.807 × 10²⁴ atoms. One mole of oxygen gas is 6.022 × 10²³ O₂ molecules and therefore 1.204 × 10²⁴ oxygen atoms.
Ionic compounds are counted in formula units rather than molecules, because an ionic solid is a continuous lattice with no discrete molecules in it. One mole of sodium chloride is 58.44 g and contains 6.022 × 10²³ formula units, which is 6.022 × 10²³ Na⁺ ions together with 6.022 × 10²³ Cl⁻ ions - 1.204 × 10²⁴ ions in total.
- 1 mol of iron: 55.845 g, 6.022 × 10²³ Fe atoms.
- 1 mol of water: 18.015 g, 6.022 × 10²³ molecules, 1.807 × 10²⁴ atoms.
- 1 mol of carbon dioxide: 44.009 g, 6.022 × 10²³ molecules, 1.807 × 10²⁴ atoms.
- 1 mol of sodium chloride: 58.44 g, 6.022 × 10²³ formula units, 1.204 × 10²⁴ ions.
- 'A mole of oxygen' is ambiguous; 'a mole of O₂' and 'a mole of O atoms' are not.
Moles in reactions and in gases
The coefficients in a balanced equation are mole ratios, which is what makes the mole so useful. In N₂ + 3 H₂ → 2 NH₃, one mole of nitrogen reacts with three moles of hydrogen to give two moles of ammonia. Turn that into masses with molar mass and you get 28.014 g of nitrogen plus 6.048 g of hydrogen producing 34.062 g of ammonia - and 28.014 + 6.048 = 34.062, exactly as conservation of mass requires.
Gases add a shortcut. Equal amounts of any ideal gas occupy equal volumes at the same temperature and pressure, so one mole occupies about 22.7 L at 0 °C and 100 kPa, the current definition of standard temperature and pressure. Older courses and textbooks often use 1 atm instead, which gives 22.4 L per mole. Neither is wrong; check which convention your syllabus uses before quoting a figure.
Everything here rests on molar mass, so if the conversions feel shaky, practise those first. ChemTable's element list and tools give you real atomic masses to work with, and drilling half a dozen conversions with substances you can picture is worth more than rereading the definition.
Frequently asked questions
Is a mole a mass or a number?
A number. One mole is exactly 6.02214076 × 10²³ entities, whatever those entities are. A mole of different substances has different masses because their particles have different masses.
Why was the mole redefined in 2019?
To fix it to an exact number instead of a physical sample. The mole used to be defined by the atoms in 12 g of carbon-12, which meant Avogadro's number carried experimental uncertainty. Now the number is exact by definition and the carbon-12 link is a very close consequence.
How do I convert grams to particles?
Go through moles. Divide the mass by the molar mass to get moles, then multiply by 6.022 × 10²³. For 25.0 g of CO₂: 25.0 ÷ 44.009 = 0.568 mol, and 0.568 × 6.022 × 10²³ = 3.42 × 10²³ molecules.
What is the difference between a molecule and a formula unit?
A molecule is a discrete group of covalently bonded atoms, like H₂O. A formula unit is the simplest whole-number ratio of ions in a lattice, like NaCl, where no discrete molecule exists. Moles count either, as long as you say which.