Molar MassThe mole and the Avogadro constant
The mole is the unit chemists use to count particles. Its symbol is mol. One mole of anything contains exactly 6.02214076 × 1023 of those things. That number, per mole, is the Avogadro constant, written NA.
A counting unit, nothing more
A pair is 2, a dozen is 12, a gross is 144. A mole is 602,214,076,000,000,000,000,000. The idea is the same: a name for a number. It has to be this large because atoms are so small. A mole of water molecules is only about 18 millilitres of water, a small sip.
Always say what you are counting. One mole of oxygen atoms and one mole of oxygen molecules are different amounts of gas, because each molecule, O2, has two atoms. One mole of O2 molecules contains two moles of oxygen atoms.
The definition changed in 2019
For many years the mole was defined through carbon: the number of atoms in exactly 12 grams of carbon-12. Since 20 May 2019 the International System of Units defines it the other way round. The Avogadro constant is fixed as an exact number, 6.02214076 × 1023 per mole, and a mole is that many particles. For school and college sums nothing changes. The molar mass of carbon-12 is still 12 g/mol to more decimal places than any balance can show.
Moles to particles and back
number of particles = moles × 6.022 × 1023
moles = number of particles ÷ 6.022 × 1023
Example. How many molecules are in 0.25 mol of carbon dioxide? 0.25 × 6.022 × 1023 = 1.506 × 1023 molecules. Each has three atoms, so the sample contains 4.517 × 1023 atoms in all.
Example. How many moles is 3.011 × 1023 atoms of iron? 3.011 × 1023 ÷ 6.022 × 1023 = 0.5 mol. Its mass is 0.5 × 55.845 = 27.92 g.
From grams to particles in two steps
Most questions give a mass and ask for a number of particles. Go through moles.
- Grams to moles: divide by the molar mass.
- Moles to particles: multiply by the Avogadro constant.
Example. How many molecules are in 9 g of water? 9 ÷ 18.02 = 0.4996 mol. Then 0.4996 × 6.022 × 1023 = 3.009 × 1023 molecules.
The mass of one molecule
Turn the idea around and you can find the mass of a single particle: divide the molar mass by the Avogadro constant. One water molecule has a mass of 18.02 ÷ 6.022 × 1023 = 2.991 × 10-23 g. It is this unimaginably small figure that makes the mole necessary.
Who was Avogadro?
Amedeo Avogadro was an Italian scientist who proposed in 1811 that equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. He never knew the value of the constant that carries his name. It was measured much later and named in his honour.
Try the conversions with your own numbers in the grams, moles and particles converter.
Which values? This site uses the abridged standard atomic weights published by IUPAC (CIAAW), read on 12 November 2026. Your textbook or question paper may round them differently, for example H = 1 and O = 16, so its answer can differ slightly. In an exam, use the values the paper gives.