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6.022 140 76 × 10²³. It’s probably the most famous number in chemistry, and at first sight it looks completely arbitrary. Why that value? Why not a nice round 10²⁴?
The answer is that Avogadro’s number isn’t arbitrary at all. It’s the exact number needed to make the atomic mass scale and the gram line up — and that one convenience is what makes practical chemistry possible.
What it is
The Avogadro constant, N_A, is the number of particles in one mole of anything:
N_A = 6.022 140 76 × 10²³ per mole
A mole of carbon atoms, a mole of water molecules and a mole of sodium chloride formula units each contain exactly that many particles. The mole is a counting unit, like a dozen — just an astronomically bigger one.
Why this particular number?
Atomic masses are measured in daltons (also called atomic mass units), where a carbon-12 atom is defined as exactly 12. A hydrogen atom is about 1, oxygen about 16, and so on.
Chemists wanted a bridge from that tiny scale to grams, so that “12” on the atomic scale would correspond to “12 grams” in the lab. The question was: how many carbon-12 atoms do you need to make exactly 12 grams?
The answer is about 6.022 × 10²³. That number is Avogadro’s number.
Because of that choice, the numbers on the periodic table do double duty. Iron’s atomic weight is 55.845, so:
- one iron atom has a mass of 55.845 daltons, and
- one mole of iron atoms has a mass of 55.845 grams.
This is why you can convert grams to moles just by dividing by the atomic weight.
Who was Avogadro?
Amedeo Avogadro, an Italian scientist, proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. He never knew how many particles that was — the number was named in his honour much later, in the early 20th century, by the French physicist Jean Perrin.
How was it measured?
Counting atoms directly is impossible, so scientists found clever indirect routes, and the fact that they all agreed was powerful evidence that atoms were real:
- Brownian motion. Perrin’s experiments around 1908–1909 on the jittery motion of tiny particles in water, analyzed with Einstein’s theory, gave a value of roughly 6–7 × 10²³. Perrin won the 1926 Nobel Prize in Physics partly for this work.
- Electrolysis and the electron charge. The charge carried by a mole of electrons (the Faraday constant) divided by the charge of one electron (measured by Millikan) gives N_A.
- X-ray crystallography. Measuring the spacing between atoms in a perfect crystal and the crystal’s density lets you count atoms per gram.
The last method was taken to extraordinary precision in the 2010s, using near-perfect spheres of silicon-28 — some of the roundest objects ever made — to count atoms with uncertainties of a few parts in a hundred million.
Exact since 2019
On 20 May 2019, the International System of Units was redefined in terms of fixed constants of nature. The Avogadro constant was fixed at exactly 6.022 140 76 × 10²³ mol⁻¹, and the mole was redefined as that exact number of particles.
A side effect: the mass of a mole of carbon-12 is no longer exactly 12 grams by definition. It’s 12 grams to within about one part in a billion — far below anything that matters in a chemistry lab.
Just how big is it?
- If you had 6.022 × 10²³ grains of fine sand, they’d cover a large country in a deep layer.
- A mole of seconds is about 19 million billion years — more than a million times the age of the universe.
- Yet a mole of water is only about 18 mL — roughly a tablespoon and a half.
That last comparison is the real point. Atoms and molecules are so small that an amount you could hold in a spoon contains an unimaginable number of them.
Using it in calculations
The constant converts between moles and numbers of particles:
- particles = moles × 6.022 × 10²³
- moles = particles ÷ 6.022 × 10²³
How many molecules are in 2.5 mol of CO₂? 2.5 × 6.022 × 10²³ = 1.51 × 10²⁴ molecules — and three times that many atoms, 4.52 × 10²⁴, since each molecule has three.
What is the mass of one gold atom? 196.97 g/mol ÷ 6.022 × 10²³ = 3.27 × 10⁻²² g.
Quick answers
Is Avogadro’s number the same as the Avogadro constant? Strictly, the Avogadro constant has units (per mole) and Avogadro’s number is the pure number. In everyday use they’re interchangeable.
Why isn’t it a round number? Because it was chosen to match the gram to the atomic mass scale, and nature didn’t make that ratio a round number.
Is 6.02 × 10²³ accurate enough? For almost every chemistry calculation, yes.
Try it
The grams to moles converter converts between grams, moles and number of particles for any formula, using the exact Avogadro constant.
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