The Mole and Avogadro's Number: Chemistry's Counting Unit
Source: BIPM. Published: 2025-06-15.
What Is a Mole?
The mole is the SI unit of amount of substance — one of the seven SI base units, alongside the metre, kilogram, second, ampere, kelvin, and candela. Before 2019, one mole was defined as the number of atoms in exactly 12 grams of carbon-12. This definition tied the mole to a physical artefact (a specific isotope of carbon at a specific mass) rather than to a fundamental constant. After the 2019 revision, the mole was redefined by fixing the value of Avogadro's number — the number of elementary entities (atoms, molecules, ions, or other particles) in one mole — to exactly 6.022 140 76 × 10²³. This constant is now exact by definition, not a measured quantity, making the mole independent of any physical substance.
Who Was Avogadro, and What Did He Discover?
Amedeo Avogadro was a nineteenth-century Italian scientist who proposed in 1811 that equal volumes of gases at the same temperature and pressure contain the same number of molecules, regardless of the chemical nature of the gas. This insight — now known as Avogadro's law — was a foundational step toward atomic theory and the quantitative understanding of chemical reactions. Avogadro did not determine the actual number of molecules in a given volume; that would come later. The constant that bears his name was first estimated by Josef Loschmidt in 1865 and refined over a century of increasingly precise experiments. The modern value of 6.022 140 76 × 10²³ is the result of coordinated measurements by national metrology institutes, culminating in the 2019 SI revision that fixed it exactly.
The Avogadro Project: Counting Silicon Atoms
The most precise experimental route to Avogadro's constant before the 2019 SI revision involved the Avogadro Project — an international collaboration that produced near-perfect spheres of highly enriched silicon-28. By measuring the diameter and crystal lattice spacing of these spheres with X-ray interferometry, scientists could calculate the exact number of silicon atoms each sphere contained and thereby determine Avogadro's constant with unprecedented precision. The spheres, known as kilogram-spheres, were among the roundest objects ever manufactured: their departure from perfect spherical geometry was less than the diameter of a silicon atom. The project's results, combined with measurements from the Kibble balance, provided the confidence needed to fix both Avogadro's constant and Planck's constant in the 2019 redefinition.
Why Chemistry Needs the Mole
The mole solves a practical problem: atoms and molecules are so small that any chemically useful quantity of substance contains an astronomically large number of them. A single gram of hydrogen gas contains approximately 6 × 10²³ hydrogen atoms. Without a counting unit that bridges the macroscopic and atomic scales, chemical equations would be hopelessly unwieldy. By defining one mole as 6.022 × 10²³ entities, chemists can work in laboratory-scale quantities (grams, litres) while accounting for the atomic-scale ratios prescribed by chemical formulae. A molecule of water (H₂O) contains two hydrogen atoms for every oxygen atom, and this 2:1 ratio holds whether you are counting individual molecules or moles of molecules.
Avogadro's Number and the 2019 SI Revision
Before 2019, Avogadro's constant was a measured quantity with a small but non-zero uncertainty. The 2019 revision fixed it exactly, simultaneously redefining the mole. This change was philosophically significant: the mole, like all other SI base units after 2019, is now defined by a fixed constant of nature rather than a physical artefact or a material-dependent experiment. Any laboratory anywhere in the world can now realise the mole from first principles, without reference to a physical standard or a specific chemical substance. The change also resolved a subtle circularity in the pre-2019 SI, where the kilogram, mole, and atomic mass unit were all defined in terms of each other via carbon-12, creating a chain of dependence that the constant-based definitions have now severed.
The Mole in Everyday Science and Industry
Though the mole rarely appears on product labels or road signs, it is indispensable in chemistry, pharmaceuticals, materials science, and environmental monitoring. Drug dosages are ultimately determined by counting molecules — the pharmacological effect of a substance depends on how many molecules interact with receptors, not on the mass in grams. Industrial chemical processes are designed around molar stoichiometry to ensure complete reactions and minimise waste. Environmental standards for pollutants like ozone (parts per billion by volume) can be converted to molar concentrations to assess chemical reactivity. The mole is the bridge between the human-scale world of grams and litres and the molecular world where chemistry actually happens.
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