Avogadro constant

The Avogadro constant, commonly denoted N_A or L, is an SI defining constant with an exact value of 6.02214076×10²³ mol^-1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, or ions) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In practice, its value is often approximated as 6.02×10²³ mol^-1 or 6.022×10²³ mol^-1. The constant is named after the physicist and chemist Amedeo Avogadro (1776–1856).

The Avogadro constant N_A is also the factor that converts the average mass of one particle, in grams, to the molar mass of the substance, in grams per mole (g/mol).

The constant N_A also relates the molar volume (the volume per mole) of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/mol, the volume occupied by one molecule of water is about 18/6.022×10⁻²³ mL, or about 0.030 nm³ (cubic nanometres). For a crystalline substance, N₀ relates the volume of a crystal with one mole worth of repeating unit cells, to the volume of a single cell (both in the same units).

In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, ${\displaystyle {\mathsf {N}}^{-1}}$. The Avogadro number, sometimes denoted N₀, is the numeric value of the Avogadro constant (i.e., without units), namely the dimensionless number 6.02214076×10²³.

The Avogadro constant was historically derived from the old definition of the mole as the amount of substance in 12 grams of carbon-12 (¹²C); or, equivalently, the number of daltons in a gram, where the dalton is defined as 1⁄12 of the mass of a ¹²C atom. By this old definition, the numerical value of the Avogadro constant in mol^-1 (the Avogadro number) was a physical constant that had to be determined experimentally.

The redefinition of the mole in 2019, as being the amount of substance containing exactly 6.02214076×10²³ particles, meant that the mass of 1 mole of a substance is now exactly the product of the Avogadro number and the average mass of its particles. The dalton however is still defined as 1⁄12 of the mass of a ¹²C atom, which must be determined experimentally and is known only with finite accuracy. The prior experiments that aimed to determine the Avogadro constant are now re-interpreted as measurements of the value in grams of the dalton.

By the old definition of mole, the numerical value of the mass of one mole of a substance, expressed in grams, was exactly equal to the average mass of one molecule (or atom) of the substance in daltons. With the new definition, this numerical equivalence is no longer exact, and is affected by the uncertainty of the value of the dalton; but it still holds for all practical purposes. For example, the average mass of one molecule of water is about 18.0153 daltons, and of one mole of water is about 18.0153 grams. Also, the Avogadro number is the approximate number of nucleons (protons and neutrons) in one gram of ordinary matter.

In older literature, the Avogadro number was also denoted N, although that conflicts with the symbol for number of particles in statistical mechanics.