Historical perspective: Unit of amount of substance, mole


Following the discovery of the fundamental laws of chemistry, units called, for example, "gram-atom" and "gram molecule", were used to specify amounts of chemical elements or compounds. These units had a direct connection with "atomic weights" and "molecular weights", which are in fact relative atomic and molecular masses. The first compilations of "Atomic weights" were originally linked to the atomic weight of oxygen, which was, by general agreement, taken as being 16. Whereas physicists separated the isotopes in a mass spectrometer and attributed the value 16 to one of the isotopes of oxygen, chemists attributed the same value to the (slightly variable) mixture of isotopes 16, 17 and 18, which for them constituted the naturally occurring element oxygen. An agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959-1960. Physicists and chemists had agreed to assign the value 12, exactly, to the so-called atomic weight, correctly referred to as the relative atomic mass Ar, of the isotope of carbon with mass number 12 (carbon 12, 12C). The unified scale thus obtained gives the relative atomic and molecular masses, also known as the atomic and molecular weights, respectively. This agreement is unaffected by the redefinition of the mole.

The quantity used by chemists to specify the amount of chemical elements or compounds is called "amount of substance". Amount of substance, symbol n, is defined to be proportional to the number of specified elementary entities N in a sample, the proportionality constant being a universal constant which is the same for all entities. The proportionality constant is the reciprocal of the Avogadro constant NA, so that n = N/NA. The unit of amount of substance is called the mole, symbol mol. Following proposals by the IUPAP, IUPAC and ISO, the CIPM developed a definition of the mole in 1967 and confirmed it in 1969, by specifying that the molar mass of carbon 12 should be exactly 0.012 kg/mol. This allowed the amount of substance nS(X) of any pure sample S of entity X to be determined directly from the mass of the sample mS and the molar mass M(X) of entity X, the molar mass being determined from its relative atomic mass Ar (atomic or molecular weight) without the need for a precise knowledge of the Avogadro constant, by using the relations

nS(X) = mS/(M(X), and M(X) = Ar(X) g/mol

Thus, this definition of the mole was dependent on the artefact definition of the kilogram.

The numerical value of the Avogadro constant defined in this way was equal to the number of atoms in 12 grams of carbon 12. However, because of recent technological advances, this number is now known with such precision that a simpler and more universal definition of the mole has become possible, namely, by specifying exactly the number of entities in one mole of any substance, thus fixing the numerical value of the Avogadro constant. This has the effect that the new definition of the mole and the value of the Avogadro constant are no longer dependent on the definition of the kilogram. The distinction between the fundamentally different quantities 'amount of substance' and 'mass' is thereby emphasized. The present definition of the mole based on a fixed numerical value for the Avogadro constant,NA, was adopted in Resolution 1 of the 26th CGPM (2018).

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CGPM Resolution 3 (1971)

SI unit of amount of substance (mole)

CGPM Resolution 1 (2018)

On the revision of the International System of Units (SI)