# Amount of substance (mole)

The amount of substance is a basic (or fundamental) quantity that indicates a set of elementary entities and its value is proportional to the number of entities contained in the system. The entities can be atoms, molecules, ions, radicals, or other, and must be specified each time to replace the word “substance“ (for example the chemical quantity of H2O molecules, the chemical quantity of ionizable protons, the chemical quantity of sulfate, quantity chemistry of calcium ions, etc.).

### Amount of substance unit (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 masses. “Atomic weights” were originally referred to the atomic weight of oxygen, by general agreement taken as 16. But 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 was for them the naturally occurring element oxygen.

Finally, 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 1959/60. Physicists and chemists have ever since agreed to assign the value 12, exactly, to the so-called atomic weight of the isotope of carbon with mass number 12 (carbon 12, 12C), correctly called the relative atomic mass Ar(12C). The unified scale thus obtained gives the relative atomic and molecular masses, also known as the atomic and molecular weights, respectively.

The quantity used by chemists to specify the amount of chemical elements or compounds is now called “amount of substance.” Amount of substance is defined to be proportional to the number of specified elementary entities in a sample, the proportionality constant being a universal constant which is the same for all samples. The unit of amount of substance is called the mole, symbol mol, and the mole is defined by specifying the mass of carbon 12 that constitutes one mole of carbon 12 atoms. By international agreement this was fixed at 0.012 kg, i.e. 12 g. Following proposals by the IUPAP, the IUPAC, and the ISO, the CIPM gave a definition of the mole in 1967 and confirmed it in 1969. This was adopted by the 14th CGPM (1971):

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol.”
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

It follows that the molar mass of carbon 12 is exactly 12 grams per mole, M(12C) = 12 g/mol. In 1980 the CIPM approved the report of the CCU (1980) which specified that: In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. The definition of the mole also determines the value of the universal constant that relates the number of entities to the amount of substance for any sample. This constant is called the Avogadro constant, symbol $$N_A$$ or $$L$$. If $$N(X)$$ denotes the number of entities $$X$$ in a specified sample, and if $$n(X)$$ denotes the amount of substance of entities $$X$$ in the same sample, the relation is:

$n(X) = \dfrac{N(X)}{N_A}$

Note that since $$N(X)$$ is dimensionless, and $$n(X)$$ has the SI unit mole, the Avogadro constant has the coherent SI unit reciprocal mole. In the name “amount of substance,” the words “of substance” could for simplicity be replaced by words to specify the substance concerned in any particular application, so that one may, for example, talk of “amount of hydrogen chloride, HCl,” or “amount of benzene, C6H6.”

It is important to always give a precise specification of the entity involved (as emphasized in the second sentence of the definition of the mole); this should preferably be done by giving the empirical chemical formula of the material involved. Although the word “amount” has a more general dictionary definition, this abbreviation of the full name “amount of substance” may be used for brevity. This also applies to derived quantities such as “amount of substance concentration,” which may simply be called “amount concentration.” However, in the field of clinical chemistry the name “amount of substance concentration” is generally abbreviated to “substance concentration.”