Mole (mol)
Definition, realization and amount of substance in the International System of Units
Amount of substance is a fundamental quantity in chemistry, physics and materials science. It counts how many elementary entities (such as atoms, molecules, ions or other particles) a system contains. The SI unit of amount of substance is the mole. Despite its central role in the sciences, how the mole is actually defined, and how that definition relates to mass and the number of particles, is often unclear.
The modern definition of the mole is no longer linked to any particular mass or chemical reference, but to an exact number of elementary entities. To understand this it is, as with the other SI base units, necessary to distinguish between definition, realization and practical use.
The definition of the mole in the SI system
Since 2019, the mole has been defined within the International System of Units (SI) according to the following principle:
The mole is the SI unit of amount of substance. It is defined by giving the Avogadro constant Nₐ the exact numerical value
6.022 140 76 × 10²³ mol⁻¹.
This means that:
One mole contains exactly 6.022 140 76 × 10²³ elementary entities.
The elementary entity must always be specified and may be, for example, an atom, a molecule, an ion, an electron or another particle.
The mole is thus a counting unit, analogous to concepts such as the dozen, but with a much larger and exactly fixed number.
Historical background and the 2019 SI reform
Before 2019, the mole was defined indirectly through its link to the kilogram. One mole was defined as the amount of substance containing as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.
This definition tied the mole and the kilogram together in a way that made amount of substance dependent on the unit of mass. With the 2019 SI reform, a direct definition through an exact value of the Avogadro constant was introduced instead.
The transition brought a clarification of principle: the mole is now a pure counting unit, independent of mass, while the relationship between the mole and the kilogram is instead described through molar mass.
Definition, realization and use
For amount of substance too, it is important to distinguish between three levels:
The definition states what the mole is in principle and is tied to the Avogadro constant.
The realization refers to how amount of substance can be determined experimentally in practice.
The use refers to how the mole is used in chemistry, physics, biology and engineering.
Realizing the mole
Unlike the meter, the second and the kilogram, the mole is not realized through a specific measuring instrument. In practice, amount of substance is determined by counting entities indirectly, usually via mass, volume or electric charge, in combination with known physical and chemical relationships.
The central relationship is that between amount of substance n, mass m and molar mass M:n=Mm
The molar mass M is expressed in the unit kg·mol⁻¹ and is a property of the substance in question.
The Avogadro constant and the number of particles
The Avogadro constant states the number of elementary entities per mole and forms the link between the microscopic world (individual particles) and the macroscopic world (measurable quantities).
By fixing the value of the Avogadro constant, the SI system has made amount of substance an exact counting quantity, in the same way that the second is tied to an exact number of atomic oscillations.
The mole’s relationship to mass and the kilogram
Although the mole is no longer defined via the kilogram, there is a close relationship between amount of substance and mass. This relationship is expressed through molar mass, which in turn is related to atomic and molecular masses.
For example, carbon-12 by definition has a molar mass of exactly 12 g·mol⁻¹. For other substances, the molar mass is determined by measurement and tabulated with high accuracy.
The kilogram and the mole are thus no longer linked by definition, but remain practically connected through molar masses.
The role of the mole in derived quantities
The mole appears in several derived SI quantities, for example:
- molar concentration (mol·m⁻³),
- molar energy (J·mol⁻¹),
- molar heat capacity (J·mol⁻¹·K⁻¹).
A clear and consistent definition of the mole is therefore central to chemical thermodynamics, reaction kinetics and materials science.
Practical use of the mole
In practical chemistry, the mole is used to:
- balance chemical reactions
- calculate reaction yields
- connect experimental masses to chemical equations
Through the concept of the mole it becomes possible to work with very large numbers of particles in a systematic and manageable way.
Summary
The mole is today defined as an exact number of elementary entities and is thus a pure counting unit within the SI system. By fixing the Avogadro constant, amount of substance has been decoupled from the unit of mass, which has clarified the role of the mole and strengthened the logical structure of the SI system.
The mole works as a bridge between the microscopic and the macroscopic world, and it is one of the core quantities in chemistry, physics and related sciences.