Amount of substance, symbol (n), is a physical quantity that measures the number of specified elementary entities in a system. These entities may be atoms, molecules, ions, electrons, other particles, or explicitly defined groups of particles. It is one of the seven base quantities of the International System of Units (SI), and its unit is the mole, symbol mol. Also called chemical amount, it connects microscopic particle numbers with quantities measured in laboratory samples. (goldbook.iupac.org)
Definition and particle number
Amount of substance is related to the number of specified entities, (N), by
[ n=\frac{N}{N_{\mathrm A}}, ]
where (N_{\mathrm A}) is the Avogadro constant. In the SI,
[ N_{\mathrm A}=6.02214076\times10^{23}\ \mathrm{mol^{-1}} ]
exactly. Consequently, one mole contains exactly (6.02214076\times10^{23}) specified entities. The same constant applies regardless of their chemical identity. Equal amounts therefore contain equal numbers of entities, although their masses and other properties may differ. (bipm.org)
Particle number and amount of substance are distinct quantities. (N) is a dimensionless count, whereas (n) has the SI dimension of amount of substance and is expressed in moles. The factor (N_{\mathrm A}), with unit (\mathrm{mol^{-1}}), converts between them. Amount of substance is not a special kind of mass; its definition concerns entity numbers rather than how much those entities weigh. (bipm.org)
Specifying the entities
An amount-of-substance value is meaningful only when the entities are identified. For example, one mole of oxygen molecules, (\mathrm{O_2}), contains two moles of oxygen atoms. The expressions (n(\mathrm O)) and (n(\mathrm{O_2})) thus refer to different quantities even when they describe the same sample. This follows directly from counting the atoms within each molecule. (goldbook.iupac.org)
The word “elementary” in this definition does not mean that an entity must be a fundamental particle. A molecule or a specified group of particles also qualifies. For an ionic solid, the specified entity can be a formula unit representing its composition, rather than a discrete molecule. The chemical formula and the entity description establish what is being counted. (goldbook.iupac.org)
Amount of substance is an extensive quantity: for a fixed entity specification, the amounts in separate subsystems add. Combining two portions without changing their chemical composition gives the sum of their original amounts. This additivity distinguishes it from properties that do not scale with sample size. (goldbook.iupac.org)
Relation to mass and measurement
The molar mass (M) of a substance is its mass divided by its amount:
[ M=\frac{m}{n}, \qquad n=\frac{m}{M}. ]
Its SI unit is (\mathrm{kg,mol^{-1}}), although (\mathrm{g,mol^{-1}}) is widely used in chemistry. Thus, different substances with the same mass generally have different amounts because their molar masses differ. (goldbook.iupac.org)
Laboratory determination usually does not involve counting every entity individually. Instead, amount is inferred from measured quantities and an appropriate physical or chemical relationship. Weighing a sufficiently characterized substance and dividing by its molar mass is a common route. Where a sample contains impurities, the calculation must use the mass attributable to the specified substance rather than the total sample mass. (bipm.org)
Other routes include gas measurements and electrochemical measurements. Under the ideal-gas approximation,
[ n=\frac{pV}{RT}, ]
where (p) is pressure, (V) is volume, (T) is thermodynamic temperature, and (R) is the gas constant. Real-gas measurements may require corrections. Electrochemical determinations can relate transferred charge to amount through the Faraday constant and the reaction stoichiometry. (bipm.org)
Mixtures and concentration
Several composition quantities are built from amount of substance. Amount concentration, often called molar concentration, is
[ c_i=\frac{n_i}{V}, ]
where (V) is the volume of the entire mixture, not merely that of one component. Its SI unit is (\mathrm{mol,m^{-3}}); (\mathrm{mol,L^{-1}}) is also commonly used. (goldbook.iupac.org)
The amount fraction, or mole fraction, is
[ x_i=\frac{n_i}{\sum_j n_j}. ]
It is dimensionless and equals the corresponding number fraction of the specified entities. By contrast, molality divides a solute’s amount by the mass of the solvent, normally giving units of (\mathrm{mol,kg^{-1}}). These quantities use different denominators and are not interchangeable. (goldbook.iupac.org)
Chemical reactions
Amount of substance provides the quantitative basis of stoichiometry. The coefficients in a balanced chemical equation describe ratios of entities and therefore ratios of amounts consumed or produced. They do not generally represent equal mass ratios. (old.iupac.org)
For a specified chemical reaction, the extent of reaction (\xi) relates changes in component amounts through
[ \mathrm dn_i=\nu_i,\mathrm d\xi, ]
where (\nu_i) is negative for a reactant and positive for a product. Extent has the unit mole. Individual species amounts can change during reaction, so amount of substance summed over all species is not, in general, conserved. (goldbook.iupac.org)
Historical development
Earlier chemical practice used expressions such as “gram-atom” and “gram-molecule,” linking laboratory quantities to relative atomic and molecular masses. In 1971, the General Conference on Weights and Measures adopted the mole as an SI base unit, defining it through the number of atoms in 0.012 kilogram of carbon-12. (bipm.org)
A revised definition was adopted in November 2018 and took effect on May 20, 2019. It fixed the Avogadro constant exactly, replacing the carbon-12-based definition. The mole thereby became independent of the definition of the kilogram. Carbon-12’s molar mass, formerly exactly (0.012\ \mathrm{kg,mol^{-1}}), is now experimentally determined rather than fixed by definition. (goldbook.iupac.org)