The mole, symbol mol, is the unit of amount of substance in the International System of Units (SI), and one of its seven base units. One mole contains exactly (6.02214076\times10^{23}) specified elementary entities. These may be atoms, molecules, ions, electrons, or other specified particles or groups of particles. The mole connects microscopic particle counts with macroscopic quantities used in chemistry. Its definition depends on the fixed value of the Avogadro constant, rather than on a particular material sample. (bipm.org)
Definition and particle counting
The Avogadro constant is exactly
[ N_{\mathrm A}=6.02214076\times10^{23}\ \mathrm{mol}^{-1}. ]
For a sample containing (N) specified entities, its amount of substance (n) is
[ n=\frac{N}{N_{\mathrm A}}, \qquad N=nN_{\mathrm A}. ]
The particle count (N) is dimensionless, whereas (n) is a physical quantity expressed in moles. Thus, although the mole functions as a counting unit, amount of substance and number of entities remain distinct quantities in SI. The numerical value (6.02214076\times10^{23}), without the reciprocal-mole unit, is often called the Avogadro number. (bipm.org)
The identity of the counted entity must be stated. For example, one mole of water molecules contains two moles of hydrogen atoms and one mole of oxygen atoms. Likewise, one mole of molecular nitrogen, N₂, contains two moles of nitrogen atoms. These are consequences of molecular formulas, not different definitions of the mole. Entities need not exist as separate molecules: an ionic solid can be described using specified formula units. (bipm.org)
Relationship to mass
The mole is not a unit of mass. Equal amounts of different substances contain equal numbers of specified entities but generally have different masses. The connecting quantity is molar mass, (M), defined as mass divided by amount of substance:
[ M=\frac{m}{n}, \qquad n=\frac{m}{M}. ]
Its coherent SI unit is kilograms per mole, although grams per mole are widely used in chemical calculations. A sample with a molar mass of (18.0\ \mathrm{g,mol^{-1}}) and a mass of (9.00\ \mathrm g), for example, has an amount of (0.500\ \mathrm{mol}). (goldbook.iupac.org)
Molar masses depend on composition, including isotopic composition. For a chemical element, molar mass is related to relative atomic mass through the molar mass constant. Before the 2019 redefinition, that constant was exactly (1\ \mathrm{g,mol^{-1}}); it is now experimentally determined and extremely close to that value. Consequently, familiar conversions between relative atomic masses and molar masses remain suitable for ordinary chemical work, but their formerly exact numerical correspondence is no longer part of the definition. (bipm.org)
Chemical reactions and composition
The mole is central to stoichiometry, which relates quantities of substances participating in a chemical reaction. Coefficients in a balanced chemical equation express ratios of entities and therefore ratios of amounts in moles. For example,
[ 2\mathrm{H_2}+\mathrm{O_2}\rightarrow2\mathrm{H_2O} ]
indicates that two moles of hydrogen molecules react with one mole of oxygen molecules to form two moles of water molecules, assuming complete conversion according to that equation. The coefficients do not express mass ratios; masses must be obtained using the respective molar masses. (iupac.org)
Several composition quantities incorporate amount of substance:
- Amount concentration, (c=n/V), divides the amount of a constituent by the volume of the mixture. Its coherent SI unit is (\mathrm{mol,m^{-3}}); (\mathrm{mol,L^{-1}}) is common.
- Molality, (b=n_{\text{solute}}/m_{\text{solvent}}), divides solute amount by the mass of the solvent, usually in (\mathrm{mol,kg^{-1}}).
- Mole fraction, (x_i=n_i/\sum_j n_j), gives a constituent’s amount relative to the total amount and is dimensionless. (iupac.org)
These quantities are not interchangeable. In particular, amount concentration uses the volume of the entire mixture, while molality uses the solvent’s mass. (media.iupac.org)
Gases and molar quantities
For an ideal gas, amount of substance enters the equation of state
[ pV=nRT, ]
where (p) is pressure, (V) is volume, (T) is absolute temperature, and (R) is the molar gas constant. Its molar volume is therefore (V/n=RT/p). A mole of gas has no universally fixed volume: volume depends on temperature, pressure, and departures from ideal behavior. The frequently quoted value of approximately 22.4 litres applies to an ideal gas at 273.15 K and one atmosphere. (openstax.org)
In thermodynamics, dividing an extensive quantity by amount of substance produces a molar quantity. Examples include molar enthalpy, expressed in joules per mole, and molar heat capacity, expressed in joules per mole per kelvin. Such quantities permit comparisons on a common amount-of-substance basis. (iupac.org)
Historical definition and practical realization
Earlier chemical practice used terms such as “gram-atom” and “gram-molecule.” 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. A replacement definition was adopted on November 16, 2018, and took effect on May 20, 2019, fixing the Avogadro constant exactly and separating the mole’s definition from the kilogram. (bipm.org)
An exact definition does not make every laboratory measurement exact. Practical determinations depend on measured mass, purity, composition, and molar mass, or on other validated measurement methods. In high-precision metrology, enriched silicon crystals allow atom numbers to be inferred from crystal volume and lattice spacing, with corrections for impurities and surface effects. The resulting amount still has measurement uncertainty, even though the defining constant does not. (bipm.org)