Mole (unit)

The mole (symbol mol) is the International System of Units (SI) base unit for amount of substance. One mole represents an exact aggregate of 6.02214076×10²³ elementary entities—these can be atoms, molecules, ions, ion pairs, or other particles. That number, 602,214,076,000,000,000,000,000, is roughly 602 sextillion, or 602 billion multiplied by one trillion. The count of particles in a mole is called the Avogadro number (symbol N₀), while the Avogadro constant (symbol Nₐ) carries units of mol⁻¹. Their relationship is given by 1 mol = N₀ / Nₐ = 6.02214076×10²³ / Nₐ.

The current SI value of the mole stems from its historical definition: the amount of substance equal to the number of atoms in 12 grams of carbon-12. That definition made the molar mass of a compound, in grams per mole, numerically equal to its average molecular or formula mass expressed in daltons. After the 2019 SI revision, this numerical equivalence is only approximate, though still highly accurate.

Conceptually, the mole works like the word "dozen" or "pair"—it describes a set of identical objects, not just a number. The daunting aspect is the sheer size of the set: the Avogadro number is enormous because atoms are so small that trillions upon trillions are needed to create a sample large enough for a chemistry lab.

In chemistry, the mole is a standard way to express amounts of reactants and products. For instance, the equation 2 H₂ + O₂ → 2 H₂O means that for every 2 moles of molecular hydrogen and 1 mole of molecular oxygen that react, 2 moles of water form. Solution concentration is often given as molar concentration, typically in moles per litre (mol/L).

The number of entities (N) in a one-mole sample equals the Avogadro number (N₀), a dimensionless quantity. The Avogadro constant (Nₐ) is N₀ multiplied by the unit reciprocal mole (mol⁻¹), so Nₐ = N₀ / mol. The amount of substance (n) is then n = N / Nₐ, with the unit mole. The Avogadro constant was determined by measuring the number of silicon-28 atoms in a single crystalline sample.

The elementary entity counted can be an atom, molecule, ion, ion pair, or subatomic particle like a proton. For example, 10 moles of water and 10 moles of mercury contain the same number of particles—one mercury atom for each water molecule—even though their volumes and masses differ. The mole corresponds to a fixed count (an Avogadro number) of these entities. Usually, the entities are chemically identical and distinct, such as dissolved molecules in a solution. In a solid, the entities are fixed in a lattice but remain separable without losing chemical identity, so the solid is described by a certain number of moles of those entities. In cases like diamond, where the whole crystal is essentially a single molecule, the mole still counts the atoms bound together rather than molecules. Common chemical conventions define the constituent entities for a substance; where needed, exact definitions are specified. The molar mass of a substance equals its relative atomic or molecular mass multiplied by the molar mass constant, which is almost exactly 1 g/mol.

Chemical engineers also use the mole extensively, though industrial processes often employ different multiples. For example, the SI unit for volume is the cubic metre—much larger than the litre used in labs. When amount of substance is expressed in kmol (1000 mol) on an industrial scale, the numerical value of molarity remains the same, as kmol/m³.