Mole (unit)

Definition and numerical value

Since 2019 the mole has been defined by fixing the numerical value of the Avogadro constant to exactly 6.02214076×10²³ when expressed in the unit mol⁻¹. In words: one mole of a specified elementary entities contains exactly 6.02214076×10²³ of those entities. That fixed number is commonly called Avogadro's constant or Avogadro's number. The mole therefore counts molecules, atoms or other designated entities in a defined, reproducible way.

Relationship to mass and the atomic scale

Although the mole counts entities, chemists usually relate it to mass through the concept of molar mass. The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g·mol⁻¹). Because the atomic masses listed in tables are given in unified atomic mass units (u), the numerical value of an element's relative atomic mass in u is equal to its molar mass in grams per mole. For example, one mole of water molecules has a molar mass close to 18 g·mol⁻¹. The link between atomic-scale masses and laboratory masses makes the mole practical for preparing solutions and measuring chemical yields; see concepts of mass and the gram equivalence gram.

History and development

The idea of relating amounts of gas or elements to numbers of particles evolved through the 19th and 20th centuries. The name and number are associated with Amedeo Avogadro, and the constant itself is often called Avogadro's number. Historically, the mole was tied to a specified mass of carbon-12, but advances in measurement and a decision by the metrology community led to the modern definition based on a fixed numerical value of Avogadro's constant. Experimental determinations of the constant used many techniques, including studies of carbon compounds and precise measurements on crystals.

Uses, examples and practical significance

• Stoichiometry: Chemists use moles to relate reactants and products in balanced chemical equations so quantities can be measured and predicted.
• Concentration: Molar concentration (molarity) expresses moles of solute per liter of solution, a common laboratory unit.
• Comparisons: Because one mole always contains the same number of entities, it permits direct comparison of quantities of different substances regardless of individual particle mass; one mole of hydrogen atoms and one mole of oxygen atoms contain the same number of atoms though their masses differ. For context, a single mole of hydrogen atoms is related to the mass of hydrogen in grams.

Notable distinctions and facts

Although any entity can be counted in moles, the magnitude of Avogadro's number means that one mole often corresponds to a small laboratory mass for atoms and molecules (grams or tens of grams) but to an impractically large count for macroscopic objects (one mole of apples would vastly exceed planetary mass). The mole is therefore a counting unit like the dozen or gross, but tailored to atomic and molecular scales. For further reading on related concepts see SI unit and additional resources on molecules and atoms, along with technical summaries available at specialist sites hydrogen, carbon metrology pages and other references mass, gram.