Mole (unit)

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, an SI base quantity proportional to the number of elementary entities of a substance. One mole is an aggregate of exactly 6.02214076×10²³ elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N₀) and the numerical value of the Avogadro constant (symbol N_A) has units of mol⁻¹. The relationship between the mole, Avogadro number, and Avogadro constant can be expressed in the following equation:$${\displaystyle 1{\text{ mol}}={\frac {N_{0}}{N_{\text{A}}}}={\frac {6.02214076\times 10^{23}}{N_{\text{A}}}}}$$The current SI value of the mole is based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of ¹²C, which made the molar mass of a compound in grams per mole, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 revision of the SI, the numerical equivalence is now only approximate, but may still be assumed with high accuracy.

Conceptually, the mole is similar to the concept of dozen or other convenient grouping used to discuss collections of identical objects. Because laboratory-scale objects contain a vast number of tiny atoms, the number of entities in the grouping must be huge to be useful for work.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and amounts of products of chemical reactions. For example, the chemical equation 2 H₂ + O₂ → 2 H₂O can be interpreted to mean that for each 2 mol molecular hydrogen (H₂) and 1 mol molecular oxygen (O₂) that react, 2 mol of water (H₂O) form. The concentration of a solution is commonly expressed by its molar concentration, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is mole per litre (mol/L).

Conceptually a mole is similar to words like "pair" or "dozen". These words describe a set of identical objects—i.e. a collection or aggregate of the objects themselves, not the numbers 2 or 12. The unusual and daunting aspect of a mole is that the number of objects in the set, given by the Avogadro number, is difficult to comprehend. To be useful as a unit, the mole needs to describe the amount in a sample containing a number of atoms (or other elementary entities) that can be manipulated in an ordinary chemistry lab. Atoms are so small that not just trillions but trillions-of-trillions of atoms are needed to create an aggregate large enough to work with.

The number of entities (symbol N) in a one-mole sample equals the Avogadro number (symbol N₀), a dimensionless quantity. The Avogadro constant (symbol N_A) is given by the Avogadro number multiplied by the unit reciprocal mole (mol⁻¹), i.e. N_A = N₀/mol. The ratio n = N/N_A is a measure of the amount of substance (with the unit mole). The Avogadro constant was determined by a measurement of the number of ²⁸Si atoms in a single crystalline sample.

Depending on the nature of the substance, an elementary entity may be an atom, a molecule, an ion, an ion pair, or a subatomic particle such as a proton. For example, 10 moles of water (a chemical compound) and 10 moles of mercury (a chemical element) contain equal numbers of particles of each substance, with one atom of mercury for each molecule of water, despite the two quantities having different volumes and different masses.^{[citation needed]}

The mole is an amount corresponding to a given count (an Avogadro number) of elementary entities. Usually, the entities counted are chemically identical and individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, the constituent entities in a solid are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity. Thus, the solid is composed of a certain number of moles of such entities. In yet other cases, such as diamond, where the entire crystal is essentially a single molecule, the mole is still used to express the number of atoms bound together, rather than a count of molecules. Thus, common chemical conventions apply to the definition of the constituent entities of a substance, in other cases exact definitions may be specified. The molar mass of a substance is equal to its relative atomic (or molecular) mass multiplied by the molar mass constant, which is almost exactly 1 g/mol.^{[citation needed]}

Like chemists, chemical engineers use the unit mole extensively, but different unit multiples may be more suitable for industrial use. For example, the SI unit for volume is the cubic metre, a much larger unit than the commonly used litre in the chemical laboratory. When amount of substance is also expressed in kmol (1000 mol) in industrial-scaled processes, the numerical value of molarity remains the same, as ${\textstyle {\frac {\text{kmol}}{{\text{m}}^{3}}}={\frac {1000{\text{ mol}}}{1000{\text{ L}}}}={\frac {\text{mol}}{\text{L}}}}$. Chemical engineers once used the kilogram-mole (notation kg-mol), which is defined as the number of entities in 12 kg of ¹²C, and often referred to the mole as the gram-mole (notation g-mol), then defined as the number of entities in 12 g of ¹²C, when dealing with laboratory data.