Mole (unit)

 ( Si Base Units ) 

The equation can be rearranged as an explicit expression for the mole: . Letting ent denote the amount of substance equal to one Molecular entity, the smallest particle of a substance (retaining its chemical properties), one mole is the amount of substance containing  entities, i.e. . Thus, amount of substance is dimensionally equivalent to the reciprocal of the Avogadro constant (), which is an amount consisting of exactly one elementary entity, i.e. an elementary amount.

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.

Late 20th-century chemical engineering practice came to use the kilomole (kmol), which was numerically identical to the kilogram-mole (until the 2019 revision of the SI, which redefined the mole by fixing the value of the Avogadro constant, making it very nearly equivalent to but no longer exactly equal to the gram-mole), but whose name and symbol adopt the SI convention for standard multiples of metric units – thus, kmol means 1000 mol. This is equivalent to the use of kg instead of g. The use of kmol is not only for "magnitude convenience" but also makes the equations used for modelling chemical engineering systems coherent. For example, the conversion of a flowrate of kg/s to kmol/s only requires dividing by the molar mass in kg/kmol (which is equivalent to g/mol, as $\backslash frac\{\backslash text\{kg\}\}\{\backslash text\{kmol\}\}=\backslash frac\{1000\backslash text\{\; g\}\}\{1000\backslash text\{\; mol\}\}=\backslash frac\{\backslash text\{g\}\}\{\backslash text\{mol\}\}$) without multiplying by 1000 unless the basic SI unit of mol/s were to be used, which would otherwise require the molar mass to be converted to kg/mol.

For convenience in avoiding conversions in the Imperial units (or US customary units), some engineers adopted the pound-mole (notation lb-mol or lbmol), which is defined as the number of entities in 12 lb of ¹²C. One lb-mol is equal to , which is the same numerical value as the number of grams in an international avoirdupois pound.

Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1 mol photons ≈ photons. The obsolete unit einstein is variously defined as the energy in one mole of photons and also as simply one mole of photons.

One femtomole is exactly molecules; attomole and smaller quantities do not correspond to a whole number of entities. The yoctomole, equal to around 0.6 of an individual molecule, did make appearances in scientific journals in the year the yocto- prefix was officially implemented.

The first table of standard atomic weight was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the Stoichiometry proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to atomic theory (an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic masses (promoted by proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from relative atomic masses by an integer factor), which would last throughout much of the nineteenth century.

Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of relative atomic masses to ever-increasing accuracy. He was also the first chemist to use oxygen as the standard to which other masses were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especially metals. However, he chose to fix the atomic mass of oxygen as 100, which did not catch on.

Charles Frédéric Gerhardt (1816–56), Henri Victor Regnault (1810–78) and Stanislao Cannizzaro (1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic masses attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had reverted to defining the atomic mass of hydrogen as 1, although at the level of precision of measurements at that time – relative uncertainties of around 1% – this was numerically equivalent to the later standard of oxygen = 16. However the chemical convenience of having oxygen as the primary atomic mass standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic mass determinations.

The name mole is an 1897 translation of the German unit Mol, coined by the chemist Wilhelm Ostwald in 1894 from the German word Molekül (molecule). Some sources place the date of first usage in English as 1902. Merriam–Webster proposes

an etymology from ''Molekulärgewicht'' ([[molecular weight]]).
From p. 119: ''"Nennen wir allgemein das Gewicht in Grammen, welches dem Molekulargewicht eines gegebenen Stoffes numerisch gleich ist, ein Mol, so ... "''  (If we call in general the weight in grams, which is numerically equal to the molecular weight of a given substance, a "mol", then ... ) The related concept of [[equivalent mass]] had been in use at least a century earlier.'''mole''', '''''n.''''', Oxford English Dictionary, Draft Revision Dec. 2008
     

In chemistry, it has been known since Joseph Proust law of definite proportions (1794) that knowledge of the mass of each of the components in a chemical system is not sufficient to define the system. Amount of substance can be described as mass divided by Proust's "definite proportions", and contains information that is missing from the measurement of mass alone. As demonstrated by John Dalton law of partial pressures (1803), a measurement of mass is not even necessary to measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable one being the ideal gas law (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties.

The oxygen-16 definition was replaced with one based on carbon-12 during the 1960s. The International Bureau of Weights and Measures defined the mole as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12." Thus, by that definition, one mole of pure ¹²C had a mass of exactly 12 Gram. The four different definitions were equivalent to within 1%.

Because a dalton, a unit commonly used to measure atomic mass, is exactly 1/12 of the mass of a carbon-12 atom, this definition of the mole entailed that the mass of one mole of a compound or element in grams was numerically equal to the average mass of one molecule or atom of the substance in daltons, and that the number of daltons in a gram was equal to the number of elementary entities in a mole. Because the mass of a nucleon (i.e. a proton or neutron) is approximately 1 dalton and the nucleons in an atom's nucleus make up the overwhelming majority of its mass, this definition also entailed that the mass of one mole of a substance was roughly equivalent to the number of nucleons in one atom or molecule of that substance.

Since the definition of the gram was not mathematically tied to that of the dalton, the number of molecules per mole N_A (the Avogadro constant) had to be determined experimentally. The experimental value adopted by CODATA in 2010 is . physics.nist.gov/ Fundamental Physical Constants: Avogadro Constant In 2011 the measurement was refined to .

The mole was made the seventh SI base unit in 1971 by the 14th CGPM.

In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed to a plan for a possible revision of the SI base unit definitions at an undetermined date.

On 16 November 2018, after a meeting of scientists from more than 60 countries at the CGPM in Versailles, France, all SI base units were defined in terms of physical constants. This meant that each SI unit, including the mole, would not be defined in terms of any physical objects but rather they would be defined by physical constants that are, in their nature, exact.

Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly elementary entities" of that substance. CIPM Report of 106th Meeting Retrieved 7 April 2018

• the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity that can be expressed simply as a number, not requiring a distinct base unit;
• The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies
• The mole is not a true metric (i.e. measuring) unit, rather it is a parametric unit, and amount of substance is a parametric base quantity