Mole (unit)

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This article is about the chemistry unit "Mole". For other uses, see Mole (disambiguation).
"Nmol" redirects here. For the mathematical technique, see Method of lines.
Unit system SI base unit
Unit of Amount of substance
Symbol mol 

Mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as the amount of any substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of pure carbon-12 (12C), the isotope of carbon with relative atomic mass of exactly 12 by definition. This corresponds to the Avogadro constant, which has a value of 6.02214129(27)×1023 elementary entities of the substance. It is one of the base units in the International System of Units, and has the unit symbol mol and corresponds with the dimension symbol N.[1] In honour of the unit, some chemists celebrate October 23 (a reference to the 1023 part of Avogadro's number) as "Mole Day".

The mole is widely used in chemistry instead of units of mass or volume as a convenient way to express amounts of reactants or of products of chemical reactions. For example, the chemical equation 2 H2 + O2 → 2 H2O implies that 2 mol of dihydrogen (H2) and 1 mol of dioxygen (O2) react to form 2 mol of water (H2O). The mole may also be used to express the number of atoms, ions, or other elementary entities in a given sample of any substance. The concentration of a solution is commonly expressed by its molarity, defined as the number of moles of the dissolved substance per litre of solution.

The number of molecules in a mole (known as Avogadro's constant) is defined such that the mass of one mole of a substance, expressed in grams, is exactly equal to the substance's mean molecular mass. For example, the mean molecular mass of natural water is about 18.015, so one mole of water is about 18.015 grams. Making use of this equation considerably simplifies many chemical and physical computations.

The term gram-molecule was formerly used for essentially the same concept.[1] The term gram-atom (abbreviated gat.) has been used for a related but distinct concept, namely a quantity of a substance that contains Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgB2 is 1 gram-molecule of MgB2 but 3 gram-atoms of MgB2.[2][3]

Definition and related concepts[edit]

As of 2011, the mole is defined by BIPM to be the amount of substance of a system which contains as many elementary entities (e.g. atoms, molecules, ions, electrons) as there are atoms in 0.012 kilograms of carbon-12 (12C), the isotope of carbon with relative atomic mass 12.[1] Thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance.

The mass per mole of a substance is called its molar mass. Since the standard unit for expressing the mass of molecules or atoms (atomic mass unit or the dalton) is defined as 1/12 of the mass of a 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is exactly equal to its mean molecular or atomic mass, measured in unified atomic mass units or daltons; which is to say, to the substance's mean molecular or relative atomic mass.

The number of elementary entities in a sample of a substance is technically called its (chemical) amount. Therefore, the mole is a convenient unit for that physical quantity. One can determine the chemical amount of a known substance, in moles, by dividing the sample's mass by the substance's molar mass.[4] Other methods include the use of the molar volume or the measurement of electric charge.[4]

The mass of one mole of a substance depends not only on its molecular formula, but also on the proportion of the isotopes of each element present in it. For example, one mole of calcium-40 is 39.96259098 ± 2.2×10−7 grams, whereas one mole of calcium-42 is 41.95861801 ± 2.7×10−7 grams, and one mole of calcium with the normal isotopic mix is 40.078 ± 0.004 grams.

Since the definition of the gram is not (as of 2011) mathematically tied to that of the atomic mass unit, the number NA of molecules in a mole (Avogadro's number) must be determined experimentally. The value adopted by CODATA in 2010 is NA = 6.02214129×1023 ± 2.7×10−7×1023.[5] In 2011 the measurement was refined to 6.02214078×1023 ± 1.8×10−7×1023.[6]


The history of the mole is intertwined with that of molecular mass, atomic mass unit, Avogadro's number and related concepts.




Developments in mass spectrometry led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen.[citation needed] The current definition of the mole, based on carbon-12, was approved during the 1960s.[1][7] The four different definitions were equivalent to within 1%.

Scale basis Scale basis
relative to 12C = 12
Relative deviation
from the 12C = 12 scale

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).[8][9][10] However, the related concept of equivalent mass had been in use at least a century earlier.[11]

The mole was made the seventh SI base unit in 1971 by the 14th CGPM.[12]

The mole as a unit[edit]

Since its adoption into the International System of Units in 1971, there have been a number of criticisms of the concept of the mole as a unit like the metre or the second:

  • the number of molecules, etc. in a given lump of material is a fixed dimensionless quantity that can be expressed simply as a number, so does not require its own base unit;[7]
  • the SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies;[13]


Other units called "mole"[edit]

Chemical engineers use the concept extensively, but the unit is rather small for industrial use.[16] For convenience in avoiding conversions, some American engineers adopted the pound-mole (noted lb-mol or lbmol), which is defined as the number of entities in 12 lbm of 12C. One lb-mol is equal to 453.59237 mol.[17] In the metric system, chemical engineers once used the kilogram-mole (noted 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 (noted g-mol), when dealing with laboratory data.[17] However modern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units. Concentrations expressed as kmol/m3 are the same numbers as those in mol/dm3 or molarity conventionally used by chemists for bench measurements, which is convenient for scale-up.

Proposed future definition[edit]

Main article: New SI definitions

In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed a plan for a possible revision of the SI base unit definitions on an as yet undetermined date. This plan, set forward in the meeting's first resolution, included a proposal to redefine the mole in a way that will fix “the Avogadro constant to be equal to exactly 6.022 14X ×1023 when it is expressed in the SI unit mol-1.”[18]

Related units[edit]


The unit's holiday[edit]

October 23 is called Mole Day.[19] It is an informal holiday in honour of the unit among chemists. The date is derived from Avogadro's number, which is approximately 6.022×1023. It starts at 6:02 a.m. and ends at 6:02 p.m.

See also[edit]

Notes and references[edit]

  1. ^ a b c d International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 114–15, ISBN 92-822-2213-6 
  2. ^ Wang, Yuxing et al.; Bouquet, Fr d ric; Sheikin, Ilya; Toulemonde, Pierre; Revaz, Bernard; Eisterer, Michael; Weber, Harald W; Hinderer, Joerg; Junod, Alain (2003). "Specific heat of MgB2 after irradiation". Journal of Physics: Condensed Matter 15 (6): 883–893. arXiv:cond-mat/0208169. Bibcode:2003JPCM...15..883W. doi:10.1088/0953-8984/15/6/315. 
  3. ^ Lortz, R. et al.; Wang, Y.; Abe, S.; Meingast, C.; Paderno, Yu.; Filippov, V.; Junod, A. (2005). "Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductor ZrB12". Phys. Rev. B 72 (2): 024547. arXiv:cond-mat/0502193. Bibcode:2005PhRvB..72b4547L. doi:10.1103/PhysRevB.72.024547. 
  5. ^ [1]
  6. ^ Andreas, Birk; et al (2011). "Determination of the Avogadro Constant by Counting the Atoms in a 28Si Crystal". Physical Review Letters 106 (3): 30801. arXiv:1010.2317. Bibcode:2011PhRvL.106c0801A. doi:10.1103/PhysRevLett.106.030801. 
  7. ^ a b de Bièvre, P.; Peiser, H.S. (1992). "'Atomic Weight'—The Name, Its History, Definition, and Units". Pure Appl. Chem. 64 (10): 1535–43. doi:10.1351/pac199264101535. 
  8. ^ Helm, Georg (1897). The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena. transl. by Livingston, J.; Morgan, R. New York: Wiley. p. 6. 
  10. ^ Ostwald, Wilhelm (1893). Hand- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen. Leipzig. p. 119. 
  12. ^ 14th CGPM (1971):Resolution 3
  13. ^ Price, Gary (2010). "Failures of the global measurement system. Part 1: the case of chemistry". Accreditation and Quality Assurance 15 (7): 421–427. doi:10.1007/s00769-010-0655-z. [2].
  14. ^ Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units, and dimensions.". Metrologia 47 (3): 219–230. Bibcode:2010Metro..47..219J. doi:10.1088/0026-1394/47/3/012. 
  15. ^ Cooper, G; Humphry, S (2010). "The ontological distinction between units and entities". Synthese 187 (2): 393. doi:10.1007/s11229-010-9832-1. 
  16. ^ In particular, when the mole is used, alongside the SI unit of volume of a cubic metre, in thermodynamic calculations such as the ideal gas law, a factor of 1000 is introduced which engineering practice chooses to simplify by adopting the kilomole.
  19. ^ History of National Mole Day Foundation, Inc

External links[edit]