Chemistry:Mole (unit)

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Short description: SI unit of amount of substance
Unit systemInternational system of units (SI)
Unit ofAmount of substance

The mole, symbol mol, is the SI base unit of amount of substance.[1][2][3] The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. Depending on what the substance is, an elementary entity may be an atom, a molecule, an ion, an ion pair, or a subatomic particle such as an electron. For example, if beaker A contains 10 moles of water (a chemical compound) and beaker B contains 10 moles of mercury (a chemical element), they contain equal amounts of substance and beaker B contains exactly 1 atom of mercury for each molecule of water in beaker A, despite the two beakers' containing different volumes and very different masses of liquid.

The mole is defined as exactly 6.02214076×1023 elementary entities.[clarification needed] This definition was adopted in November 2018 and came into force on May 20, 2019, superseding the previous definition of a mole as a number of elementary entities equal to that of 12 grams of carbon-12, the most common isotope of carbon. Because a dalton, a unit commonly used to measure atomic mass, is exactly 1/12 of the mass of a carbon-12 atom, the definition of the mole in use before 2019 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, the pre-2019 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. For example, a water molecule formed from the most common isotope of oxygen and of hydrogen contains 10 protons plus 8 neutrons for a total mass of 18.015 daltons, and a mole of water has a mass of 18.015 grams.

The number of elementary entities in 1 mole is known as the Avogadro number. Prior to 2019, it could only be estimated based on experimental data. The value 6.02214076×1023 was adopted based on the best estimates available in 2018, allowing the new definition to very closely approximate the earlier definition and avoid the need to recalibrate measuring equipment or update published data tables.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that for each 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) that react, 2 mol of water (H2O) form. The mole may also be used to measure the amount of atoms, ions, electrons, or other entities. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance in mole(s) per unit volume of solution, for which the unit typically used is moles per litre (mol/L), commonly abbreviated M.

The term gram-molecule (g mol) was formerly used for "mole of molecules",[4] and gram-atom (g atom) for "mole of atoms". For example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.[5][6]


Nature of the particles

The mole is essentially a count of particles.[7] Usually the particles counted are chemically identical entities, individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, in a solid the constituent particles 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 particles. 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 multiple molecules. Thus, common chemical conventions apply to the definition of the constituent particles of a substance, in other cases exact definitions may be specified. The mass of 1 mole of a substance is equal to its relative atomic or molecular mass in grams.

Molar mass

The molar mass of a substance is the mass of 1 mole of that substance, in multiples of the gram. The amount of substance is the number of moles in the sample. For most practical purposes, the magnitude of molar mass is numerically the same as that of the mean mass of one molecule, expressed in daltons. For example, the molar mass of water is 18.015 g/mol.[8] Other methods include the use of the molar volume or the measurement of electric charge.[8]

The number of moles of a substance in a sample is obtained by dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about 5.551 mol of water.[8]

The molar mass of a substance depends not only on its molecular formula, but also on the distribution of isotopes of each chemical element present in it. For example, the mass of one mole of calcium-40 is 39.96259098±0.00000022 grams, whereas the mass of one mole of calcium-42 is 41.95861801±0.00000027 grams, and of one mole of calcium with the normal isotopic mix is 40.078±0.004 grams.

Molar concentration

The molar concentration, also called molarity, of a solution of some substance is the number of moles per unit of volume of the final solution. In the SI its standard unit is mol/m3, although more practical units, such as mole per litre (mol/L) are used.

Molar fraction

The molar fraction or mole fraction of a substance in a mixture (such as a solution) is the number of moles of the compound in one sample of the mixture, divided by the total number of moles of all components. For example, if 20 g of NaCl is dissolved in 100 g of water, the amounts of the two substances in the solution will be (20 g)/(58.443 g/mol) = 0.34221 mol and (100 g)/(18.015 g/mol) = 5.5509 mol, respectively; and the molar fraction of NaCl will be 0.34221/(0.34221 + 5.5509) = 0.05807.

In a mixture of gases, the partial pressure of each component is proportional to its molar ratio.


Avogadro, who inspired the Avogadro constant

The history of the mole is intertwined with that of molecular mass, atomic mass units, and the Avogadro number.

The first table of standard atomic weight (atomic mass) 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 stoichiometric 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).[9][10][11] The related concept of equivalent mass had been in use at least a century earlier.[12]


Developments in mass spectrometry led to the adoption of oxygen-16 as the standard substance, in lieu of natural oxygen.

The oxygen-16 definition was replaced with one based on carbon-12 during the 1960s. The mole was defined by International Bureau of Weights and Measures as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12." Thus, by that definition, one mole of pure 12C had a mass of exactly 12 g.[4][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
Atomic mass of hydrogen = 1 1.00794(7) −0.788%
Atomic mass of oxygen = 16 15.9994(3) +0.00375%
Relative atomic mass of 16O = 16 15.9949146221(15) +0.0318%

Since the definition of the gram was not mathematically tied to that of the dalton, the number of molecules per mole NA (the Avogadro constant) had to be determined experimentally. The experimental value adopted by CODATA in 2010 is NA = (6.02214129±0.00000027)×1023 mol−1.[13] In 2011 the measurement was refined to (6.02214078±0.00000018)×1023 mol−1.[14]

The mole was made the seventh SI base unit in 1971 by the 14th CGPM.[15]

2019 redefinition of SI base units

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 constants that are, in their nature, exact.[2]

Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly 6.02214076×1023 elementary entities" of that substance.[16][17]


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

  • 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;[7][18]r
  • The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies[19]
  • 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[20]
  • the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between entities and units of continuous quantities[21]

In chemistry, it has been known since Proust's 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 Dalton's 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.

Similar units

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.

For convenience in avoiding conversions in the imperial (or American 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 453.59237 mol,[22] which value is the same as the number of grams in an international avoirdupois pound.

In the metric system, 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), when dealing with laboratory data.[22]

Late 20th-century chemical engineering practice came to use the kilomole (kmol), which is numerically identical to the kilogram-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 the molecular mass without the factor 1000 unless the basic SI unit of mol/s were to be used.

Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1 mol photons = 6.02×1023 photons.[23]


SI multiples of mole (mol)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1 mol dmol decimole 101 mol damol decamole
10−2 mol cmol centimole 102 mol hmol hectomole
10−3 mol mmol millimole 103 mol kmol kilomole
10−6 mol µmol micromole 106 mol Mmol megamole
10−9 mol nmol nanomole 109 mol Gmol gigamole
10−12 mol pmol picomole 1012 mol Tmol teramole
10−15 mol fmol femtomole 1015 mol Pmol petamole
10−18 mol amol attomole 1018 mol Emol examole
10−21 mol zmol zeptomole 1021 mol Zmol zettamole
10−24 mol ymol yoctomole 1024 mol Ymol yottamole
Common multiples are in bold face

Like other SI units, the mole can modified by adding a prefix that multiplies it by a power of 10.


A yoctomole (ymol) is one septillionth of a mole (10−24 mol). It is equal to 0.602214076 elementary entities. While the metric prefix system entails the existence of this unit, in practice it would be more convenient to simply express such extremely small quantities of amount of substance by stating the number of elementary entities directly.


A zeptomole (zmol) is one sextillionth of a mole (10−21 mol). It is equal to 602.214076 elementary entities.


An attomole (amol) is one quintillionth of a mole (10−18 mol). It is equal to 602,214.076 elementary entities.


A femtomole (fmol) is one quadrillionth of a mole (10−15 mol). It is equal to 602,214,076 elementary entities.


A picomole (pmol) is one trillionth of a mole (10−12 mol). It is equal to 602,214,076,000 elementary entities.


A nanomole (nmol) is one billionth of a mole (10−9 mol). It is equal to 602,214,076,000,000 or 6.02214076×1014 elementary entities.


A micromole (μmol) is one millionth of a mole (10−6 mol). It is equal to 602,214,076,000,000,000 or 6.02214076×1017 elementary entities, the approximate number of elementary charges in 0.096485 coulombs.


A millimole (mmol) is one one thousandth of a mole (0.001 mol or 10−3 mol). It is equal to 6.02214076×1020 elementary entities, the approximate number of atoms in 1/5 of a gram of mercury.


A centimole (cmol) is one one hundredth of a mole (0.01 mol or 10−2 mol). It is equal to 6.02214076×1021 elementary entities, slightly more than the number of atoms in a gram of ruthenium metal.


A decimole (dmol) is one tenth of a mole (0.1 mol or 10−1 mol). It is equal to 6.02214076×1022 elementary entities, somewhat more than the number of atoms in a gram of boron and somewhat less than the number of atoms in a gram of beryllium.


A decamole (damol) is ten moles (10 mol or 101 mol). It is equal to 6.02214076×1024 elementary entities, the approximate number of molecules in a 180 ml glass of water.


A hectomole (hmol) is one hundred moles (100 mol or 102 mol). It is equal to 6.02214076×1025 elementary entities.


A kilomole (kmol) is one thousand moles (1000 mol or 103 mol). It is equal to 6.02214076×1026 elementary entities, the approximate number of molecules in an 18 litre (4.755 US gallon) tub of water.


A megamole (Mmol) is one million moles (106 mol). It is equal to 6.02214076×1029 elementary entities, the approximate number of water molecules in an 18 cubic metre pond.


A gigamole (Gmol) is one billion moles (109 mol). It is equal to 6.02214076×1032 elementary entities, the approximate number of water molecules in an 18,000 cubic metre lake.


A teramole (Tmol) is one trillion moles (1012 mol). It is equal to 6.02214076×1035 elementary entities, the approximate number of water molecules in Blithfield Reservoir in Staffordshire, United Kingdom , when full to capacity.


A petamole (Pmol) is one quadrillion moles (1015 mol). It is equal to 6.02214076×1038 elementary entities, a little less than the number of water molecules in Crater Lake, Oregon, the deepest lake in the United States .


An examole (Emol) is one quintillion moles (1018 mol). It is equal to 6.02214076×1041 elementary entities, a little less than the number of water molecules in Lake Tanganyika, the largest lake in Africa and the third largest in the world by volume.


A zettamole (Zmol) is one sextillion moles (1021 mol). It is equal to 6.02214076×1044 elementary entities, a little less than the number of water molecules in the Arctic Ocean.[24]


A yottamole (Ymol) is one septillion moles (1024 mol). It is equal to 6.02214076×1047 elementary entities, approximately 13.5 times the number of water molecules in all oceans on Earth.[24]

Mole Day

October 23, denoted 10/23 in the US, is recognized by some as Mole Day.[25] It is an informal holiday in honor of the unit among chemists. The date is derived from the Avogadro number, which is approximately 6.022×1023. It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 (06/02), June 22 (6/22), or 6 February (06.02), a reference to the 6.02 or 6.022 part of the constant.[26][27][28]

See also


  1. IUPAC Gold Book. IUPAC - mole (M03980). International Union of Pure and Applied Chemistry. doi:10.1351/goldbook.M03980. 
  2. 2.0 2.1 "On the revision of the International System of Units - International Union of Pure and Applied Chemistry". 16 November 2018. 
  3. BIPM (20 May 2019). "Mise en pratique for the definition of the mole in the SI". 
  4. 4.0 4.1 International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 114–15, ISBN 92-822-2213-6, 
  5. Wang, Yuxing et al. (2003). "Specific heat of MgB2 after irradiation". Journal of Physics: Condensed Matter 15 (6): 883–893. doi:10.1088/0953-8984/15/6/315. Bibcode2003JPCM...15..883W. 
  6. Lortz, R. et al. (2005). "Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductor ZrB12". Phys. Rev. B 72 (2): 024547. doi:10.1103/PhysRevB.72.024547. Bibcode2005PhRvB..72b4547L. 
  7. 7.0 7.1 7.2 de Bièvre, Paul; Peiser, H. Steffen (1992). "'Atomic Weight' — The Name, Its History, Definition, and Units". Pure and Applied Chemistry 64 (10): 1535–43. doi:10.1351/pac199264101535. 
  8. 8.0 8.1 8.2 International Bureau of Weights and Measures. "Realising the mole ." Retrieved 25 September 2008.
  9. 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. Some sources place the date of first usage in English as 1902. Merriam–Webster proposes an etymology from Molekulärgewicht (molecular weight).
  11. Ostwald, Wilhelm (1893). Hand- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen. Leipzig, Germany: Wilhelm Engelmann. p. 119.;view=1up;seq=131.  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 ... )
  12. mole, n.8, Oxford English Dictionary, Draft Revision Dec. 2008
  13. Fundamental Physical Constants: Avogadro Constant
  14. Andreas, Birk (2011). "Determination of the Avogadro Constant by Counting the Atoms in a 28Si Crystal". Physical Review Letters 106 (3): 30801. doi:10.1103/PhysRevLett.106.030801. PMID 21405263. Bibcode2011PhRvL.106c0801A. 
  15. "BIPM – Resolution 3 of the 14th CGPM". 
  16. CIPM Report of 106th Meeting Retrieved 7 April 2018
  17. "Redefining the Mole". NIST. 2018-10-23. 
  18. Barański, Andrzej (2012). "The Atomic Mass Unit, the Avogadro Constant, and the Mole: A Way to Understanding". Journal of Chemical Education 89 (1): 97–102. doi:10.1021/ed2001957. Bibcode2012JChEd..89...97B. 
  19. 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. 
  20. Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units, and dimensions". Metrologia 47 (3): 219–230. doi:10.1088/0026-1394/47/3/012. Bibcode2010Metro..47..219J. 
  21. Cooper, G.; Humphry, S. (2010). "The ontological distinction between units and entities". Synthese 187 (2): 393–401. doi:10.1007/s11229-010-9832-1. 
  22. 22.0 22.1 Himmelblau, David (1996). Basic Principles and Calculations in Chemical Engineering (6 ed.). pp. 17–20. ISBN 978-0-13-305798-0. 
  23. "Lighting Radiation Conversion". 
  24. 24.0 24.1 "Volumes of the World's Oceans from ETOPO1". National Oceanic and Atmospheric Administration. 
  25. History of National Mole Day Foundation, Inc. .
  26. Happy Mole Day! , Mary Bigelow. SciLinks blog, National Science Teachers Association. October 17, 2013.
  27. What Is Mole Day? – Date and How to Celebrate. , Anne Marie Helmenstine.
  28. The Perse School (Feb 7, 2013), The Perse School celebrates moles of the chemical variety, Cambridge Network,, retrieved Feb 11, 2015, "As 6.02 corresponds to 6th February, the School has adopted the date as their 'Mole Day'." 

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