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In chemistry, the amount of substance is the number of discrete particles of some specified nature, such as molecules, atoms, ions, electrons, etc., in some sample of matter. For example, it is the number of molecules in a sample of a chemical compound. It is sometimes referred to as the chemical amount.

The number of particles in macroscopic samples is conveniently expressed as a number of moles. The mole (symbol "mol") is a unit of the International System of Units defined as NA particles, where NA is the Avogadro constant, which is defined as exactly 6.02214076×1023.[1] In other words, a mole contains exactly 6.02214076×1023 particles. This number was chosen so that the mass of one mole of a compound, in grams, is numerically equal (for all practical purposes) to the mass of one molecule of the compound, in atomic mass units. For example, a molecule of water has a mass of about 18.015 atomic mass units on average, whereas a mole of water (which contains 6.02214076×1023 water molecules) has a total mass of about 18.015 grams.

In chemistry, because of the law of multiple proportions, it is often much more convenient to work with amounts of substances (that is, moles, or number of molecules) than with masses (grams) or volumes (liters). For example, "1 mole of oxygen O
will react with 2 moles of hydrogen H
to form 2 moles of water H
O". Or, equivalently, "6.022×1023 molecules of oxygen will react with 1.204 × 1024 molecules of hydrogen to make 1.204 × 1024 molecules of water". The same chemical fact, expressed in terms of masses, would be "32 g of oxygen will react with approximately 2.0156 g of hydrogen to make approximately 18.0152 g of water" (and the numbers would depend on the isotopic composition of the reagents). In terms of volume, the numbers would depend on the pressure and temperature of the reagents and products. For the same reasons, the concentrations of reagents and products in liquids is often specified in moles per liter, rather than grams per liter.

The amount of substance is also a convenient concept in thermodynamics. For example, the pressure of a certain quantity of a noble gas in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through the ideal gas law), not to its mass.

The technical term "amount of substance" should not be confused with the more general English word "amount". The general term "amount" can refer to other measurements such as mass or volume,[2] whereas "amount of substance" specifically refers to the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms.[2][3]



When quoting an amount of substance, it is necessary to specify the entity involved, unless there is no risk of ambiguity. One mole of chlorine could refer either to chlorine atoms, as in 58.44 g of sodium chloride, or to chlorine molecules, as in 22.711 liters of chlorine gas at STP. The simplest way to avoid ambiguity is to replace the term substance by the name of the entity or to quote the empirical formula.[4][5] For example:

Amount of substance replaces the term "number of moles" which should no longer be used according to IUPAC recommendation, just as the quantity mass should not be called "number of kilograms".[6] However, confusion can arise due to the everyday usage of the term "amount", so the terms "enplethy"[3] and "stoichiometric amount"[2] have been suggested for international usage to replace "amount of substance".

Derived quantitiesEdit

When amount of substance enters into a derived quantity, it is usually as the denominator: such quantities are known as molar quantities.[7] For example, the quantity which describes the volume occupied by a given amount of substance is called the molar volume, while the quantity which describes the mass of a given amount of substance is the molar mass. Molar quantities are sometimes denoted by a subscript Latin "m" in the symbol,[7] e.g. Cp,m, molar heat capacity at constant pressure: the subscript may be omitted if there is no risk of ambiguity, as is often the case in pure chemistry.

The main derived quantity in which amount of substance enters into the numerator is amount of substance concentration, c. This name is often abbreviated to amount concentration,[8] except in clinical chemistry where substance concentration is the preferred term[9] to avoid ambiguity with mass concentration. The term molar concentration is incorrect,[10] but commonly used.


The alchemists, and especially the early metallurgists, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758, Mikhail Lomonosov questioned the idea that mass was the only measure of the quantity of matter,[11] but he did so only in relation to his theories on gravitation. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.

  • 1777: Wenzel publishes Lessons on Affinity, in which he demonstrates that the proportions of the "base component" and the "acid component" (cation and anion in modern terminology) remain the same during reactions between two neutral salts.[12]
  • 1789: Lavoisier publishes Treatise of Elementary Chemistry, introducing the concept of a chemical element and clarifying the Law of conservation of mass for chemical reactions.[13]
  • 1792: Richter publishes the first volume of Stoichiometry or the Art of Measuring the Chemical Elements (publication of subsequent volumes continues until 1802). The term "stoichiometry" is used for the first time. The first tables of equivalent weights are published for acid–base reactions. Richter also notes that, for a given acid, the equivalent mass of the acid is proportional to the mass of oxygen in the base.[12]
  • 1794: Proust's Law of definite proportions generalizes the concept of equivalent weights to all types of chemical reaction, not simply acid–base reactions.[12]
  • 1805: Dalton publishes his first paper on modern atomic theory, including a "Table of the relative weights of the ultimate particles of gaseous and other bodies".[14]
The concept of atoms raised the question of their weight. While many were skeptical about the reality of atoms, chemists quickly found atomic weights to be an invaluable tool in expressing stoichiometric relationships.
The ideal gas law was the first to be discovered of many relationships between the number of atoms or molecules in a system and other physical properties of the system, apart from its mass. However, this was not sufficient to convince all scientists of the existence of atoms and molecules, many considered it simply being a useful tool for calculation.
  • 1834: Faraday states his Laws of electrolysis, in particular that "the chemical decomposing action of a current is constant for a constant quantity of electricity".[23]
  • 1856: Krönig derives the ideal gas law from kinetic theory.[24] Clausius publishes an independent derivation the following year.[25]
  • 1860: The Karlsruhe Congress debates the relation between "physical molecules", "chemical molecules" and atoms, without reaching consensus.[26]
  • 1865: Loschmidt makes the first estimate of the size of gas molecules and hence of number of molecules in a given volume of gas, now known as the Loschmidt constant.[27]
  • 1886: van't Hoff demonstrates the similarities in behaviour between dilute solutions and ideal gases.
  • 1886: Eugen Goldstein observes discrete particle rays in gas discharges, laying the foundation of mass spectrometry, a tool subsequently used to establish the masses of atoms and molecules.
  • 1887: Arrhenius describes the dissociation of electrolyte in solution, resolving one of the problems in the study of colligative properties.[28]
  • 1893: First recorded use of the term mole to describe a unit of amount of substance by Ostwald in a university textbook.[29]
  • 1897: First recorded use of the term mole in English.[30]
  • By the turn of the twentieth century, the concept of atomic and molecular entities was generally accepted, but many questions remained, not least the size of atoms and their number in a given sample. The concurrent development of mass spectrometry, starting in 1886, supported the concept of atomic and molecular mass and provided a tool of direct relative measurement.
  • 1905: Einstein's paper on Brownian motion dispels any last doubts on the physical reality of atoms, and opens the way for an accurate determination of their mass.[31]
  • 1909: Perrin coins the name Avogadro constant and estimates its value.[32]
  • 1913: Discovery of isotopes of non-radioactive elements by Soddy[33] and Thomson.[34]
  • 1914: Richards receives the Nobel Prize in Chemistry for "his determinations of the atomic weight of a large number of elements".[35]
  • 1920: Aston proposes the whole number rule, an updated version of Prout's hypothesis.[36]
  • 1921: Soddy receives the Nobel Prize in Chemistry "for his work on the chemistry of radioactive substances and investigations into isotopes".[37]
  • 1922: Aston receives the Nobel Prize in Chemistry "for his discovery of isotopes in a large number of non-radioactive elements, and for his whole-number rule".[38]
  • 1926: Perrin receives the Nobel Prize in Physics, in part for his work in measuring the Avogadro constant.[39]
  • 1959/1960: Unified atomic weight scale based on 12C = 12 adopted by IUPAP and IUPAC.[40]
  • 1968: The mole is recommended for inclusion in the International System of Units (SI) by the International Committee for Weights and Measures (CIPM).[41]
  • 1972: The mole is approved as the SI base unit of amount of substance.[41]

See alsoEdit



  1. ^ "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  2. ^ a b c Giunta, Carmen J. (2016). "What's in a Name? Amount of Substance, Chemical Amount, and Stoichiometric Amount". Journal of Chemical Education. 93 (4): 583–586. Bibcode:2016JChEd..93..583G. doi:10.1021/acs.jchemed.5b00690.
  3. ^ a b "E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, "Quantities, Units and Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008)" (PDF). p. 4. Archived from the original (PDF) on 2016-12-20. Retrieved 2019-05-24.
  4. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "amount of substance, n". doi:10.1351/goldbook.A00297
  5. ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 46. Electronic version.
  6. ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 4. Electronic version.
  7. ^ a b International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 7. Electronic version.
  8. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "amount-of-substance concentration". doi:10.1351/goldbook.{{{file}}}
  9. ^ International Union of Pure and Applied Chemistry (1996). "Glossary of Terms in Quantities and Units in Clinical Chemistry" (PDF). Pure Appl. Chem. 68: 957–1000. doi:10.1351/pac199668040957.
  10. ^ "Molar concentration" should refer to a concentration per mole, i.e. an amount fraction. The use of molar as a unit, equal to 1 mol/dm3, symbol M, is frequent, but, as of May 2007, not condoned by IUPAC: International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 42 (n. 15). Electronic version.
  11. ^ Lomonosov, Mikhail (1970). "On the Relation of the Amount of Material and Weight". In Leicester, Henry M. (ed.). Mikhail Vasil'evich Lomonosov on the Corpuscular Theory. Cambridge, MA: Harvard University Press. pp. 224–33 – via Internet Archive.
  12. ^ a b c d e "Atome". Grand dictionnaire universel du XIXe siècle. Paris: Pierre Larousse. 1: 868–73. 1866.. ‹See Tfd›(in French)
  13. ^ Lavoisier, Antoine (1789). Traité élémentaire de chimie, présenté dans un ordre nouveau et d'après les découvertes modernes. Paris: Chez Cuchet.. ‹See Tfd›(in French)
  14. ^ Dalton, John (1805). "On the Absorption of Gases by Water and Other Liquids". Memoirs of the Literary and Philosophical Society of Manchester, 2nd Series. 1: 271–87.
  15. ^ Dalton, John (1808). A New System of Chemical Philosophy. Manchester: London.
  16. ^ Gay-Lussac, Joseph Louis (1809). "Memoire sur la combinaison des substances gazeuses, les unes avec les autres". Mémoires de la Société d'Arcueil. 2: 207. English translation.
  17. ^ Avogadro, Amedeo (1811). "Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons". Journal de Physique. 73: 58–76. English translation.
  18. ^ Excerpts from Berzelius' essay: Part II; Part III.
  19. ^ Berzelius' first atomic weight measurements were published in Swedish in 1810: Hisinger, W.; Berzelius, J.J. (1810). "Forsok rorande de bestamda proportioner, havari den oorganiska naturens bestandsdelar finnas forenada". Afh. Fys., Kemi Mineral. 3: 162.
  20. ^ Prout, William (1815). "On the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms". Annals of Philosophy. 6: 321–30.
  21. ^ Petit, Alexis Thérèse; Dulong, Pierre-Louis (1819). "Recherches sur quelques points importants de la Théorie de la Chaleur". Annales de Chimie et de Physique. 10: 395–413. English translation
  22. ^ Clapeyron, Émile (1834). "Puissance motrice de la chaleur". Journal de l'École Royale Polytechnique. 14 (23): 153–90.
  23. ^ Faraday, Michael (1834). "On Electrical Decomposition". Philosophical Transactions of the Royal Society. 124: 77–122. doi:10.1098/rstl.1834.0008.
  24. ^ Krönig, August (1856). "Grundzüge einer Theorie der Gase". Annalen der Physik. 99 (10): 315–22. Bibcode:1856AnP...175..315K. doi:10.1002/andp.18561751008.
  25. ^ Clausius, Rudolf (1857). "Ueber die Art der Bewegung, welche wir Wärme nennen". Annalen der Physik. 176 (3): 353–79. Bibcode:1857AnP...176..353C. doi:10.1002/andp.18571760302.
  26. ^ Wurtz's Account of the Sessions of the International Congress of Chemists in Karlsruhe, on 3, 4, and 5 September 1860.
  27. ^ Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle". Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien. 52 (2): 395–413. English translation Archived February 7, 2006, at the Wayback Machine.
  28. ^ Arrhenius, Svante (1887). Zeitschrift für Physikalische Chemie. 1: 631.CS1 maint: Untitled periodical (link) English translation Archived 2009-02-18 at the Wayback Machine.
  29. ^ Ostwald, Wilhelm (1893). Hand- und Hilfsbuch zur ausführung physiko-chemischer Messungen. Leipzig.
  30. ^ Helm, Georg (1897). The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena. (Transl. Livingston, J.; Morgan, R.). New York: Wiley. p. 6.
  31. ^ Einstein, Albert (1905). "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen". Annalen der Physik. 17 (8): 549–60. Bibcode:1905AnP...322..549E. doi:10.1002/andp.19053220806.
  32. ^ Perrin, Jean (1909). "Mouvement brownien et réalité moléculaire". Annales de Chimie et de Physique. 8e Série. 18: 1–114. Extract in English, translation by Frederick Soddy.
  33. ^ Soddy, Frederick (1913). "The Radio-elements and the Periodic Law". Chemical News. 107: 97–99.
  34. ^ Thomson, J.J. (1913). "Rays of positive electricity". Proceedings of the Royal Society A. 89 (607): 1–20. Bibcode:1913RSPSA..89....1T. doi:10.1098/rspa.1913.0057.
  35. ^ Söderbaum, H.G. (November 11, 1915). Statement regarding the 1914 Nobel Prize in Chemistry.
  36. ^ Aston, Francis W. (1920). "The constitution of atmospheric neon". Philosophical Magazine. 39 (6): 449–55. doi:10.1080/14786440408636058.
  37. ^ Söderbaum, H.G. (December 10, 1921). Presentation Speech for the 1921 Nobel Prize in Chemistry.
  38. ^ Söderbaum, H.G. (December 10, 1922). Presentation Speech for the 1922 Nobel Prize in Chemistry.
  39. ^ Oseen, C.W. (December 10, 1926). Presentation Speech for the 1926 Nobel Prize in Physics.
  40. ^ Holden, Norman E. (2004). "Atomic Weights and the International Committee—A Historical Review". Chemistry International. 26 (1): 4–7.
  41. ^ a b International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14