Amount of substance

Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units (SI) defines the amount of substance to be proportional to the number of elementary entities present. The SI unit for amount of substance is the mole. It has the unit symbol mol. The proportionality constant is the inverse of the Avogadro constant.

The mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 12g of the isotope carbon-12.^[1] This number is called Avogadro's number and has the value 6.022140857(74)×10²³.^[2] It is the numerical value of the Avogadro constant which has the unit 1/mol, and relates the molar mass of an amount of substance to its mass. Therefore, the amount of substance of a sample is calculated as the sample mass divided by the molar mass of the substance.

Amount of substance appears in thermodynamic relations such as the ideal gas law, and in stoichiometric relations between reacting molecules as in the law of multiple proportions.

Another unit of amount of substance in use in chemical engineering in the United States is the pound-mole, having the symbol lb-mol.^[3][4] One pound-mole is 453.59237 mol.^{[notes 1]}

Terminology

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.^[5][6] For example:

• amount of chloroform (molecules), CHCl₃
• amount of sodium (atoms), Na
• amount of hydrogen (atoms), H
• n(C₂H₄)

This is a technical definition of the term amount, a usage which is also found in the names of certain derived quantities, while in common English, amount does not apply to discrete counts of items.

Derived quantities

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. C_p,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.

History

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.

• 1808: Publication of Dalton's A New System of Chemical Philosophy, containing the first table of atomic weights (based on H = 1).^[15]
• 1809: Gay-Lussac's Law of combining volumes, stating an integer relationship between the volumes of reactants and products in the chemical reactions of gases.^[16]
• 1811: Avogadro hypothesizes that equal volumes of different gases contain equal numbers of particles, now known as Avogadro's law.^[17]
• 1813/1814: Berzelius publishes the first of several tables of atomic weights based on the scale of O = 100.^[12][18][19]
• 1815: Prout publishes his hypothesis that all atomic weights are integer multiple of the atomic weight of hydrogen.^[20] The hypothesis is later abandoned given the observed atomic weight of chlorine (approx. 35.5 relative to hydrogen).
• 1819: Dulong–Petit law relating the atomic weight of a solid element to its specific heat capacity.^[21]
• 1819: Mitscherlich's work on crystal isomorphism allows many chemical formulae to be clarified, resolving several ambiguities in the calculation of atomic weights.^[12]
• 1834: Clapeyron states the ideal gas law.^[22]

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 observed discrete particle rays in gas discharges that laid the foundation of mass spectrometry, a tool later 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 Avogadro's 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).^[1]
• 1972: The mole is approved as the SI base unit of amount of substance.^[1]

See also

• Amount fraction
• International System of Quantities

Notes

1. This relation is exact, from the definition of the international avoirdupois pound.

References

1. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6
2. "CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-25.
3. Talty, John T. (1988). Industrial Hygiene Engineering: Recognition, Measurement, Evaluation, and Control. William Andrew. p. 142. ISBN 0-8155-1175-2.
4. Lee, C.C. (2005). Environmental Engineering Dictionary (4th ed.). Rowman & Littlefield. p. 506. ISBN 0-86587-848-X.
5. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "amount of substance, n".
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. 46. Electronic version.
7. 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".
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.
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. Mikhail Vasil'evich Lomonosov on the Corpuscular Theory. Cambridge, MA: Harvard University Press. pp. 224–33 – via Internet Archive.
12. "Atome". Grand dictionnaire universel du XIXe siècle (Paris: Pierre Larousse) 1: 868–73. 1866.. (French)
13. Lavoisier, Antoine (1789). Traité élémentaire de chimie, présenté dans un ordre nouveau et d'après les découvertes modernes. Paris: Chez Cuchet.. (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.
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.
28. Arrhenius, Svante (1887). Zeitschrift für Physikalische Chemie 1: 631. English translation.
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" (PDF). 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. 8^e 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.