Definitions

# Amount of substance

The amount of substance, n, of a sample or system is a physical quantity which is proportional to the number of elementary entities present. "Elementary entities" may be atoms, molecules, ions, electrons, or particles, the choice of which is dependent upon context and must be stated. Amount of substance is sometimes referred to as chemical amount or, incorrectly, as number of moles.

Amount of substance is a quantity that measures the size of an ensemble of entities. It appears in thermodynamic relations such as the ideal gas law, and in stoichiometric relations between reacting molecules as in the law of multiple proportions.

The SI unit for amount of substance is the mole (symbol: mol), which is defined as the amount of substance that has an equal number of elementary entities as there are atoms in 12 g of carbon-12. That number is the Avogadro constant, NA, which has a value of . The only other unit of amount of substance in current use is the pound mole (symbol: lb-mol.), which is sometimes used in chemical engineering in the United States.

1 lb-mol. ≡ 453.592 37 mol (this relation is exact, from the definition of the international avoirdupois pound).

## Rationale

Why use amount of substance instead of mass or volume to tell how much of a substance there is? This is because in chemical reactions, the reagents react molecule-to-molecule, ion-to-ion, etc. Since different atoms and therefore molecules have different masses, 100 grams of some substance is not same amount of some other substance. For example, 100 grams of carbon has more molecules than 100 grams of oxygen.

See: Stoichiometry

## 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 of chlorine gas at STP). The simplest way to avoid ambiguity is to replace the term "substance" by the name of the entity and/or to quote the empirical formula. For example:
amount of chloroform, CHCl3
amount of sodium, Na
amount of hydrogen (atoms), H
n(C2H4)
This can be considered to be a technical definition of the word "amount", a usage which is also found in the names of certain derived quantities (see below).

## Derived quantities

When amount of substance enters into a derived quantity, it is usually as the denominator: such quantities are known as "molar quantities". 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, 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", except in clinical chemistry where "substance concentration" is the preferred term (to avoid any possible ambiguity with mass concentration). The name "molar concentration" is incorrect, if commonly used.

## History

The alchemists, and especially the early metallurgists, probably has some notion of amount of substance, but there are no surviving records of their having generalised the idea beyond a set of "recipes". Lomonosov in 1758 questioned the idea that mass was the only measure of the quantity of matter, but 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.
• 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.
• 1792: Richter publishes the first volume of Stoichiometry of the Art of Measuring the Chemical Elements (publication of subsequent volumes continues until 1802). The term "stoichiometry" used for the first time. The first tables of equivalent masses 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.
• 1794: Proust's Law of definite proportions generalises the concept of equivalent masses to all types of chemical reaction, not simply acid–base reactions.

With the concept of atoms came the notion of atomic weight. While many were sceptical about the reality of atoms, chemists quickly found atomic weights to be an invaluable tool in expressing stoichiometric relationships.

• 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".
• 1808: Publication of Dalton's A New System of Chemical Philosophy, containing the first table of atomic weights (based on H = 1).
• 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.
• 1811: Avogadro hypothesizes that equal volumes of different gases contain equal numbers of particles, now known as Avogadro's law.
• 1813/1814: Berzelius publishes the first of several tables of atomic weights based on the scale of O = 100.
• 1815: Prout publishes his hypothesis that all atomic weights are integer multiple of the atomic weight of hydrogen. 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.
• 1819: Mitscherlich's work on crystal isomorphism allows many chemical formulae to be clarified, resolving several ambiguities in the calculation of atomic weights.

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 that atoms and molecules had a physical reality, rather than simply being useful tools for calculation.

• 1834: Clapeyron states the ideal gas law.
• 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".
• 1856: Krönig derives the ideal gas law from kinetic theory. Clausius publishes an independent derivation the following year.
• 1860: The Karlsruhe Congress debates the relation between "physical molecules", "chemical molecules" and atoms, without reaching consensus.
• 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.
• 1886: van't Hoff demonstrates the similarities in behaviour between dilute solutions and ideal gases.
• 1887: Arrhenius describes the dissociation of electrolyte in solution, resolving one of the problems in the study of colligative properties.
• 1893: First recorded use of the term "mole" to describe a unit of amount of substance, by Ostwald in a university textbook.
• 1897: First recorded use of the term "mole" in English.
• 1901: van't Hoff receives the very first Nobel Prize in Chemistry, partly for determining the laws of osmotic pressure.
• 1903: Arrhenius receives the Nobel Prize in Chemistry, in part for his work on the dissociation of electrolytes.

By the turn of the twentieth century, the supporters of atomic theory had more or less won the day, but many questions remained, not least the size of atoms and their number. The devolopment of mass spectrometry of one of the techniques that revolutionized the way that physicists and chemists made connections between the microscopic world of atoms and molecules and the macroscopic observations of laboratory experiments.

• 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.
• 1909: Perrin coins the name "Avogadro constant" and makes an estimate of its value.
• 1913: Discovery of isotopes of non-radioactive elements by Soddy and Thomson.
• 1914: Richards receives the Nobel Prize in Chemistry for "for his determinations of the atomic weight of a large number of elements".
• 1920: Aston proposes the whole number rule, an updated version of Prout's hypothesis.
• 1921: Soddy receives the Nobel Prize in Chemistry "for his work on the chemistry of radioactive substances and investigations into isotopes".
• 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".
• 1926: Perrin receives the Nobel Prize in Physics, in part for his work in measuring the Avogadro constant.
• 1959/1960: Unified atomic weight scale based on C = 12 adopted by IUPAP and IUPAC.
• 1968: The mole recommended for inclusion in the International System of Units (SI) by the International Committee for Weights and Measures (CIPM).
• 1972: The mole approved as the SI base unit of amount of substance.