Amount of substance
Encyclopedia
Amount of substance is a standards-defined quantity
Quantity
Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...

  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
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

 (SI) defines the amount of substance to be proportional
Proportionality
Proportionality may refer to:*Proportionality , the relationship of two variables whose ratio is constant*Proportionality , A legal principle under municipal law in which the punishment of a certain crime should be in proportion to the severity of the crime itself, and under international law an...

 to the number of elementary entities present. The SI unit for amount of substance is the mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

. It has the unit symbol mol. The mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in of the isotope carbon-12
Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....

. This number is called Avogadro's number and has the value . 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.

Amount of substance appears in thermodynamic relations such as the ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

, and in stoichiometric relations between reacting molecules as in the law of multiple proportions
Law of multiple proportions
In chemistry, the law of multiple proportions is one of the basic laws of stoichiometry, alongside the law of definite proportions. It is sometimes called Dalton's Law after its discoverer, the English chemist John Dalton.The statement of the law is:...

.

The only other unit of amount of substance in current use is the pound mole with the symbol lb-mol, which is sometimes used in chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...

 in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

.  ≡ .This relation is exact, from the definition of the international avoirdupois pound
Pound (mass)
The pound or pound-mass is a unit of mass used in the Imperial, United States customary and other systems of measurement...

.

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
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

 could refer either to chlorine atoms, as in 58.44 g of sodium chloride
Sodium chloride
Sodium chloride, also known as salt, common salt, table salt or halite, is an inorganic compound with the formula NaCl. Sodium chloride is the salt most responsible for the salinity of the ocean and of the extracellular fluid of many multicellular organisms...

, or to chlorine molecules, as in of chlorine gas at STP
Standard conditions for temperature and pressure
Standard condition for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data...

. The simplest way to avoid ambiguity is to replace the term substance by the name of the entity or to quote the empirical formula
Empirical formula
In chemistry, the empirical formula of a chemical compound is the simplest positive integer ratio of atoms of each element present in a compound. An empirical formula makes no reference to isomerism, structure, or absolute number of atoms. The empirical formula is used as standard for most ionic...

. For example:
  • amount of chloroform
    Chloroform
    Chloroform is an organic compound with formula CHCl3. It is one of the four chloromethanes. The colorless, sweet-smelling, dense liquid is a trihalomethane, and is considered somewhat hazardous...

    , CHCl3
  • amount of sodium
    Sodium
    Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

    , Na
  • amount of hydrogen
    Hydrogen
    Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

     (atoms), H
  • n(C2H4
    Ethylene
    Ethylene is a gaseous organic compound with the formula . It is the simplest alkene . Because it contains a carbon-carbon double bond, ethylene is classified as an unsaturated hydrocarbon. Ethylene is widely used in industry and is also a plant hormone...

    )

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
Molar volume
The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...

, while the quantity which describes the mass of a given amount of substance is the molar mass
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

. Molar quantities are sometimes denoted by a subscript Latin "m" in the symbol, e.g. Cp,m, molar heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

 at constant pressure: the subscript may be omitted if there is no risk of ambiguity, as is often the case in pure chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

.

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
Mass concentration
In astronomy or astrophysics mass concentration or mascon is a region of a planet or moon's crust that contains a large positive gravitational anomaly. In general, the word "mascon" can be used as a noun to describe an excess distribution of mass on or beneath the surface of a planet , such as Hawaii...

). The name "molar concentration" is incorrect, if commonly used.

History

The alchemists
Alchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...

, 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
Mikhail Lomonosov
Mikhail Vasilyevich Lomonosov was a Russian polymath, scientist and writer, who made important contributions to literature, education, and science. Among his discoveries was the atmosphere of Venus. His spheres of science were natural science, chemistry, physics, mineralogy, history, art,...

 questioned the idea that mass was the only measure of the quantity of matter, but he did so only in relation to his theories on gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.
  • 1777: Wenzel
    Carl Friedrich Wenzel
    Carl Friedrich Wenzel was a German chemist and metallurgist who determined the reaction rates of various chemicals, establishing, for example, that the amount of metal that dissolves in an acid is proportional to the concentration of acid in the solution...

     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
    Antoine Lavoisier
    Antoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...

     publishes Treatise of Elementary Chemistry, introducing the concept of a chemical element
    Chemical element
    A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

     and clarifying the Law of conservation of mass for chemical reactions.
  • 1792: Richter
    Jeremias Benjamin Richter
    Jeremias Benjamin Richter was a German chemist. He was born at Hirschberg in Silesia, became a mining official at Breslau in 1794, and in 1800 was appointed assessor to the department of mines and chemist to the royal porcelain factory at Berlin, where he died.-Developer of titration:To him...

     publishes the first volume of Stoichiometry or the Art of Measuring the Chemical Elements (publication of subsequent volumes continues until 1802). The term "stoichiometry
    Stoichiometry
    Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...

    " used for the first time. The first tables of equivalent weight
    Equivalent weight
    Equivalent weight is a term which has been used in several contexts in chemistry. In its most general usage, it is the mass of one equivalent, that is the mass of a given substance which will:...

    s 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
    Joseph Proust
    Joseph Louis Proust was a French chemist.-Life:Joseph L. Proust was born on September 26, 1754 in Angers, France. His father served as an apothecary in Angers. Joseph studied chemistry in his father’s shop and later came to Paris where he gained the appointment of apothecary in chief to the...

     Law of definite proportions
    Law of definite proportions
    In chemistry, the law of definite proportions, sometimes called Proust's Law, states that a chemical compound always contains exactly the same proportion of elements by mass. An equivalent statement is the law of constant composition, which states that all samples of a given chemical compound have...

     generalizes the concept of equivalent weights to all types of chemical reaction, not simply acid–base reactions.
  • 1805: Dalton
    John Dalton
    John Dalton FRS was an English chemist, meteorologist and physicist. He is best known for his pioneering work in the development of modern atomic theory, and his research into colour blindness .-Early life:John Dalton was born into a Quaker family at Eaglesfield, near Cockermouth, Cumberland,...

     publishes his first paper on modern atomic theory
    Atomic theory
    In chemistry and physics, atomic theory is a theory of the nature of matter, which states that matter is composed of discrete units called atoms, as opposed to the obsolete notion that matter could be divided into any arbitrarily small quantity...

    , including a "Table of the relative weights of the ultimate particles of gaseous and other bodies".
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 weight
    Atomic weight
    Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

    s (based on H = 1).
  • 1809: Gay-Lussac's
    Joseph Louis Gay-Lussac
    - External links :* from the American Chemical Society* from the Encyclopædia Britannica, 10th Edition * , Paris...

     Law of combining volumes
    Gay-Lussac's law
    The expression Gay-Lussac's law is used for each of the two relationships named after the French chemist Joseph Louis Gay-Lussac and which concern the properties of gases, though it is more usually applied to his law of combining volumes, the first listed here...

    , 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
    Avogadro's law
    Avogadro's law is a gas law named after Amedeo Avogadro who, in 1811, hypothesized that two given samples of an ideal gas, at the same temperature, pressure and volume, contain the same number of molecules...

    .
  • 1813/1814: Berzelius
    Jöns Jakob Berzelius
    Jöns Jacob Berzelius was a Swedish chemist. He worked out the modern technique of chemical formula notation, and is together with John Dalton, Antoine Lavoisier, and Robert Boyle considered a father of modern chemistry...

     publishes the first of several tables of atomic weights based on the scale of O = 100.
  • 1815: Prout
    William Prout
    William Prout FRS was an English chemist, physician, and natural theologian. He is remembered today mainly for what is called Prout's hypothesis.-Biography:...

     publishes his hypothesis
    Prout's hypothesis
    Prout's hypothesis was an early 19th century attempt to explain the existence of the various chemical elements through a hypothesis regarding the internal structure of the atom...

     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
    Chlorine
    Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

     (approx. 35.5 relative to hydrogen).
  • 1819: Dulong–Petit law
    Dulong–Petit law
    The Dulong–Petit law, a chemical law proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states the classical expression for the molar specific heat capacity of a crystal...

     relating the atomic weight of a solid element to its specific heat capacity.
  • 1819: Mitscherlich's
    Eilhard Mitscherlich
    Eilhard Mitscherlich was a German chemist, who is perhaps best remembered today for his law of isomorphism , which states that compounds crystallizing together probably have similar structures and compositions...

     work on crystal
    Crystal
    A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

     isomorphism
    Isomorphism
    In abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations.  If there exists an isomorphism between two structures, the two structures are said to be isomorphic.  In a certain sense, isomorphic structures are...

     allows many chemical formula
    Chemical formula
    A chemical formula or molecular formula is a way of expressing information about the atoms that constitute a particular chemical compound....

    e to be clarified, resolving several ambiguities in the calculation of atomic weights.
  • 1834: Clapeyron
    Benoit Paul Émile Clapeyron
    Benoît Paul Émile Clapeyron was a French engineer and physicist, one of the founders of thermodynamics.-Life:...

     states the ideal gas law.
The ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's 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
    Michael Faraday
    Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....

     states his Laws of electrolysis
    Faraday's laws of electrolysis
    Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834.-Statements of the laws:Several versions of the laws can be found in textbooks and the scientific literature...

    , in particular that "the chemical decomposing action of a current is constant for a constant quantity of electricity".
  • 1856: Krönig
    August Krönig
    August Karl Krönig was a German chemist and physicist who published an account of the kinetic theory of gases in 1856, probably after reading a paper by John James Waterston....

     derives the ideal gas law from kinetic theory
    Kinetic theory
    The kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...

    . Clausius
    Rudolf Clausius
    Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...

     publishes an independent derivation the following year.
  • 1860: The Karlsruhe Congress
    Karlsruhe Congress
    The Karlsruhe Congress was an international meeting of chemists held in Karlsruhe, Germany from 3 to 5 September, 1860. It was the first international conference of chemistry worldwide.- The meeting :...

     debates the relation between "physical molecules", "chemical molecules" and atoms, without reaching consensus.
  • 1865: Loschmidt
    Johann Josef Loschmidt
    Jan or Johann Josef Loschmidt , who referred to himself mostly as 'Josef' , was a notable Austrian scientist who performed groundbreaking work in chemistry, physics , and crystal forms.Born in Carlsbad, a town located in the Austrian Empire , 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
    Jacobus Henricus van 't Hoff
    Jacobus Henricus van 't Hoff, Jr. was a Dutch physical and organic chemist and the first winner of the Nobel Prize in chemistry. He is best known for his discoveries in chemical kinetics, chemical equilibrium, osmotic pressure, and stereochemistry...

     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
    Mass spectrometry
    Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

    , a tool later used to establish the masses of atoms and molecules.
  • 1887: Arrhenius
    Svante Arrhenius
    Svante August Arrhenius was a Swedish scientist, originally a physicist, but often referred to as a chemist, and one of the founders of the science of physical chemistry...

     describes the dissociation of electrolyte
    Electrolyte
    In chemistry, an electrolyte is any substance containing free ions that make the substance electrically conductive. The most typical electrolyte is an ionic solution, but molten electrolytes and solid electrolytes are also possible....

     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
    Wilhelm Ostwald
    Friedrich Wilhelm Ostwald was a Baltic German chemist. He received the Nobel Prize in Chemistry in 1909 for his work on catalysis, chemical equilibria and reaction velocities...

     in a university textbook.
  • 1897: First recorded use of the term mole in English.
  • 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
    Mass spectrometry
    Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

    , starting in 1886, supported the concept of atomic and molecular mass and provided a tool of direct relative measurement.
  • 1905: Einstein's
    Albert Einstein
    Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

     paper on Brownian motion
    Brownian motion
    Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

     dispels any last doubts on the physical reality of atoms, and opens the way for an accurate determination of their mass.
  • 1909: Perrin
    Jean Baptiste Perrin
    Jean Baptiste Perrin was a French physicist and Nobel laureate.-Early years:Born in Lille, France, Perrin attended the École Normale Supérieure, the elite grande école in Paris. He became an assistant at the school during the period of 1894-97 when he began the study of cathode rays and X-rays...

     coins the name Avogadro constant and estimates its value.
  • 1913: Discovery of isotope
    Isotope
    Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

    s of non-radioactive elements by Soddy
    Frederick Soddy
    Frederick Soddy was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also proved the existence of isotopes of certain radioactive elements...

     and Thomson
    J. J. Thomson
    Sir Joseph John "J. J." Thomson, OM, FRS was a British physicist and Nobel laureate. He is credited for the discovery of the electron and of isotopes, and the invention of the mass spectrometer...

    .
  • 1914: Richards
    Theodore William Richards
    Theodore William Richards was the first American scientist to receive the Nobel Prize in Chemistry, earning the award "in recognition of his exact determinations of the atomic weights of a large number of the chemical elements."- Biography :Theodore Richards was born in Germantown, Philadelphia,...

     receives the Nobel Prize in Chemistry for "for his determinations of the atomic weight of a large number of elements".
  • 1920: Aston
    Francis William Aston
    Francis William Aston was a British chemist and physicist who won the 1922 Nobel Prize in Chemistry for his discovery, by means of his mass spectrograph, of isotopes, in a large number of non-radioactive elements, and for his enunciation of the whole-number rule...

     proposes the whole number rule
    Whole number rule
    The whole number rule states that the masses of the elements are whole number multiples of the mass of the hydrogen atom. The rule can be formulated from Prout's hypothesis put forth in 1815. In 1920, Francis W...

    , an updated version of Prout's hypothesis
    Prout's hypothesis
    Prout's hypothesis was an early 19th century attempt to explain the existence of the various chemical elements through a hypothesis regarding the internal structure of the atom...

    .
  • 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
    Nobel Prize in Physics
    The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...

    , in part for his work in measuring Avogadro's constant.
  • 1959/1960: Unified atomic weight scale based on C = 12 adopted by IUPAP and IUPAC.
  • 1968: The mole is recommended for inclusion in the International System of Units
    International System of Units
    The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

     (SI) by the International Committee for Weights and Measures
    International Committee for Weights and Measures
    The Interglobal Committee for Weights and Measures is the English name of the Comité international des poids et mesures . It consists of eighteen persons from Member States of the Metre Convention...

     (CIPM).
  • 1972: The mole is approved as the SI base unit
    SI base unit
    The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

    of amount of substance.
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