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The Avogadro constant, commonly denoted or , is the
proportionality factor In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a Constant (mathematics), constant ratio, which is called the coefficient of proportionality or p ...
that relates the number of constituent particles (usually
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s,
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s or
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
s) in a sample with the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
in that sample. It is an SI defining constant with an exact value of . It is named after the Italian scientist
Amedeo Avogadro Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian scientist, most noted for his contribution to molecular theory now known as Avogadro's law, which states that equal volumes ...
by
Stanislao Cannizzaro Stanislao Cannizzaro ( , also , ; 13 July 1826 – 10 May 1910) was an Italian chemist. He is famous for the Cannizzaro reaction and for his influential role in the atomic-weight deliberations of the Karlsruhe Congress in 1860. Biography ...
, who explained this number four years after Avogadro's death while at the
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 The Karlsruhe Congress was called so that Euro ...
in 1860. The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted or , which is the number of particles that are contained in one mole, exactly . The Avogadro number is the approximate number of
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
s (
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s or
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s) in one gram of ordinary
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
. The value of the Avogadro constant was chosen so that the mass of one mole of a
chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
, in
gram The gram (originally gramme; SI unit symbol g) is a Physical unit, unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure wate ...
s, is approximately the number of nucleons in one constituent particle of the substance. It is numerically equal (for all practical purposes) to the average mass of one molecule (or atom) the compound in daltons (unified atomic mass units); one dalton being of the mass of one
carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
atom. For example, the average mass of one molecule of
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
is about 18.0153 daltons, and one mole of water ( molecules) is about 18.0153 grams. Thus, the Avogadro constant is the
proportionality factor In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a Constant (mathematics), constant ratio, which is called the coefficient of proportionality or p ...
that relates the
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, p ...
of a substance to the average
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
of one molecule. The Avogadro constant also relates the
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/ mol, the volume occupied by one molecule of water is about , or about (cubic
angstrom The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
s). For a
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
line substance, it similarly relates its molar volume (in mol/mL), the volume of the repeating
unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
of the crystals (in mL), to the number of molecules in that cell. The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by
Josef Loschmidt Johann Josef Loschmidt (15 March 1821 – 8 July 1895), who referred to himself mostly as Josef Loschmidt (omitting his first name), was a notable Austrian scientist who performed ground-breaking work in chemistry, physics (thermodynamics, optics, ...
in 1865. (Avogadro's number is closely related to the
Loschmidt constant The ''Loschmidt constant'' or Loschmidt's number (symbol: ''n''0) is the number of particles (atoms or molecules) of an ideal gas in a given volume (the number density), and usually quoted at standard temperature and pressure. The 2014 CODATA reco ...
, and the two concepts are sometimes confused.) It was initially defined by
Jean Perrin Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids ( sedimentation equilibrium), verified Albert Einstein’s explanation of this ...
as the number of atoms in 16 grams of
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
. It was later redefined in the 14th conference of the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM) as the number of atoms in 12 grams of the isotope
carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
(12C). In each case, the mole was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when carbon-12 was the reference, one mole of carbon-12 was exactly 12 grams of the element. These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number as the exact value , and redefined the mole as the amount of a substance under consideration that contains constituent particles of the substance. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is times the average mass of one of its constituent particles – a physical quantity whose precise value has to be determined experimentally for each substance.


History


Origin of the concept

The Avogadro constant is named after the Italian scientist
Amedeo Avogadro Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian scientist, most noted for his contribution to molecular theory now known as Avogadro's law, which states that equal volumes ...
(1776–1856), who, in 1811, first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s or
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s regardless of the nature of the gas. The name ''Avogadro's number'' was coined in 1909 by the physicist
Jean Perrin Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids ( sedimentation equilibrium), verified Albert Einstein’s explanation of this ...
, who defined it as the number of molecules in exactly 16 grams of
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
. The goal of this definition was to make the mass of a mole of a substance, in grams, be numerically equal to the mass of one molecule relative to the mass of the hydrogen atom; which, because of the
law of definite proportions In chemistry, the law of definite proportions, sometimes called Proust's law, or law of constant composition states that a given chemical compound always contains its component elements in fixed ratio (by mass) and does not depend on its source an ...
, was the natural unit of atomic mass, and was assumed to be 1/16 of the atomic mass of oxygen.


First measurements

The value of Avogadro's number (not yet known by that name) was first obtained indirectly by
Josef Loschmidt Johann Josef Loschmidt (15 March 1821 – 8 July 1895), who referred to himself mostly as Josef Loschmidt (omitting his first name), was a notable Austrian scientist who performed ground-breaking work in chemistry, physics (thermodynamics, optics, ...
in 1865, by estimating the number of particles in a given volume of gas. This value, the
number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
of particles in an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
, is now called the
Loschmidt constant The ''Loschmidt constant'' or Loschmidt's number (symbol: ''n''0) is the number of particles (atoms or molecules) of an ideal gas in a given volume (the number density), and usually quoted at standard temperature and pressure. The 2014 CODATA reco ...
in his honor, and is related to the Avogadro constant, , by :n_0 = \frac, where is the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, is the
gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
, and is the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
. Because of this work, the symbol is sometimes used for the Avogadro constant, and, in
German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...
literature, that name may be used for both constants, distinguished only by the
units of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
. (However, should not be confused with the entirely different
Loschmidt constant The ''Loschmidt constant'' or Loschmidt's number (symbol: ''n''0) is the number of particles (atoms or molecules) of an ideal gas in a given volume (the number density), and usually quoted at standard temperature and pressure. The 2014 CODATA reco ...
in English-language literature.) Perrin himself determined Avogadro's number by several different experimental methods. He was awarded the 1926
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
, largely for this work. The electric charge per
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
of electrons is a constant called the
Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
and has been known since 1834, when
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
published his works on electrolysis. In 1910,
Robert Millikan Robert Andrews Millikan (March 22, 1868 – December 19, 1953) was an American experimental physicist honored with the Nobel Prize for Physics in 1923 for the measurement of the elementary electric charge and for his work on the photoelectric e ...
obtained the first measurement of the charge on an electron. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.


SI definition of 1971

In 1971, the International Bureau of Weights and Measures (BIPM) decided to regard the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
as an independent dimension of measurement, with the mole as its base unit in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI). Specifically, the mole was defined as an amount of a substance that contains as many elementary entities as there are atoms in . By this definition, the common rule of thumb that "one gram of matter contains nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes. On the other hand, one mole of any substance contained exactly as many molecules as one mole of any other substance. As a consequence of this definition, in the SI system the Avogadro constant had the
dimensionality In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordin ...
of reciprocal of amount of substance rather than of a pure number, and had the approximate value with units of mol. By this definition, the value of inherently had to be determined experimentally. The BIPM also named the "Avogadro ''constant''", but the term "Avogadro number" continued to be used especially in introductory works.


SI redefinition of 2019

In 2017, the BIPM decided to change the definitions of mole and amount of substance. The mole was redefined as being the amount of substance containing exactly elementary entities. One consequence of this change is that the mass of a mole of 12C atoms is no longer exactly 0.012 kg. On the other hand, the dalton ( universal atomic mass unit) remains unchanged as of the mass of 12C. Thus, the
molar mass constant The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) multipl ...
is no longer exactly 1 g/mol, although the difference ( in relative terms, as of March 2019) is insignificant for practical purposes.


Connection to other constants

The Avogadro constant is related to other physical constants and properties. * It relates the
molar gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
and the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
, which in the SI is defined to be exactly : *:  * It relates the
Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
and the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, which in the SI is defined as exactly : *:  * It relates the
molar mass constant The molar mass constant, usually denoted by ''M''u, is a physical constant defined as one twelfth of the molar mass of carbon-12: ''M''u = ''M''(12C)/12. The molar mass of any element or compound is its relative atomic mass (atomic weight) multipl ...
and the
atomic mass constant The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at ...
currently *: 


See also

*
Mole Day Mole Day is an unofficial holiday celebrated among chemists, chemistry students and chemistry enthusiasts on October 23, between 6:02 a.m. and 6:02 p.m., making the date 6:02 10/23 in the American style of writing dates. The time and ...
*
CODATA 2018 The Committee on Data of the International Science Council (CODATA) was established in 1966 as the Committee on Data for Science and Technology, originally part of the International Council of Scientific Unions, now part of the International ...


References


External links


1996 definition of the Avogadro constant
from the
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
''
Compendium of Chemical Terminology The International Union of Pure and Applied Chemistry publishes many books which contain its complete list of definitions. The definitions are divided into seven "colour books": Gold, Green, Blue, Purple, Orange, White, and Red. There is also an ...
'' ("''Gold Book''")
Some Notes on Avogadro's Number,
''(historical notes)''
An Exact Value for Avogadro's Number
– ''
American Scientist __NOTOC__ ''American Scientist'' (informally abbreviated ''AmSci'') is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Society. In the beginning of 2000s the headquarters was in New ...
''
Avogadro and molar Planck constants for the redefinition of the kilogram
* * Scanned version of "Two hypothesis of Avogadro", 1811 Avogadro's article, on
BibNum
' {{Authority control Amount of substance Fundamental constants Dimensionless numbers of chemistry Physical constants