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The mole, symbol mol, is the unit of amount of substance in the International System of Units (SI). The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. The mole is defined as containing exactly elementary entities. Depending on what the substance is, an elementary entity may be an
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, ...
, a
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 bioche ...
, an
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 conve ...
, an ion pair, or a subatomic particle such as an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
. For example, 10 moles of
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
(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 ...
) and 10 moles of mercury (a
chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
), contain equal amounts of substance and the mercury contains exactly one atom for each molecule of the water, despite the two having different volumes and different masses. The number of elementary entities in one mole is known as the
Avogadro number The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining co ...
, which 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 ( protons 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 part ...
. The previous definition of a mole was simply the number of elementary entities equal to that of 12
gram The gram (originally gramme; SI unit symbol g) is a 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 water equal to th ...
s of carbon-12, the most common isotope of carbon. The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation can be interpreted to mean that for each 2 mol
dihydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, a ...
(H2) and 1 mol
dioxygen There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are: * ...
(O2) that react, 2 mol of water (H2O) form. The
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', '' number concentration'', ...
of a solution is commonly expressed by its
molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per
litre The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3 ...
(mol/L). The term gram-molecule was formerly used for "mole of molecules", and gram-atom for "mole of atoms". For example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.


Concepts


Nature of the particles

The mole corresponds to a given count of particles. Usually the particles counted are chemically identical entities, individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, in a solid the constituent particles are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity. Thus the solid is composed of a certain number of moles of such particles. In yet other cases, such as
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...
, where the entire crystal is essentially a single molecule, the mole is still used to express the number of atoms bound together, rather than a count of molecules. Thus, common chemical conventions apply to the definition of the constituent particles of a substance, in other cases exact definitions may be specified. The mass of a substance is equal to its relative atomic (or molecular) mass multiplied by 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) multip ...
, which is almost exactly 1 g/mol.


Molar mass

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, ...
of a substance is the ratio of the
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 eleme ...
of a sample of that substance to its amount of substance. The amount of substance is given as the number of moles in the sample. For most practical purposes, the numerical value of the molar mass expressed with the unit gram per mole is the same as that of the mean mass of one molecule of the substance expressed with the unit
dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor ch ...
. For example, the molar mass of water is 18.015 g/mol.
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 ...

Realising the mole
. Retrieved 25 September 2008.
Other methods include the use of 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 ...
or the measurement of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
. The number of moles of a substance in a sample is obtained by dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about 5.551 mol of water. The molar mass of a substance depends not only on its
molecular formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
, but also on the distribution of
isotopes Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
of each chemical element present in it. For example, the molar mass of calcium-40 is , whereas the molar mass of calcium-42 is , and of
calcium Calcium is a chemical element with the symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar t ...
with the normal isotopic mix is .


Molar concentration

The
molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
, also called ''molarity'', of a solution of some substance is the number of moles per unit of volume of the final solution. In the SI its standard unit is mol/ m3, although more practical units, such as mole per litre (mol/L) are used.


Molar fraction

The
molar fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ...
or
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
of a substance in a mixture (such as a solution) is the number of moles of the compound in one sample of the mixture, divided by the total number of moles of all components. For example, if 20 g of is dissolved in 100 g of water, the amounts of the two substances in the solution will be (20 g)/(58.443 g/mol) = 0.34221 mol and (100 g)/(18.015 g/mol) = 5.5509 mol, respectively; and the molar fraction of will be . In a mixture of gases, the partial pressure of each component is proportional to its molar ratio.


History

The history of the mole is intertwined with that of
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
,
atomic mass unit 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 ...
s, and the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining c ...
. The first table of standard atomic weight was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
was defined as 1. These relative atomic masses were based on the
stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...
proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to
atomic theory Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter ...
(an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic masses (promoted by proponents of atomic theory) and
equivalent weight In chemistry, equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is ...
s (promoted by its opponents and which sometimes differed from relative atomic masses by an integer factor), which would last throughout much of the nineteenth century. Jöns Jacob Berzelius (1779–1848) was instrumental in the determination of relative atomic masses to ever-increasing accuracy. He was also the first chemist to use
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 ...
as the standard to which other masses were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, especially
metals A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typical ...
. However, he chose to fix the atomic mass of oxygen as 100, which did not catch on. Charles Frédéric Gerhardt (1816–56),
Henri Victor Regnault Henri Victor Regnault (21 July 1810 – 19 January 1878) was a French chemist and physicist best known for his careful measurements of the thermal properties of gases. He was an early thermodynamicist and was mentor to William Thomson in ...
(1810–78) and
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. Biograph ...
(1826–1910) expanded on Berzelius' works, resolving many of the problems of unknown stoichiometry of compounds, and the use of atomic masses attracted a large consensus by the time of 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 ...
(1860). The convention had reverted to defining the atomic mass of hydrogen as 1, although at the level of precision of measurements at that time – relative uncertainties of around 1% – this was numerically equivalent to the later standard of oxygen = 16. However the chemical convenience of having oxygen as the primary atomic mass standard became ever more evident with advances in analytical chemistry and the need for ever more accurate atomic mass determinations. The name ''mole'' is an 1897 translation of the German unit ''Mol'', coined by the
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe t ...
Wilhelm Ostwald Friedrich Wilhelm Ostwald (; 4 April 1932) was a Baltic German chemist and philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst, and Svante Arrhen ...
in 1894 from the German word ''Molekül'' (
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 bioche ...
). The related concept of
equivalent mass Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry *Equivalence class (music) *''Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *''Equivale ...
had been in use at least a century earlier.


Standardization

Developments in mass spectrometry led to the adoption of
oxygen-16 Oxygen-16 (16O) is a stable isotope of oxygen, having 8 neutrons and 8 protons in its nucleus. It has a mass of . Oxygen-16 is the most abundant isotope of oxygen and accounts for 99.762% of oxygen's natural abundance. The relative and absol ...
as the standard substance, in lieu of natural oxygen. The oxygen-16 definition was replaced with one based on carbon-12 during the 1960s. The mole was defined by International Bureau of Weights and Measures as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12." Thus, by that definition, one mole of pure 12C had a mass of ''exactly'' 12  g. The four different definitions were equivalent to within 1%. Because a
dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor ch ...
, a unit commonly used to measure
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nb ...
, is exactly 1/12 of the mass of a carbon-12 atom, this definition of the mole entailed that the mass of one mole of a compound or element in grams was numerically equal to the average mass of one molecule or atom of the substance in daltons, and that the number of daltons in a gram was equal to the number of elementary entities in a mole. Because the mass of a
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 ...
(i.e. a proton 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 ...
) is approximately 1 dalton and the nucleons in an atom's nucleus make up the overwhelming majority of its mass, this definition also entailed that the mass of one mole of a substance was roughly equivalent to the number of nucleons in one atom or molecule of that substance. Since the definition of the gram was not mathematically tied to that of the
dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor ch ...
, the number of molecules per mole ''N''A (the Avogadro constant) had to be determined experimentally. The experimental value adopted by CODATA in 2010 is . In 2011 the measurement was refined to . The mole was made the seventh SI base unit in 1971 by the 14th CGPM.


2019 redefinition of SI base units

In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed to a plan for a possible revision of the SI base unit definitions at an undetermined date. On 16 November 2018, after a meeting of scientists from more than 60 countries at the CGPM in Versailles, France, all SI base units were defined in terms of physical constants. This meant that each SI unit, including the mole, would not be defined in terms of any physical objects but rather they would be defined by physical constants that are, in their nature, exact. Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly elementary entities" of that substance.


Criticism

Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the
metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
or the second have arisen: * the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity that can be expressed simply as a number, not requiring a distinct base unit; * The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies * The mole is not a true metric (i.e. measuring) unit, rather it is a ''parametric'' unit, and amount of substance is a ''parametric'' base quantity * the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between ''entities'' and ''units of continuous quantities'' In chemistry, it has been known since Proust's
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 ...
(1794) that knowledge of the mass of each of the components in a chemical system is not sufficient to define the system. Amount of substance can be described as mass divided by Proust's "definite proportions", and contains information that is missing from the measurement of mass alone. As demonstrated by Dalton's
law of partial pressures Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by Joh ...
(1803), a measurement of mass is not even necessary to measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable one being the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
(where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these
colligative properties In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ...
.


Similar units

Like chemists, chemical engineers use the unit mole extensively, but different unit multiples may be more suitable for industrial use. For example, the SI unit for volume is the cubic metre, a much larger unit than the commonly used litre in the chemical laboratory. When amount of substance is also expressed in kmol (1000 mol) in industrial-scaled processes, the numerical value of molarity remains the same. For convenience in avoiding conversions in the imperial (or
US customary units United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English uni ...
), some engineers adopted the ''pound-mole'' (notation ''lb-mol'' or ''lbmol''), which is defined as the number of entities in 12 lb of 12C. One lb-mol is equal to , which value is the same as the number of grams in an international avoirdupois pound. In the metric system, chemical engineers once used the ''kilogram-mole'' (notation ''kg-mol''), which is defined as the number of entities in 12 kg of 12C, and often referred to the mole as the ''gram-mole'' (notation ''g-mol''), when dealing with laboratory data. Late 20th-century chemical engineering practice came to use the ''kilomole'' (kmol), which is numerically identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units – thus, kmol means 1000 mol. This is equivalent to the use of kg instead of g. The use of kmol is not only for "magnitude convenience" but also makes the equations used for modelling chemical engineering systems coherent. For example, the conversion of a flowrate of kg/s to kmol/s only requires the molecular mass without the factor 1000 unless the basic SI unit of mol/s were to be used. Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1 mol photons = photons. One mole of photons is sometimes referred to as an einstein.


Derived units and SI multiples

The only SI derived unit with a special name derived from the mole is the
katal The katal (symbol: kat) is the unit of catalytic activity in the International System of Units (SI) used for quantifying the catalytic activity of enzymes (that is, measuring the enzymatic activity level in enzyme catalysis) and other catalyst ...
, defined as one mole per second of catalytic activity. Like other SI units, the mole can also be modified by adding a
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pr ...
that multiplies it by a
power of 10 A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The f ...
: One fmol is exactly 602,214,076 molecules; attomole and smaller quantities cannot be exactly realized. The yoctomole, equal to around 0.6 of an individual molecule, did make appearances in scientific journals in the year the yocto- prefix was officially implemented.


Mole Day

October 23, denoted 10/23 in the US, is recognized by some as Mole Day. It is an informal holiday in honor of the unit among chemists. The date is derived from the Avogadro number, which is approximately . It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 (), June 22 (), or 6 February (), a reference to the 6.02 or 6.022 part of the constant.


See also

* * * * * *


References


External links

* {{DEFAULTSORT:Mole (Unit) SI base units Units of amount of substance Units of chemical measurement Dimensionless numbers of chemistry Units of amount