Mole (unit)
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The mole, symbol mol, is the unit of
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
(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 atomic nucleus, 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, l ...
, 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 pair, or a
subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of n ...
such as an
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
. 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 entity, molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A homonuclear molecule, molecule co ...
) 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 atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
), 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 particle number, number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an I ...
, 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, mass number (nucleon number). Until the 1960s, n ...
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 atomic nucleus, nuclei of atoms. Since protons and ...
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 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 Volume is a measure ...
s of
carbon-12 Carbon-12 (12C) is the most abundant of the two Stable isotope, stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of Periodic table, element carbon on Earth; its abundance is due to the triple-alpha process by which it is ...
, 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 (H2) and 1 mol dioxygen (O2) that react, 2 mol of water (H2O) form. The
concentration In chemistry, concentration is the Abundance (chemistry), abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: ''mass concentration (chemistry), mass 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 (chemistry), solution, in terms of amount of substance pe ...
, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (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 In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material ...
, 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, 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 mole (unit), moles. The molar mass is a bulk, not ...
of a substance is the ratio of the
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
of a sample of that substance to its
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
. 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 cha ...
. 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 List of intergovernmental organizations, intergovernmental organisation, through which its 59 member-states act together on measur ...

Realising the mole
. Retrieved 25 September 2008.
Other methods include the use of the molar volume 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 electron ...
. 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, but also on the distribution of isotopes 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 A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemica ...
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 (chemistry), solution, in terms of amount of substance pe ...
, 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 or mole fraction 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 In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas ...
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 isotope Isotopes are two or more ty ...
,
atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity ...
s, and the Avogadro constant. The first table of standard atomic weight was published by
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
(1766–1844) in 1805, based on a system in which the relative atomic mass of
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the chemical ...
was defined as 1. These relative atomic masses were based on the
stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and Product (chemistry), products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of ...
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 (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 weights (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 chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...
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 ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
. 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 (1810–78) and Stanislao Cannizzaro (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 (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 th ...
Wilhelm Ostwald 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 had been in use at least a century earlier.


Standardization

Developments in
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is us ...
led to the adoption of oxygen-16 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 cha ...
, a unit commonly used to measure atomic mass, 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, mass number (nucleon number). Until the 1960s, n ...
(i.e. a
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 ...
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 atomic nucleus, nuclei of atoms. Since protons and ...
) 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 cha ...
, the number of molecules per mole ''N''A (the Avogadro constant) had to be determined experimentally. The experimental value adopted by
CODATA 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 ...
in 2010 is . In 2011 the measurement was refined to . The mole was made the seventh
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which a ...
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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(CGPM) agreed to a plan for a possible revision of the
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which a ...
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 constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant (mathematics), constant value in time. It is contrasted with a ...
s 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 The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
in 1971, numerous criticisms of the concept of the mole as a unit like the
metre The metre (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
or the
second The second (symbol: s) is the unit of Time in physics, time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally t ...
have arisen: * the number of molecules, etc. in a given amount of material is a fixed
dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no Dimension (physics), physical dimension is assigned, with a corresponding International Sys ...
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 (1794) that knowledge of the mass of each of the components in a chemical
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
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 (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 s ...
(where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties.


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), 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, defined as one mole per
second The second (symbol: s) is the unit of Time in physics, time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally t ...
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: 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