View source for Mole (unit)

{{Short description|SI unit of amount of substance}}
{{Infobox Unit
| name = mole
| caption = Unit of scientific measurement
| standard = SI
| quantity = [[Physics:Amount of substance|amount of substance]]
| symbol = mol
| dimension = N
}}

The '''mole''' (symbol '''mol''') is the [[Unit of measurement|unit of measurement]] for ''[[Physics:Amount of substance|amount of substance]]'', a quantity proportional to the [[Physics:Particle number|number of elementary entities]] of a substance. It is a [[SI base unit|base unit]] in the [[International System of Units]] (SI). One mole contains exactly {{val|6.02214076|e=23}} elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, or other [[Physics:Particle|particle]]s. The number of particles in a mole is the '''Avogadro number''' (symbol ''N''<sub>0</sub>) and the numerical value of the ''[[Physics:Avogadro constant|Avogadro constant]]'' (symbol ''N''<sub>A</sub>) expressed in '''mol<sup>-1</sup>'''.<ref name="SI9" /> The value was chosen based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12&nbsp;[[Gram|gram]]s of [[Physics:Carbon-12|<sup>12</sup>C]],<ref name=SI9>{{SIbrochure9th}}</ref> which made the mass of a mole of a compound expressed in grams numerically equal to the average molecular mass of the compound expressed in [[Dalton (unit)|daltons]]. With the [[2019 redefinition of the SI base units|2019 redefinition of the SI base units]], the numerical equivalence is now only approximate but may be assumed for all practical purposes.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and amounts of products of [[Chemistry:Chemical reaction|chemical reaction]]s. For example, the chemical equation {{nowrap|2 H<sub>2</sub> + O<sub>2</sub> → 2 H<sub>2</sub>O}} can be interpreted to mean that for each 2&nbsp;mol molecular hydrogen (H<sub>2</sub>) and 1&nbsp;mol [[Chemistry:Dioxygen|molecular oxygen]] (O<sub>2</sub>) that react, 2&nbsp;mol of water (H<sub>2</sub>O) form. The [[Chemistry:Concentration|concentration]] of a solution is commonly expressed by its [[Physics:Molar concentration|molar concentration]], defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is mole per [[Litre|litre]] (mol/L).

== Concepts ==

=== Relation to the Avogadro constant ===
The number of entities (symbol ''N'') in a one-mole sample equals the ''[[Chemistry:Avogadro number|Avogadro number]]'' (symbol ''N''<sub>0</sub>), a [[Physics:Dimensionless quantity|dimensionless quantity]].<ref name=SI9/>
Historically, ''N''<sub>0</sub> approximates the number of [[Physics:Nucleon|nucleon]]s ([[Physics:Proton|proton]]s or [[Physics:Neutron|neutron]]s) in one gram of ordinary [[Physics:Matter|matter]].
The ''[[Physics:Avogadro constant|Avogadro constant]]'' (symbol {{nowrap|1=''N''<sub>A</sub> = ''N''<sub>0</sub>/mol}}) has numerical multiplier given by the Avogadro number with the unit '''reciprocal mole''' (mol<sup>−1</sup>).<ref name="Gold Book mole"/>
The ratio {{nowrap|1=''n'' = ''N''/''N''<sub>A</sub>}} is a measure of the amount of substance (with the unit mole).<ref name="Gold Book mole">{{Cite book |url=https://goldbook.iupac.org/terms/view/M03980 |title=IUPAC – mole (M03980) |author=IUPAC Gold Book |publisher=[[Organization:International Union of Pure and Applied Chemistry|International Union of Pure and Applied Chemistry]]|doi=10.1351/goldbook.M03980 |s2cid=241546445 }}</ref><ref name=IUPACrev>{{cite web | title=On the revision of the International System of Units – International Union of Pure and Applied Chemistry | publisher=International Union of Pure and Applied Chemistry | date=16 November 2018 | url=https://iupac.org/on-the-revision-of-the-international-system-of-units/ | access-date=1 March 2021}}</ref><ref name="MEP for mole 2019">{{Cite web|last=BIPM|date=20 May 2019|title=Mise en pratique for the definition of the mole in the SI|url=https://www.bipm.org/documents/20126/41489679/SI-App2-mole.pdf/be4dea74-a526-e49b-f497-11b393665401?version=1.6&t=1637238198610&download=false|access-date=18 February 2022|website=BIPM.org}}</ref>

=== Nature of the entities {{anchor|Elementary entities}} ===

Depending on the nature of the substance, an '''elementary entity''' may be an [[Physics:Atom|atom]], a [[Physics:Molecule|molecule]], an [[Physics:Ion|ion]], an ion pair, or a [[Physics:Subatomic particle|subatomic particle]] such as a [[Physics:Proton|proton]]. For example, 10 moles of [[Chemistry:Water|water]] (a [[Chemistry:Chemical compound|chemical compound]]) and 10 moles of [[Chemistry:Mercury (element)|mercury]] (a [[Chemistry:Chemical element|chemical element]]) contain equal amounts of substance, and the mercury contains exactly one atom for each molecule of the water, despite the two substances having different volumes and different masses.

The mole corresponds to a given count of entities.<ref name="IUPAChist" /> Usually the entities counted are chemically identical and 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 entities 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 entities. In yet other cases, such as [[Chemistry:Diamond|diamond]], 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 entities of a substance, in other cases exact definitions may be specified.
The mass of a substance is equal to its [[Physics:Relative atomic mass|relative atomic (or molecular) mass]] multiplied by the [[Physics:Molar mass constant|molar mass constant]], which is almost exactly 1&nbsp;g/mol.

== History ==
[[File:Amadeo Avogadro.png|thumb|upright|[[Biography:Amedeo Avogadro|Avogadro]], who inspired the Avogadro constant]]
The history of the mole is intertwined with that of units of [[Physics:Molecular mass|molecular mass]], and the [[Physics:Avogadro constant|Avogadro constant]].

The first table of [[Physics:Standard atomic weight|standard atomic weight]] was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of [[Chemistry:Hydrogen|hydrogen]] was defined as 1. These relative atomic masses were based on the [[Chemistry:Stoichiometry|stoichiometric]] proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to [[Physics:Atomic theory|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 [[Chemistry:Equivalent weight|equivalent weight]]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.

[[Biography:Jöns Jacob Berzelius|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 [[Chemistry:Oxygen|oxygen]] 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. However, he chose to fix the atomic mass of oxygen as 100, which did not catch on.

Charles Frédéric Gerhardt (1816–56), [[Biography:Henri Victor Regnault|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 [[Chemistry:Karlsruhe Congress|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|chemist]] [[Biography:Wilhelm Ostwald|Wilhelm Ostwald]] in 1894 from the German word ''Molekül'' ([[Physics:Molecule|molecule]]).<ref>
{{Cite book
|first=Georg
|last=Helm
|year=1897
|title=The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena
|url=https://archive.org/details/principlesmathe00helmgoog
|others=transl. by Livingston, J.; Morgan, R.
|place=New York
|publisher=Wiley
|page=[https://archive.org/details/principlesmathe00helmgoog/page/n20 6]
}}</ref><ref>Some sources place the date of first usage in English as 1902. Merriam–Webster [http://www.merriam-webster.com/dictionary/mole%5B5%5D proposes] {{webarchive|url=https://web.archive.org/web/20111102181728/http://www.merriam-webster.com/dictionary/mole%5B5%5D |date=2011-11-02 }} an etymology from ''Molekulärgewicht'' ([[Physics:Molecular weight|molecular weight]]).</ref><ref>{{cite book
|first=Wilhelm
|last=Ostwald
|year=1893
|publisher=Wilhelm Engelmann
|location=Leipzig, Germany
|title=Hand- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen
|trans-title=Handbook and Auxiliary Book for Conducting Physico-Chemical Measurements
|page=119
|url=https://babel.hathitrust.org/cgi/pt?id=uc1.b4584562;view=1up;seq=131
}} From p. 119: ''"Nennen wir allgemein das Gewicht in Grammen, welches dem Molekulargewicht eines gegebenen Stoffes numerisch gleich ist, ein Mol, so ... "''  (If we call in general the weight in grams, which is numerically equal to the molecular weight of a given substance, a "mol", then ... )</ref> The related concept of [[Physics:Equivalent mass|equivalent mass]] had been in use at least a century earlier.<ref>'''mole''', '''''n.{{sup|8}}''''', Oxford English Dictionary, Draft Revision Dec. 2008</ref>

=== Standardization ===
Developments in [[Physics:Mass spectrometry|mass spectrometry]] led to the adoption of [[Physics:Oxygen-16|oxygen-16]] as the standard substance, in lieu of natural oxygen.<ref>{{cite journal |last1=Busch |first1=Kenneth |title=Units in Mass Spectrometry |journal=Current Trends in Mass Spectrometry |date=May 2, 2003 |volume=18 |issue=5S |pages=S32-S34 [S33] |url=https://cdn.sanity.io/files/0vv8moc6/spectroscopy/cfb6f4cb3d02243b516bce3b11dc3584733be2b1.pdf/article-55961.pdf |access-date=29 April 2023}}</ref>

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 <sup>12</sup>C had a mass of ''exactly'' 12&nbsp;[[Gram|g]].<ref name="SI114-15" /><ref name="IUPAChist">{{AtomicWeightHistory}}</ref> The four different definitions were equivalent to within 1%.

{|class="wikitable" align="center" style="margin:.5em;"
! Scale basis
! Scale basis<br />relative to {{sup|12}}C = 12
! Relative deviation<br />from the {{sup|12}}C = 12 scale
|-
| Atomic mass of hydrogen = 1
| 1.00794(7)
| align="center" | −0.788%
|-
| Atomic mass of oxygen = 16
| {{val|15.9994|(3)}}
| align="center" | +0.00375%
|-
| Relative atomic mass of {{sup|16}}O = 16
| {{val|15.9949146221|(15)}}
| align="center" | +0.0318%
|-
|}

Because a [[Dalton (unit)|dalton]], a unit commonly used to measure [[Physics:Atomic mass|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 [[Physics:Nucleon|nucleon]] (i.e. a [[Physics:Proton|proton]] or [[Physics:Neutron|neutron]]) 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 (unit)|dalton]], the number of molecules per mole ''N''<sub>A</sub> (the Avogadro constant) had to be determined experimentally. The experimental value adopted by [[Organization:Committee on Data for Science and Technology|CODATA]] in 2010 is {{nowrap|1=''N''<sub>A</sub> = {{val|6.02214129|(27)|e=23|u=mol-1}}}}.<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?na physics.nist.gov/] {{webarchive|url=https://web.archive.org/web/20150629063615/http://physics.nist.gov/cgi-bin/cuu/Value?na |date=2015-06-29 }} Fundamental Physical Constants: Avogadro Constant</ref>
In 2011 the measurement was refined to {{val|6.02214078|(18)|e=23|u=mol-1}}.<ref>{{cite journal | first = Birk | last = Andreas | title = Determination of the Avogadro Constant by Counting the Atoms in a <sup>28</sup>Si Crystal | journal=Physical Review Letters | volume = 106 | issue = 3 | year=2011 | pages = 30801 | doi=10.1103/PhysRevLett.106.030801 | pmid = 21405263 | bibcode=2011PhRvL.106c0801A|arxiv = 1010.2317 | s2cid = 18291648 |display-authors=0}}</ref>

The mole was made the seventh [[SI base unit]] in 1971 by the 14th CGPM.<ref>{{cite web|url=http://www.bipm.org/en/CGPM/db/14/3/|title=BIPM – Resolution 3 of the 14th CGPM|website=www.bipm.org|access-date=1 May 2018|url-status=dead|archive-url=https://web.archive.org/web/20171009112117/http://www.bipm.org/en/CGPM/db/14/3|archive-date=9 October 2017}}</ref>

=== 2019 redefinition of SI base units ===

Before the [[2019 redefinition of the SI base units|2019 redefinition of the SI base units]], the mole was defined as the amount of substance of a system that contains as many elementary entities as there are atoms in 12 [[Gram|gram]]s of [[Physics:Carbon-12|carbon-12]] (the most common [[Physics:Isotopes of carbon|isotope of carbon]]).<ref name=SI8>{{SIbrochure8th}}</ref>
The term ''gram-molecule'' was formerly used to mean one mole of molecules, and ''gram-atom'' for one mole of atoms.<ref name="SI114-15">{{SIbrochure8th|pages=114–15}}</ref> For example, 1 mole of MgBr<sub>2</sub> is 1&nbsp;gram-molecule of MgBr<sub>2</sub> but 3&nbsp;gram-atoms of MgBr<sub>2</sub>.<ref>
{{cite journal
| doi=10.1088/0953-8984/15/6/315
| last1=Wang | first1=Yuxing
| last2=Bouquet | first2= Frédéric
| last3=Sheikin | first3=Ilya
| last4=Toulemonde | first4=Pierre
| last5=Revaz | first5=Bernard
| last6=Eisterer | first6=Michael
| last7=Weber | first7=Harald W.
| last8=Hinderer | first8=Joerg
| last9=Junod | first9=Alain
| display-authors=0
| title=Specific heat of MgB<sub>2</sub> after irradiation
| journal=Journal of Physics: Condensed Matter | year=2003
| volume=15
| issue=6 | pages=883–893|arxiv = cond-mat/0208169 |bibcode = 2003JPCM...15..883W| s2cid=16981008 }}</ref><ref>{{cite journal
| doi=10.1103/PhysRevB.72.024547
| last1=Lortz | first1=R.
| last2=Wang | first2=Y.
| last3=Abe | first3=S.
| last4=Meingast | first4=C.
| last5=Paderno | first5=Yu.
| last6=Filippov | first6=V.
| last7=Junod | first7=A.
| display-authors=0
| title=Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductor ZrB<sub>12</sub>
| journal=Phys. Rev. B | year=2005
| volume=72
| issue=2 | pages=024547
| arxiv = cond-mat/0502193
| bibcode = 2005PhRvB..72b4547L
| s2cid=38571250
}}</ref>

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 [[Physics:Physical constant|physical constant]]s that are, in their nature, exact.<ref name="IUPACrev" />

Such changes officially came into effect on 20 May 2019. Following such changes, "one mole" of a substance was redefined as containing "exactly {{val|6.02214076|e=23}} elementary entities" of that substance.<ref>[https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23 CIPM Report of 106th Meeting] {{webarchive|url=https://web.archive.org/web/20180127202612/https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23 |date=2018-01-27 }} Retrieved 7 April 2018</ref><ref>{{cite journal |title=Redefining the Mole |url=https://www.nist.gov/si-redefinition/redefining-mole |journal=NIST |access-date=24 October 2018|date=2018-10-23 }}</ref>

== 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|metre]] or the [[Second|second]] have arisen:
* the number of molecules, etc. in a given amount of material is a fixed [[Physics:Dimensionless quantity|dimensionless quantity]] that can be expressed simply as a number, not requiring a distinct base unit;<ref name="IUPAChist" /><ref name="Giunta 2015">{{cite journal | url=http://dx.doi.org/10.1021/ed2001957 | doi=10.1021/ed2001957 | title=The Atomic Mass Unit, the Avogadro Constant, and the Mole: A Way to Understanding | year=2012 | last1=Barański | first1=Andrzej | journal=Journal of Chemical Education | volume=89 | issue=1 | pages=97–102 | bibcode=2012JChEd..89...97B }}</ref>
* The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to advanced economies<ref>{{cite journal |last=Price |first=Gary |year=2010 |title=Failures of the global measurement system. Part 1: the case of chemistry |journal=Accreditation and Quality Assurance |volume=15 |issue=7 |pages=421–427 |doi=10.1007/s00769-010-0655-z|s2cid=95388009 }}</ref>
* 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<ref>{{cite journal
| url = http://stacks.iop.org/0026-1394/47/i=3/a=012
| title = Metrological thinking needs the notions of ''parametric'' quantities, units, and dimensions
| year = 2010
| journal = Metrologia
| volume = 47
| issue = 3
| pages = 219–230
| first = Ingvar
| last = Johansson
| bibcode = 2010Metro..47..219J
| doi = 10.1088/0026-1394/47/3/012 | s2cid = 122242959
}}</ref>
* the SI defines numbers of entities as quantities of dimension one, and thus ignores the ontological distinction between ''entities'' and ''units of continuous quantities''<ref>{{cite journal
| doi = 10.1007/s11229-010-9832-1
| title = The ontological distinction between units and entities
| year = 2010
| journal = Synthese
| volume = 187
| issue = 2
| pages = 393–401
| first = G.
| last = Cooper
| author2 = Humphry, S.| s2cid = 46532636
}}</ref>

In chemistry, it has been known since Proust's [[Physics:Law of definite proportions|law of definite proportions]] (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 (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 [[Physics:Ideal gas law|ideal gas law]] (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these [[Chemistry:Colligative properties|colligative properties]].<ref>{{cite book | url=https://openlibrary.org/books/OL7204743M/The_scientific_foundations_of_analytical_chemistry | ol=7204743M | title=The scientific foundations of analytical chemistry: Treated in an elementary manner | year=1900 | publisher=Macmillan and co., limited }}</ref>

== 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&nbsp;mol) in industrial-scaled processes, the numerical value of molarity remains the same, as <math display="inline">\frac{\text{kmol}}{\text{m}^3}=\frac{1000\text{ mol}}{1000\text{ L}}=\frac{\text{mol}}{\text{L}}</math>. Chemical engineers once used the ''kilogram-mole'' (notation ''kg-mol''), which is defined as the number of entities in 12&nbsp;kg of <sup>12</sup>C, and often referred to the mole as the ''gram-mole'' (notation ''g-mol''), then defined as the number of entities in 12&nbsp;g of <sup>12</sup>C, when dealing with laboratory data.<ref name="Himmelblau">{{cite book |last=Himmelblau |first=David |title=Basic Principles and Calculations in Chemical Engineering |year=1996 |isbn=978-0-13-305798-0 |edition=6 |pages=17–20|publisher=Prentice Hall PTR }}</ref>

Late 20th-century chemical engineering practice came to use the ''kilomole'' (kmol), which was numerically identical to the kilogram-mole (until the [[2019 redefinition of the SI base units|2019 redefinition of SI units]], which redefined the mole by fixing the value of the Avogadro constant, making it very nearly equivalent to but no longer exactly equal to the gram-mole), but whose name and symbol adopt the SI convention for standard multiples of metric units – thus, kmol means 1000&nbsp;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 [[Coherence (units of measurement)|coherent]]. For example, the conversion of a flowrate of kg/s to kmol/s only requires dividing by the molar mass in g/mol (as <math display="inline">\frac{\text{kg}}{\text{kmol}}=\frac{1000\text{ g}}{1000\text{ mol}}=\frac{\text{g}}{\text{mol}}</math>) without multiplying by 1000 unless the basic SI unit of mol/s were to be used, which would otherwise require the molar mass to be converted to kg/mol.

For convenience in avoiding conversions in the [[Imperial units|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 [[Pound (mass)|lb]] of <sup>12</sup>C. One lb-mol is equal to {{val|453.59237|u=g-mol}},<ref name="Himmelblau" /> which is the same numerical value as the number of grams in an international avoirdupois pound.

Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where 1&nbsp;mol photons ≈ {{val|6.02|e=23}} photons.<ref>{{cite web|title=Lighting Radiation Conversion|url=http://www.egc.com/useful_info_lighting.php|access-date=March 10, 2016|url-status=live|archive-url=https://web.archive.org/web/20160311131342/http://www.egc.com/useful_info_lighting.php|archive-date=March 11, 2016}}</ref> The obsolete unit [[Physics:Einstein (unit)|einstein]] is variously defined as the energy in one mole of photons and also as simply one mole of photons.

== Derived units and SI multiples ==
The only [[SI derived unit#Derived units with special names|SI derived unit with a special name]] derived from the mole is the [[Katal|katal]], defined as one mole per [[Second|second]] of catalytic activity. Like other SI units, the mole can also be modified by adding a [[Metric prefix|metric prefix]] that multiplies it by a [[Power of 10|power of 10]]:
{{SI multiples
| unit=mole
| symbol=mol
}}

One femtomole 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.<ref>{{cite journal | first = Da Yong | last = Chen | title = Low-cost, high-sensitivity laser-induced fluorescence detection for DNA sequencing by capillary gel electrophoresis | journal = Journal of Chromatography | volume = 559 | year = 1991 | issue = 1–2 | pages = 237–246 | doi = 10.1016/0021-9673(91)80074-Q | pmid = 1761625 | display-authors=0 }}</ref>

== Mole Day ==
October 23, denoted 10/23 in the US, is recognized by some as Mole Day.<ref>[https://www.moleday.org/history-of-the-foundation History of National Mole Day Foundation, Inc.] {{webarchive|url=https://web.archive.org/web/20101023075040/http://www.moleday.org/htdocs/history.html |date=2010-10-23 }}.</ref> It is an informal holiday in honor of the unit among chemists. The date is derived from the Avogadro number, which is approximately {{val|6.022|e=23}}. It starts at 6:02&nbsp;a.m. and ends at 6:02&nbsp;p.m. Alternatively, some chemists celebrate June&nbsp;2 ({{abbr|06/02|in mm/dd/yyyy format}}), June&nbsp;22 ({{abbr|6/22|in m/d/y format}}), or 6&nbsp;February ({{abbr|06.02|in dd.mm.yyyy format}}), a reference to the 6.02 or 6.022 part of the constant.<ref>[http://nstacommunities.org/blog/2013/10/17/happy-mole-day/ Happy Mole Day!] {{webarchive|url=https://web.archive.org/web/20140729135936/http://nstacommunities.org/blog/2013/10/17/happy-mole-day/ |date=2014-07-29 }}, Mary Bigelow. SciLinks blog, National Science Teachers Association. October 17, 2013.</ref><ref>[http://chemistry.about.com/od/historyofchemistry/a/mole-day.htm What Is Mole Day? – Date and How to Celebrate]. {{webarchive|url=http://archive.wikiwix.com/cache/20140730061148/http://chemistry.about.com/od/historyofchemistry/a/mole-day.htm |date=2014-07-30 }}, Anne Marie Helmenstine. About.com.</ref><ref>{{Citation |url=http://www.cambridgenetwork.co.uk/news/perse-school-celebrates-moles-of-chemical-variety/ |publisher=Cambridge Network |title=The Perse School celebrates moles of the chemical variety |quote=As 6.02 corresponds to 6th February, the School has adopted the date as their 'Mole Day'. |author=The Perse School |date=Feb 7, 2013 |access-date=Feb 11, 2015 |url-status=live |archive-url=https://web.archive.org/web/20150211183911/http://www.cambridgenetwork.co.uk/news/perse-school-celebrates-moles-of-chemical-variety/ |archive-date=2015-02-11 |}}</ref>

== See also ==
{{div col}}
* {{annotated link|Chemistry:Element-reactant-product table}}
* {{annotated link|Physics:Faraday constant}}
* {{annotated link|Chemistry:Mole fraction}}
* {{annotated link|Dalton (unit)}}
* {{annotated link|Physics:Molecular mass}}
* {{annotated link|Physics:Molar mass}}
{{Div col end}}

== References ==
{{Reflist}}

== External links ==
* {{webarchive |url=https://web.archive.org/web/20071222072256/http://dbhs.wvusd.k12.ca.us/webdocs/Mole/Origin-of-Mole.html |date=December 22, 2007 |title=ChemTeam: The Origin of the Word 'Mole' }}

{{SI units}}
{{Mole concepts}}

{{DEFAULTSORT:Mole (Unit)}}
[[Category:SI base units]]
[[Category:Units of amount of substance]]
[[Category:Units of chemical measurement]]
[[Category:Units of amount]]

{{Sourceattribution|Mole (unit)}}