View source for Mole (unit)

{{Short description|SI unit of amount of substance}}
{{Redirect|Nmol|the mathematical technique|Method of lines}}
{{Infobox Unit
| name = mole
| image = Mole_carbon-12_diagram.svg
| imagesize = 350px
| caption = One mole is exactly {{val|6.02214076|e=23}} elementary entities, approximately equivalent to the number of atoms in 12 grams of carbon-12 in the historical definition
| standard = [[SI]]
| quantity = [[amount of substance]]
| symbol = mol
| dimension = N
}}

The '''mole''' (symbol '''mol''') is a [[unit of measurement]], the [[SI base unit|base unit]] in the [[International System of Units]] (SI) for ''[[amount of substance]]'', an SI base quantity proportional to the [[Particle number|number of elementary entities]] of a substance. One mole is an aggregate of exactly {{val|6.02214076|e=23}} elementary entities (approximately 602 [[sextillion]] or 602 billion times a trillion), which can be [[atom]]s, [[molecule]]s, [[ion]]s, [[Ion pair|ion pairs]], or other [[particle]]s. The number of particles in a mole is the '''Avogadro number''' (symbol {{Math|''N''<sub>0</sub>}}) and the numerical value of the ''[[Avogadro constant]]'' (symbol {{Math|''N''<sub>A</sub>}}) expressed in '''mol<sup>−1</sup>'''.<ref name="SI9" /> The relationship between the mole, Avogadro number, and Avogadro constant can be expressed in the following equation:<ref name="SI9" /><math display="block">1\text{ mol} = \frac{N_0}{N_{\text{A}}} = \frac{6.02214076\times10^{23}}{N_{\text{A}}} </math>The current SI value of the mole is based on the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12&nbsp;[[gram]]s of [[Carbon-12|<sup>12</sup>C]],<ref name=SI9>{{SIbrochure9th}}</ref> which made the [[molar mass]] of a compound in grams per mole, numerically equal to the average [[molecular mass]] or formula mass of the compound expressed in [[Dalton (unit)|daltons]]. With the [[2019 revision of the SI]], the numerical equivalence is now only approximate, but may still be assumed with high accuracy. 

Conceptually, the mole is no different than the concept of [[dozen]] or other convenient grouping used to discuss collections of identical objects. Because laboratory-scale objects contain a vast number of tiny atoms, the number of entities in the grouping must be huge to be useful for  work.

The mole is widely used in [[chemistry]] as a convenient way to express amounts of [[reactant]]s and amounts of [[product (chemistry)|products]] of [[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 [[dihydrogen|molecular hydrogen]] (H<sub>2</sub>) and 1&nbsp;mol [[dioxygen|molecular oxygen]] (O<sub>2</sub>) that react, 2&nbsp;mol of water (H<sub>2</sub>O) form. The [[concentration]] of a solution is commonly expressed by its [[molar concentration]], defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is mole per [[litre]] (mol/L).

== Concepts ==

=== Relation to the Avogadro constant ===
The [[number of particles|number of entities]] (symbol ''N'') in a one-mole sample equals the '''Avogadro number''' (symbol {{Math|''N''<sub>0</sub>}}), a [[dimensionless quantity]].<ref name=SI9/> Historically, {{Math|''N''<sub>0</sub>}} approximates the number of [[nucleon]]s ([[proton]]s or [[neutron]]s) in one&nbsp;[[gram]] of ordinary [[matter]]. The ''[[Avogadro constant]]'' (symbol {{Math|''N''<sub>A</sub>}}) is given by the Avogadro number multiplied by the unit '''reciprocal mole''' (mol<sup>−1</sup>), i.e. {{Math|1=''N''<sub>A</sub> = ''N''<sub>0</sub>/mol}}.<ref name="Gold Book mole"/> The ratio {{Math|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=[[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>

The equation {{Math|1=''N''<sub>A</sub> = ''N''<sub>0</sub>/mol}} can be rearranged as an explicit expression for the mole: {{Math|1=1 mol = ''N''<sub>0</sub>/''N''<sub>A</sub>}}. Letting '''ent''' denote the amount of substance equal to one&nbsp;[[Molecular entity|entity]], the smallest particle of a substance (retaining its chemical properties), one&nbsp;mole is the amount of substance containing {{Math|''N''<sub>0</sub>}}&nbsp;entities, i.e. {{Math|1=1 mol = ''N''<sub>0</sub> ent}}. Thus, amount of substance is dimensionally equivalent to the reciprocal of the Avogadro constant ({{Math|1/''N''<sub>A</sub>}}).

=== Nature of the entities <span class="anchor" id="Elementary entities"></span> ===
{{see also|Amount of substance#Nature of the particles}}

Depending on the nature of the substance, an '''elementary entity''' may be an atom, a molecule, an ion, an ion pair, or a [[subatomic particle]] such as a [[proton]]. For example, 10&nbsp;moles of [[water]] (a [[chemical compound]]) and 10&nbsp;moles of [[mercury (element)|mercury]] (a [[chemical element]]) contain equal numbers of particles of each substance, with one atom of mercury for each molecule of water, despite the two quantities 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, the constituent entities in a solid 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 [[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 [[molar mass]] of a substance is equal to its [[Relative atomic mass|relative atomic (or molecular) mass]] multiplied by the [[molar mass constant]], which is almost exactly 1&nbsp;g/mol.

== 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 revision of the SI]], 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 kg/kmol (which is equivalent to 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 [[United States customary units|US customary units]]), some engineers adopted the ''pound-mole'' (notation ''lb-mol'' or ''lbmol''), which is defined as the number of entities in 12&nbsp;[[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 [[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]], defined as one mole per [[second]] of [[catalytic activity]]. Like other SI units, the mole can also be modified by adding a [[metric prefix]] that multiplies it by a [[power of 10]]:
{{SI multiples
| unit=mole
| symbol=mol
}}

One femtomole is exactly {{val|602,214,076}} molecules; attomole and smaller quantities do not correspond to a whole number of entities. 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=etal }}</ref>

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

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]] was defined as 1. These relative atomic masses were based on the [[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 [[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 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.

[[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]] 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), [[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]] [[Wilhelm Ostwald]] in 1894 from the German word ''Molekül'' ([[molecule]]).<ref>
{{cite book
| last=Helm |first=Georg
| 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'' ([[molecular weight]]).</ref><ref>
{{cite book
 | last=Ostwald |first=Wilhelm |author-link=Wilhelm 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 [[equivalent mass]] had been in use at least a century earlier.<ref>'''mole''', '''''n.{{sup|8}}''''', [[Oxford English Dictionary]], Draft Revision Dec. 2008</ref>

In chemistry, it has been known since [[Joseph Proust|Proust's]] [[law of definite proportions]] (1794) that knowledge of the mass of each of the components in a chemical [[system (thermodynamics)|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 [[John Dalton|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]] (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these [[colligative properties]].<ref>{{cite book |last=Ostwald |first=Wilhelm |others=McGowan, George (transl.) |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 |edition=Second English |location=London | publisher=Macmillan and Co. }}</ref>

=== Standardization ===
Developments in [[mass spectrometry]] led to the adoption of [[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 International Bureau of Weights and Measures defined the mole as "the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012&nbsp;kilograms 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 [[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]] (i.e. a [[proton]] or [[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, the number of molecules per mole ''N''<sub>A</sub> (the Avogadro constant) had to be determined experimentally. The experimental value adopted by [[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=etal}}</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 revision of the SI ===

Before the [[2019 revision of the SI]], the mole was defined as the amount of substance of a system that contains as many elementary entities as there are atoms in 12&nbsp;[[gram]]s of [[carbon-12]] (the most common [[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&nbsp;mole of [[MgBr2|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=etal
| 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=etal
| 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 [[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]] 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;<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 | url-access=subscription }}</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
| url-access = subscription
}}</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>
* the mole is often used interchangeably and inconsistently to refer to both a unit and a quantity without appropriate use of amount of substance potentially causing confusion for novice chemistry students.<ref>
{{cite journal
| doi = 10.1021/acs.jchemed.2c00199
| title = Inconsistent language use in online resources explaining the mole has implications for students' understanding
| year = 2022
| journal = Journal of Chemical Education
| volume = 99
| issue = 7
| pages = 2446–2450
| first = S. W.
| last = Rees
| author2 = Bruce, M.
}}</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 |author-link=The Perse School}}</ref>

== See also ==
{{div col}}
* {{annotated link|Element–reactant–product table}}
* {{annotated link|Faraday constant}}
* {{annotated link|Mole fraction}}
* {{annotated link|Dalton (unit)}}
* {{annotated link|Molecular mass}}
* {{annotated link|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}}
{{Authority control}}

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