Editing Avogadro constant

{{Short description|Fundamental metric system constant defined as the number of particles per mole}}
{{good article}}
{{use dmy dates|date=October 2022|cs1-dates=l}}
{{Infobox
| above   = Avogadro constant
| image   = [[File:Amadeo Avogadro.png|150px|upright=1]]
| caption = [[Amedeo Avogadro]], the constant's namesake
| label1  = {{longitem|Common symbols}}
| data1   = {{mvar|N{{sub|{{ni|A}}}}}}, {{mvar|L}}
| label2  = [[International System of Units|SI&nbsp;unit]]
| data2   = [[mole (unit)|mol]]{{sup|−1}}
| header3 = Exact value
| label4  = {{nobold|reciprocal mole|reciprocal moles]]}}
| data4   = {{physconst|NA|unit=no|ref=no}}
}}
The '''Avogadro constant''', commonly denoted {{math|'''''N''{{sub|A}}'''}}<ref name=bipm9th/> or {{math|'''''L'''''}},<ref name=iupac1996/> is an [[SI defining constant]] with an exact value of {{val|6.02214076|e=23|u=mol-1}} ([[reciprocal mole]]s).<ref name="SI2019">
{{cite book
 | last1 = Newell
 | first1 = David B.
 | last2 = Tiesinga
 | first2 = Eite
 | year = 2019
 | title = The International System of Units (SI)
 | series = NIST Special Publication 330
 | publisher = National Institute of Standards and Technology
 | location = Gaithersburg, Maryland
 | url = https://www.nist.gov/si-redefinition/meet-constants
 | doi = 10.6028/nist.sp.330-2019
 | s2cid = 242934226
 | doi-access = free
}}</ref><ref name=ciaaw/> It defines the [[particle number|number of constituent particle]]s in one [[Mole (unit)|mole]], where the particles in question can be either [[molecule]]s, [[atom]]s, [[ion]]s, ion pairs, or any other elementary entities. The number {{val|6.02214076|e=23|u=}} is a [[dimensionless physical constant]] known as the '''Avogadro number''', commonly denoted {{math|''N''{{sub|0}}}}<ref name="feynman" /><ref name="born" /> and often confused with the constant. Both are named after the Italian physicist and chemist [[Amedeo Avogadro]].

The Avogadro constant is used as a [[proportionality factor|normalization factor]] in relating the ''[[amount of substance]]'' <math display="inline">n(\mathrm{X})</math>, in a sample of a substance <math>\mathrm{X}</math>, to the corresponding number of elementary entities <math>N(\mathrm{X})</math>:

<math>n(\mathrm{X}) = \frac{N(\mathrm{X})}{N_{\mathrm{A}}} = N(\mathrm{X})\,\left(\frac{1\;\mathrm{mol}}{N_0}\right)</math>

The Avogadro constant {{math|''N''{{sub|A}}}} is also the factor that converts the average [[mass]] (<math>m</math>) of one particle, in [[gram]]s, to the [[molar mass]] (<math>M</math>) of the substance, in grams per mole (g/mol).<ref name="okun" /> That is, <math>M = m\cdot N_{\text{A}}</math>. Historically, this was precisely true, but since the [[2019 revision of the SI]], the relation is now merely approximate.

The constant {{math|''N''{{sub|A}}}} also relates the [[molar volume]] (the volume per mole) of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about {{nowrap|18 [[millilitre|mL]]/mol}}, the volume occupied by one molecule of water is about {{nowrap|18/(6.022{{e|23}}) mL}}, or about {{val|0.030|u=nm3}} (cubic [[nanometre]]s). For a [[crystal]]line substance, {{math|''N''{{sub|0}}}} relates the volume of a crystal with one mole worth of repeating [[crystal structure|unit cells]], to the volume of a single cell (both in the same units).

== Definition ==
[[Image:Mole carbon-12 diagram.svg|thumb|400px|Approximate definition of a mole based on 12 grams of carbon-12]]

The Avogadro constant was historically derived from the old definition of the mole as the amount of substance in 12&nbsp;[[gram|grams]] of [[carbon-12]] (<sup>12</sup>C); or, equivalently, the number of [[dalton (unit)|daltons]] in a gram, where the dalton is defined as {{sfrac|1|12}} of the mass of a <sup>12</sup>C atom.<ref name="bipm8th" /> By this old definition, the numerical value of the Avogadro constant in mol<sup>−1</sup> (the Avogadro number) was a physical constant that had to be determined experimentally.

The redefinition of the mole in 2019, as being the amount of substance containing exactly {{val|6.02214076|e=23}} particles,<ref name=NIST2019/> meant that the mass of 1 mole of a substance is now exactly the product of the Avogadro number and the average mass of its particles. The dalton, however, is still defined as {{sfrac|1|12}} of the mass of a <sup>12</sup>C atom, which must be determined experimentally and is known only with finite [[accuracy and precision|accuracy]]. The prior experiments that aimed to determine the Avogadro constant are now re-interpreted as measurements of the value in grams of the dalton.

By the old definition of mole, the numerical value of the mass of one mole of a substance, expressed in grams, was precisely equal to the average mass of one particle in daltons. With the new definition, this numerical equivalence is no longer exact, as it is affected by the uncertainty of the value of the dalton in SI units. However, it is still applicable for all practical purposes. For example, the average mass of one molecule of [[water]] is about 18.0153&nbsp;daltons, and of one mole of water is about 18.0153&nbsp;grams. Also, the Avogadro number is the approximate number of [[nucleon]]s ([[proton]]s and [[neutron]]s) in one gram of ordinary [[matter]]. 

In older literature, the Avogadro number was also denoted {{mvar|N}},<ref name=pauling/><ref name=mcgraw/> although that conflicts with the symbol for [[number of particles]] in [[statistical mechanics]].

== History ==

=== Origin of the concept ===
[[File:Jean Perrin 1926.jpg|right|thumb|Jean Perrin in 1926]]
The Avogadro constant is named after the Italian scientist [[Amedeo Avogadro]] (1776–1856), who, in 1811, first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of [[atom]]s or [[molecule]]s regardless of the nature of the gas.<ref name=avog1811/>

Avogadro's hypothesis was popularized four years after his death by [[Stanislao Cannizzaro]], who advocated Avogadro's work at the [[Karlsruhe Congress]] in 1860.<ref>{{Cite web |date=June 2016 |title=Stanislao Cannizzaro {{!}} Science History Institute |url=https://www.sciencehistory.org/historical-profile/stanislao-cannizzaro |access-date=June 2, 2022 |website=Science History Institute}}</ref>

The name ''Avogadro's number'' was coined in 1909 by the physicist [[Jean Baptiste Perrin|Jean Perrin]], who defined it as the number of molecules in exactly 32 grams of [[oxygen]] gas.<ref name="perrin1909" /> The goal of this definition was to make the mass of a mole of a substance, in grams, be numerically equal to the mass of one molecule relative to the mass of the hydrogen atom; which, because of the [[law of definite proportions]], was the natural unit of atomic mass, and was assumed to be {{sfrac|1|16}} of the atomic mass of oxygen.

=== First measurements ===
[[File:Johann Josef Loschmidt portrait plaque.jpg|right|thumb|Josef Loschmidt]]
The value of Avogadro's number (not yet known by that name) was first obtained indirectly by [[Johann Josef Loschmidt|Josef Loschmidt]] in 1865, by estimating the number of particles in a given volume of gas.<ref name=losch1865/> This value, the [[number density]] {{math|''n''{{sub|0}}}} of particles in an [[ideal gas]], is now called the [[Loschmidt constant]] in his honor, and is related to the Avogadro constant, {{math|''N''{{sub|A}}}}, by
: <math>n_0 = \frac{p_0N_{\rm A}}{R\,T_0},</math>
where {{math|''p''{{sub|0}}}} is the [[pressure]], {{math|''R''}} is the [[gas constant]], and {{math|''T''{{sub|0}}}} is the [[absolute temperature]]. Because of this work, the symbol {{math|''L''}} is sometimes used for the Avogadro constant,<ref name=bipm1971/> and, in [[German language|German]] literature, that name may be used for both constants, distinguished only by the [[units of measurement]].<ref name=virgo1933/> (However, {{math|''N''{{sub|A}}}} should not be confused with the entirely different [[Loschmidt constant]] in English-language literature.)

Perrin himself determined the Avogadro number, which he called "Avogadro's constant" (constante d'Avogadro), by several different experimental methods. He was awarded the 1926 [[Nobel Prize in Physics]], largely for this work.<ref name=oseen1926/>

The electric charge per [[Mole (unit)|mole]] of electrons is a constant called the [[Faraday constant]] and has been known since 1834, when [[Michael Faraday]] published [[Faraday's laws of electrolysis|his works on electrolysis]]. In 1910, [[Robert Millikan]] with the help of [[Harvey Fletcher]] obtained the first measurement of the [[elementary charge|charge on an electron]]. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.<ref name=ebrit1974/>

=== SI definition of 1971 ===
In 1971, in its 14th conference, the [[International Bureau of Weights and Measures]] (BIPM) decided to regard the [[amount of substance]] as an independent [[dimensional analysis|dimension of measurement]], with the mole as its [[SI unit|base unit]] in the [[International System of Units]] (SI).<ref name=bipm1971/> Specifically, the mole was defined as the amount of a substance that contains as many elementary entities as there are atoms in {{nowrap|12 grams}} ({{nowrap|0.012 [[kilogram]]s}}) of [[carbon-12]] (<sup>12</sup>C).<ref name=bipm8th/> Thus, in particular, an amount of one mole of carbon 12 had a corresponding mass that was ''exactly'' {{nowrap|12 grams}} of that element.  

By this definition, one mole of any substance contained exactly as many elementary entities as one mole of any other substance. However, this number {{math|''N''{{sub|0}}}} was a physical constant that had to be experimentally determined since it depended on the mass (in grams) of one atom of <sup>12</sup>C, and therefore, it was known only to a limited number of decimal digits.<ref name=bipm1971/> The common rule of thumb that "one gram of matter contains {{math|''N''{{sub|0}}}} nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes.

In the same conference, the BIPM also named {{math|''N''{{sub|A}}}} (the factor that related the amount of a substance to the corresponding number of particles) the "Avogadro ''constant''". However, the term "Avogadro number" continued to be used, especially in introductory works.<ref name=kotz2008/> As a consequence of this definition, {{math|''N''{{sub|A}}}} was not a pure number, but had the [[dimensional analysis|metric dimension]] of reciprocal of amount of substance (mol<sup>−1</sup>).

=== SI redefinition of 2019 ===
{{main|2019 revision of the SI}}
In its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro constant {{math|''N''{{sub|A}}}} as the exact value {{val|6.02214076|e=23|u=mol-1}}, thus redefining the mole as exactly {{val|6.02214076|e=23}} constituent particles of the substance under consideration.<ref name=cipm106/><ref name=NIST2019/> One consequence of this change is that the mass of a mole of <sup>12</sup>C atoms is no longer exactly 0.012&nbsp;kg. On the other hand, the dalton ({{aka}} universal atomic mass unit) remains unchanged as {{sfrac|1|12}} of the mass of <sup>12</sup>C.<ref name=pave2018/><ref name=IUPAC/> Thus, the [[molar mass constant]] remains very close to but no longer exactly equal to 1&nbsp;g/mol, although the difference ({{val|4.5|e=-10}} in relative terms, as of March 2019) is insignificant for all practical purposes.<ref name=NIST2019/><ref name=bipm9th/>

== Connection to other constants ==
The Avogadro constant {{math|''N''{{sub|A}}}} is related to other physical constants and properties.
* It relates the [[molar gas constant]] {{mvar|R}} and the [[Boltzmann constant]] {{math|''k''{{sub|B}}}}, which in the SI is defined to be exactly {{val|1.380649|e=−23|u=J/K}}:<ref name=NIST2019/>
*: {{math|1=''R'' = ''k''{{sub|B}} ''N''{{sub|A}} =}}&nbsp;{{physconst|R|ref=no}}
* It relates the [[Faraday constant]] {{mvar|F}} and the [[elementary charge]] {{mvar|e}}, which in the SI is defined as exactly {{val|1.602176634|e=−19|u=[[coulomb]]s}}:<ref name=NIST2019/>
*: {{math|1=''F'' = ''e N''{{sub|A}} =}}&nbsp;{{physconst|F|ref=no}}
* It relates the [[molar mass constant]] {{math|''M''{{sub|u}}}} and the [[atomic mass constant]] {{math|''m''{{sub|u}}}} currently {{physconst|mu|after=:}}
*: {{math|1=''M''{{sub|u}} = ''m''{{sub|u}} ''N''{{sub|A}} =}}&nbsp;{{physconst|Mu|ref=no}}

== See also ==
* [[CODATA 2018]]
* [[List of scientists whose names are used in physical constants]]
* [[Mole Day]]

== References ==
{{reflist|3| refs=

<ref name=NIST2019>David B. Newell and Eite Tiesinga (2019): [https://www.nist.gov/si-redefinition/meet-constants ''The International System of Units (SI)'']. NIST Special Publication 330, National Institute of Standards and Technology. {{doi|10.6028/nist.sp.330-2019}} {{s2cid|242934226}}</ref>

<ref name="perrin1909">{{cite journal|first = Jean|last = Perrin|author-link = Jean Baptiste Perrin|title = Mouvement brownien et réalité moléculaire |trans-title= Brownian movement and molecular reality |journal = [[Annales de Chimie et de Physique]] |series=8th series |volume = 18 |pages = 1–114 |year = 1909 |url = https://babel.hathitrust.org/cgi/pt?id=inu.30000091630800&seq=9 |language=fr }} [http://web.lemoyne.edu/~giunta/perrin.html Extract in English, translation by Frederick Soddy].</ref>

<ref name="losch1865">{{cite journal|first = J.|last = Loschmidt|author-link = Johann Josef Loschmidt|title = Zur Grösse der Luftmoleküle |trans-title = On the size of air molecules |journal = Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Classe. Wien |volume = 52|issue = 2|pages = 395–413 |year = 1865 |url = https://books.google.com/books?id=ppEAAAAAYAAJ&pg=PA395 | language = de}} [https://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation].</ref>

<ref name=bipm8th>{{SIbrochure8th|pages=114–115}}</ref>

<ref name=bipm9th>Bureau International des Poids et Mesures (2019): ''[https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf The International System of Units (SI)]'', 9th edition, English version, p. 134. Available at the [https://www.bipm.org/en/publications/si-brochure/ BIPM website].</ref>

<ref name=feynman>[https://www.feynmanlectures.caltech.edu/II_08.html#Ch8-S3-p4 Richard P. Feynman: ''The Feynman Lectures on Physics'', Volume II]</ref>

<ref name=mcgraw>Marvin Yelles (1971): ''McGraw-Hill Encyclopedia of Science and Technology'', Vol. 9, 3rd ed.; 707 pages. {{isbn|978-0070797987}}</ref>

<ref name=born>Max Born (1969): ''[https://books.google.com/books?id=zv3DAgAAQBAJ&pg=PA3 Atomic Physics]'', 8th ed., Dover ed., reprinted by Courier in 2013; 544 pages. {{isbn|978-0486318585}}</ref>

<ref name=bipm1971>Bureau International des Poids et Mesures (1971): ''[https://www.bipm.org/jsp/en/ListCGPMResolution.jsp?CGPM=14 14th Conference Générale des Poids et Mesures] {{Webarchive|url=https://web.archive.org/web/20200923114009/https://www.bipm.org/jsp/en/ListCGPMResolution.jsp?CGPM=14 |date=2020-09-23 }}'' Available at the [https://www.bipm.org/ BIPM website].</ref>

<ref name=iupac1996>H. P. Lehmann, X. Fuentes-Arderiu, and L. F. Bertello (1996): "Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)"; p. 963, item "[http://goldbook.iupac.org/terms/view/A00543 Avogadro constant]". ''Pure and Applied Chemistry'', vol. 68, iss. 4, pp. 957–1000. {{doi|10.1351/pac199668040957}}</ref>

<ref name=ciaaw>{{cite journal|title=Atomic Weight: The Name, Its History, Definition and Units|last1=de Bievre|first1=P.|last2=Peiser|first2=H. S.|journal=[[Pure and Applied Chemistry]]|year=1992|volume=64|issue=10|pages=1535–1543|doi=10.1351/pac199264101535|s2cid=96317287|doi-access=free}}</ref>

<ref name=okun>{{cite book|last = Okun|first = Lev B.|author2= Lee, A. G.|title = Particle Physics: The Quest for the Substance of Substance|url = https://books.google.com/books?id=UBidG9OKrQ8C|page= 86|year = 1985|publisher = OPA Ltd.|isbn = 978-3-7186-0228-5}}</ref>

<ref name=pauling>Linus Pauling (1970), ''[https://books.google.com/books?id=FjKlBQAAQBAJ&pg=PA96 General Chemistry]'', p. 96. Dover Edition, reprinted by Courier in 2014; 992 pages. {{isbn|978-0486134659}}</ref>

<ref name=avog1811>{{cite journal|first = Amedeo|last = Avogadro|author-link = Amedeo Avogadro|title = Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons|journal = Journal de Physique|year = 1811|volume = 73|pages = 58–76}} [http://web.lemoyne.edu/~giunta/avogadro.html English translation].</ref>

<ref name=oseen1926>[[Carl Wilhelm Oseen|Oseen, C.W.]] (December 10, 1926). ''[http://nobelprize.org/nobel_prizes/physics/laureates/1926/press.html Presentation Speech for the 1926 Nobel Prize in Physics]''.</ref>

<ref name=virgo1933>{{cite journal|last=Virgo |first=S.E. |url=http://gemini.tntech.edu/~tfurtsch/scihist/loschmid.html |title=Loschmidt's Number |journal=Science Progress |volume=27 |year=1933 |pages=634–649 |url-status=dead |archive-url=https://web.archive.org/web/20050404003919/http://gemini.tntech.edu/~tfurtsch/scihist/loschmid.html |archive-date=2005-04-04 }}</ref>

<ref name=ebrit1974>(1974): ''[https://physics.nist.gov/cuu/Constants/historical1.html Introduction to the constants for nonexperts, 1900–1920]'' From the ''Encyclopaedia Britannica'', 15th ed.; reproduced by [[NIST]]. Accessed on 2019-07-03.</ref>

<ref name=kotz2008>{{cite book|last = Kotz|first = John C.|author2 = Treichel, Paul M.|author3 = Townsend, John R.|title = Chemistry and Chemical Reactivity|edition = 7th|url = http://cengagesites.com/academic/kotz.cfm?site=2719&section=home|archive-url = https://web.archive.org/web/20081016082922/http://cengagesites.com/academic/kotz.cfm?site=2719&section=home|url-status = dead|archive-date = 2008-10-16|year = 2008|publisher = Brooks/Cole|isbn = 978-0-495-38703-9}}</ref>

<ref name=cipm106>International Bureau for Weights and Measures (2017): ''[https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf Proceedings of the 106th meeting of the International Committee for Weights and Measures (CIPM), 16-17 and 20 October 2017]'', p. 23. Available at the [https://www.bipm.org/en/committees/cipm/meeting/106.html BIPM website] {{Webarchive|url=https://web.archive.org/web/20210221105820/https://www.bipm.org/en/committees/cipm/meeting/106.html |date=2021-02-21 }}.</ref>

<ref name=pave2018>{{Cite journal|last=Pavese|first=Franco|date=January 2018|title=A possible draft of the CGPM Resolution for the revised SI, compared with the CCU last draft of the 9th SI Brochure|journal=Measurement|volume=114|pages=478–483|doi=10.1016/j.measurement.2017.08.020|bibcode=2018Meas..114..478P|issn=0263-2241}}</ref>

<ref name=IUPAC>{{cite book |doi=10.1351/goldbook.U06554 |doi-access=free |chapter=Unified atomic mass unit |title=The IUPAC Compendium of Chemical Terminology |year=2014 }}</ref>

<!-- <ref name=mosh2023>Michael Mosher, Paul Kelter (2023): ''An Introduction to Chemistry'', 2nd edition. Springer Nature. {{isbn|9783030902674}}, 1067 pages</ref> -->

}}

== External links ==
* [https://goldbook.iupac.org/terms/view/A00543 1996 definition of the Avogadro constant] from the [[IUPAC]] ''[[Compendium of Chemical Terminology]]'' ("''Gold Book''")
* [https://web.archive.org/web/20140428004944/http://iweb.tntech.edu/tfurtsch/scihist//avogadro.htm Some Notes on Avogadro's Number, {{val|6.022|e=23}}] ''(historical notes)''
* [https://www.americanscientist.org/article/an-exact-value-for-avogadros-number An Exact Value for Avogadro's Number] – ''[[American Scientist]]''
* [https://web.archive.org/web/20110717124427/http://www.inrim.it/Nah/Web_Nah/home.htm Avogadro and molar Planck constants for the redefinition of the kilogram]
* {{cite journal |doi=10.1002/1522-2675(20010613)84:6<1314::AID-HLCA1314>3.0.CO;2-Q|title=Avogadro and His Constant|year=2001|last1=Murrell|first1=John N.|journal=Helvetica Chimica Acta|volume=84|issue=6|pages=1314–1327}}
* Scanned version of "Two hypothesis of Avogadro", 1811 Avogadro's article, on ''[https://translate.google.com/translate?&us=auto&tl=en&u=https%3A%2F%2Fwww.bibnum.education.fr%2Fchimie%2Ftheorie-chimique%2Fles-deux-hypotheses-d-avogadro-en-1811 BibNum]''

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[[Category:Amount of substance]]
[[Category:Fundamental constants]]
[[Category:Physical constants]]
[[Category:Units of amount]]