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| [[File:Avogadro Amedeo.jpg|right|180px|thumb|[[Amedeo Avogadro]]]]
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| In [[chemistry]] and [[physics]], the '''Avogadro constant''' (symbols: '''''L''''', '''''N''<sub>A</sub>''') is defined as the number of [[Particle number|constituent particle]]s (usually [[atom]]s or [[molecule]]s) per [[mole (unit)|mole]] of a given substance, where the mole is one of the seven [[base units]] in the [[International System of Units]] (SI). The Avogadro constant has dimensions of reciprocal mol and its value is equal to {{val|fmt=commas|6.02214129|(27)|e=23|u=mol<sup>−1</sup>}}.<ref name=CODATA>
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| {{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?na}}</ref><ref>
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| {{cite journal
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| |title=Atomic Weight: The Name, Its History, Definition and Units
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| |last=[[International Union of Pure and Applied Chemistry]] Commission on Atomic Weights and Isotopic Abundances
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| |journal=[[Pure and Applied Chemistry]]
| |
| |year=1992
| |
| |volume=64
| |
| |issue=10
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| |pages=1535–43
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| |doi=10.1351/pac199264101535
| |
| |first1=P.
| |
| |last2=Peiser
| |
| |first2=H. S.
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| }}</ref><ref>{{cite journal
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| |title=Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)
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| |volume=68
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| |issue=4
| |
| |pages=957–1000
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| |year=1996
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| |last=[[International Union of Pure and Applied Chemistry]] Commission on Quantities and Units in Clinical Chemistry|coauthors=International Federation of Clinical Chemistry Committee on Quantities and Units
| |
| |doi=10.1351/pac199668040957
| |
| |first1=H. P.
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| }}</ref>
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| Previous definitions of chemical quantity involved '''Avogadro's number''', a historical term closely related to the Avogadro constant but defined differently: Avogadro's number was initially defined by [[Jean Baptiste Perrin]] as the number of atoms in one [[gram-molecule]] of [[hydrogen]]. It was later redefined as the number of atoms in 12 [[gram]]s of the isotope [[carbon-12]] and still later generalized to relate amounts of a substance to their molecular weight.<ref name="SI">{{SIbrochure8th|pages=114–15}}</ref> For instance, to a first approximation, 1 gram of hydrogen, which has a mass number of 1 (atomic number 1), has {{val|6.022|e=23|}} hydrogen atoms. Similarly, 12 grams of carbon 12, with the mass number of 12 (atomic number 6), has the same number of carbon atoms, {{val|6.022|e=23|}}. Avogadro's number is a dimensionless quantity and has the numerical value of the Avogadro constant given in base units.
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| The Avogadro constant is fundamental to understanding both the makeup of molecules and their interactions and combinations. For instance, since one atom of oxygen will combine with two atoms of hydrogen to create one molecule of water (H<sub>2</sub>O), one can similarly see that one mol of oxygen ({{val|6.022|e=23|}} of O atoms) will combine with two mol of hydrogen (2 × {{val|6.022|e=23|}} of H atoms) to make one mol of H<sub>2</sub>O.
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| Revisions in the base set of SI units necessitated redefinitions of the concepts of chemical quantity and so Avogadro's number, and its definition, was deprecated in favor of the Avogadro constant and its definition. Changes in the SI units are proposed that will precisely fix the value of the constant to exactly {{gaps|6.022|14X|×|10<sup>23</sup>}} when it is expressed in the unit mol<sup>−1</sup> (see [[New SI definitions]], in which an "X" at the end of a number means one or more final digits yet to be agreed upon).
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| {| class="wikitable" style="float: right; margin: 0 0 0 0.5em;"
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| ! Value of ''N''<sub>A</sub><ref>[http://physics.nist.gov/cgi-bin/cuu/Value?na Avogadro constant]. 2010 CODATA recommended values. NIST</ref> in various units
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| | {{val|fmt=commas|6.02214129|(27)|e=23}} mol<sup>−1</sup>
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| | {{val|fmt=commas|2.73159734|(12)|e=26}} (lb-mol)<sup>−1</sup>
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| | {{val|fmt=commas|1.707248434|(77)|e=25}} (oz-mol)<sup>−1</sup>
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| |-
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| |}
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| ==History==
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| The Avogadro constant is named after the early 19th century Italian scientist [[Amedeo Avogadro]], 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>{{cite journal|first = Amedeo|last = Avogadro|authorlink = 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> The French physicist [[Jean Baptiste Perrin|Jean Perrin]] in 1909 proposed naming the constant in honor of Avogadro.<ref name="Perrin">{{cite journal|first = Jean|last = Perrin|authorlink = Jean Baptiste Perrin|title = Mouvement brownien et réalité moléculaire|journal = [[Annales de Chimie et de Physique]] |series=8<sup>e</sup> Série|volume = 18|pages = 1–114|year = 1909|postscript = .}} [http://web.lemoyne.edu/~giunta/perrin.html Extract in English, translation by Frederick Soddy].</ref> Perrin won the 1926 [[Nobel Prize in Physics]], largely for his work in determining the Avogadro constant by several different methods.<ref>[[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>
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| The value of the Avogadro constant was first indicated by [[Johann Josef Loschmidt]] who in 1865 estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas.<ref>{{cite journal|first = J.|last = Loschmidt|authorlink = Johann Josef Loschmidt|title = Zur Grösse der Luftmoleküle|journal = Sitzungsberichte der kaiserlichen Akademie der Wissenschaften Wien|volume = 52|issue = 2|pages = 395–413|year =1865}} [http://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation].</ref> This latter value, the [[number density]] <math>n_0</math> of particles in an [[ideal gas]], is now called the [[Loschmidt constant]] in his honor, and is related to the Avogadro constant, ''N''<sub>A</sub>, by
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| :<math>n_0 = \frac{p_0N_{\rm A}}{RT_0}</math>
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| where ''p''<sub>0</sub> is the [[pressure]], ''R'' is the [[gas constant]] and ''T''<sub>0</sub> is the [[absolute temperature]]. The connection with Loschmidt is the root of the symbol ''L'' sometimes used for the Avogadro constant, and [[German language]] literature may refer to both constants by the same name, distinguished only by the [[units of measurement]].<ref>{{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 = 634–49}}</ref>
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| Accurate determinations of Avogadro's number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist [[Robert Millikan]] measured the [[elementary charge|charge on an electron]] in 1910. The electric charge per [[Mole (unit)|mole]] of electrons is a constant called the [[Faraday constant]] and had been known since 1834 when [[Michael Faraday]] published [[Faraday's laws of electrolysis|his works on electrolysis]]. By dividing the charge on a mole of electrons by the charge on a single electron the value of Avogadro's number is obtained.<ref>[http://physics.nist.gov/cuu/Constants/historical1.html NIST Introduction to physical constants]</ref> Since 1910, newer calculations have more accurately determined the values for the Faraday constant and the elementary charge. (''[[Avogadro constant#Measurement|See below]]'')
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| [[Jean Baptiste Perrin|Perrin]] originally proposed the name Avogadro's number (''N'') to refer to the number of molecules in one [[gram-molecule]] of [[oxygen]] (exactly {{gaps|32|g}} of oxygen, according to the definitions of the period),<ref name="Perrin" /> and this term is still widely used, especially in introductory works.<ref name="Kotz">{{cite book|last = Kotz|first = John C.|coauthors = Treichel, Paul M.; Townsend, John R.|title = Chemistry and Chemical Reactivity|edition = 7th|url = http://cengagesites.com/academic/kotz.cfm?site=2719§ion=home|year = 2008|publisher = Brooks/Cole|isbn = 0-495-38703-7}}</ref> The change in name to ''Avogadro constant'' (''N''<sub>A</sub>) came with the introduction of the mole as a [[SI base unit|base unit]] in the [[International System of Units]] (SI) in 1971,<ref>Resolution 3, 14th [[General Conference of Weights and Measures]] (CGPM), 1971.</ref> which recognized [[amount of substance]] as an independent [[Dimensional analysis|dimension of measurement]].<ref name="IUPAChist">{{cite journal|first = P.|last = de Bièvre|coauthors = Peiser, H.S.|year = 1992|title = 'Atomic Weight'—The Name, Its History, Definition, and Units|journal = [[Pure and Applied Chemistry]]|volume = 64|issue = 10|pages = 1535–43|doi = 10.1351/pac199264101535}}</ref> With this recognition, the Avogadro constant was no longer a pure number, but had a [[unit of measurement]], the reciprocal mole (mol<sup>−1</sup>).<ref name="IUPAChist" />
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| While it is rare to use units of amount of substance other than the mole, the Avogadro constant can also be expressed in units such as the [[pound mole]] (lb-mol) and the [[ounce mole]] (oz-mol).
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| :''N''{{sub|A}} = {{val|fmt=commas|2.73159757|(14)|e=26|u=(lb-mol)<sup>−1</sup>}} = {{val|fmt=commas|1.707248479|(85)|e=25|u=(oz-mol)<sup>−1</sup>}}
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| ==General role in science==
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| Avogadro's constant is a scaling factor between macroscopic and microscopic ([[atomic unit|atomic scale]]) observations of nature. As such, it provides the relation between other physical constants and properties. For example, it establishes a relationship between the [[gas constant]] ''R'' and the [[Boltzmann constant]] ''k''<sub>B</sub>,
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| :<math>R = k_{\rm B} N_{\rm A} = 8.314\,472(15)\ {\rm J\,mol^{-1}\,K^{-1}}\,</math>
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| and the [[Faraday constant]] ''F'' and the [[elementary charge]] ''e'',
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| :<math>F = N_{\rm A} e = 96\,485.3383(83)\ {\rm C\,mol^{-1}}. \,</math>
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| The Avogadro constant also enters into the definition of the [[unified atomic mass unit]], u, | |
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| :<math>1\ {\rm u} = \frac{M_{\rm u}}{N_{\rm A}} = 1.660 \, 538\, 782(83)\times 10^{-24}\ {\rm g}</math>{{Dubious|date=January 2014}}
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| where ''M''<sub>u</sub> is the [[molar mass constant]].
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| ==Measurement==
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| ===Coulometry===
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| The earliest accurate method to measure the value of the Avogadro constant was based on [[coulometry]]. The principle is to measure the [[Faraday constant]], ''F'', which is the [[electric charge]] carried by one mole of electrons, and to divide by the [[elementary charge]], ''e'', to obtain the Avogadro constant.
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| :<math>N_{\rm A} = \frac{F}{e}</math>
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| The classic experiment is that of Bowers and Davis at [[NIST]],<ref>This account is based on the review in {{CODATA1998}}</ref> and relies on dissolving [[silver]] metal away from the [[anode]] of an [[electrolysis]] cell, while passing a constant [[electric current]] ''I'' for a known time ''t''. If ''m'' is the mass of silver lost from the anode and ''A''{{sub|r}} the atomic weight of silver, then the Faraday constant is given by:
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| :<math>F = \frac{A_{\rm r}M_{\rm u}It}{m}.</math>
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| The NIST scientists devised a method to compensate for silver lost from the anode by mechanical causes, and conducted an [[isotope analysis]] of the silver used to determine its atomic weight. Their value for the conventional Faraday constant is ''F''{{sub|90}} = {{val|fmt=commas|96485.39|(13)|u=C/mol}}, which corresponds to a value for the Avogadro constant of {{val|fmt=commas|6.0221449|(78)|e=23|u=mol<sup>−1</sup>}}: both values have a relative standard uncertainty of {{val|1.3|e=-6}}.
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| ===Electron mass measurement===
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| The Committee on Data for Science and Technology ([[CODATA]]) publishes values for physical constants for international use. It determines the Avogadro constant<ref name="CODATA2002">{{CODATA2002}}</ref> from the ratio of the molar mass of the [[electron]] ''A''{{sub|r}}(''e'')''M''{{sub|u}} to the rest mass of the electron ''m''{{sub|e}}:
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| :<math>N_{\rm A} = \frac{A_{\rm r}({\rm e})M_{\rm u}}{m_{\rm e}}.</math>
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| The relative atomic mass of the electron, ''A''{{sub|r}}(''e''), is a directly-measured quantity, and the [[molar mass constant]], ''M''{{sub|u}}, is a defined constant in the SI. The electron rest mass, however, is calculated from other measured constants:<ref name="CODATA2002" />
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| :<math>m_{\rm e} = \frac{2R_{\infty}h}{c\alpha^2}.</math>
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| As may be observed in the table of 2006 CODATA values below,<ref name="CODATA2006">{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?na |page=94}}</ref> the main limiting factor in the precision of the Avogadro constant is the uncertainty in the value of the [[Planck constant]], as all the other constants that contribute to the calculation are known more precisely.
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| {| class="wikitable"
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| |-
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| ! Constant
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| ! Symbol
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| ! 2006 CODATA value
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| ! Relative standard uncertainty
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| ! Correlation coefficient<br />with ''N''{{sub|A}}
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| |-
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| | Electron relative atomic mass
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| | align="center"|''A''{{sub|r}}(''e'')
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| | 5.485 799 0943(23){{e|–4}}
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| | align="center"|4.2{{e|–10}}
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| | 0.0082
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| |-
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| | [[Molar mass constant]]
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| | align="center"|''M''{{sub|u}}
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| | 0.001 kg/mol
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| | align="center"|defined
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| | —
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| |-
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| | [[Rydberg constant]]
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| | align="center"|''R''{{sub|∞}}
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| | 10 973 731.568 527(73) m<sup>−1</sup>
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| | align="center"|6.6{{e|–12}}
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| | 0.0000
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| |-
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| | [[Planck constant]]
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| | align="center"|''h''
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| | 6.626 068 96(33){{e|–34}} Js
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| | align="center"|5.0{{e|–8}}
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| | −0.9996
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| |-
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| | [[Speed of light]]
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| | align="center"|''c''
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| | 299 792 458 m/s
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| | align="center"|defined
| |
| | —
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| |-
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| | [[Fine structure constant]]
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| | align="center"|''α''
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| | 7.297 352 5376(50){{e|–3}}
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| | align="center"|6.8{{e|–10}}
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| | 0.0269
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| |-
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| | '''Avogadro constant'''
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| | align="center"|''N''{{sub|A}}
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| | 6.022 141 79(30){{e|23}} mol<sup>−1</sup>
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| | align="center"|5.0{{e|–8}}
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| | 1
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| |-
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| |}
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| ===X-ray crystal density (XRCD) methods===
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| [[Image:Silicon-unit-cell-labelled-3D-balls.png|thumb|right|200px|[[Ball-and-stick model]] of the [[unit cell]] of [[silicon]]. X-ray diffraction measures the cell parameter, ''a'', which is used to calculate a value for Avogadro's constant.]]
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| A modern method to determine the Avogadro constant is the use of [[X-ray crystallography]]. [[Silicon]] single crystals may be produced today in commercial facilities with extremely high purity and with few lattice defects. This method defines the Avogadro constant as the ratio of the [[molar volume]], ''V''{{sub|m}}, to the atomic volume ''V''<sub>atom</sub>:<br />
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| :<math>N_{\rm A} = \frac{V_{\rm m}}{V_{\rm atom}}</math>, where <math>V_{\rm atom} = \frac{V_{\rm cell}}{n}</math> and ''n'' is the number of atoms per unit cell of volume ''V''<sub>cell</sub>.
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| The unit cell of silicon has a cubic packing arrangement of 8 atoms, and the unit cell volume may be measured by determining a single unit cell parameter, the length of one of the sides of the cube, ''a''.<ref>{{cite web
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| |url=http://webmineral.com/help/CellDimensions.shtml
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| |accessdate=2007-12-09
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| |title=Unit Cell Formula
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| |last=Mineralogy Database
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| |date=2000-2005
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| }}</ref>
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| In practice, measurements are carried out on a distance known as ''d''{{sub|220}}(Si), which is the distance between the planes denoted by the [[Miller index|Miller indices]] {220}, and is equal to ''a''/√8. The 2006 CODATA value for ''d''{{sub|220}}(Si) is {{val|fmt=commas|192.0155762|(50)|u=pm}}, a relative uncertainty of {{val|fmt=commas|2.8|e=-8}}, corresponding to a unit cell volume of {{val|fmt=commas|1.60193304|(13)|e=-28|u=m<sup>3</sup>}}.
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| The [[isotope]] proportional composition of the sample used must be measured and taken into account. Silicon occurs in three stable isotopes (<sup>28</sup>Si, <sup>29</sup>Si, <sup>30</sup>Si), and the natural variation in their proportions is greater than other uncertainties in the measurements. The [[atomic weight]] ''A''{{sub|r}} for the sample crystal can be calculated, as the [[relative atomic mass]]es of the three [[nuclide]]s are known with great accuracy. This, together with the measured [[density]] ''ρ'' of the sample, allows the molar volume ''V''{{sub|m}} to be determined:
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| :<math>V_{\rm m} = \frac{A_{\rm r}M_{\rm u}}{\rho}</math>
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| where ''M''{{sub|u}} is the molar mass constant. The 2006 CODATA value for the molar volume of silicon is 12.058 8349(11) cm<sup>3</sup>mol<sup>−1</sup>, with a relative standard uncertainty of {{val|9.1|e=-8}}.<ref>{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?mvolsil|search_for=molar+volume+of+silicon}}</ref>
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| As of the 2006 CODATA recommended values, the relative uncertainty in determinations of the Avogadro constant by the X-ray crystal density method is {{val|1.2|e=-7}}, about two and a half times higher than that of the electron mass method.
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| ====International Avogadro Coordination====
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| [[File:Silicon sphere for Avogadro project.jpg|thumb|right|One of the master opticians at the [http://www.acpo.csiro.au/ Australian Centre for Precision Optics] (ACPO) holding a one-kilogram single-crystal silicon sphere for the International Avogadro Coordination.]]
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| The International Avogadro Coordination (IAC), often simply called the "[[Avogadro project]]", is a collaboration begun in the early 1990s between various national metrology institutes to measure the Avogadro constant by the X-ray crystal density method to a relative uncertainty of 2{{e|−8}} or less.<ref>{{cite web| title = Avogadro Project | url = http://www.npl.co.uk/engineering-measurements/mass-force-pressure/mass/research/avogadro-project | publisher = National Physical Laboratory | accessdate = 2010-08-19}}</ref> The project is part of the efforts to redefine the [[kilogram]] in terms of a universal [[physical constant]], rather than the [[International Prototype Kilogram]], and complements the measurements of the [[Planck constant]] using [[watt balance]]s.<ref name="Leonard">{{cite journal| first = B. P. | last = Leonard | title = On the role of the Avogadro constant in redefining SI units for mass and amount of substance | journal = Metrologia | volume = 44 | issue = 1 | pages = 82–86 | year = 2007 | doi = 10.1088/0026-1394/44/1/012|bibcode = 2007Metro..44...82L }}</ref><ref name="Jabbour">{{cite journal| first = Zeina J. | last = Jabbour | title = Getting Closer to Redefining The Kilogram | url = http://www.nist.gov/customcf/get_pdf.cfm?pub_id=903635 | journal = Weighing & Measurement Magazine | year = 2009 | issue = October | pages = 24–26}}</ref> Under the current definitions of the [[International System of Units]] (SI), a measurement of the Avogadro constant is an indirect measurement of the Planck constant: | |
| :<math>h = \frac{c\alpha^2 A_{\rm r}({\rm e})M_{\rm u}}{2R_{\infty} N_{\rm A}}.</math>
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| The measurements use highly polished spheres of silicon with a mass of one kilogram. Spheres are used to simplify the measurement of the size (and hence the density) and to minimize the effect of the oxide coating that inevitably forms on the surface. The first measurements used spheres of silicon with natural isotopic composition, and had a relative uncertainty of 3.1{{e|−7}}.<ref>{{cite journal| first = Peter | last = Becker | year = 2003 | title = Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal | journal = Metrologia | volume = 40 | issue = 6 | pages = 366–75 | doi = 10.1088/0026-1394/40/6/008|bibcode = 2003Metro..40..366B }}</ref><ref>{{cite journal| author=Fujii, K. ''et al.'' |title = Present State of the Avogadro Constant Determination From Silicon Crystals With Natural Isotopic Compositions | journal = IEEE Trans. Instrum. Meas. | volume = 54 | issue = 2 | pages = 854–59 | year = 2005 | doi = 10.1109/TIM.2004.843101}}</ref><ref>{{cite journal| last = Williams | first = E. R. | year = 2007 | title = Toward the SI System Based on Fundamental Constants: Weighing the Electron | journal = IEEE Trans. Instrum. Meas. | volume = 56 | issue = 2 | pages = 646–50 | doi = 10.1109/TIM.2007.890591}}</ref> These first results were also inconsistent with values of the Planck constant derived from watt balance measurements, although the source of the discrepancy is now believed to be known.<ref name="Jabbour"/>
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| The main residual uncertainty in the early measurements was in the measurement of the isotopic composition of the silicon to calculate the atomic weight so, in 2007, a 4.8-kg single crystal of isotopically-enriched silicon (99.94% <sup>28</sup>Si) was grown,<ref>{{cite journal| author=Becker, P. ''et al.''| title = Large-scale production of highly enriched 28Si for the precise determination of the Avogadro constant | journal = Meas. Sci. Technol. | volume = 17 | issue = 7 | pages = 1854–60 | year = 2006 | doi =10.1088/0957-0233/17/7/025|bibcode = 2006MeScT..17.1854B }}</ref><ref>{{cite journal | author= Devyatykh, G. G. ''et al.''| journal = Dokl. Akad. Nauk | volume = 421 | issue = 1 | pages = 61–64 | year = 2008}}; {{cite journal | author = Devyatykh, G. ''et al.'' | title = High-Purity Single-Crystal Monoisotopic Silicon-28 for Precise Determination of Avogadro's Number | journal = Dokl. Chem. | year = 2008 | volume = 421 | issue = 1 | pages = 157–60 | doi =10.1134/S001250080807001X}}</ref> and two one-kilogram spheres cut from it. Diameter measurements on the spheres are repeatable to within 0.3 nm, and the uncertainty in the mass is 3 µg. Full results from these determinations were expected in late 2010.<ref>{{cite web | title = Report of the 11th meeting of the Consultative Committee for Mass and Related Quantities (CCM) | url = http://www.bipm.org/utils/common/pdf/CCM11.pdf | publisher = International Bureau of Weights and Measures | year = 2008 | page = 17}}</ref>
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| Their paper, published in January 2011, summarized the result of the International Avogadro Coordination and presented a measurement of the Avogadro constant to be {{val|fmt=commas|6.02214078|(18)|e=23}} mol<sup>−1</sup>.<ref>{{cite journal| author= Andreas, B. ''et al.''| title = An accurate determination of the Avogadro constant by counting the atoms in a <sup>28</sup>Si crystal | journal = Phys. Rev. Lett. | volume = 106 | issue = 3 | page = 030801 (4 pages) | year = 2011 | doi = 10.1103/PhysRevLett.106.030801 | bibcode=2011PhRvL.106c0801A|arxiv = 1010.2317 }}</ref>
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| ==See also==
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| * [[Mole Day]]
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| ==References==
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| {{reflist|2}}
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| ==External links==
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| * [http://www.iupac.org/goldbook/A00543.pdf 1996 definition of the Avogadro constant] from the [[IUPAC]] ''[[Compendium of Chemical Terminology]]'' ("''Gold Book''")
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| * [http://gemini.tntech.edu/~tfurtsch/scihist/avogadro.htm Some Notes on Avogadro's Number, 6.022{{e|23}}] ''(historical notes)''
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| * [http://www.americanscientist.org/issues/pub/2007/2/an-exact-value-for-avogadros-number An Exact Value for Avogadro's Number] – [[American Scientist]]
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| * [http://www.inrim.it/Nah/Web_Nah/home.htm Avogadro and molar Planck constants for the redefinition of the kilogram]
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| * {{cite web|last=Poliakoff|first=Martyn|title=Avogadro's Number – N<sub>A</sub> = 6.02214 x 10<sup>23</sup>|url=http://www.numberphile.com/videos/mole.html|work=Numberphile|publisher=[[Brady Haran]]|authorlink=Martyn Poliakoff}}
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| * [http://onlinelibrary.wiley.com/doi/10.1002/1522-2675%2820010613%2984:6%3C1314::AID-HLCA1314%3E3.0.CO;2-Q/abstract;jsessionid=2BF5A65667EEDDCD40A985289CFDDC0B.f01t01?deniedAccessCustomisedMessage=&userIsAuthenticated=false Murrell, J. 2001 ''Avogadro and his Constant'', Helvitica Chemica Acta, '''84''', 6, p.1314-1327]
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| {{DEFAULTSORT:Avogadro Constant}}
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| [[Category:Amount of substance]]
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| [[Category:Physical constants]]
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| {{Link GA|zh}}
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