Lihat sumber Bilangan Avogadro

[[Berkas:Avogadro Amedeo.jpg|ka|180px|jmpl|[[Amedeo Avogadro]]]]
'''Bilangan Avogadro''' (lambang: ''L'', atau ''N''<sub>A</sub>), juga dinamakan sebagai '''tetapan Avogadro''' atau '''konstanta Avogadro''', adalah banyaknya "entitas" (biasanya [[atom]] atau [[molekul]]) dalam satu [[mol]]<ref>{{cite book|last=[[International Union of Pure and Applied Chemistry]] Commission on Physiochemical Symbols Terminology and Units|title=Quantities, Units and Symbols in Physical Chemistry (2nd Edition)|publisher=Blackwell Scientific Publications|location=Oxford|date=1993
|url=http://www.iupac.org/publications/books/gbook/green_book_2ed.pdf|id=ISBN 0-632-03583-8|accessdate=2006-12-28}} {{cite journal|title=Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)| |url=http://www.iupac.org/publications/pac/1996/pdf/6804x0957.pdf|journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]]|volume=68|pages=957–1000|year=1996|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|accessdate=2006-12-28}}</ref><ref>{{cite journal|url=http://www.iupac.org/publications/pac/1992/pdf/6410x1535.pdf|title=Atomic Weight: The Name, Its History, Definition and Units|last=[[International Union of Pure and Applied Chemistry]] Commission on Atomic Weights and Isotopic Abundances|journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]]|year=1992|volume=64|pages=1535–43|accessdate=2006-12-28}}</ref>, yang merupakan jumlah [[atom]] karbon-12 dalam 12 [[gram]] (0,012 [[kilogram]]) karbon-12 dalam keadaan dasarnya. Perkiraan terbaik terakhir untuk angka ini adalah:<ref>[[CODATA]] [http://physics.nist.gov/cgi-bin/cuu/Value?na|search_for=abbr_in! (2006)].</ref>

:<math>N_A = (6.022 \, 141 \, 79\pm 0.000 \, 000 \, 30)\,\times\,10^{23} \mbox{ mol}^{-1} \,</math>

Nilai ini kebetulan sangat dekat (hanya berbeda 0.37% lebih kecil) dengan 2<sup>79</sup> mol<sup>−1</sup>, sehingga angka ini berguna sebagai perkiraan pada fisika nuklir pada waktu menghitung laju pertumbuhan reaksi berantai.

{|  class="wikitable" style="float: right; margin: 0 0 0 0.5em;"
! Nilai ''N''<sub>A</sub><ref>[http://physics.nist.gov/cgi-bin/cuu/Value?na konstanta Avogadro]. Nilai yang direkomendasi oleh 2010 CODATA. NIST</ref> dalam berbagai satuan
|-
| {{val|fmt=commas|6.02214129|(27)|e=23}} mol<sup>−1</sup>
|-
| {{val|fmt=commas|2.73159734|(12)|e=26}} (lb-mol)<sup>−1</sup>
|-
| {{val|fmt=commas|1.707248434|(77)|e=25}} (oz-mol)<sup>−1</sup>
|-
|}

== Sejarah ==
Konstanta Avogadro dinamakan menurut seorang ilmuwan Italia dari awal abad ke-19, [[Amedeo Avogadro]], yang pada tahun 1811 pertama kalinya mengemukakan bahwa volume suatu gas (pada tekanan dan suhu tertentu) berbanding lurus dengan jumlah [[atom]] atau [[molekul]] tanpa tergantung dari jenis 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> Fisikawan Prancis, [[Jean Baptiste Perrin|Jean Perrin]], pada tahun 1909 mengusulkan penamaan konstanta ini untuk menghormati 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 mendapat penghargaan [[Nobel Prize in Physics]] tahun 1926, terutama karena karyanya dalam menentukan bilangan Avogadro dengan beberapa metode.<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>

Nilai bilangan Avogadro ini pertama kali diperkirakan oleh [[:en:Johann Josef Loschmidt|Johann Josef Loschmidt]], yang pada 1865 menghitung diameter rata-rata molekul di udara dengan metode yang sama dengan menghitung jumlah partikel di dalam volume gas tertentu dalam keadaan standar.<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> Nilai ini, [[:en:number density|densitas jumlah]] <math>n_0</math> partikel dalam suatu [[gas ideal]], sekarang disebut [[:en:Loschmidt constant|Tetapan atau Konstanta Loschmidt]] untuk menghormatinya, dan terkait dengan bilangan Avogadro, ''N''<sub>A</sub>, melalui persamaan:
:<math>n_0 = \frac{p_0N_{\rm A}}{RT_0}</math>
di mana ''p''<sub>0</sub> adalah [[tekanan]], ''R'' adalah [[:en:gas constant|konstanta gas]] dan ''T''<sub>0</sub> adalah [[:en:absolute temperature|suhu mutlak]]. Hubungan dengan Loschmidt adalah akar dari lambang ''L'' yang kadang digunakan untuk bilangan Avogadro constant, dan kepustakaan [[bahasa Jerman]] dapat merujuk kedua konstanta ini dengan nama yang sama, dibedakan hanya dari satuan ukurannya.<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>

== Peranan umum dalam sains ==
Bilangan Avogadro merupakan faktor skala antara pengamatan makroskopik dan mikroskopik ([[:en:atomic unit|skala atom]]) dari alam, yaitu mengkaitkan sejumlah konstanta fisika dengan sifat-sifat. Misalnya, konstanta ini memberikan hubungan antara [[konstanta gas]] ''R'' dan [[konstanta Boltzmann]] ''k''<sub>B</sub>,

:<math>R = k_{\rm B} N_{\rm A} = 8.314\,472(15)\ {\rm J\,mol^{-1}\,K^{-1}}\,</math>

dan [[konstanta Faraday]] ''F'' dan [[:en:elementary charge|muatan elementer]] ''e'',

:<math>F = N_{\rm A} e = 96\,485.3383(83)\ {\rm C\,mol^{-1}}. \,</math>

Bilangan Avogadro juga masuk ke dalam definisi [[:en:unified atomic mass unit|satuan massa atom bersatu]], u,

:<math>1\ {\rm u} = \frac{M_{\rm u}}{N_{\rm A}}  = 1.660 \, 538\, 921(73)\times 10^{-24}\ {\rm g}</math>
di mana ''M''<sub>u</sub> merupakan [[:en:molar mass constant|konstanta massa molar]].

== Pengukuran ==

=== Coulometry ===
Metode akurat paling awal untuk mengukur bilangan Avogadro didasarkan pada metode [[:en:coulometry|''coulometry'']]. Prinsipnya adalah pengukuran [[konstanta Faraday]], ''F'', yaitu [[muatan listrik]] yang dibawa oleh satu mol elektron, dan dibagi dengan [[:en:elementary charge|muatan elementer]], ''e'', untuk mendapatkan bilangan Avogadro.
:<math>N_{\rm A} = \frac{F}{e}</math>
Eksperimen yang klasik dilakukan oleh Bower dan Davis pada [[NIST]],<ref>Kisah ini didasarkan pada tinjauan dalam {{CODATA1998}}</ref> dan berpatokan pada pelarutan logam [[perak]] dari [[anoda]] suatu sel [[elektrolisis]], ketika dilewati oleh suatu [[aliran listrik]] konstan ''I'' selama waktu ''t'' yang diketahui. Jika ''m'' adalah massa perak yang hilang dari anode dan ''A''{{sub|r}} adalah berat atom perak, maka konstanta Faraday dapat dihitung melalui:
:<math>F = \frac{A_{\rm r}M_{\rm u}It}{m}.</math>
Ilmuwan-ilmuwan NIST merancang suatu metode untuk mengkompensasi perak yang hilang dari anode karena sebab mekanik, dan menjalankan sebuah [[:en:isotope analysis|analisis isotop]] perak yang digunakan untuk menentukan berat atomnya. Nilai yang mereka dapatkan untuk konstanta Faraday konvensional adalah ''F''{{sub|90}}&nbsp;= {{val|fmt=commas|96485.39|(13)|u=C/mol}}, yang bersesuaian dengan nilai bilangan Avogadro {{val|fmt=commas|6.0221449|(78)|e=23|u=mol<sup>−1</sup>}}: kedua nilai ini mempunyai ketidakpastian standar relatif sebesar {{val|1.3|e=-6}}.

=== Pengukuran massa elektron ===
'''Committee on Data for Science and Technology''' ([[CODATA]]) menerbitkan nilai-nilai konstanta fisika untuk penggunaan internasional. Bilangan Avogadro ditentukan<ref name="CODATA2002">{{CODATA2002}}</ref> dari rasio massa molar suatu [[elektron]] ''A''{{sub|r}}(''e'')''M''{{sub|u}} dengan massa diam elektron ''m''{{sub|e}}:
:<math>N_{\rm A} = \frac{A_{\rm r}({\rm e})M_{\rm u}}{m_{\rm e}}.</math>
Massa atom relatif dari elektron, ''A''{{sub|r}}(''e''), merupakan kuantitas yang langsung terukur, dan [[konstanta massa molar]], ''M''{{sub|u}}, merupkana konstanta yang didefinisikan dalam [[SI]]. Namun, massa diam elektron dihitung dari konstanta-kontanta lain yang terukur:<ref name="CODATA2002" />
:<math>m_{\rm e} = \frac{2R_{\infty}h}{c\alpha^2}.</math>
Sebagaimana dapat dilihat pada tabel nilai-nila CODATA 2006 di bawah ini,<ref name="CODATA2006">{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?na |page=94}}</ref> faktor pembatas utama dalam ketepatan bilangan Avogadro adalah ketidakpastian dari nilai [[Konstanta Planck]], karena konstanta lain yang terlibat semuanya diketahui lebih tepat nilainya.

{| class="wikitable"
|-
! Konstanta
! Simbol
! Nilai CODATA 2006
! Ketidakpastian standar relatif
! Koefisien korelasi<br />dengan ''N''{{sub|A}}
|-
| Massa atom relatif suatu elektron
| align="center"|''A''{{sub|r}}(''e'')
| 5.485 799 0943(23){{e|–4}}
| align="center"|4.2{{e|–10}}
| 0.0082
|-
| [[Konstanta massa molar]]
| align="center"|''M''{{sub|u}}
| 0.001&nbsp;kg/mol = 1 g/mol
| align="center"|defined
| —
|-
| [[Konstanta Rydberg]]
| align="center"|''R''{{sub|∞}}
| 10 973 731.568 527(73) m<sup>−1</sup>
| align="center"|6.6{{e|–12}}
| 0.0000
|-
| [[Konstanta Planck]]
| align="center"|''h''
| 6.626 068 96(33){{e|–34}} J s
| align="center"|5.0{{e|–8}}
| −0.9996
|-
| [[Kecepatan cahaya]]
| align="center"|''c''
| 299 792 458&nbsp;m/s
| align="center"|di
| —
|-
| [[:en:Fine structure constant|Konstanta struktur halus]]
| align="center"|''α''
| 7.297 352 5376(50){{e|–3}}
| align="center"|6.8{{e|–10}}
| 0.0269
|-
| '''Bilangan Avogadro'''
| align="center"|''N''{{sub|A}}
| 6.022 141 79(30){{e|23}} mol<sup>−1</sup>
| align="center"|5.0{{e|–8}}
| 1
|-
|}
<!--
===X-ray crystal density (XRCD) methods===
[[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.]]
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 />
:<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>.

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
|url=http://webmineral.com/help/CellDimensions.shtml
|accessdate=2007-12-09
|title=Unit Cell Formula
|last=Mineralogy Database
|date=2000–2005
}}</ref>

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>}}.

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:
:<math>V_{\rm m} = \frac{A_{\rm r}M_{\rm u}}{\rho}</math>
where ''M''{{sub|u}} is the molar mass constant. The 2006 CODATA value for the molar volume of silicon is 12.058&nbsp;8349(11)&nbsp;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>

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.

====International Avogadro Coordination====
[[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.]]
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>

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"/>

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&nbsp;nm, and the uncertainty in the mass is 3&nbsp;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.html | publisher = International Bureau of Weights and Measures | year = 2008 | page = 17}}</ref>
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>
-->
== Lihat pula ==
* [[Mol]]

== Referensi ==
{{reflist}}

== Pranala luar ==
* {{en}} [http://www.iupac.org/goldbook/A00543.pdf Definisi tahun 1996 untuk tetapan Avogadro] dari ''[[Compendium of Chemical Terminology]]'' ("''Gold Book''") terbitan [[IUPAC]]
* {{en}} [http://gemini.tntech.edu/~tfurtsch/scihist/avogadro.htm Some Notes on Avogadro's Number, 6.022{{e|23}}]
* {{en}} [http://www.americanscientist.org/template/AssetDetail/assetid/54773 An Exact Value for Avogadro's Number] -- [[American Scientist]]

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