Avogadro constant

The Avogadro constant, commonly denoted N_A^[1] or L,^[2] is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of 6.02214076×10²³ reciprocal moles.^[3][4] It is named after the Italian scientist Amedeo Avogadro^[5] by Stanislao Cannizzaro, who explained this number four years after Avogadro's death while at the Karlsruhe Congress in 1860.^[6]

Avogadro constant
Amedeo Avogadro, the constant's namesake
Common symbols	NA, L
SI unit	mol^−1
Exact value
mole (unit)	6.02214076×10^23

The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted N^[7][8] or N₀,^[9][10] which is the number of particles that are contained in one mole, exactly 6.02214076×10²³.^[3]

The Avogadro number is the approximate number of nucleons (protons and neutrons) in one gram of ordinary matter. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, expressed in grams, is approximately the number of nucleons in one constituent particle of the substance. It is numerically equal (for all practical purposes) to the average mass of one molecule (or atom) of a compound in daltons (unified atomic mass units); one dalton being 1/12 of the mass of one carbon-12 atom. For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water (N molecules) is about 18.0153 grams. Thus, the Avogadro constant N_A is the proportionality factor that relates the molar mass of a substance to the average mass of one molecule.^[11]

The Avogadro constant also relates the molar volume 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 18 mL/mol, the volume occupied by one molecule of water is about 18/6.022×10⁻²³ mL, or about 30 Å³ (cubic angstroms). For a crystalline substance, it similarly relates its molar volume (in mol/mL), the volume of the repeating unit cell of the crystals (in mL), to the number of molecules in that cell.

The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by Josef Loschmidt in 1865.^[12] (Avogadro's number is closely related to the Loschmidt constant, and the two concepts are sometimes confused.) It was initially defined by Jean Perrin as the number of atoms in 16 grams of oxygen.^[5] It was later redefined in the 14th conference of the International Bureau of Weights and Measures (BIPM) as the number of atoms in 12 grams of the isotope carbon-12 (¹²C).^[13] In each case, the mole was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when carbon-12 was the reference, one mole of carbon-12 was exactly 12 grams of the element.

These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number N as the exact value 6.02214076×10²³, and redefined the mole as the amount of a substance under consideration that contains N constituent particles of the substance. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is N times the average mass of one of its constituent particles – a physical quantity whose precise value has to be determined experimentally for each substance.

History

Origin of the concept

 

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 atoms or molecules regardless of the nature of the gas.^[14]

The name Avogadro's number was coined in 1909 by the physicist Jean Perrin, who defined it as the number of molecules in exactly 16 grams of oxygen.^[5] 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 1/16 of the atomic mass of oxygen.

First measurements

 

Josef Loschmidt

The value of Avogadro's number (not yet known by that name) was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas.^[12] This value, the number density n₀ of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, N_A, by

${\displaystyle n_{0}={\frac {p_{0}N_{\rm {A}}}{R\,T_{0}}}}$ ,

where p₀ is the pressure, R is the gas constant, and T₀ is the absolute temperature. Because of this work, the symbol L is sometimes used for the Avogadro constant,^[15] and, in German literature, that name may be used for both constants, distinguished only by the units of measurement.^[16] (However, N_A should not be confused with the entirely different Loschmidt constant in English-language literature.)

Perrin himself determined Avogadro's number by several different experimental methods. He was awarded the 1926 Nobel Prize in Physics, largely for this work.^[17]

The electric charge per mole of electrons is a constant called the Faraday constant and has been known since 1834, when Michael Faraday published his works on electrolysis. In 1910, Robert Millikan with the help of Harvey Fletcher obtained the first measurement of the 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.^[18]

SI definition of 1971

In 1971, the International Bureau of Weights and Measures (BIPM) decided to regard the amount of substance as an independent dimension of measurement, with the mole as its base unit in the International System of Units (SI).^[15] Specifically, the mole was defined as an amount of a substance that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.

By this definition, the common rule of thumb that "one gram of matter contains N₀ nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes. On the other hand, one mole of any substance contained exactly as many molecules as one mole of any other substance.

As a consequence of this definition, in the SI system the Avogadro constant N_A had the dimensionality of reciprocal of amount of substance rather than of a pure number, and had the approximate value 6.02×10²³ with units of mol⁻¹.^[15] By this definition, the value of N_A inherently had to be determined experimentally.

The BIPM also named N_A the "Avogadro constant", but the term "Avogadro number" continued to be used especially in introductory works.^[19]

SI redefinition of 2019

Main article: 2019 redefinition of the SI base units

In 2017, the BIPM decided to change the definitions of mole and amount of substance.^[20][3] The mole was redefined as being the amount of substance containing exactly 6.02214076×10²³ elementary entities. One consequence of this change is that the mass of a mole of ¹²C atoms is no longer exactly 0.012 kg. On the other hand, the dalton (a.k.a. universal atomic mass unit) remains unchanged as 1/12 of the mass of ¹²C.^[21][22] Thus, the molar mass constant is no longer exactly 1 g/mol, although the difference (4.5×10⁻¹⁰ in relative terms, as of March 2019) is insignificant for practical purposes.^[3][1]

Connection to other constants

The Avogadro constant N_A is related to other physical constants and properties.

• It relates the molar gas constant R and the Boltzmann constant k_B, which in the SI is defined to be exactly 1.380649×10⁻²³ J/K:^[3]

  R = k_B N_A = 8.314462618... J⋅mol⁻¹⋅K⁻¹

• It relates the Faraday constant F and the elementary charge e, which in the SI is defined as exactly 1.602176634×10⁻¹⁹ coulombs:^[3]

  F = e N_A = 9.648533212...×10⁴ C⋅mol⁻¹

• It relates the molar mass constant M_u and the atomic mass constant m_u currently 1.66053906660(50)×10⁻²⁷ kg:^[23]

  M_u = m_u N_A = 0.99999999965(30)×10⁻³ kg⋅mol⁻¹

• σ = 1 / {N_A }^[24]

See also

• Mole Day
• CODATA 2018

References

1. Bureau International des Poids et Mesures (2019): The International System of Units (SI), 9th edition, English version, page 134. Available at the BIPM website.
2. 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)"; page 963, item "Avogadro constant". Pure and Applied Chemistry, volume 68, issue 4, pages 957–1000. doi:10.1351/pac199668040957
3. Newell, David B.; Tiesinga, Eite (2019). "The International System of Units (SI)". Nist. NIST Special Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. S2CID 242934226.
4. de Bievre, P.; Peiser, H. S. (1992). "Atomic Weight: The Name, Its History, Definition and Units". Pure and Applied Chemistry. 64 (10): 1535–1543. doi:10.1351/pac199264101535. S2CID 96317287.
5. Perrin, Jean (1909). "Mouvement brownien et réalité moléculaire". Annales de Chimie et de Physique. 8^e Série. 18: 1–114. Extract in English, translation by Frederick Soddy.
6. "Stanislao Cannizzaro | Science History Institute". Science History Institute. June 2016. Retrieved 2 June 2022.
7. Linus Pauling (1970), General Chemistry, page 96. Dover Edition, reprinted by Courier in 2014; 992 pages. ISBN 9780486134659
8. Marvin Yelles (1971): McGraw-Hill Encyclopedia of Science and Technology, Volume 9, 3rd edition; 707 pages. ISBN 9780070797987
9. Richard P. Feynman: The Feynman Lectures on Physics, Volume II
10. Max Born (1969): Atomic Physics, 8th Edition. Dover edition, reprinted by Courier in 2013; 544 pages. ISBN 9780486318585
11. Okun, Lev B.; Lee, A. G. (1985). Particle Physics: The Quest for the Substance of Substance. OPA Ltd. p. 86. ISBN 978-3-7186-0228-5.
12. Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle". Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien. 52 (2): 395–413. .
13. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6, (PDF) from the original on 4 June 2021, retrieved 16 December 2021
14. Avogadro, Amedeo (1811). "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 de Physique. 73: 58–76. English translation.
15. Bureau International des Poids et Mesures (1971): 14th Conference Générale des Poids et Mesures 2020-09-23 at the Wayback Machine Available at the BIPM website.
16. Virgo, S.E. (1933). . Science Progress. 27: 634–649. Archived from the original on 4 April 2005.
17. Oseen, C.W. (December 10, 1926). Presentation Speech for the 1926 Nobel Prize in Physics.
18. (1974): Introduction to the constants for nonexperts, 1900–1920 From the Encyclopaedia Britannica, 15th edition; reproduced by NIST. Accessed on 2019-07-03.
19. Kotz, John C.; Treichel, Paul M.; Townsend, John R. (2008). (7th ed.). Brooks/Cole. ISBN 978-0-495-38703-9. Archived from the original on 16 October 2008.
20. International Bureau for Weights and Measures (2017): Proceedings of the 106th meeting of the International Committee for Weights and Measures (CIPM), 16-17 and 20 October 2017, page 23. Available at the BIPM website 2021-02-21 at the Wayback Machine.
21. Pavese, Franco (January 2018). "A possible draft of the CGPM Resolution for the revised SI, compared with the CCU last draft of the 9th SI Brochure". Measurement. 114: 478–483. Bibcode:2018Meas..114..478P. doi:10.1016/j.measurement.2017.08.020. ISSN 0263-2241.
22. "Unified atomic mass unit". The IUPAC Compendium of Chemical Terminology. 2014. doi:10.1351/goldbook.U06554.
23. "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
24. Brown, Richard J. C. (10 April 2019). "Future requirements for non-decimal unit prefixes in chemical measurement". Accreditation and Quality Assurance [de]. 24 (3): 245–247. doi:10.1007/s00769-019-01374-y. S2CID 146005120. from the original on 20 December 2022. Retrieved 20 December 2022.

External links

• 1996 definition of the Avogadro constant from the IUPAC Compendium of Chemical Terminology ("Gold Book")
• (historical notes)
• An Exact Value for Avogadro's Number – American Scientist
• Murrell, John N. (2001). "Avogadro and His Constant". Helvetica Chimica Acta. 84 (6): 1314–1327. doi:10.1002/1522-2675(20010613)84:6<1314::AID-HLCA1314>3.0.CO;2-Q.
• Scanned version of "Two hypothesis of Avogadro", 1811 Avogadro's article, on BibNum