Avogadro constant

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Avogadro constant


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{Quote} The Avogadro constant NA is a proportionality constant between the quantity amount of substance (with unit mole) and the quantity for counting entities ... One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number {Bureau International des Poids et Mesures 2019 The International System of Units (SI) end of quote}. Thus the Avogadro constant NA has the SI unit 'per mole' [mol-1], but more strictly the unit for counting entities per amount is 'units per mole' [x·mol-1] (compare elementary charge). Therefore, NA is 'count per amount' with units 'counting units per mole'. The Avogadro constant times elementary charge is the Faraday constant.

Abbreviation: NA [x·mol-1]

Reference: Bureau International des Poids et Mesures 2019 The International System of Units (SI), Gnaiger 2020 BEC MitoPathways

Communicated by Gnaiger Erich (2018-10-18) last update 2020-05-20
in: Anastrophe XX Entity X and the elementary unit x of A X-mass Carol


In a critical article on dimensionless units in the SI, Mohr and Phillips (2015) comment on the Avogadro constant, NA: "Evidently, this constant can be viewed as the conversion factor between entities and moles." The unit mole [mol], however, is the SI base unit for amount of substance, defined by IUPAC (Cohen et al 2008) as: "Amount of substance is proportional to the number of specified elementary entities of that substance". Therefore, NA is not the conversion factor between entities and moles, but NA is the conversion factor between count and amount, expressed in counting units of entities and moles of entities. Thus, the unit 'ent' suggested by Mohr and Phillips (2015) for the quantity count would imply, that they should consider 'mol ent' as the unit for amount of substance. In this case, the unit of NA should be [ent/(mol ent) = mol-1], in line with SI, but contrary to the valid intention of Mohr and Phillips (2015).
NA is the conversion factor between countable entities, expressed in counting units [x], and amount of entities (amount of substance), expressed in moles [mol]. Therefore, the unit of NA is 'counting units per mole' [x·mol-1].


Bioblast linkReferenceYear
Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0.2019
Cohen ER, Cvitas T, Frey JG, Holmström B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry. IUPAC Green Book 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge.2008
Gibney E (2017) New definitions of scientific units are on the horizon. Nature 550:312–13.2017
Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2:112 pp. https://doi.org/10.26124/bec:2020-00022020
Gnaiger E (2021) The elementary unit — canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprints 2020.4.v2. doi:10.26124/mitofit:200004.v22021-09-06
Mohr Peter J, Phillips William D (2015) Dimensionless units in the SI. Metrologia 52:40-7.2015


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Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment
elementary UX elementary unit [x] UX, UB; [x] not in SI
count NX elementary unit [x] NX, NB; [x] not in SI
number N - dimensionless = NX·UX-1
amount of substance nB mole [mol] nX, nB
electric current I ampere [A] A = C·s-1
time t second [s]
length l meter [m] SI: metre
mass m kilogram [kg]
thermodynamic temperature T kelvin [K]
luminous intensity IV candela [cd]
Fundamental relationships
» Avogadro constant NA
» Boltzmann constant k
» elementary charge e
» Faraday constant F
» gas constant R
» electrochemical constant f
SI and related concepts
» International System of Units
» SI prefixes
» International Union of Pure and Applied Chemistry, IUPAC
» entity
» quantity
» dimension
» format
» motive unit
» iconic symbols

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