Avogadro constant

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Avogadro constant

Description

The Avogadro constant, N_A, has the SI unit 'per mole' [mol^-1] (IUPAC), but more strictly the unit for counting entities per amount is 'units per mole' [x·mol^-1] (compare elementary charge). Therefore, the reciprocal of the Avogadro constant is the proportionality factor between the amount of substance and the number of specified elementary entities of that substance, or 'count per amount' with units 'counting units per mole'. The Avogadro constant times elementary charge is the Faraday constant.

Abbreviation: N_A [x·mol^-1]

Reference: Gibney 2017 Nature

Communicated by Gnaiger Erich 2018-10-18, last update 2020-05-19

Discussion

In a critical article on dimensionless units in the SI, Mohr and Phillips (2015) comment on the Avogadro constant, N_A: "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, N_A is not the conversion factor between entities and moles, but N_A 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 N_A should be [ent/(mol ent) = mol^-1], in line with SI, but contrary to the valid intention of Mohr and Phillips (2015).

N_A 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 N_A is 'counting units per mole' [x·mol^-1].

References

Bioblast link	Reference	Year
Brown 2018 Metrologia	Brown RJC (2018) The evolution of chemical metrology: distinguishing between amount of substance and counting quantities, now and in the future. Metrologia 55:L25. https://doi.org/10.1088/1681-7575/aaace8	2018
Brown 2021 Metrologia	Brown RJC (2021) A metrological approach to quantities that are counted and the unit one. Metrologia 58:035014. https://doi.org/10.1088/1681-7575/abf7a4	2021
Bureau International des Poids et Mesures 2019 The International System of Units (SI)	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 2008 IUPAC Green Book	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
Cooper 2012 Synthese	Cooper G, Humphry SM (2012) The ontological distinction between units and entities. Synthese 187:393–401. https://doi.org/10.1007/s11229-010-9832-1	2012
Gibney 2017 Nature	Gibney E (2017) New definitions of scientific units are on the horizon. Nature 550:312–13.	2017
Gnaiger 2020 BEC MitoPathways	Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5^th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-0002	2020
Gnaiger 2020 MitoFit x	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. https://doi.org/10.26124/mitofit:200004.v2	2021
Mohr 2015 Metrologia	Mohr Peter J, Phillips William D (2015) Dimensionless units in the SI. Metrologia 52:40-7. https://doi.org/10.1088/0026-1394/52/1/40	2015

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Entity, count, and number, and SI base quantities / SI base units

Quantity name	Symbol	Unit name	Symbol	Comment
elementary	U_X	elementary unit	[x]	U_X, U_B; [x] not in SI
count	N_X	elementary unit	[x]	N_X, N_B; [x] not in SI
number	N	-	dimensionless	= N_X·U_X^-1
amount of substance	n_B	mole	[mol]	n_X, n_B
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	I_V	candela	[cd]