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 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. The Avogadro constant times elementary charge is the Faraday constant.

Abbreviation: N_A [x·mol^-1]

Reference: Gibney 2017 Nature

Communicated by Gnaiger E 2018-10-18, last update 2020-05-14

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 the number of entities and moles of entities. Thus, the unit 'ent' suggested by Mohr and Phillips (2015) for the number of entities 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 entities expressed as countable entities, unit [x], and entities expressed as amount (of substance), mole [mol]. Therefore, the unit of N_A is 'units per mole' [x·mol^-1].

References

Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - »Open Access pdf«
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. - »Bioblast link«
Gnaiger E (2019) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Mitochondr Physiol Network 24.05. Oroboros MiPNet Publications, Innsbruck:112 pp. - »Bioblast link«
Mohr PJ, Phillips WD (2015) Dimensionless units in the SI. Metrologia 52:40-7. - »Bioblast link«

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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]