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## Description

{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 {End of Quote: Bureau International des Poids et Mesures 2019 The International System of Units (SI)}.

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]

```Communicated by Gnaiger Erich (2018-10-18) last update 2022-08-16
in: Anastrophe XX Entity X and the elementary unit x of A X-mass Carol
```

## Discussion

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 (count) and moles of entities (amount). 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].

## References

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/aaace82018
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/abf7a42021
Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216. ISBN 978-92-822-2272-02019
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 G, Humphry SM (2012) The ontological distinction between units and entities. Synthese 187:393–401. https://doi.org/10.1007/s11229-010-9832-12012
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. 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 2020.04.v2. https://doi.org/10.26124/mitofit:200004.v22021
Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3. https://doi.org/10.26124/mitofit:2024-00032024
Mohr Peter J, Phillips William D (2015) Dimensionless units in the SI. Metrologia 52:40-7. https://doi.org/10.1088/0026-1394/52/1/402015

Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
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
» Boltzmann constant k
» elementary charge e
» gas constant R
» electrochemical constant f
SI and related concepts
» International System of Units
» elementary unit x
» SI prefixes
» International Union of Pure and Applied Chemistry, IUPAC
» entity
» quantity
» dimension
» format
» motive unit
» iconic symbols

## NA applied to cell respiration

A cell respiring O2 at 100 amol·s-1·x-1 consumes 60 million O2 molecules per second per cell.
InO2 = 100 amol·s-1·x-1 = 10-16 mol·s-1·x-1 = 10-16 (mol O2)·s-1·(x cell)-1
INO2 = InO2 · NA
NA = 6.022 140 76·1023 x·mol-1 = 602.2140 76 Zx·mol-1
INO2 = 10-16 (mol O2)·s-1·(x cell)-1 · 6.02 × 1023 (x O2)·(mol O2)-1
INO2 = 60.2·106 (x O2)·s-1·(x cell)-1

MitoPedia concepts: Ergodynamics

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