Description
{Quote} The Avogadro constant N_{A} 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 × 10^{23} elementary entities. This number is the fixed numerical value of the Avogadro constant, N_{A}, 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 N_{A} 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, N_{A} is '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: 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 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 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 (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 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 |
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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. MitoFit Preprints 2020.04.v2. https://doi.org/10.26124/mitofit:200004.v2 | 2021 |
Gnaiger 2024 MitoFit | Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3. https://doi.org/10.26124/mitofit:2024-0003 | 2024 |
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]
- Fundamental relationships
- » Avogadro constant N_{A}
- » Boltzmann constant k
- » elementary charge e
- » Faraday constant F
- » gas constant R
- » electrochemical constant f
- Fundamental relationships
- SI and related concepts
N_{A} applied to cell respiration
- A cell respiring O_{2} at 100 amol·s^{-1}·x^{-1} consumes 60 million O_{2} molecules per second per cell.
- I_{n}_{O2} = 100 amol·s^{-1}·x^{-1} = 10^{-16} mol·s^{-1}·x^{-1} = 10^{-16} (mol O_{2})·s^{-1}·(x cell)^{-1}
- see SI prefixes
- I_{n}_{O2} = 100 amol·s^{-1}·x^{-1} = 10^{-16} mol·s^{-1}·x^{-1} = 10^{-16} (mol O_{2})·s^{-1}·(x cell)^{-1}
- I_{N}_{O2} = I_{n}_{O2} · N_{A}
- N_{A} = 6.022 140 76·10^{23} x·mol^{-1} = 602.2140 76 Zx·mol^{-1}
- see Format
- N_{A} = 6.022 140 76·10^{23} x·mol^{-1} = 602.2140 76 Zx·mol^{-1}
- I_{N}_{O2} = I_{n}_{O2} · N_{A}
- I_{N}_{O2} = 10^{-16} (mol O_{2})·s^{-1}·(x cell)^{-1} · 6.02 × 10^{23} (x O_{2})·(mol O_{2})^{-1}
- I_{N}_{O2} = 60.2·10^{6} (x O_{2})·s^{-1}·(x cell)^{-1}
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Ergodynamics