Amount of substance

high-resolution terminology - matching measurements at high-resolution

Amount of substance

Description

The amount of substance n is a base physical quantity, and the corresponding SI unit is the mole [mol]. Amount of substance (sometimes abbreviated as 'amount' or 'chemical amount') is proportional to the number N_X of specified elementary entities X, and the universal proportionality constant is the reciprocal value of the Avogadro constant (SI),

n_X = N_X·N_A^-1

n_X contained in a system can change due to internal and external transformations,

dn_X = d_in_X + d_en_X

In the absence of nuclear reactions, the amount of any atom is conserved, e.g., for carbon d_in_C = 0. This is different for chemical substances or ionic species which are produced or consumed during the advancement of a reaction r,

A change in the amount of X_i, dn_i, in an open system is due to both the internal formation in chemical transformations, d_rn_i, and the external transfer, d_en_i, across the system boundaries. dn_i is positive if X_i is formed as a product of the reaction within the system. d_en_i is negative if X_i flows out of the system and appears as a product in the surroundings (Cohen 2008 IUPAC Green Book).

Abbreviation: n [mol]

Reference: Cohen 2008 IUPAC Green Book, Gnaiger 1993 Pure Appl Chem, Gnaiger 2020 BEC MitoPathways

Communicated by Gnaiger E (last update 2020-05-27)

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
Gnaiger 1993 Pure Appl Chem	Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. http://dx.doi.org/10.1351/pac199365091983	1993
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
BEC 2020.1 doi10.26124bec2020-0001.v1	Gnaiger E et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/10.26124/bec:2020-0001.v1	2020

Quantity	Symbol for quantity Q	Symbol for dimension	Name of abstract unit u_Q	Symbol for unit u_Q [*]
elementary entity ^*,$	U_X	U	elementary unit	x
count ^*,$	N_X = N·U_X	X	elementary unit	x
amount of substance ^*,§	n_X = N_X·N_A^-1	N	mole	mol
charge ^*,€	Q_el = z_X·e·N_X	I·T	coulomb	C = A·s

length	l	L	meter	m
mass	m	M	kilogram	kg
time	t	T	second	s
electric current	I	I	ampere	A
thermodynamic temperature	T	Θ	kelvin	K
luminous intensity	I_v	J	candela	cd

[*] SI units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments, related to iconic symbols.

^* For the elementary quantities N_X, n_X, and Q_el, the entity-type X of the elementary entity U_X has to be specified in the text and indicated by a subscript: n_O₂; N_ce; Q_el.

^$ Count N_X equals the number of elementary entities U_X. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). An elementary entity U_X is a material unit, it is not a count (U_X is not a number of U_X). N_X has the dimension X of a count and U_X has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].

^§ Amount n_X is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant N_A.

^€ Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge e, or converting moles [mol] into coulombs [C] using the Faraday constant F. z_X is the charge number per elementary entity U_X, which is a constant for any defined elementary entity U_X. Q_el = z_X·F·n_X

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	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]