Density

high-resolution terminology - matching measurements at high-resolution

Density

Description

Density, mass density ρ = m·V^-1 [kg·m^-3], is mass m divided by volume V. Surface density ρ_A = m·A^-1 [kg·m^-2] (SI). For a pure sample S, the mass density ρ_S = m_S·V_S^-1 [kg·m^-3] is the mass m of pure sample S per volume V_S of the pure sample. With density ρ thus defined, the 'amount density' of substance B is ρ_B = n_B·V_B^-1 [mol·m^-3]. This is not a commonly used expression, but the inverse is defined as the molar volume of a pure substance (IUPAC), V_m,B = V_B·n_B^-1 [m³·mol^-1]. The pure sample is a pure gas, pure liquid or pure solid of a defined elementary entity. The amount concentration, c_B = n_B·V^-1 [mol·m^-3] is the amount n_B of substance B divided by the volume V of the mixture (IUPAC), and this is not called an 'amount density'. The term 'amount density' is reserved for an amount of substance per volume V_S of the pure substance. This explicit distinction between 'density' related to the volume of the sample and 'concentration' related to the total volume of the mixture is very helpful to avoid confusion. Further clarification is required in cases, when the mass density ρ_s of the sample in the mixture differs from the mass density ρ_S of the pure sample before mixing. Think of a sample S of pure ethanol with a volume of 1 L at 25 °C, which is mixed with a volume of 1 L of pure water at 25 °C: after the temperature of the mixture has equilibrated to 25 °C, the total volume of the mixture is less than 2 L, such that the volume V_S of 1 L pure ethanol has diminished to a smaller volume V_s of ethanol in the mixture; the density of ethanol in the mixture is higher than the density of pure ethanol (this is incomplete additivity). The volume V_s of sample s in a mixture is by definition smaller than the total volume V of the mixture. Sample volume V_S and system volume V are identical, but this applies only to the case of a pure sample. Concentration is related to samples s per total volume V of the mixture, whereas density is related to samples S or s per volume V_S = V or V_s < V, respectively (BEC 2020.1).

Abbreviation: ρ, C, D

Reference: BEC 2020.1, Gnaiger MitoFit Preprints 2020.4

Communicated by Gnaiger E (2018-08-23) last update 2020-05-30

Concentration and density

Concentration and density in different formats

Concentration is an extensive quantity divided by volume V, or a count divided by volume V. The elementary entities X (or B) or the sample type s have to be specified in the text or indicated by a subscript or in parentheses. Examples: cell-count concentration C_ce; count concentration of protons C_H⁺; molar concentration of protons c_H⁺. Density is not only 'mass density ρ, but is used for many extensive quantities divided by volume or area.

Concentration	Symbol	Definition	Unit	Note
Count concentration	C_X	= N_X·V^-1	[x·L^-1]	The IUPAC term 'number concentration' should be replaced by 'count concentration' (or 'number of entities concentration').
Amount concentration	c_B	= n_B·V^-1	[mol·L^-1]	Amount concentration is a counting concentration, converting the elementary unit [x] into moles [mol] using the Avogadro constant.
Charge concentration	C_{Q_X}	= Q_X·V^-1	[C·L^-1]	Charge concentration is a counting concentration, converting the elementary unit [x] into coulombs C using the elementary charge, or converting moles [mol] into coulombs [C] using the Faraday constant. Charge density in electricity is 'charge per volume'.
Mass concentration of X	C_{m_X}	= m_X·V^-1	[kg·L^-1]	Mass concentration C_{m_X} is mass of entities X per volume V of the mixture.
Mass density of S	ρ_S	= m_S·V_S^-1	[kg·L^-1]	Mass density ρ_S is mass of the pure sample S per volume V_S of the pure sample; ρ_S is the reciprocal of specific volume.
Volume concentration of X	C_{V_X}	= V_X·V^-1	[L·L^-1]	Volume concentration C_{V_X} is the volume of entities X per volume V of the mixture.
Volume density	Φ_X	= V_X·V^-1	[L·L^-1]	Volume density is equivalent to the volume fraction.

References

Bioblast link	Reference	Year
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
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
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