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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} [m^{3}·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_{QX} = 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_{mX} = m_{X}·V^{-1} [kg·L^{-1}] Mass concentration C_{mX} 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_{VX} = V_{X}·V^{-1} [L·L^{-1}] Volume concentration C_{VX} 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. https://doi.org/10.26124/bec:2020-0002 | BEC 2020.2 |
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. https://doi.org/10.26124/mitofit:200004.v2 | 2021-09-06 |
BEC 2020.1 doi10.26124bec2020-0001.v1 | Gnaiger E et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. https://doi.org/10.26124/bec:2020-0001.v1 | BEC 2020.1 |
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