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 ρA = m·A-1 [kg·m-2] (SI). For a pure sample S, the mass density ρS = mS·VS-1 [kg·m-3] is the mass m of pure sample S per volume VS of the pure sample. With density ρ thus defined, the 'amount density' of substance B is ρB = nB·VB-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), Vm,B = VB·nB-1 [m3·mol-1]. The pure sample is a pure gas, pure liquid or pure solid of a defined elementary entity. The amount concentration, cB = nB·V-1 [mol·m-3] is the amount nB 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 VS 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 ρs of the sample in the mixture differs from the mass density ρS 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 VS of 1 L pure ethanol has diminished to a smaller volume Vs 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 Vs of sample s in a mixture is by definition smaller than the total volume V of the mixture. Sample volume VS 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 VS = V or Vs < 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
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## 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 Cce; count concentration of protons CH+; molar concentration of protons cH+. 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 CX = NX·V-1 [x·L-1] The IUPAC term 'number concentration' should be replaced by 'count concentration' (or 'number of entities concentration').
Amount concentration cB = nB·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 CQX = QX·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 CmX = mX·V-1 [kg·L-1] Mass concentration CmX is mass of entities X per volume V of the mixture.
Mass density of S ρS = mS·VS-1 [kg·L-1] Mass density ρS is mass of the pure sample S per volume VS of the pure sample; ρS is the reciprocal of specific volume.
Volume concentration of X CVX = VX·V-1 [L·L-1] Volume concentration CVX is the volume of entities X per volume V of the mixture.
Volume density ΦX = VX·V-1 [L·L-1] Volume density is equivalent to the volume fraction.