DOI: 10.1039/D0AY90126A
(AMC Technical Brief)
Anal. Methods, 2020, Advance Article

Analytical Methods Committee, AMCTB No. 99

Received
15th September 2020

First published on 2nd October 2020

It is universally accepted that a measurement of a quantity of interest should be presented as the product of a numerical value and a unit (we should also include an estimate of measurement uncertainty, but this is beyond the scope of this Technical Brief). The International System of Units (the SI) provides the world’s only practical system of coherent units of measurement for this purpose. For ease of expression and understanding it is generally preferred that the numerical value presented is between 1 and 100. One might refer to these as ‘human-scale’ numbers that are easy to relate to, conceptualise and communicate. The SI uses ‘SI prefixes’ to achieve this aim, allowing us to write 2.3 km rather than 2300 m. Equally we could use scientific nomenclature to write, arguably more inelegantly, 2.3 × 10^{3} m. Deviation from these agreed practices may risk confusion in the communication of measurement results. This Technical Brief outlines the SI units and quantities available for use in analytical chemistry and explains the care that must be taken if alternative approaches are followed. One principle remains essential to aid understanding: the description of the quantity being expressed should always be stated unambiguously in words as part of the presentation of a measurement result.

Analytical chemistry is largely concerned with determining the composition of mixtures. The result of analysis for a component in a mixture should comprise a ‘numerical value’ and a ‘unit’ in order to express the value of the ‘quantity’ being measured (and an associated statement of uncertainty, of course

Quantity | Symbol | Definition | SI unit | Other common units |
---|---|---|---|---|

Mass fraction | w | w_{i} = m_{i}/∑m_{j} |
kg kg^{−1} |
g g^{−1}, μg g^{−1}, ng g^{−1}, mg kg^{−1}, μg kg^{−1}, etc. |

Volume fraction | ϕ | ϕ_{i} = V_{i}/∑V_{j} |
m^{3} m^{−3} |
L L^{−1}, mL L^{−1}, etc. |

Amount fraction | x | x_{i} = n_{i}/∑n_{j} |
mol mol^{−1} |
mmol mol^{−1}, μmol mol^{−1}, nmol mol^{−1}, etc. |

Mass concentration | γ | γ_{i} = m_{i}/V |
kg m^{−3} |
g dm^{−3}, g L^{−1}, mg dm^{−3}, mg L^{−1}, etc. |

Volume concentration | σ | σ_{i} = V_{i}/V |
m^{3} m^{−3} |
L L^{−1}, mL L^{−1}, etc. |

Amount concentration (molarity) | c | c_{i} = n_{i}/V |
mol m^{−3} |
M, mol dm^{−3}, mol L^{−1}, mM, mmol dm^{−3}, mmol L^{−1}, etc. |

Molality | b | b_{i} = n_{i}/m_{solv} |
mol kg^{−1} |
mmol kg^{−1}, μmol kg^{−1}, etc. |

Volume content | κ | κ_{i} = V_{i}/m |
m^{3} kg^{−1} |
cm^{3} g^{−1}, etc. |

Amount content | k | k_{i} = n_{i}/m |
mol kg^{−1} |
mmol kg^{−1}, μmol kg^{−1}, etc. |

Quantities involving volumes are more limited in their application because their magnitude is dependent on temperature, and pressure (for gaseous mixtures), and therefore for mass concentrations and amount concentrations it is often necessary to state at what temperature and pressure the value of the quantity is applicable. Indeed the use of volume fraction and volume concentration is discouraged without reiteration of what is being expressed, since definitions vary as to whether the volume of the whole mixture is measured before or after the mixing of individual components. Only when discussing the general concept, and there is no risk of any confusion, should the term ‘concentration’ be used in isolation, perhaps because the quantity being expressed has already been described in detail.

The use of ‘ppm’ and ‘ppb’ and similar terms is widespread in analytical chemistry, in particular when proper units are omitted because the quantity being expressed is a fraction where the units can be simplified to one. When these terms are used it is essential that a full description of the quantity being measured is provided so there can be no ambiguity in the interpretation of the result of a measurement (since ‘ppm’ could represent any type of fraction) and that the meaning of the terms used is explained (for instance there are different meanings for ‘billion’, ‘trillion’, etc., across the world).^{7} The use of ‘ppm’ and ‘ppb’ in specific situations may afford some advantages: used to express amount fraction they are the main route to document workplace exposure limits across the world and so usually involve more ‘rounded’, memorable values than the equivalent numerical value expressed as a mass concentration in mg m^{−3}. However, whenever possible the terms ‘ppm’ and ‘ppb’ should not be used to express concentrations. By its definition (in Table 1) a concentration does not have units that simplify to one (except for the rather obscure quantity volume concentration). The use of ‘ppm’ and ‘ppb’ might also allow otherwise complicated unit expressions to be simplified. For instance uptake rate of gaseous diffusive samplers expressed in (ng ppm^{−1}) min^{−1} rather than (ng (μmol mol^{−1})^{−1}) min^{−1}.

• The amount fraction of calcium, x(Ca) = 2.3 × 10^{−6} mol mol^{−1}, or

• The amount fraction of calcium, x(Ca) = 2.3 μmol mol^{−1}.

It is arguably less rigorous to state that:

• The amount fraction of calcium, x(Ca) = 2.3 × 10^{−6}, or

• The amount fraction of calcium, x(Ca) = 2.3 ppm.

And it is ambiguous to state that:

x(Ca) = 2.3 ppm.

In the final example, the use of ‘ppm’ does not unambiguously distinguish between quantities such as mass fraction, amount fraction, volume fraction and volume concentration. The reader is left to guess whether the symbol x has been employed to represent the quantity amount fraction, or not.

This Technical Brief has presented, from the viewpoint of the SI, the internationally agreed units and quantities available to express measurement results in analytical chemistry, with best practice guidelines suggested – noting that some units must be used with care since their numerical values are sensitive to environmental conditions. There are also other expressions that are in common usage and the Technical Brief has explained the care that must be taken to avoid confusion when employing these alternatives. In all cases, the key principle that must be followed to ensure unambiguous communication is to state clearly in words the description of the quantity being expressed as part of the presentation of a measurement result.

Dr Richard J. C. Brown (National Physical Laboratory)

This Technical Brief was prepared for the Analytical Methods Committee, with contributions from Michael Healy (Environment Agency), Matthew Rawlinson (Affinity Water Ltd) and Ian Pengelly (Health and Safety Executive), and approved on 31^{st} August 2020.

- EURACHEM/CITAC Guide CG 4, Quantifying Uncertainty in Analytical Measurement, ed. S. L. R. Ellison and A. Williams, EURACHEM/CITAC, 3rd edn, 2012 Search PubMed.
- AMC TB, Revision of the International System of Units, Anal. Methods, 2019, 11, 1577–1579 RSC.
- T. Cvitas, Quantities describing compositions of mixtures, Metrologia, 1996, 33, 35–39 CrossRef.
- Quantities Units and Symbols in Physical Chemistry, ed. I. Mills, et al., RSC Publishing, Cambridge, 3rd edn, 2007 Search PubMed.
- The International System of Units, BIPM, 9th edn, 2019, https://www.bipm.org/en/publications/si-brochure/ Search PubMed.
- T. J. Quinn and I. M. Mills, The use and abuse of the terms percent, parts per million and parts in 10⁁n, Metrologia, 1998, 35, 807–810 CrossRef.
- Long and short scales, https://en.wikipedia.org/wiki/Long_and_short_scales, accessed June 2020 Search PubMed.
- R. J. C. Brown, Quantities and units in analytical chemistry, Int. J. Environ. Anal. Chem., 2008, 88, 681–687 CrossRef CAS.

## Footnotes |

† Each of the seven base quantities used in the SI (mass, length, time, amount of substance, etc.) is regarded as having its own independent dimension. Derived quantities written in terms of the base quantities, whose dimensions cannot be simplified to one, are quantities with dimension, e.g. velocity in m s^{−1}, area in m^{2}, etc. |

‡ The unit here has been expressed as a quotient, as in g/kg, but could equally have been expressed as products using negative exponents, as in g · kg^{−1} or g kg^{−1}, as in the rest of the paper.^{4} |

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