Brown 2018 Metrologia

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Brown RJC (2018) The evolution of chemical metrology: distinguishing between amount of substance and counting quantities, now and in the future. Metrologia 55:L25.

ยป IOPscience

Brown RJC (2018) Metrologia

Abstract: This discussion article begins by highlighting the benefits of the mole's incorporation within the international system of units (SI), in particular by bringing chemical measurement within formal metrology structures. The origins of the confusion that has consistently existed between amount of substance (the base quantity of which the mole is the SI base unit) and counting quantities are examined in detail and their differentiating characteristics fully elaborated on. The importance and benefits of distinguishing between these different quantities and the role that the Avogadro constant plays in doing this are highlighted. It is proposed that these issues are becoming increasingly important for two reasons. First, as chemistry and biology consider increasingly small size domains, measurements are being made of significantly reduced collections of entities. Second, the proposed re-definition of the mole makes the link between amount of substance and the number of elementary entities more transparent. Finally, proposals for new ways of expressing very low amounts of substance in terms of new prefixes based on the numerical value of the Avogadro constant are presented as a way to encourage the use of the mole, when appropriate, even for ultra-low level chemical measurement.

โ€ข Bioblast editor: Gnaiger E

Selected quotes

  • There are few if any that address the differences between amount of substance and counting quantities.
  • In this paper, where possible, the term โ€˜elementary entitiesโ€™ is used to describe items which could be considered together as amount of substance, whereas the term โ€˜entitiesโ€™ is used to describe items in the most general sense (a specific subset of which are elementary entities).
  • There is an ontological difference between continuous quantities and countable aggregatesโ€”the distinction being the basis of the differences between real and natural numbers and the natural lower limit that exists for countable aggregates (i.e. one entity) that does not exist for continuous quantities [13].
  • These quantities are often referred to as those quantities having the nature of a count, number of (items being counted), counting number or, simply, counting quantities. There is no international agreement on the nomenclature for counting quantities but ISO 80000-1:2013 uses โ€˜counting numberโ€™ [16]. As shall be discussed later, counting quantities have the unit one, symbol 1, and have dimension one (or number).
  • Counting quantities are often referred to as being dimensionless or having the dimension one. More rigorously [21] we should refer to these as having the dimension โ€˜numberโ€™.
  • The use of โ€˜1/m3โ€™ explicitly highlights the nature of the unit as a ratio of number (unit โ€˜1โ€™) to volume (unit โ€˜m3โ€™) and is preferred by the author to โ€˜mโˆ’3โ€™ which, whilst also correct, loses this distinction.
  • The presence of the unit โ€˜1โ€™ in such a way also reminds us not to attempt to use any description of the quantity in the unit: such as โ€˜cells/cm2โ€™, โ€˜particles/m3โ€™ or โ€˜particles(10 nmโˆ’1 ฮผm)/m3โ€™. This use is strongly deprecated as are similar examples for amount of substance, such as โ€˜mmol Hg/m3โ€™. Such โ€˜unitsโ€™ could propagate uncontrollably if this usage was allowed with no clear distinction between them or definitions associated with them. Proposals to create taxonomies for such counting โ€˜unitsโ€™ [22] do not address these concerns since they neither set any limits for the number of such units that could be created and used nor explain how they would be officially controlled within the SI. Such units also violate the general principle that the name of the quantity should never be mixed with the name of the unit.
  • .. amount of substance still has the outward appearance of a continuous quantity, but is more clearly exposed as having the character of a countable aggregate.

Cited by

Gnaiger 2024 Ambiguity crisis.jpg
Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3.


Amount of substance, Avogadro constant, Count, Dimension, Elementary entity, Entity, International System of Units, Mass, Number, Unit, Gnaiger 2024 MitoFit 

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