Numerosity versus mass

Abstract

The particulate nature of matter was not evident for a long time in early history. Demokritos (460–370 BC) is mostly credited with the concept of particulate matter, probably based on philosophical grounds. But it was centuries later before the concept was really established by the systematic scientific work of Antoine-Laurent Lavoisier (1743–1794), John Dalton (1766–1844), Jons Jakob Berzelius (1779– 1848), and others. It is no wonder that an ‘‘amount’’ of matter was measured (determined in common parlance) as mass, especially since a simple instrument—a balance—and a property of any material—its ‘‘mass’’—made it easy to perform the desired measurement, i.e. compare an unknown mass to a known mass, agreed by convention to be the measurement unit for mass measurements. The property of mass was easy to understand, even after the term ‘‘inertia’’ was introduced as a more adequate formulation of it. Paradoxically, an intelligent use of the balance—and therefore of the property of ‘‘inertia’’—enabled the above-quoted chemists to discover that other property of matter known as ‘‘numerosity’’, using it to uncover the principle that chemical interactions of atoms and molecules could be described in terms of simple ratios of integer numbers of interacting particles, using the concept of ‘‘atomic weight’’. The particulate nature of matter was now coming to light very directly and could be described in simple number ratios. Fully consistent with that, chemists then insisted that an amount of matter involved in chemical interactions (the very essence of chemistry), could be expressed simply by a number of particles (general name: ‘‘entities’’). Eventually, this was to give rise to a new base quantity in the SI: ‘‘amount-of-substance’’ and a corresponding base unit, the mole (symbol: mol). This new insight was agreed by both IUPAP and IUPAC, and ‘‘cast in stone’’ by the International Conference for Weights and Measures, CGPM, in 1971. Now the chemists had ‘‘their’’ unit. But no sooner did they have it, or interest in it declined in practice, with the possible exception of clinical chemistry where it was applied rather consistently. The reasons for such a decline still require investigation. Was it the shift to more instrumental (spectrometric) measurement methods rather than wet chemistry with its requirements for stoichiometric substances? Or was it the automation of instrumental analysis, which loosens the link between analyst and principles of the measurement method? The very notion of ‘‘amount’’ being a base quantity (like time, length, mass, electric current, etc.) was based on this other property of matter known as ‘‘numerosity’’. Numerosity is independent of gravity and enables the simplest form of measurement: counting. It is also far more selective than mass. It requires the substance to be specified, i.e. when counting, the counted particles must be identical and specified. The fact that it is very difficult to handle (or count) very large numbers of entities (typically in the range of 10– 10) is overcome by not choosing the most natural unit for amount-of-substance, i.e. one entity, symbol ‘‘1’’, but rather a large number of entities: 6.02214 · 10 and call that the unit for amount measurements, i.e. the mole. In fact, this large number is just a known and fixed multiple of the natural unit: 1 entity. This notion is important for modern analytical instrumentation intended to measure ratios, R, of large numbers of neutral entities (e.g. in the comparison of P. De Bievre (&) Duineneind 9, 2460 Kasterlee, Belgium e-mail: paul.de.bievre@skynet.be