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Accreditation and Quality Assurance: Journal for Quality, Comparability and Reliability in Chemical Measurement (v.16, #3)
Integer numbers and their ratios are key concepts in describing the interactions of atoms and molecules
by Paul De Bièvre (pp. 117-120).
A skeptic’s review of the New SI by Gary Price (pp. 121-132).
Proposals in draft form have been circulated for new Système International (SI) measurement units that are expected to be official instruments of the Treaty of the Metre by 2015. This review outlines the substance of the proposals and examines some of the consequences of the continuing evolution of the SI toward inter-dependence of base units and quantities since its introduction in 1960. The proposals in question fix at an exact value a number of inter-related fundamental natural constants such as the speed of light, the Planck constant, the elementary charge and Boltzmann’s constant. All SI units are then so defined that their magnitude is set by those fixed values. Notably, the ongoing confusions about chemical measurements and the thermodynamic ‘mole’ are exacerbated. On the big principles of the basic purpose of the SI to facilitate communication and the fixing of fundamental physical constants of nature, there are significant problems and unanswered questions. They risk: damage to the enterprise of science; wide economic loss including increased transaction costs and barriers to global trade; barriers to new technologies and to improvements in measurement accuracy; loss of measurement compatibility or consistency; and a circular global measurement system vulnerable to undetectable systematic errors with serious adverse consequences for environmental decision making among many other vital human activities. The New SI requires frank and open discussion throughout science, technology, industry, trade, and global policy well before irreversible decisions are made.
Keywords: Measurement units; Physical constants; SI quantities; Policy
Why the invariant atomic-scale unit, entity, is essential for understanding stoichiometry without ‘Avogadro anxiety’ by B. P. Leonard (pp. 133-141).
The Avogadro constant is generally considered to be the relevant physical invariant for stoichiometry, intimately associated with the SI base unit for the amount of a specified substance. Unfortunately, it has dimensions of reciprocal amount rather than of amount itself, and this appears to be the source of the widespread confusion permeating this subject. It would make sense, instead, to use its reciprocal—an amount consisting of a single representative entity—as the fundamental invariant for amount. Major simplifications in comprehension then result. In particular, the mole would be redefined in a straightforward way as a designated exact number of elementary entities, making stoichiometric calculations much more easily comprehended. Unfortunately, acceptance by the CIPM of recent CCU recommendations for redefining the mole and kilogram (while keeping the inexactly known carbon-12-based dalton definition) would inject even more confusion into this subject, because the proposed definitions violate a basic compatibility condition relating the mole, kilogram and dalton, stemming from the fundamental concept of the mole itself. However, there are a number of alternative mole-concept-compatible and easily comprehended definitions worthy of consideration, where, in each case, a compatible dalton must be an exact sub-multiple of the (redefined) kilogram. These alternatives should receive much wider discussion before final decisions are made in the major restructuring of the international system of units.
Keywords: Redefinition of SI units; Atomic-scale unit entity; Avogadro’s number; Stoichiometry; Violation of the mole concept
The International System of Units—a case for reconsideration by Ulrich Feller (pp. 143-153).
The International System of Units (SI) follows a concept that goes back to Maxwell. At that time, a logic sound foundation of mathematics was not yet available. This has lead to concepts and terms that are contradictory and in conflict with today’s standard mathematical concepts. The inconsistencies that have evolved in metrology due to the lack of appropriate notions are pointed out. This is most important, as the metrology is a field that is internationally well organized under the umbrella of the Meter Convention, an international treaty for acting on all matters relating to units of measurement. Committees and working groups under the Meter Convention have a leading role in the elaboration of important metrological guides, among others the International Vocabulary of Metrology. Therefore, it is highly desirable that their publications use well-founded concepts and terminology. It is consensus that it is desirable to find a system of units on invariant properties of nature and not on human artifacts, e.g., the prototype of the kilogram. However, the current proposals to improve that are in conflict with standard scientific concepts. It is shown in the paper how these inconsistencies can be avoided. The argumentation is based on the interpretation of numbers developed by mathematicians like Cantor, Dedekind, Peano, and others that have led the logic foundation of mathematics with set and number theory. This foundation excludes dogmas that have been forwarded in the last century under the umbrella of the Meter Convention.
Keywords: System of units; System of quantities; Quantity calculus; Base unit; Derived unit; Number; Quantity; Measurement; Dimension; Constant of nature
Reproposition of numerosity as the SI base quantity whose unit is the mole by Romeu C. Rocha-Filho (pp. 155-159).
‘Amount of substance’ was introduced in the end of the 1950s as the physical quantity whose unit of measurement is the mole. Fundamental problems associated with this physical quantity have caused a never-ending discussion that continues to this day. One of the reasons for this is the fact that the expression ‘amount of substance’ is not a good choice, due to its generality and inclusion of the word ‘substance’. Considering that samples of matter commonly handled by chemists are extremely numerous in entities and that the quality of being numerous or many is referred to as numerosity (a concept related to numerical cognition), this concept is reproposed as a replacement for amount of substance. Then, taking into account ongoing discussions toward a redefinition of the mole, the following definition is proposed for this SI base unit: “the mole is the numerosity of a sample of entities numbering exactly 6.022 141 794 × 1023”. The relationships between four extensive properties of matter (mass, volume, numerosity and number of entities) are detailed and the resulting intensive physical quantities (proportionality constants) are discussed. The concept numerosity is not the product of an invented synonym; furthermore, as a consequence of its generality, it can be used to express the quantity of entities in samples of matter, as well as of light, chemical reactions, etc. The acceptance that mole is the SI unit of numerosity might also solve most of the pedagogic problems associated heretofore with teaching of mole and amount of substance.
Keywords: International System of Units; Amount of substance; Avogadro’s number; Metrology in chemistry
Some reflections on the proposed redefinition of the unit for the amount of substance and of other SI units by Franco Pavese (pp. 161-165).
Proposals on the floor at CIPM are aiming at defining basic units by stipulating a consensus value for a number of fundamental constants. The paper indicates the author’s viewpoint about a number of issues that, in his view, should be better understood before such a choice becomes indisputable. They include the count nature of the Avogadro number; the correct expression of its stipulated numerical value; the check for the consistency of the SI system; the shift to the unit of the experimental uncertainty; the loss of the concept of base unit; the possibility of checking the correctness of the future standards; implications for the future reductions in uncertainty; the meaning of ‘fundamental’ related to the constants; and some lexical problems.
Keywords: Basic units; Definition of units; Fundamental constants; SI
The mole: definition versus practical use by G. Meinrath (pp. 167-170).
Most base units in the SI relate to specific sensoric qualities our body is able to observe: space, heat, brightness, etc. The base unit ‘mole’ incorporates intellectual insight: the atomistic perception of the world. This perception is a quintessence of over 300 years of scientific research. The quintessence, from Dalton’s ‘The sceptical chymist’ to Perrin’s Nobel Prize in 1926 and Pauling’s ‘Nature of the Chemical Bond’ in 1939, results in the conclusion that the base unit of the SI quantity ‘amount of substance’ is not the mole but the dimensionless entity.
Keywords: Mole; Amount of substance; Avogadro number; Dimensionless quantity; Number of entities