On the dimensionality of the Avogadro constant and the definition of the mole

Abstract

There is a common misconception among educators, and even some metrologists, that the Avogadro constant N A is (or should be) a pure number, and not a constant of dimension N -1 (where N is the dimension amount of substance). Amount of substance is measured, and has always been measured, as ratios of other physical quantities, and not in terms of a specified pure number of elementary entities. Hence the Avogadro constant has always been defined in terms of the unit of amount of substance, and not vice versa. The proposed redefinition of the mole in terms of a fixed value of the Avogadro constant would cause additional conceptual complexity for no metrological benefit.

A sorites paradox in the conventional definition of amount of substance

“…The second sentence of the current definition, which attempts to define the term "elementary entity" by example, should be moved to the Mise en pratique, while the 1980 clarification from the CIPM ("unbound, at rest and in the ground state") should be incorporated into the main definition. Three possible revised wordings are given in [4]. As is discussed elsewhere [4,27], there is no reason to change the basis of the definition of the mole to a fixed numerical value of the Avogadro constant: indeed, the present author believes that such a move would only aggravate the confusion surrounding the quantity amount of substance.…”

“…Three possible revised wordings are given in [4]. As is discussed elsewhere [4,27], there is no reason to change the basis of the definition of the mole to a fixed numerical value of the Avogadro constant: indeed, the present author believes that such a move would only aggravate the confusion surrounding the quantity amount of substance.…”

“…Some authors have attempted to resolve this paradox by saying that amount of substance is (or should be) a quantity of dimension 1 [2,3]: several reasons why this approach is unsatisfactory have been discussed elsewhere [4]. This paper explains why amount of substance, as that term is generally understood, must be a continuous quantity.…”

“…Problems with differentiation can be resolved by taking a separate physical quantity which is both continuous and proportional to amount of substance: for example, chemical potential can also be defined by (3), and this is closer to Gibbs' original definition [7]. 3 µ = M(∂G/∂m) T,p (3) The many problems caused by ignoring the separate quantity dimension of amount of substance are discussed elsewhere [4]. For the purposes of this discussion, it is sufficient to note that the mass of a given chemical substance is just as discrete at the microscopic scale as the number of entities.…”

“…In other words, if there is a significant difference in measurement result by adding a single entity, the measurement is a count of number of entities; if there is no significant difference in measurement 4 The present author prefers to see temperature as a property of an ensemble of particles, and use the term "thermal energy" for the property of a single particle. Nevertheless, the use of the term "temperature" for a single particle is widespread in the literature.…”