Analysis of Two Definitions of the Mole That Are in Simultaneous Use, and Their Surprising Consequences

Abstract

This paper highlights the use of two related but distinct definitions of the mole in chemistry, often in the same text, and analyzes their consequences. The mole is officially defined by IUPAC as a unit for "amount of substance" and is not a number, since otherwise it could not be a base unit in the international system of units (SI); this definition relies on an outdated continuum view of matter. By contrast, in chemical practice the mole can simply be treated as a large number (1 mol = 6.022... × 1023). Which of these definitions is implied in a specific instance can be determined by checking whether "amount of" or "mole of" is followed by a singular word for a substance (e.g., "water"), or a plural word for atoms, molecules, ions, or electrons. For discrete elementary entities, the "amount" of entities is the number of the entities; for instance, 1 mol electrons = 6.022 × 1023 electrons. In short, when applied to elementary entities, the mole must be a number. Most textbooks initially recite the official definition of the mole but later implicitly use the number definition when referring to moles of electrons or of ions such as H+(aq). While most practicing chemists ignore the subtleties of the official definition, its ambiguity trying to link a continuum substance concept with a number of countable entities must confuse students. Like previous authors, we argue that a substance essentially equals the molecules of which it consists, and therefore, "amount of substance" is equal to the "number of molecules". In this framework, the mole is a number unit analogous to dozen or percent. The number definition has interesting consequences that have not been exploited due to its unofficial status: If 1 mol = 6.022 × 1023, then the gas and Boltzmann constants are equal, R = kB. Since 1 mol = 6.022 × 1023 for electrons, the Faraday constant equals the elementary charge, F = 96,485 C/6.022 × 1023 = 1.602 × 10-19 C = e, and 1 eV = 96.5 kJ/mol. These unifying equalities will make it easier to learn and teach chemistry.