Solution to the Avogadro constant challenge.

The Avogadro constant has long been defined as the number of molecules of a substance in a gram molecular weight [1]. In a modern parlance, it is a fundamental physical constant representing the number of entities comprising 1 mol. It is clear that any modification to the definition of macroscopic (kilogram) or microscopic mass scales (atomic mass) will affect the numerical value of the Avogadro constant. The definition of kilogram has remained unaltered since the very first Conférence Générale des Poids et Mesures in September of 1889, when it was declared that the international prototype of the kilogram “shall henceforth be considered to be the unit of mass,” not so with the definition of the atomic mass scale. In 1803/1805, John Dalton established the first atomic mass scale in which hydrogen was assigned Ar(H)=1, whereas the current definition sets Ar( C)=12. In addition, there were numerous other scales used during the intervening years (Table 1). Though Dalton's H=1 mass scale was used in chemistry for nearly a century, many of these alternative scales, following a suggestion by Wollaston, employed oxygen as the standard instead—an idea which resurfaced near the end of the nineteenth century as the O=16 scale. With the discovery of isotopes, the oxygen scale was refined to the O isotope, albeit only among physicists. The most recent change in the atomic mass scale occurred during the height of the cold war when the oxygen scale, Ar( O)=16, was abandoned in favor of the current Ar( C)= 12 by the International Union of Pure and Applied Physics (Ottawa 1960) and by the International Union of Pure and Applied Chemistry (Montreal 1961) [2]. The relative atomic mass of the O isotope in the C-scale is 15.9949—a difference of 0.03% from the “old” value of 16.0000. This shift, in turn, alters the value of the Avogadro constant from 6.024×10 to 6.022×10 mol. This “change” in the numerical value of the Avogadro constant can be easily spotted by inspection of twentieth century chemistry textbooks [3]. It may be of interest here to mention an earlier story regarding the value of the Avogadro constant when determination of NA involved measurements of lattice spacing in crystals [4]. In 1919, at a time when wavelengths could not be measured directly, Manne Siegbahn (1924 Table 1 Relative atomic mass scales through the centuries