History and progress in the accurate determination of the Avogadro constant

Abstract

The Avogadro constant, N A , is a fundamental physical constant that relates any quantity at the atomic scale to its corresponding macroscopic scale. Inspired by the kinetic gas theory Avogadro proposed his hypothesis in 1811, in order to describe chemical reactions as an atomic process between atoms or molecules. Starting from his pioneering findings, the determination of this large number has fascinated generations of scientists up to this day. The review of methods aimed at finding a value for N A starts with the calculations made by Loschmidt (1865; N A ≈ 72 × 10 23 mol −1 ) who evaluated the number of molecules in a given gas volume, derived from estimates of molecular diameters and the mean free path length. Consideration of Brownian motion led to some more accurate determinations of N A around the beginning of the 20th century (Perrin (1908); N A ≈ 6.7 × 10 23 mol −1 ). Other methods developed in the following years are based on Millikan's oil drop experiment (1917, N A ≈ 6.064(6) × 10 23 mol −1 ), on the counting of alpha particles emitted from radium or uranium (Rutherford (1909); N A ≈ 6.16 × 10 23 mol −1 ) and on investigations of molecular monolayers on liquids (Nuoy (1924); N A ≈ 6.004 × 10 23 mol −1 ).A modern method to derive N A from the density, the relative atomic mass, and the unit cell length was introduced by Bragg in 1913. It makes use of the diffraction of x-rays by the interatomic spacings of a crystal lattice and its periodic arrangement. The accuracy of this method is extremely affected by the fact that the lattice scale of the structurally imperfect lattice can be calibrated only approximately in SI units. Data of N A were, therefore, found to be in disagreement with other fundamental constants (Bearden (1931); N A ≈ 6.019(3) × 10 23 mol −1 ). A break though was achieved with perfect crystals of silicon and x-ray interferometry making available very precise data of atomic distances, expressed in SI units (Bonse and Hart 1965).Today, metrology has re-discovered the Avogadro constant and uses it as one of several possible routes to a re-definition of the kilogram because the old platinum iridium artefact exhibits long-term stability problems. This application of the Avogadro constant presupposes a final measurement uncertainty of about 1×10 −8 , a challenge for the experimental determination of the quantities involved, i.e. macroscopic density, isotopic composition, and unit cell volume of a silicon crystal. Many years of research work were centred on the problem of how far the perfection of a real crystal is away from the ideal state. At present, it is widely accepted that,

Determination of the Atomic Weight of 28Si-Enriched Silicon for a Revised Estimate of the Avogadro Constant

“…1,2 The measurements, for a number of technical reasons, use highly polished one-kilogram spheres of silicon. 3,4 An overall relative target uncertainty of less than 2 in 10 8 is desired for the Avogadro constant to ensure a smooth transition between the definitions.…”

A new definition for the mole based on the Avogadro constant: a journey from physics to chemistry

“…In 1909, Perrin [9] made further measurements of the Brownian motion of particles, which, together with the formulae derived by Einstein, enabled him to determine a value of 6.7 × 10 23 for N [2]. Perrin explained clearly how he used the gram-molecule:…”

“…The first application of the method was to single crystals of calcite [2]. The major limitation of the method at that time was in the determination of the length of the unit cell of the crystal.…”

“…Equation (4.2) is given using current notation in the following section. 2 In Stille's text, Molzahl is a dimensionless quantity. He advocated its retention in this form rather than the introduction of an alternative German term Stoffmenge (literally 'amount of substance') as a new base unit with an associated definition for the term Mol of the 'Stoffmenge that contains as many entities as there are in A r (O) g of atomic oxygen'.…”

“…In addition, the history of the Avogadro constant has been reviewed [2]. However, the parallel developments in the understanding of amount of substance, the quantity of which the mole is the base unit, have not been discussed in detail.…”