mass
'no magic to the mole'
amount
molar mass
concentration
solution volume
gas volume
molar gas volume
Avogadro
constant, L
number of
entities, N
Now try the following question.
G11. EVOLUTION OF THE AVOGADRO CONSTANT & THE 2018 S.I. UNIT MOLE
How was the Avogadro constant determined ?
Adapted from Feb 16, 2004
Scientific American article
Despite what many people might assume, Avogadro’s constant – the number of elementary entities (aka elementary particles) in the unit for the physical quantity amount of substance, i.e., per mole
– was neither invented, discovered nor measured by Amadeo Avogadro (1776–1856).
An ecclesiastical lawyer more interested in mathematics and physics, Avogadro was Italy’s first professor of physics when appointed to the University of Turin (1820), the city then being the newly restored capital of the Savoyard Kingdom of Sardinia. He is most famous for his postulate that
‘equal volumes of different gases at the same temperature and pressure contain the same number of particles’ (1811), an excellent approximation almost unrecognized until some 50-odd years later. This was championed by Stanislao Cannizzaro (1826–1910) at the first ever scientific congress, held in Karlsruhe (1860). With an appreciation of atoms and molecules being then unclear to chemists and physicists, there was also wide disagreement on the atomic weights of several of the known elements.
The term ‘Avogadro number’ was introduced by French physicist Jean-Baptiste Perrin. He reported (1909) an experimentally determined estimate of this number confirming the findings of Einstein’s theoretical paper (1905) on Brownian motion which predicted that colloidal particles should obey the experimental gas laws. Working with colloids, Perrin was able to observe this random, haphazard movement of suspended microscopic particles and thence to calculate Avogadro’s number, ‘the number of molecules per gram molecule of a gas’. A variety of experimental techniques has been used subsequently to estimate the magnitude of this important physical constant.
Precise determinations of Avogadro’s number require measurement of a single quantity on both the nanoscopic and macroscopic scales using the same unit of measurement. This was realised when US experimental physicists Robert A. Millikan (1868–1953) and Harvey Fletcher (1884–1981) measured the charge on an electron in their famous oil drop experiment (1909). The charge on one mole of electrons had
Over time, revisions in the base set of S.I. units necessitated re-definitions of the concepts of chemical quantity. Avogadro's number was deprecated in favour of the Avogadro constant. The former has made something of
a comeback as far as the wording of the 2018 BIPM revisions are concerned, however.
An alternative approach to determining Avogadro’s constant begins with careful macroscopic measurements of the density of an ultra-pure sample of silicon. The density of this material on the nanoscopic scale is then measured using X-ray diffraction (XRD) techniques to determine the number of atoms per unit cell in the crystal lattice, and the distance between equivalent lattice points that define the unit cell, the points in space about which the atoms in the crystal are free to vibrate.
(see Physical Review Letters, 1974, volume 33, issue 8, 463).
Such a method was adopted in the 2018 re-definition of the mole - XRD determination of the precise density of an ultra-pure silicon sample, highly enriched in the 28-Si nuclide. Experimental details, the so-called
Mise en pratique, are viewable at: Practical realization of the definition of the mole with the smallest uncertainty.
