Chemists use Avogadro's Number, 6.022 x 1023 every day.
It is a very valuable
number for a chemist to know how to use, and use properly. Where did Avogadro's number
come from? Did Avogadro himself do all the calculations? Was it just arbitrarily made up?
How can it be measured? Some possible answers follow.
Amadeo Avogadro (1776-1856) was the author of Avogadro's
Hypothesis in 1811, which, together with Gay-Lussac's Law of
Combining Volumes, was used to elegantly remove all doubt about
the establishment of the atomic weight scale at the Karlsruhe
Conference of 1860.
The name "Avogadro's Number" is just an honorary name attached
to the calculated value of the number of atoms, molecules, etc. in a
gram mole of any chemical substance. If we used some other mass
unit for the mole such as "pound mole", the "number" would be
different than 6.022 x 1023.
The best modern values for what we now call "Avogadro's Number" are the result of the x-ray
diffraction measurement of lattice distances in metals and salts. The earliest attempts at using
this method are reviewed in Virgo's paper
One example, from x-ray data the one can determine that titanium (Ti)
 Ti metal has a body-centered cubic unit cell (i.e. there are two Ti atoms per unit cell) and
an edge length of 330.6 A.
 One can also find that the density of Ti metal is 4.401 g/cm3.
 The number of grams of Ti in a mole of Ti (47.88 g),
Avogadro's Number, can be calculated as follows:*
Today's best experimental value of 6.022 141 99 x 1023 mol-1 atoms per mol (obtained from
NIST web site) is the best average for measurements using the best methods available. The
experiments are often very difficult to carry out. That the number today has 8 significant figures
is a testament to the quality of modern experimental methods.
*
(General Chemistry, Whitten, Davis and Peck, Saunders College Publishing, 6ed, 2000, p. 523):