AVOGADRO'S NUMBER

    A principle stated in 1811 by the Italian chemist Amadeo Avogadro (1776-1856) that equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties. This number (Avogadro's number) is 6.023 X 10²³. It is the number of molecules of any gas present in a volume of 22.41 L and is the same for the lightest gas (hydrogen) as for a heavy gas such as carbon dioxide or bromine.

Avogadro's number is one of the fundamental constants of chemistry. It permits one to compare the different atoms or molecules of given substances where the same number of atoms or molecules are being compared.
It also makes possible determination of how much heavier a simple molecule of one gas is than that of another, as a result the relative molecular weights of gases can be ascertained by comparing the weights of equal volumes.

Avogadro - his contribution to chemistry

In order to understand the contribution that Avogadro made, we must consider some of the ideas
being developed at this time. Chemistry was just beginning to become an exact science. The Law of
Definite Proportions and the Law of Multiple Proportions were well accepted by 1808, at
which time John Dalton published his New System of Chemical Philosophy.

Dalton proposed that the atoms of each element had a characteristic atomic weight, and that it was
atoms that were the combining units in chemical reactions. Dalton had no method of measuring
atomic weights unambiguously, so made the incorrect assumption that in the most common
compound between two elements, there was one atom of each.

At around this time, Gay-Lussac was studying the chemical reactions of gases, and found that the
ratios of volumes of the reacting gases were small integer numbers. This provided a more logical
method of assigning atomic weights. Gay-Lussac did not carry through the full implications of his
work. However, Dalton realised that a simple integral relation between volumes of reacting gases
implied an equally simple relation between reacting particles. Dalton still equated particles with
atoms, and could not accept how one particle of oxygen could yield two particles of water. This was
a direct threat to the relatively new atomic theory, and therefore Dalton tried to discredit the work of
Gay-Lussac.

In 1811, Avogadro published an article in Journal de physique that clearly drew the distinction
between the molecule and the atom. He pointed out that Dalton had confused the concepts of atoms
and molecules. The "atoms" of nitrogen and oxygen are in reality "molecules" containing two atoms
each. Thus two molecules of hydrogen can combine with one molecule of oxygen to produce two
molecules of water.

Avogadro suggested that equal volumes of all gases at the same temperature and pressure contain the same number of molecules which is now known as Avogadro's Principle.

The work of Avogadro was almost completely neglected until it was forcefully presented by
Stanislao Cannizarro at the Karlsruhe Conference in 1860. He showed that Avogadro's Principle
could be used to determine not only molar masses, but also, indirectly, atomic masses. The reason
for the earlier neglect of Avogadro's work was probably the deeply rooted conviction that chemical
combination occurred by virtue of an affinity between unlike elements. After the electrical discoveries
of Galvani and Volta, this affinity was generally ascribed to the attraction between unlike charges.
The idea that two identical atoms of hydrogen might combine into the compound molecular hydrogen
was abhorrent to the chemical philosophy of the early nineteenth century.

Avogadro - his number

It was long after Avogadro that the idea of a mole was introduced. Since a molecular weight in
grams (mole) of any substance contains the same number of molecules, then according to
Avogadro's Principle, the molar volumes of all gases should be the same. The number of molecules
in one mole is now called Avogadro's number. It must be emphasised that Avogadro, of course,
had no knowledge of moles, or of the number that was to bear his name. Thus the number was never
actually determined by Avogadro himself.

As we all know today, Avogadro's number is very large, the presently accepted value being
6.0221367 x 10²³. The size of such a number is extremely difficult to comprehend. There are many
awe-inspiring illustrations to help visualize the enormous size of this number. For example:

An Avogadro's number of standard soft drink cans would cover the surface of the earth to a depth of over 200 miles.

If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.

If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.
 

Determination of the number

Cannizarro, around 1860, used Avogadro's ideas to obtain a set of atomic weights, based upon
oxygen having an atomic weight of 16. In 1865, Loschmidt used a combination of liquid density,
gaseous viscosity, and the kinetic theory of gases, to establish roughly the size of molecules, and
hence the number of molecules in 1 cm3 of gas.

During the latter part of the nineteenth century, it was possible to obtain reasonable estimates for
Avogadro's number from sedimentation measurements of colloidal particles. Into the twentieth
century, then Mullikens oil drop experiment gave much better values, and was used for many years.

A more modern method is to calculate the Avogadro number from the density of a crystal, the
relative atomic mass, and the unit cell length, determined from x-ray methods. To be useful for this
purpose, the crystal must be free of defects. Very accurate values of these quantities for silicon have
been measured at the National Institute for Standards and Technology (NIST).

To use this approach, it is necessary to have accurate values of atomic weights, often obtained by
measuring the mass of atomic ions. For example, an ion trap, employing extremely uniform and
stable magnetic and electric fields should allow such measurements to be made to better than 1 part
in 1010. The relative atomic mass of silicon is particularly important, since silicon crystals are used in
the x-ray methods mentioned above.

As a continuation of this approach, one of the 1999 NIST Precision Measurement Grants has been
awarded to David Pritchard, physics professor at the Massachusetts Institute of Technology. He will
conduct cyclotron frequency measurements on ions that could achieve a 100-fold improvement in
the accuracy of atomic mass measurements. MIT has developed the world's most accurate mass
spectrometer capable of measuring the atomic mass of atoms to one part in 10 billion. Pritchard
proposes to simultaneously measure the cyclotron frequencies of two different ions in order to
improve the values of several fundamental constants, including Avogadro's number.

At the present time, information on Avogadro's number from many different experiments is pooled
with other observations on other physical constants. A most probable and self-consistent set of
physical constants that best fits all reliable data is then found by statistical methods.

The size of Avogadro's number is determined by our definition of the mole. What it does
demonstrate is how small an atom or molecule is compared to the amounts of material we are
familiar with in everyday life, since the definition of the mole involves amounts of material we are
completely familiar with.

If you are a scholar on the life and works of Avogadro, and have information that might be usefully
included on this page, then why not mail me the details. Contributions will be acknowledged.

Special thanks to  Chris Johnson for his insightful presentation.