Technologies for Measuring Avogadro's Number

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 Mullikan's 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 was 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.

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