Avogadro's Number N_A

N_A the number 6.02 x 10²³ (or more accurately 6.022 1415 x 10²³ with an uncertainty of 0.000 0010 x 10²³) has been estimated in a number of ways. 

Early estimates of N_A's value were made by calculations that estimated the number of molecules in a given volume, based on estimates of molecular diameter, and mean free path (Loschmidt 1865). In 1873 Maxwell estimated that Loschmidt's number (the number of molecules in 1 cm³ of gas at normal temperature and pressure) was 1.9 x 10¹⁹. Given that there are 22,400 cm³ in a mole of gas at normal temperature and pressure, this leads to an estimate of the number of molecules in a mole of 4.3 x 10²³. Slightly later, Kelvin obtained an estimate of the number of molecules in a gas from the scattering of light, and his data would give a value of 5 x 10²³.

Consideration of Brownian motion led to some of the more accurate determinations of Loschmidt's number around the beginning of the 1900's. J. Perrin (1908) is the first person to have used the term Avogadro's number for the number of particles in a mole. He estimated it to be between 6.5 x 10²³ and 6.9 x 10²³ from studies of Brownian motion. By 1914 Brownian motion methods had led to an estimate of 6.03 x 10²³. 

Radioactive methods were used by a number of investigators to directly count the number of alpha particles emitted from radium and uranium. Rutherford and Geiger estimated that Avogadro's number was 6.2 x 10²³. 

Thin films of sodium oleate assumed to be monolayers on the surface of water led Lecomte du Nouy to estimate the size of a molecule, and from that the number of molecules in a mole as 6.004 x 10²³ in 1924. A variation of this experiment is sometimes done today by beginning chemistry students. 

Modern methods of determining Avogadro's number rely on the use of x-ray crystallography to get precise dimensions in crystals. These can produce extremely precise values of N_A with an error of less than 0.000 000 01. Further information about physical constants and standards is available at the National Institute of Standards and Technology. 

References: 
A. J. Berry, From Classical to Modern Chemistry, Dover Publications, 1968 

Copyright © 1996 David Dice