# With such limited resources of his time, how did Avogadro come up with his number (the number of molecules in a mole of gas)?

Asked by: Chris Redgate### Answer

The short answer is:**he didn't!**

Avogadro stated the theory that equal volumes of gases at the same temperature and pressure contained equal numbers of molecules, being the first to tease out the discrepancy between molecules and atoms. Unfortunately no one listened to him (probably because he was going against the ideas of one of the most revered proto-chemists of his day, Dalton) Avogadro died before anyone looked at his paper and saw the wisdom in his ideas.

In any case, someone had to come up with the number of particles in these volumes of gas Avogadro was talking about. Loschmidt, Maxwell, and Kelvin made early estimates of how many molecules could be found in a given volume of gas at standard temp and pressure based on estimates of molecular diameters, the mean free path of a molecule according to the kinetic theory of gases, and some fancy calculation.

Plank, Einstein, Millikan and Perrin all tried to use the new mathematical tools presented by quantum theory to refine estimates of how many molecules are in a given volume of gas early in the 20th century. In the meantime, the actual number searched for shifted to the number of oxygen atoms in 16 grams of O, since it was known that Oxygen was 16 times heavier than hydrogen (just lucky that they were both diatomic!) Once atomic structure came to be known, the value sought was understood to be the number of times 1 atomic mass unit can be divided into one gram. (this is often stated as the number of protons in one gram, but 1 AMU is actually closer the mass of 1 proton plus one half of an electron, or 1/12 the mass of an atom of C-12)

This number was called 'Avogadro's Number' by Perrin, who wished to honor the man who never received recognition during his life for his substantial contributions to early chemistry.

You can read more about Avogadro and Avogadro's Number at:

Notes on Avogadro's Number

Avogadro's Number

History of Avogadro's Number

Answered by: Rob Landolfi, Science Teacher, Washington, DC

'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'

(

**Godfrey Hardy**(

*1877-1947*)