In 1811, the Italian scientist Amedeo Avogadro postulated that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This was based upon the 1805 evidence of the French chemist and physicist Joseph Louis Gay-Lussac, that when gases react together, they do so in volumes that are simple multiples of each other. And their products, if gases, also have these volumes.

It was not until 1865 that an estimate was made of the number of molecules in a gas volume. This estimate was made by the Austrian physicist and chemist Johann Josef Loschmidt, who used a value for the collision cross-section of molecules. Improvements in the theory of gas kinetics, and better measurements, increased the accuracy through to the end of the nineteenth century. Then, several other big names in physics used other methods to give even better answers.

Albert Einstein had this as the subject of his PhD thesis, in 1905. His answer was not very good, only because there was a mistake in his mathematics. Today, Avogadro's constant - the number of molecules in a mole - is known with great accuracy, from X-ray and density measurements on pure silicon crystals. Avogadro's constant is approximately 6.022 × 10₂₃. This is roughly the number of water molecules in 18 millilitres of water.

Molecules exist, and are very small. Not everyone was convinced of this until the end of the nineteenth century. Having a value for an atomic mass, and Avogadro's constant, means that we do not need a separate standard for macroscopic mass, based upon that kilogram of platinum kept somewhere in France.

John Murrell is coauthor of Properties of Liquids and Solutions (buy this book from Amazon (UK) or Amazon (USA)), and The Chemical Bond (buy this book from Amazon (UK) or Amazon (USA)). See his website.