How was the Avogadro constant determined? Why 6.022 x 1023, and not a simpler quantity like a trillion or a septillion?
The detailed explanation can be found in the new eBook, The Mole: Theories Behind the Experiments That Define the Avogadro Constant, which explores the groundbreaking concepts that have transformed our understanding of the Avogadro constant from the 1800s to 2018.
In short, scientists require a quantity that is huge and precisely defined to conveniently count samples of atoms and molecules. In 1967, a consensus was reached and the mole was accepted as a SI base unit with the following definition:
A mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.
Having defined the mole, the next logical step was to experimentally determine the exact number of atoms in twelve grammes of carbon-12. This was accomplished using a method called x-ray diffraction, which gave a value of 6.02214076 x 1023 in 2017. The 2017 result was so accurate that the definition of the mole was, in Nov 2018, changed to:
A mole is the amount of substance of a system that contains exactly 6.02214076 x 1023 elementary entities.
With this new definition, the molar mass of carbon-12, while still 0.012 kg, has a very small degree of uncertainty that has to be determined through future experiments.
The 1967 definition of the mole states that if there are twelve grammes of carbon-12 in a container, there are 6.022 x 1023 atoms of carbon-12 or one mole of carbon-12 in the container. Applying the same train of thought, if there are m grammes of carbon-12 in a vessel, there are moles of carbon-12.
Hence, the number of moles of a substance is the ratio of the mass of the substance, m, and its mass per mole, M (also known as molar mass), i.e.:
Eq2 remains valid with regard to the 2018 definition.