Milestones related to the Avogadro constant

Why 6.022 x 10²³, and not a simpler quantity like a hundred or a septillion? The answer lies in the extraordinary work of Jean Perrin, a French scientist, and other scientists like Robert Millikan.

As mentioned in an earlier section, the Avogadro number is used to represent a large number of atoms or molecules. Perrin, in his attempt to determine the mass of a molecule of hydrogen gas, devised a way to count the number of molecules in a gas that occupied the same volume as two grammes of hydrogen gas. He obtained a constant count that averaged 7.05 x 10²³ and named the number after the Italian scientist Amedeo Avogadro. The Avogadro number, which is now equated to a mole, was subsequently improved upon by scientists to one containing more than three significant figures. However, the experiments that the scientists (including Perrin) conducted to measure the Avogadro number did not have a consistent and precise definition of the number. After much discussion, the mole was accepted as a SI base unit in 1967 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.

The choice of carbon-12 in the definition of a mole was partly because the isotope was already selected to define the unified atomic mass unit and also due to the fact that it did not significantly alter the values of the Avogadro number previously determined by scientists. With the Avogadro number well defined, scientists worked further to refine it. They used a precise and reliable experimental method called x-ray diffraction, which produced an Avogardo number of up to ten significant figures. In Nov 2018, the definition of the mole was finally changed to:

A mole is the amount of substance of a system that contains exactly 6.02214076 x 10²³ elementary entities.

The significant milestones of events and experiments related to the Avogadro constant, and links to detailed explanation of those experiments, are found in the table below.

Year	Event	Measurement	Results
1834	Michael Faraday’s experiments	One mole of charge, 1F (originally with respect to mass equivalent to 1g of H₂, subsequently with respect to different molar mass of elements). $m=\frac{Q}{F}\left ( \frac{M}{z} \right )$	Subsequently refined to 96485 C
1909	Jean Perrin’s experiments	One mole of ideal gas (via distribution of gamboge). $\frac{n}{n_{0}}=e^{-\frac{N_{A}mgh}{RT}}$	6.5 x 10²³ to 7.2 x 10²³
1909	Robert Millikan’s experiments	Charge of an electron. $N_{A}=\frac{F}{q}$	6.059 x 10^²³mol^-1
1961	SI amu definition	One carbon-12 = 12 amu amu of other isotopes determined by mass spectrometry with carbon-12 as reference isotope. $u\; of\; ^{m}\!X=\frac{\frac{u}{z}\; of\; ^{m}\!X}{\frac{u}{z}\; of\; ^{12}C}\times u\; of\; ^{12}C$
1967	SI mole definition	A mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. Prior to this, there is no proper definition of a mole. Perrin’s and Millikan’s definitions using ideal gases and the equivalent masses of electrolysed elements, respectively, are not specific. With the SI definition, all subsequent experimental values of molar mass and hence the Avogadro constant are based on 0.012 kg of carbon-12.
>1967	Molar mass refinement	The value of the molar mass of an isotope is dependent on the precision of the mass spectrometer’s amu results of $\frac{\frac{u}{z}\; of\; ^{m}\!X}{\frac{u}{z}\; of\; ^{12}C}$
>1967	X-ray diffraction experiments	Since the Avogadro constant is defined as the number of atoms in 0.012 kilogram of carbon-12, a hypothetical way to precisely evaluate the constant through X-ray diffraction is to synthesize a perfect sphere of pure carbon-12 that weighs exactly 0.012 kilogram and calculate the ratio of its molar volume to that of one-eighth of its unit cell (n = 8 carbon atoms in a unit cell). $N_{A}=\frac{V_{mol}}{a^{3}/n}$ In reality, it is impossible to carve a perfect sphere out of diamond with minimal defects and the Avogadro constant is instead determined using a sphere that is grown from highly enriched silicon-28. $N_{A}=\frac{nM}{\rho a^{3}}$ Even though the X-ray diffraction approach is by far the most accurate, it gives an Avogadro constant with a very small margin of error.	6.02214076 x 10²³mol^-1
2018	New definition	*The Avogadro constant is exactly 6.02214076 x 10²³ mol^-1. The mole is the amount of substance that contains exactly 6.02214076 x 10²³ of elementary entities.*