Happy Mole( 6.022*10^23) Day!  But where did the number come from?

1. Mole: the SI unit for amount of a substance. Mole is also the name for a small burrowing mammal.

The mole concept is one of the most fundamental concepts in Chemistry. Every year October 23rd is celebrated as the Mole day from 6.02 am to 6.02 pm since the date makes the number 10/23. 

Just like a set of 12 is a dozen, a set of 100 is a century, similarly, 1 mole is a set of 6.022*10^23. For the sake of convenience, Carbon-12 is considered as a standard for calculating this number. Earlier oxygen-16 was taken as the standard, but since the mass of Carbon-12 is exactly 12.000gm, a whole number unlike oxygen which is 15.994, carbon-12 is chosen. The calculations are much easier with carbon 12. Moreover the number of protons and neutrons is same in Carbon-12, 6 each.

2. one mole of everything contains same particles just like one dozen and one century 

So one mole is the amount of a substance that contains as many number of particles as there are atoms present in exactly 12 gm of Carbon. 12gm of Carbon is nothing but 1 mole of Carbon-12. But how many atoms are present in 12 gm of Carbon? 

For example, if a big block is made up of tiny blocks and you want to find the number of tiny blocks in it, you divide the area of the big block with the area of a single tiny block. Similarly for calculating the number of atoms in carbon 12 we need to divide 12 gm of carbon with the mass of one atom of carbon-12. The mass of 1 atom of carbon is  1/12th the mass of 12 atomic units of carbon and masses of all other atoms are calculated relative to this standard. 1 atomic mass unit=1.6605*10^-24gm. So when 12 is multiplied with 1.6605*10^-24, we get the mass of 1 atom of carbon which is 1.992684*10^-23. This was experimentally proved using a mass spectrometer. It is an instrument that ionizes the sample into fragments. The mass and charge on these fragment is then analyzed. 

12gm of carbon divided by 1.992648*10^-23 gm gives us the number 6.022*10^23 atoms which is the Avogadro constant named after the scientist Amadeo Avogadro.

In short, for carbon, mass of 1 mole=12gm, mass of 1 atom in that 1 mole =1.992684*10^-23gm and number of such atoms in 12gm of carbon=6.022*10^23.

But you know what the interesting part is? one mole remains the same even when the substance is changed. Whether you take Oxygen, nitrogen, Iron, Zinc, Copper, Helium anything, the number of atoms in 1 mole of all these remain the same. That is why it is a constant. 

For example mass of 1 mole of oxygen is 15.994gm. The mass of 1 atom in it is 2.66*10^-23. So the number of atoms is the ratio of these 2 quantities i.e. 6.022*10^23. 

1 mole of any substance contains the same number of particles. But back then, during the times of Avogadro, there weren't any mass spectrometers. Many techniques were used to calculate this number including the random motion of suspended particle( Brownian motion). Avogadro was famous because of his law, equal volumes of all gases at the same temperature and pressure contain equal number of molecules. The accurate determination of the Avogadro number was possible only after Robert Mullikan calculated the charge on an electron. The charge on one mole of electrons was known at that time 96485C/mole which is the Faraday constant named after Michael Faraday. The charge on a single electron was found to be 1.602*10^-19C. If you divide these two quantities, you get the Avogadro's number, which is 6,022*10^23 particles in 1 mole of electrons. 

Just to get an idea of how big this number is, 602213670000000000000000

Although its is a huge number, but the size of the particles is very very tiny. Just to take our imagination at a bigger level: One mole of each one of us contains the same number of particles!!!

©Neha Kanase

References

1. How Was Avogadro's Number Determined? - Scientific American

2. NCERT Class IX Chemistry textbook part 1

3. Image 1: labtopiainc.com

4. Image 2: Lumen learning