I understand how a mole works, however, I have no clue how Avogadro got the specific number of 6.02×10^23.
I have a bachelor’s degree in biochemistry, and as far as I’m aware the number itself essentially has no meaning. The concept of the mole is incredibly useful for stoichiometric equivalence, but for this the actual 6.02 * 10^23 could have been essentially any number.
Where the actual number of molecules in a mole becomes relevant, and why 6.02 * 10^23 is used, has to do with molar mass. Ever wonder why a mole of a substance has the same mass, in grams, as the atomic mass of the substance’s constituent atoms? A mole of water has a mass of 18.0528g, and a single molecule of water has a mass of 18.0528 daltons. What a coincidence!….. Or is it? In reality, by changing the number of molecules in this concept we have called a mole, we can make this conversion work perfectly. So, in short, 6.02 * 10^23 is exactly the number of molecules necessary to convert the units of mass of a molecule, called daltons, into the units of mass relevant to chemistry, grams.
It’s roughly the number of protons and neutrons in one gram of whatever you have. The mass of a proton and neutron is close enough to the same and electrons are negligible so we can ignore them. Given that, if you have one gram of something – anything – and divide it by the mass of a nucleon, you get Avagadro’s number of nucleons.
The number is based on the Kg. The value of the Kg is arbitrary but the number is the number of AMU in a Kg.
Avogadro did not get the number. The constant has his name because he was the first to suggest that it should be constant, or, more precisely, that the volume of gas at given temperature and pressure is proportional to the number of individual particles in that volume. The actual value was derived from some rather advanced thermodynamic and electrodynamic calculations and measurements
about a hundred years after Avogadro’s time.
Specifically, one way was to first determine the charge of a single electron. By observing the motion of tiny charged droplets in an electric field the electric charge of each droplet can be calculated. Since the droplets are tiny, each only has a few extra electrons on it. So the charges of all droplets are going to be integer multiples of some minimum value – the charge of one electron. After getting that, obtaining the Avogadro’s number is as simple as measuring the charge of one mole of electrons and dividing it by the charge of one electron. The charge of one mole of electrons was determined from observing electrochemical reactions (electrolysis) and comparing the amount of charge discharged and the amount (moles) of substance electrolyzed.