How should I study about moles and how they relate to things like Avogadro's number and molar mass?

Since the early days of chemistry, chemists could figure out the relative masses of atoms.

For example, they knew that a `"C"` atom had a mass 12 times that of an `"H"` atom, an `"O"` atom had 16 times the mass of an `"H"` atom, and so on.

For argument's sake, let's assume that they could put a "pile" of atoms on a balance and determine their total mass.

Then, if they measured out say, 1 g of hydrogen, 12 g of carbon, and 16 g of oxygen, they knew they had the same number of atoms in each pile, even if they didn’t know how many atoms or their individual masses.

They decided to use `"H"` as their standard pile with a mass of 1 g. The pile became a mole, after the Latin word for a pile of rocks.

Even today in England, which was occupied by the Romans, a pile of stones used as a breakwater is called a "mole".

It was natural to assign to each atom an atomic mass that had the same number as the mass of its mole.

Thus, the atomic masses became 1 unit for `"H"`, 12 units for `"C"`, and 16 units for `"H"`.

Eventually, chemists figured out how many atoms there are in a mole of atoms, and they called it Avogadro's Number (`N_"A"`).

`N_"A" = 6.022 × 10^"23"color(white)(l) "per mole"`

Then, if one mole of `"H"` atoms had a mass of 1 g, one atom must have had a mass of

`"1 g"/(6.022 × 10^"23" "atoms") ≈ 1.6 × 10^"-24" color(white)(l)"g"`

Today, we use carbon-12 atoms as our standard, and we define a mole (symbol mol) of carbon-12 as exactly 12 g of carbon-12.

We say that the molar mass of carbon-12 is exactly 12 g.

Since it contains Avogadro's number of atoms,

A mole of anything (atoms, molecules, ions, people, etc.) is Avogadro's number of those things.

The mass of an atom of carbon-12 is defined as exactly 12 unified atomic mass units (symbol u).

Thus the atomic mass of a carbon-12 atom is exactly 12 u (not amu).

Summary: The mole is a convenient way to measure a desired number of atoms or molecules.