The mole

Apparently it is difficult for some school children to comprehend what a mole is. I don't see why this should be the case, since a mole is just a numerical amount of atoms, molecules or formula units of a substance. That number, avogadros constant, is chosen in a way that makes the numbers involved easier to work with. Perhaps it is because teachers are too clever by half in explaining the concept?

Avogadros number is chosen to be the number of atoms which has a mass in grams with the same numerical value as the molecular mass of it's constituent molecules in atomic mass units. If the molecular mass of a molecule is 18.02 u, it's molar mass is 18.02 g/mole.

It would have been eminently possible to never introduce the concept of unified atomic mass units and moles; you could simply have tables that list the mass in kilograms of an average atom of an element, or specific isotopes. You could express the number of molecules as a unitless, numerical value; the actual number of molecules.

The problem with doing things this way is that any amount of substance visible to the naked eye consists of great big thundering hordes of molecules, and the mass of any molecule you're interested in will be incredibly tiny.

The choice of the unified atomic mass unit is also quite clever. It is 1/12th the mass of an atom of carbon-12. There is a slight variation in binding energy per nucleon between different atoms, and neutrons are slightly heavier than protons, but the mass of an isotope in atomic mass units is to within about 1% simply the sum of the number of protons and neutrons.

Thus U-238 should have an isotopic mass of about 238 u(actual: 238.051 u). Fe-56 should have an isotopic mass of about 56 u(actual 55.934 u). Hydrogen-1 should have an isotopic mass around 1(actual 1.0078 u).