#"Dozens, Baker's dozens, Botany Bay Dozens,"# all of these are particular numbers used to measure particular things: e.g. eggs, bread rolls, lashes. The mole is just another such number, #"a Chemist's dozen"#, admittedly it is a very large number. One mole of stuff specifies #6.02245140xx10^23# individual items of that stuff. We give this number the symbol, #N_A#, Avogadro's number, after the Italian Chemist who first recognized the utility of this numerical approach, and who realized (or theorized) that equal volumes of gases at the same temperature and pressure contain the same number of particles).
Why should we use such an absurdly large number? Well, it turns out that #N_A# is the link between the (sub!)-micro world of atoms and molecules, to the macro world of the laboratory benchtop, of grams and kilograms and litres (if the density is known).
It turns out that #N_A# #""^12C# atoms, have a MASS of #12.000# #g# precisely. On this scheme, #N_A# #""^16O# atoms, have a MASS of #16.000# #g#; and #N_A# #""^14N# atoms, have a MASS of #14.000# #g#; and and #N_A# #""^1H# atoms, have a MASS of #1.00# #g#. It follows that #N_A# #""^16O_2# molecules (i.e. #O_2#), have a mass of #32.000# #g#; or #N_A# #""^14N_2# molecules (i.e. #N_2#), have a mass of #28.000# #g#. And likewise, #N_A# #H_2O# molecules have a mass of #(16+1+1)*g=18.0*g#. Are you with me? I hope so, because if you are it will save you a whole lot of time and trouble, and it is a fundamental, conceptual notion to develop.
So, do you have to remember these molar weights and molar masses? Do you have to remember the number? The answer is no. Because for every chemistry or physics exam you will ever sit, you will be (i) given a copy of the Periodic Table, which will give the masses of a mole of ANY element (isotopically adjusted); and (ii) you should also be quoted the value of Avogadro's number. Of course, you have to be able to use it. Get cracking.
