When we balance chemical equations why do we use moles?

It is trivial to represent the complete combustion of say methane to give carbon dioxide and water....

#CH_4(g) + 2O_2(g) rarr CO_2(g) + 2H_2O(l) + Delta#

Here, we have balanced the carbons as carbon dioxide, the hydrogens as water, and then drafted in the required number of oxygen atoms, as dioxygen MOLECULES on the LHS side of the equation....

And such a reaction is likely heating your home right now. We have represented it in terms of ATOMS and molecules.....but if we specify molar quantities, then we can write....

#underbrace(CH_4(g))_(16*g) + underbrace(2O_2(g))_(64*g) rarr underbrace(CO_2(g))_(44*g) + underbrace(2H_2O(l))_(36*g) + Delta#

And as for any chemical process, BOTH MASS and CHARGE are CONSERVED ABSOLUTELY (are they?). And so the mole is the link between the micro world of atoms, and molecules, of which we can conceive, to the macro world of grams, and litres, that which we can measure in a lab. The heat evolved from the reaction is ALSO quantifiable, and may also be reported in #kJ*mol^-1#, by which we mean moles of reaction as written.

See here and links for more of the same....