A mole is just a number. A big number but its a number of particles. It’s useful for comparing amounts of substances for reactivity, because if you have a reaction where one atom of A reacts with one atom of B but a and b have different weights per atom then you can’t say 1 kg of A reacts with one kg of B but you can say one mole rescts with one mole, and then work out mass you need from the molar masses of each substance . Molar mass is also the amount that one mole weighs in grams.
Not sure what the G stands for in G formula mass though.
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