**Avogadro’s number relates the quantity of a substance to its molecular weight**: for example, the molecular weight of water is about 18 amu (atomic mass units), so one mole of water weighs about 18 grams. And it turns out there are 6.022*10^23 molecules in 18 grams of water.
Basing the mole on amu is a way to ensure we’re comparing apples to apples.
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