Because we defined one mole of protons to be the number of particles that weighs 1 gram (basically…there’s some nuance to that). And protons and neutrons weight essentially the same thing, so the atomic mass (# of protons an neutrons) will be the mass of 1 mole of the thing.
Electrons do have some weight but it’s so tiny that it doesn’t really make a difference.
That is because of the simple reason that it was defined that way to make calculations easier. Creating a new mass unit (amu) which in amount is equal to the molar mass makes converting mass between a single atom/molecule and a mole of them way easier than if the mass of a single atom/molecule was measured in yoctograms (1amu=1.66yg)
This is just definitional, isn’t it?
This is like asking “why does ten thousand 1-gram weights weigh 10 kilograms?” Molar mass is the mass of 1 mol (a quantity) of an element, and the atomic mass is that divided by the quantity. Replace the word “mol” with “million” (it’s not 1 million, but it helps you see the tautology).
Rewritten this way the question asks: “why does an atom have the same mass as 1 millionth of a million atoms?”
The atomic mass is *defined* as “the molar mass, divided by the number of atoms in a mol”
It’s because we use grams in chemistry.
Remember Avogadro? The guy with the number? All he did was ask, “if something has an atomic mass of 1, the how many atoms are in 1 gram of that stuff?”.
It turns out the number is 6.02 X 10^(23) atoms. but that’s a messy number, and it takes too long to say, so we just call it a mole.
But if the atomic mass is 12, then you’d need to weigh 12 grams of that stuff to get 6.02 x 10^(23) atoms.
If he had used pounds, instead of grams, he would have ended up with a different number.
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