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Question regarding moles: So I'm having a hard time understanding the relationship between moles, molar mass,...

Question regarding moles:

So I'm having a hard time understanding the relationship between moles, molar mass, atomic/molecular mass, and unified atomic mass units.

Is molar mass and atomic/molecular mass the same thing? It seems like atomic/molecular mass is the sum of all the atomic masses in a substance. The units for atomic/molecular mass is unified atomic units and the units for molar mass is g/moles, so it seems like some type of conversion is happening. A Helium atom has an atomic mass of 4.00 u and a molar mass of 4.00 g/mol. So is 1 u = 1 g/mol? Doesn't that go against the idea that 1 u = 1.66 * 10^-27 kg? I can see that 1g/ mol = 10^-3 kg/mol, but how do you get rid of the mol part? Is it using the notion that in 1mole of gas there are 6.022 * 10^23 molecules to get that conversion because 1.66 * 10^-27 kg needs to equal 1 g/mol if 1g/mol = 1u?

Also physically, what is the difference between the mass of the substance and the atomic/molecular mass? If the substance is just the mass of everything it contains wouldn't that be the same thing as adding up all the molecules making that substance? I'm also assuming that the atomic/molecular mass is the actual mass of the atom or molecule itself, is that the case? Or is it like the mass of the nucleus of each atom (molecular mass would then be the sum of all the masses of all the nuclei). In that case, then the atomic mass doesnt include the mass of the electrons thus creating a difference between the actual mass of the substance and the atomic/molecular mass.

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