Why is the average atomic mass of an
element referred to the "molar mass" of an
element?

“Atomic mass is expressed in atomic mass units while molar mass is expressed in grams.”

It’s true that atomic mass is expressed in atomic mass unity, called u.m.a. or dalton, but surely molar mass is expressed in the same unity too and not in grams. For example the atomic mass of hydrogen is 1.008 u.m.a.. The molar mass of water (H2O) is the sum of 2 atomic mass of hydrogen and 1 atomic mass of oxygen: 1.008x2+16=18.016 u.m.a.

Explanation:  The unit of atomic mass and molar mass is the same and it corresponds to 1/12 of the mass of the nucleus of the carbon isotope 12. Therefore both are not masses but pure dimensionless numbers. When I say that sodium (Na) has atomic mass 22.997 u.m.a., I simply say that sodium atoms weighs 22.997 time more than the atomic mass unity. When I say that CO2 has a molecular mass of 44.01 u.m.a. I say that the CO2 molecule weighs 44.01 time more than the atomic mass unity.

To move from the atomic mass to the gr-atoms, used for single atoms, or moles (gr-moles) used for molecules, both used in the stoichiometric calculations, you have simply to use the atomic mass and the molecular mass and put the dimension in grams. For the moles you can use lower dimensions (millimoles, micro moles, etc.) and higher dimensions (kilomoles, tonmoles, etc.).

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