Molar mass is an "umbrella term" as it can refer to either the atomic weight or molecular weight (which we will discuss later). The atomic weight of an element is an average of the weight of its isotopes with respect to their relative abundances (Ex: If chlorine-37 makes up 24.33% of all chlorine atoms, then it makes up that percentage of the
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Molecular weight (MW) is the sum of the atomic weights of the atoms in a molecule. (Although molecular weight is often used, the more accurate terminology is molecular mass.) A molecule can be viewed as an entity of one or more different atoms bound together by some kinds of mutual interactions. As an example, the molecular weight of water, H 2
Like "1 dozen", "1 mole" refers to an exact number. Molar mass refers to the mass of a very specific number of molecules/atoms: 1 mole. The molar mass is the mass divided by the amount (number of individual entities such as atoms or molecules) of substance measured in moles. Now 1 mole is equal of course to Avogadro's constant $\pu{N_A}$.
Molecular weight and molar mass are not exactly the same, but they are closely related terms. Molecular weight refers to the average mass of the molecule. On other hand, the molar mass is the mass of one mole of a substance. .