Atomic mass
One mole of a substance always contains almost exactly the "standard atomic weight" or "molar mass" of that substance; however, this may or may not be true for the "atomic mass," depending on whether or not the element exists naturally in more than one isotope. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The "atomic mass" of the Fe isotope is 55.935 u and one mole of Fe atoms would then in theory have a mass of 55.935 g, but such amounts of pure Fe have never been found (or separated out) on Earth. However, there are 22 mononuclidic elements of which essentially only a single isotope is found in nature (common examples are fluorine, sodium, aluminum and phosphorus) and for these elements the standard atomic weight and atomic mass are the same. Samples of these elements therefore may serve as reference standards for certain atomic mass values.
Law of definite proportions
A related early idea was Prout's hypothesis, formulated by English chemist William Prout, who proposed that the hydrogen atom was the fundamental atomic unit. From this hypothesis was derived the whole number rule, which was the rule of thumb that atomic masses were whole number multiples of the mass of hydrogen. This was later rejected in the 1820s and 30s following more refined measurements of atomic mass, notably by Jöns Jacob Berzelius, which revealed in particular that the atomic mass of chlorine was 35.45, which was incompatible with the hypothesis. Since the 1920s this discrepancy has been explained by the presence of isotopes; the atomic mass of any isotope is very close to satisfying the whole number rule, with the mass defect caused by differing binding energies being significantly smaller.