Molecular Mass - Isotopic Considerations

Isotopic Considerations

The average atomic mass of natural hydrogen is 1.00794 u and that of natural oxygen is 15.9994 u; therefore, the molecular mass of natural water with formula H₂O is (2 × 1.00794 u) + 15.9994 u = 18.01528 u. Therefore, one mole of water has a mass of 18.01528 grams. However, the exact mass of hydrogen-1 (the most common hydrogen isotope) is 1.00783, and the exact mass of oxygen-16 (the most common oxygen isotope) is 15.9949, so the mass of the most common molecule of water is 18.01056 u. The difference of 0.00472 u or 0.03% comes from the fact that natural water contain traces of water molecules containing, oxygen-17, oxygen-18 or hydrogen-2 (Deuterium) atoms. Although this difference is trivial in bulk chemistry calculations, it can result in complete failure in situations where the behavior of individual molecules matters, such as in mass spectrometry and particle physics (where the mixture of isotopes does not act as an average).

There are also situations where the isotopic distributions are not typical such as with heavy water used in some nuclear reactors which is artificially enriched with Deuterium. In these cases the computed values of molar mass and average molecular mass, which are ultimately derived from the standard atomic weights, will not be the same as the actual molar mass or average molecular mass of the sample. In this case the mass of deuterium is 2.0136 u and the average molecular mass of this water (assuming 100% deuterium enrichment) is (2 × 2.0136 u) + 15.9994 u = 20.0266 u. This is a very large difference of ~11% error from the expected average molecular mass based on the standard atomic weights. Furthermore the most abundant molecular mass is actually slightly less than the average molecular mass since oxygen-16 is still the most common. (2 × 2.0136 u) + 15.9949 u = 20.0221 u. Although this is an extreme artificial example, natural variation in isotopic distributions do occur and are measurable. For example, the atomic weight of lithium as found by isotopic analysis of 39 lithium reagents from several manufacturers varied from 6.939 to 6.996.