The molecular mass (abbreviated m) of a substance, more commonly referred to as molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of carbon-12). This is distinct from the relative molecular mass of a molecule, which is the ratio of the mass of that molecule to 1/12 of the mass of carbon 12 and is a dimensionless number. Relative molecular mass is abbreviated to Mr.
Molecular mass differs from more conventional measurements by taking into account different isotopic compositions, and as a result Molecular mass is generally more accurate then molar mass, but less used.
There are varying interpretations of this definition. Many chemists use molecular mass as a synonym of molar mass
, differing only in units (see average molecular mass below). A stricter interpretation does not equate
the two, as the mass of a single molecule is not the same as the average of an ensemble
. Because a mole of molecules may contain a variety of molecular masses due to natural isotopes
, the average mass is usually not identical to the mass of any single molecule. The actual numerical difference can be very small when considering small molecules and the molecular mass of the most common isotopomer
in which case the error only matters to physicists
and a small subset of highly specialized chemists
; however it is always more correct, accurate and consistent to use molar mass
in any bulk stoichiometric
calculations. The size of this error
becomes much larger when considering larger molecules or less abundant
isotopomers. The molecular mass of a molecule which happens to contain heavier isotopes than the average molecule in the sample can differ from the molar mass by several mass units.
The average molecular mass
(sometimes abbreviated as average mass
) is another variation
on the use of the term molecular mass. The average molecular mass is the abundance weighted mean
(average) of the molecular masses in a sample
. This is often closer to what is meant when "molecular mass" and "molar mass" are used synonymously
and may have derived
from shortening of this term. The average molecular mass and the molar mass of a particular substance in a particular sample
are in fact numerically identical
and may be interconverted
by Avogadro's constant
. It should be noted, however, that the molar mass is almost always a computed figure
derived from the standard atomic weights
, whereas the average molecular mass, in fields that need the term, is often a measured figure
specific to a sample. Therefore, they often vary since one is theoretical
and the other is experimental
. Specific samples may vary
significantly from the expected isotopic composition due to real deviations
's average isotopic abundances.
The molecular mass can be calculated as the sum of the individual isotopic masses
(as found in a table of isotopes
) of all the atoms in any molecule
. This is possible because molecules are created by chemical reactions
which, unlike nuclear reactions
, have very small binding energies
compared to the rest mass
of the atoms (
) and therefore create a negligible mass defect
. The use of average atomic masses
derived from the standard atomic weights found on a standard periodic table
will result in an average molecular mass, whereas the use of isotopic masses will result in a molecular mass consistent with the strict interpretation of the definition, i.e. that of a single molecule. However, any given molecule may contain any given combination of isotopes, so there may be multiple molecular masses for each chemical compound.
The molecular mass can also be measured directly using mass spectrometry
. In mass spectrometry, the molecular mass of a small molecule is usually reported as the monoisotopic mass
, that is, the mass of the molecule containing only the most common isotope of each element. Note that this also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass of the many possible. The masses used to compute the monoisotopic molecular mass are found on a table of isotopic masses and are not found on a typical periodic table. The average molecular mass
is often used for larger molecules since molecules with many atoms are unlikely to be composed exclusively of the most abundant isotope of each element. A theoretical average molecular mass can be calculated using the standard atomic weights
found on a typical periodic table, since there is likely to be a statistical distribution of atoms representing the isotopes throughout the molecule. This however may differ from the true average molecular mass of the sample due to natural (or artificial) variations in the isotopic distributions.
Unit Type Variation
The molar mass
of a substance is the mass of 1 mol (the SI unit for the basis SI quantity amount of substance
, having the symbol n
) of the substance. This has a numerical value which is the average molecular mass of the molecules in the substance multiplied by Avogadro's constant
. The most common units of molar mass are g/mol
because in those units the numerical value equals the average molecular mass in units of u.
Conversion Factor of average molecular mass to molar mass:
- molar mass = average molecular mass * ((1/6.022)*1023g/u)*(6.022*1023/mol)
(Note that these relations are true for theoretical and experimental values, but not between experimental and theoretical values. Molar mass is most often theoretical and average molecular mass is most often experimental)
- molar mass in g/mol= average molecular mass in u
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