# How do atomic masses reflect isotope abundances?

Feb 13, 2014

Atomic masses are weighted averages of the masses of all the element's atoms based on their isotopic abundances.

Typically, you are given a list of isotopes with their masses and their natural abundance as a percent value. You arbitrarily choose some number of atoms, calculate the numbers of each isotope, add up all their masses, and then get the average mass.

EXAMPLE:

A sample of chlorine contains 75.77 % chlorine-35 atoms and
24.23 % chlorine-37 atoms. If the atomic mass of Cl-35 is 34.969 u and the atomic mass of Cl-37 is 36.965 u, what is the atomic mass of chlorine?

Solution:

Assume that we have 10 000 Cl atoms (we could assume any number). Then we have 7577 Cl-35 atoms and 2423 Cl-37 atoms.

Mass of 7577 Cl-35 atoms = 7577 atoms × (34.969 u)/(1 atom) =
265 000 u

Mass of 2423 Cl-37 atoms = 2423 atoms × (36.965 u)/(1 atom) =
89 570 u

Mass of 10 000 atoms of Cl = 354 500 u

Average mass of a Cl atom = (354 500 u)/(10 000 atoms) = 35.45 u

The more abundant an isotope, the closer the atomic mass will be to the atomic mass of that isotope. Since Cl-35 is more abundant, the average atomic mass will be closer to 35 than to 37.