Question

How do atomic masses reflect isotope abundances?

Answer 1

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.