# How do you calculate atomic mass from isotopic composition ?

Feb 13, 2014

You calculate the atomic mass of an element by taking the average mass of all of its atoms.

The atomic mass of an element is a weighted average of the masses of all the element's isotopes based on their percentage abundances.

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:

You are given a sample containing 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) =
264 960 u

Mass of 2423 Cl-37 atoms = 2423 atoms × (36.965 u)/(1 atom) =
89 566 u

Mass of 10 000 atoms of Cl = 354 526 u

Average mass of a Cl atom = (354 526 u)/(10 000 atoms) = 35.45 u

We are allowed to use only 4 significant figures in the answer because we were given only 4 significant figures for the isotope percentages.