In the previous post, we have seen that the average atomic mass is calculated by the weighted average of the atomic masses of all the isotopes. The formula we can use for this calculation can be written as:
Average mass = (% isotope 1) x (% isotope 2) + … (% isotope n)
For example, naturally occurring chlorine consists of 75.77% chlorine-35 atoms with an atomic mass of 34.97 amu, and 24.23% chlorine-37 atoms that are 36.97 amu. To find the average atomic mass, we can write that:
Average mass = (Fraction 35Cl x Mass of 35Cl) + (Fraction 37Cl x Mass of 37Cl)
Average mass = 0.7577 x 34.97 + 0.2423 x 36.97 = 35.45
Notice that the average atomic mass is closer to 35 because the isotope with an atomic mass of 35 is more abundant in nature.
Percent Abundance of Isotopes
Let’s now suppose we need to determine the percent abundance of the two main isotopes of copper: 65Cu and 63Cu. These isotopes have an atomic mass of 64.9278 amu and 62.9296 amu respectively, and the average atomic mass of Cu is 63.5456 amu.
To do this, we set up the same equation we use for calculating the average atomic mass. The only difference is that we do not know their percent abundance, so we can set them as x and 1-x. Let’s set x for the 65Cu, and 1-x for the 63Cu isotope.
We can, therefore, write that:
Average mass = 63.5456 = 64.9278 (x) + 62.9296 (1 – x)
Simplifying the equation, we get:
63.5456 = 64.9278x + 62.9296 – 62.9296x
63.5456 – 62.9296 = 64.9278x – 62.9296x
0.616 = 1.9982x
X = 0.3083
Now, for the percentage, we multiply the answers by 100%. So, for the 65Cu, we have:
3083 x 100% = 30.83%
And for the 63Cu isotope, we have:
(1 – 0.3083) x 100% = 69.17%