The average atomic weight of oxygen (O) is 15.9994 amu. It has three naturally occurring isotopes, 16 O, 17 O and 18 O, and 0.037 percent of oxygen is made up of 17 O. If the atomic weights are 16 O = 15.995 amu, 17 O = 16.999 amu and 18 O = 17.999 amu, what are the abundances of the other two isotopes?

Abundance 18O = 0.201%

Abundance 16O = 99.768%

Explanation:

The average atomic weight of oxygen is defined as:

Average = Abundance 16O * 15.995amu + Abundance 17O * 16.999amu + Abundance 18O * 17.999amu

As average is 15.9994 amu and abundance of O17 = 0.037% = 3.7x10⁻⁴ we can write:

15.9994amu = Abundance 16O * 15.995amu + 3.7x10⁻⁴* 16.999amu + Abundance 18O * 17.999amu

15.9931 = Abundance 16O * 15.995amu + Abundance 18O * 17.999amu (1)

The abundance of each isotope = 1:

1 = Abundance 16O + Abundance 17O + Abundance 18O

1 = Abundance 16O + 3.7x10⁻⁴ + Abundance 18O

0.99963 = Abundance 16O + Abundance 18O (2)

Replacing (2) in (1):

15.9931 = (0.99963 - Abundance 18O) * 15.995amu + Abundance 18O * 17.999amu

15.9931 = 15.9891 - 15.995Abundance 18O + 17.999Abundance 18O

15.9931 = 15.9891 - 15.995Abundance 18O + 17.999Abundance 18O

4.0182x10⁻³ = 2.004Abundance 18O

2.005x10⁻³ = Abundance 18O = 0.201%

Thus, abundance of 16O in percentage is:

Abundance 16O = 100 - 0.201% - 0.031%