Question

calculate the atomic mass of oxygen if the three common isotopes of oxygen have masses of 15.995% amu (99.75% abundance), 16.995 amu (0.037% abundance), and 17.999 amu (0.204% abundance)

Answer 1

To calculate the atomic mass of oxygen based on the given isotopes and their abundances, you can use the formula for weighted averages. The formula is:

\[
\text{Atomic Mass} = \sum (\text{mass of isotope} \times \text{abundance})
\]

First, express the abundances as fractions:

- For \(^{16}\text{O}\): 99.75% = 0.9975
- For \(^{17}\text{O}\): 0.037% = 0.00037
- For \(^{18}\text{O}\): 0.204% = 0.00204

Now, multiply the mass of each isotope by its abundance:

1. For \(^{16}\text{O}\):
\[
15.995 \, \text{amu} \times 0.9975 = 15.9550125 \, \text{amu}
\]

2. For \(^{17}\text{O}\):
\[
16.995 \, \text{amu} \times 0.00037 = 0.00628815 \, \text{amu}
\]

3. For \(^{18}\text{O}\):
\[
17.999 \, \text{amu} \times 0.00204 = 0.03673996 \, \text{amu}
\]

Now, add these contributions together:

\[
\text{Atomic Mass} = 15.9550125 + 0.00628815 + 0.03673996 = 15.99804061 \, \text{amu}
\]

Therefore, the atomic mass of oxygen, calculated from the given isotopes, is approximately:

\[
\boxed{15.998 \, \text{amu}}
\]