To calculate the average atomic mass of oxygen given its isotopes and their relative abundances, we will follow a step-by-step approach. The relative abundances need to be converted from percentages to decimals. Then, we will multiply each isotope's atomic mass by its corresponding decimal abundance, and sum these products to get the average atomic mass.
### Step-by-step Calculation
1. List the Isotopes and Their Data:
- Isotope [tex]\( O-16 \)[/tex]: Atomic Mass = 15.995 amu, Relative Abundance = 99.759%
- Isotope [tex]\( O-17 \)[/tex]: Atomic Mass = 16.995 amu, Relative Abundance = 0.037%
- Isotope [tex]\( O-18 \)[/tex]: Atomic Mass = 17.999 amu, Relative Abundance = 0.204%
2. Convert Relative Abundances from Percentages to Decimals:
[tex]\[
\text{Relative Abundance} = \frac{\text{Percentage}}{100}
\][/tex]
- For [tex]\( O-16 \)[/tex]:
[tex]\[
\frac{99.759}{100} = 0.99759
\][/tex]
- For [tex]\( O-17 \)[/tex]:
[tex]\[
\frac{0.037}{100} = 0.00037
\][/tex]
- For [tex]\( O-18 \)[/tex]:
[tex]\[
\frac{0.204}{100} = 0.00204
\][/tex]
3. Multiply Each Isotope's Atomic Mass by Its Decimal Abundance:
- For [tex]\( O-16 \)[/tex]:
[tex]\[
15.995 \times 0.99759 = 15.9569105
\][/tex]
- For [tex]\( O-17 \)[/tex]:
[tex]\[
16.995 \times 0.00037 = 0.00628815
\][/tex]
- For [tex]\( O-18 \)[/tex]:
[tex]\[
17.999 \times 0.00204 = 0.0362596
\][/tex]
4. Sum These Products to Find the Average Atomic Mass:
[tex]\[
15.9569105 + 0.00628815 + 0.0362596 = 15.99945816 \text{ amu}
\][/tex]
Therefore, the average atomic mass of oxygen is [tex]\( 15.99945816 \)[/tex] amu.
