To determine the percent by mass of oxygen in carbon dioxide (CO₂), we need to use the formula:
[tex]\[ \% \text{Element} = \frac{\text{total mass of element in compound}}{\text{molar mass of compound}} \times 100 \][/tex]
Let's go through the steps:
1. Determine the atomic masses of the elements involved:
- The atomic mass of carbon (C) is 12.01 g/mol.
- The atomic mass of oxygen (O) is 16.00 g/mol.
2. Calculate the molar mass of CO₂ (carbon dioxide):
- CO₂ consists of one carbon atom and two oxygen atoms.
- Molar mass of CO₂ = (1 × atomic mass of C) + (2 × atomic mass of O)
[tex]\[ \text{Molar mass of CO}_2 = 12.01 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 44.01 \, \text{g/mol} \][/tex]
3. Calculate the total mass of oxygen in one mole of CO₂:
- There are two oxygen atoms in one molecule of CO₂.
[tex]\[ \text{Total mass of oxygen in CO}_2 = 2 \times 16.00 \, \text{g} = 32.00 \, \text{g} \][/tex]
4. Determine the percent by mass of oxygen in CO₂:
[tex]\[ \% \text{Oxygen in CO}_2 = \frac{\text{total mass of oxygen}}{\text{molar mass of CO}_2} \times 100 \][/tex]
[tex]\[ \% \text{Oxygen in CO}_2 = \frac{32.00 \, \text{g}}{44.01 \, \text{g/mol}} \times 100 \][/tex]
[tex]\[ \% \text{Oxygen in CO}_2 \approx 72.71 \% \][/tex]
Thus, the correct answer is [tex]\( \boxed{72.71 \%} \)[/tex].
