- Calculate the molar mass of \(\text{CO}_2\) using atomic masses: \(12.01 + 2 \times 16.00 = 44.01\) g/mol.
- Determine the total mass contribution of oxygen: \(2 \times 16.00 = 32.00\) g/mol.
- Apply the mass percentage formula: \(\frac{32.00}{44.01} \times 100 \approx 72.71\%\).
- The correct option is \(\boxed{72.71\%}\).
Explanation
- Analysis of the Compound Components
To determine the percent by mass of oxygen in carbon dioxide (\(\text{CO}_2\)), we must first calculate the molar mass of the compound and the total mass contributed by the oxygen atoms. We are given the atomic masses as approximately \(12.01\) g/mol for Carbon (C) and \(16.00\) g/mol for Oxygen (O). A molecule of \(\text{CO}_2\) consists of 1 atom of carbon and 2 atoms of oxygen.
- Calculating Molar and Element Masses
The molar mass of carbon dioxide (\(\text{CO}_2\)) is calculated by adding the mass of one carbon atom and two oxygen atoms:
\[\text{Molar mass of CO}_2 = 1 \times 12.01\text{ g/mol} + 2 \times 16.00\text{ g/mol} = 12.01 + 32.00 = 44.01\text{ g/mol}\]
The total mass contributed by the oxygen atoms in one mole of carbon dioxide is:
\[\text{Total mass of O} = 2 \times 16.00\text{ g/mol} = 32.00\text{ g/mol}\]
- Calculating the Percent by Mass
Using the formula for percent by mass:
\[\% \text{ Element} = \frac{\text{total mass of element in compound}}{\text{molar mass of compound}} \times 100\]
We substitute our values into this formula:
\[\% \text{ O} = \frac{32.00}{44.01} \times 100 \approx 0.727107 \times 100 \approx 72.71\%\]
Comparing this result to the provided options, we see that the percentage by mass of oxygen in \(\text{CO}_2\) is approximately \(72.71\%\).
Examples
Understanding how to calculate mass percentages is essential in fields like chemistry and nutrition. For example, a food scientist uses this knowledge to determine the precise amount of sugar or sodium in a product based on its chemical formula. Similarly, environmental scientists calculate the oxygen content in various gaseous emissions to monitor pollution levels. Mastering these calculations ensures accuracy in research, production, and public safety monitoring.