The mass percentage of oxygen in dry air is calculated by considering the mole fractions and molar masses of the constituent gases. Here's a step-by-step guide:
1. Identify the Composition of Dry Air
Dry air is primarily composed of nitrogen (N₂) and oxygen (O₂), with smaller amounts of argon (Ar) and trace gases. For this calculation, we'll focus on nitrogen and oxygen as the main components. Typical values are:
- Nitrogen (N₂): Approximately 78% by volume (mole fraction = 0.78)
- Oxygen (O₂): Approximately 21% by volume (mole fraction = 0.21)
- Argon (Ar): Approximately 1% by volume (mole fraction = 0.01)
- Note: While Argon is present, ignoring it for simplicity does not drastically affect the oxygen percentage, especially for basic approximations.
2. Determine the Molar Masses
You'll need the molar masses of nitrogen and oxygen:
- Nitrogen (N₂): Approximately 28.01 g/mol
- Oxygen (O₂): Approximately 32.00 g/mol
- Argon (Ar): Approximately 39.95 g/mol
3. Calculate the Contribution of Each Gas to the Average Molar Mass of Air
Multiply the mole fraction of each gas by its molar mass:
- Nitrogen: 0.78 * 28.01 g/mol = 21.85 g/mol
- Oxygen: 0.21 * 32.00 g/mol = 6.72 g/mol
- Argon: 0.01 * 39.95 g/mol = 0.40 g/mol
4. Calculate the Average Molar Mass of Dry Air
Sum the contributions from each gas:
Average molar mass of dry air ≈ 21.85 + 6.72 + 0.40 = 28.97 g/mol
5. Calculate the Mass Percentage of Oxygen
Divide the contribution of oxygen by the average molar mass of dry air and multiply by 100%:
Mass percentage of oxygen = (6.72 g/mol / 28.97 g/mol) * 100% ≈ 23.20%
Simplified Formula
Mass percentage of oxygen in dry air = (Mole fraction of oxygen × Molar mass of oxygen / Sum of all (Mole fraction × Molar mass)) * 100%
Example With Argon Omitted
If we consider only nitrogen and oxygen (approximating nitrogen at 79% and oxygen at 21% for simplicity), the calculation looks like this:
- Nitrogen: 0.79 * 28.01 g/mol = 22.13 g/mol
- Oxygen: 0.21 * 32.00 g/mol = 6.72 g/mol
- Average Molar Mass = 22.13 + 6.72 = 28.85 g/mol
- Mass percentage of oxygen = (6.72 / 28.85) * 100% ≈ 23.29%
As you can see, omitting Argon has a minimal impact on the final result.
Conclusion
The mass percentage of oxygen in dry air is approximately 23.2%, though this can vary slightly based on the precise composition of the air.
