Calculate the average molecular weight of air from its approximate molar composition of 79% N2, 21% aO2 and 2 from its approximate composition by mass of 76.7% N2 23.3% O2
The Correct Answer and Explanation is:
To calculate the average molecular weight of air, we will use the concept of a weighted average, which takes into account the proportions of nitrogen (N2) and oxygen (O2) in air.
We will approach this in two steps based on two different sets of compositions:
1. By molar composition (79% N2, 21% O2)
- Molar mass of N2: 28.0 g/mol
- Molar mass of O2: 32.0 g/mol
To find the average molecular weight of air based on the molar composition, we multiply each gas’s molar mass by its proportion in the air and then add the results:Average molecular weight=(0.79×28.0)+(0.21×32.0)\text{Average molecular weight} = (0.79 \times 28.0) + (0.21 \times 32.0)Average molecular weight=(0.79×28.0)+(0.21×32.0)Average molecular weight=22.12+6.72=28.84 g/mol\text{Average molecular weight} = 22.12 + 6.72 = 28.84 \text{ g/mol}Average molecular weight=22.12+6.72=28.84 g/mol
So, the average molecular weight of air based on molar composition is 28.84 g/mol.
2. By mass composition (76.7% N2, 23.3% O2)
- Molar mass of N2: 28.0 g/mol
- Molar mass of O2: 32.0 g/mol
We need to convert the mass percentages into mole fractions before we can calculate the molecular weight. First, we assume we have 100 grams of air, so:
- Mass of N2 = 76.7 grams
- Mass of O2 = 23.3 grams
Now, calculate the number of moles of each component:
- Moles of N2 = 76.7 g / 28.0 g/mol = 2.74 mol
- Moles of O2 = 23.3 g / 32.0 g/mol = 0.73 mol
Now, calculate the total moles of air:Total moles of air=2.74+0.73=3.47 mol\text{Total moles of air} = 2.74 + 0.73 = 3.47 \text{ mol}Total moles of air=2.74+0.73=3.47 mol
Next, calculate the mole fractions:
- Mole fraction of N2 = 2.74 mol / 3.47 mol = 0.79
- Mole fraction of O2 = 0.73 mol / 3.47 mol = 0.21
Finally, calculate the average molecular weight using the mole fractions and molar masses:Average molecular weight=(0.79×28.0)+(0.21×32.0)\text{Average molecular weight} = (0.79 \times 28.0) + (0.21 \times 32.0)Average molecular weight=(0.79×28.0)+(0.21×32.0)Average molecular weight=22.12+6.72=28.84 g/mol\text{Average molecular weight} = 22.12 + 6.72 = 28.84 \text{ g/mol}Average molecular weight=22.12+6.72=28.84 g/mol
In this case, the average molecular weight of air based on mass composition is also 28.84 g/mol.
Conclusion:
The average molecular weight of air is approximately 28.84 g/mol, whether you use the molar composition (79% N2, 21% O2) or the mass composition (76.7% N2, 23.3% O2).
