Example 3.2 Problem Statement:
Air is approximately 79 mole% N_{2} and 21 mole% O_{2}. Calculate the average molecular weight of air by using the following formula:
MW_{avg} = y_{N2} * MW_{N2} + y_{O2} * MW_{O2}
To solve Example 3.2:
The molecular weight of air can be calculated explicitly from the provided equation. The molecular weights of nitrogen and oxygen are known, so y_{N2} and y_{O2} are the only terms that must be calculated. Remember, y_{A} is the mole fraction of A in the mixture, which is defined as:
Equation 4: y_{A} = n_{A} /
n_{total}
Since the given information is mole % and we need mole fractions, we can assume a basis to simplify our calculations. We will assume a basis of 100 moles total, which means that our sample of air contains 79 moles of N_{2} and 21 moles of O_{2}. Now, each of the mole fractions can be calculated:
For Nitrogen:
y_{N2} = 79 moles of N_{2} / 100 moles total
y_{N2} = 0.79
For Oxygen:
y_{O2} = 21 moles of O_{2} / 100 moles total
y_{O2} = 0.21
Now, we have all of the terms we need to calculate the molecular weight of air.
MW_{N2} = 28.0 g/mole
y_{N2} = 0.79
MW_{O2} = 32.0 g/mole
y_{O2} = 0.21
MW_{avg} = 0.79 * 28.0 g/mole + 0.21 * 32.0 g/mole
MW_{avg} = 28.84 g/mole
