Question

The composition of moist air is given on a molar basis to be 78 percent \(\mathrm{N}_{2}, 20\) percent \(\mathrm{O}_{2}\), and 2 percent water vapor. Determine the mass fractions of the constituents of air. Answers: \(76.4\) percent \(\mathrm{N}_{2}, 22.4\) percent \(\mathrm{O}_{2}, 1.2\) percent \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

Answer: The mass fractions of the constituents of air are 76.4% N2, 22.4% O2, and 1.2% H2O.

Step-by-step solution

Identify the molar masses of the constituents

The molar masses of nitrogen (N2), oxygen (O2), and water vapor (H2O) should be used to convert the given molar fractions into mass fractions. The molar masses are as follows: - Molar mass of N2 is 28 g/mol - Molar mass of O2 is 32 g/mol - Molar mass of H2O is 18 g/mol

Calculate the mass of each constituent

Using the molar fractions and molar masses, we will calculate the mass of each constituent: - Mass of N2 = (molar fraction of N2) x (molar mass of N2) = 0.78 x 28 = 21.84 g - Mass of O2 = (molar fraction of O2) x (molar mass of O2) = 0.20 x 32 = 6.4 g - Mass of H2O = (molar fraction of H2O) x (molar mass of H2O) = 0.02 x 18 = 0.36 g

Calculate the total mass of the air mixture

The total mass of the air mixture will be the sum of the masses of the individual constituents: Total mass of air mixture = Mass of N2 + Mass of O2 + Mass of H2O = 21.84 + 6.4 + 0.36 = 28.6 g

Calculate the mass fractions of the constituents

Now that we have the total mass of the air mixture and the mass of each constituent, we can calculate the mass fractions by dividing the mass of each constituent by the total mass of the air mixture: - Mass fraction of N2 = (Mass of N2) / (Total mass of air mixture) = 21.84 / 28.6 = 0.764 = 76.4% - Mass fraction of O2 = (Mass of O2) / (Total mass of air mixture) = 6.4 / 28.6 = 0.224 = 22.4% - Mass fraction of H2O = (Mass of H2O) / (Total mass of air mixture) = 0.36 / 28.6 = 0.0126 = 1.2% Answers: The mass fractions of the constituents of air are 76.4% N2, 22.4% O2, and 1.2% H2O.