Question

Air is a mixture of gases with the following mass percentage composition: 75.52% N2, 23.15% O2, 1.28% Ar, and 0.046% CO2. A. Determine the molar enthalpy of mixing and the molar entropy of mixing for air at 1.100 atm and 25C. B. Is the mixing of pure gases to form air spontaneous? How does the total pressure affect spontaneity of gas mixing?

Answer 1

Solution.

Converting a mass percentage composition into a mole fractions.

Let's assume we have 1000 g of air. It contains:

755.2/28 = 26.97 moles N₂

231.5/32 = 7.234 moles O₂

12.8/40 = 0.32 moles Ar

0.46/44 = 0.0105 moles CO₂

The total number of moles is 26.97+ 7.234 + 0.32+0.0105 = 34.535 moles.

Therefore, the corresponding molar fractions are:

x₁ = 26.97/34.535 = 0.781;

x₂ =  7.234/34.535 = 0.209;

x₃ = 0.32/34.535 = 0.0093;

x₄ = 0.0105/34.535=0.000304;

The molar entropy of mixing is

The molar gibbs free energy of mixing is

Enthalpy of mixing is

The mixing of pure gases to form air spontaneous, because the Gibbs free energy change is a negative. The total pressure doesn't change mole fractions of gases, so it will not affect the spontaneity of ideal gas mixing.