Question

Air is a mixture with a composition given in the table below.

Component Percent by volume Percent by mass
Nitrogen, N₂ 78.08 75.53
Oxygen, O₂ 20.95 23.14
Argon, Ar 0.93 1.28
Carbon dioxide, CO₂ 0.031 0.047

Calculate the entropy of mixing when it is prepared from the pure (and perfect) gases.
__________ J K⁻¹ mol⁻¹

Answer 1

To calculate the entropy of mixing for air from pure gases, the mole fractions of nitrogen, oxygen, argon, and carbon dioxide are used in the entropy of mixing formula, resulting in units of J K^-1 mol^-1.

Step-by-step explanation:

The question asks us to calculate the entropy of mixing for air when it is prepared from pure (and perfect) gases. To find the entropy of mixing, we can employ the formula for the entropy change for mixing ideal gases:

Where (R) is the universal gas constant (8.314 J K-1 mol-1), is the mole fraction of each component gas in the air. We need to use the percent by volume to calculate mole fractions:

• Nitrogen (N2): 78.08%
• Oxygen (O2): 20.95%
• Argon (Ar): 0.93%
• Carbon dioxide (CO2): 0.031%

Then, we convert these percentages into fractions:

• Nitrogen (N2): 0.7808
• Oxygen (O2): 0.2095
• Argon (Ar): 0.0093
• Carbon dioxide (CO2): 0.00031

After computing the logarithms and the multiplications, sum the values, multiply by -8.314, and the resulting number will be the entropy of mixing in units of J K-1 mol-1.