Questions: Gas Mixtures and Dalton's Law of Partial Pressures

Question 1

A sealed container holds 0.6 mol of N₂ and 0.4 mol of O₂ at a total pressure of 200 kPa. What is the partial pressure of O₂?

• A. 40 kPa, because O₂ is the minority component and contributes less pressure
• B. 80 kPa, because the mole fraction of O₂ is 0.4 and partial pressure = mole fraction × total pressure
• C. 100 kPa, because each gas component occupies half the container volume
• D. 200 kPa, because ideal gases exert the same pressure regardless of composition

Answer: (B)

Partial pressure = mole fraction × total pressure. O₂ has 0.4 mol out of 1.0 mol total, so y_O₂ = 0.4. P_O₂ = 0.4 × 200 kPa = 80 kPa. Option C incorrectly applies an equal-volume split (which is not how partial pressures work); option D confuses ideal gas pressure independence from other gases with the total-pressure calculation. Each component contributes pressure proportional to its mole fraction.

Question 2

An engineer calculates the enthalpy of an ideal gas combustion exhaust containing CO₂, H₂O, N₂, and O₂ at known mole fractions. What is the correct approach?

• A. Look up enthalpy in a combustion-gas table for the specific mixture composition
• B. Use the enthalpy of air as an approximation, since exhaust is mostly nitrogen
• C. Calculate h_i for each component separately using its pure-component property table at the mixture temperature, then sum each by its mass fraction: h_mix = Σ(mf_i × h_i)
• D. Average the component enthalpies equally since they are all at the same temperature

Answer: (C)

For ideal gas mixtures, mixture enthalpy is calculated as the mass-fraction-weighted sum of pure-component enthalpies at the mixture temperature. Because ideal gas enthalpy is pressure-independent, you only need the temperature and the pure-component tables for each species — no special mixture tables required. This separability is the practical power of the ideal mixture assumption. Option D (equal averaging) ignores the different mass fractions and molecular weights of each component.

Question 3

When two different ideal gases are mixed at constant temperature and volume, the total pressure equals the sum of the individual pressures each gas would exert if it alone occupied the entire container.

• T. True
• F. False

Answer: True

This is an exact statement of Dalton's law of partial pressures for ideal gas mixtures. Because ideal gas molecules are assumed to have no intermolecular interactions, each component behaves as if the others are absent — it exerts its own partial pressure based solely on its mole fraction and the total conditions. The total pressure is the sum of all partial pressures.

Question 4

Mixing two ideal gases at the same temperature and pressure produces no change in entropy because no energy is exchanged and the total volume is unchanged.

• T. True
• F. False

Answer: False

Mixing distinct ideal gases is an irreversible process that increases entropy even with no energy transfer and no volume change. The entropy of mixing is Δs_mix = −R Σ(y_i ln y_i) per mole, which is always positive (since ln y_i < 0 for all mole fractions between 0 and 1). This reflects the increased disorder from dispersing distinguishable gas molecules throughout the container — they can no longer be separated without doing work. Entropy increases whenever distinguishable substances mix spontaneously.

Question 5

Explain why the ideal gas mixture assumption allows engineers to use pure-component property tables (like JANAF tables) for mixture calculations, rather than requiring new tables for every possible mixture composition.

Model answer: Under the ideal mixture assumption, each gas component behaves as if it were alone in the entire container — its partial pressure, enthalpy, and entropy (at its partial pressure) are determined by its own properties at the mixture temperature, independent of the other components. This means mixture properties are simply weighted sums of pure-component properties: h_mix = Σ(mf_i × h_i) and similarly for entropy (with the addition of the mixing term). Engineers need only the pure-component tables for each species plus the mole fractions — they can compute any mixture property without a new table.

The separability of mixture properties is the key engineering utility of Dalton's model. It transforms complex multi-component analysis into a set of independent single-component calculations combined by superposition. The assumption is valid when intermolecular interactions between different species are negligible — generally a good approximation for gases at moderate conditions.