Gas mixture properties and partial pressures are essential in thermodynamics, fluid mechanics, combustion, HVAC, and chemical process calculations. This cheat sheet summarizes how engineers describe mixtures of ideal gases using mole fractions, mass fractions, and component properties. It helps students quickly connect composition data to pressure, volume, mass, and molecular weight calculations.
These relationships are especially useful when analyzing air, exhaust gases, fuel mixtures, and gas storage systems.
The core idea is that each gas in an ideal mixture behaves as if it occupies the same temperature and volume as the mixture. Dalton’s law relates total pressure to the sum of partial pressures, while Amagat’s law relates total volume to component partial volumes. Mixture molecular weight connects mole-based and mass-based composition, and the ideal gas equation can be applied to the total mixture or to individual components.
Careful use of consistent units and the correct fraction basis is critical.
Key Facts
- Mole fraction is yi = ni / n_total, where ni is moles of component i and n_total is total moles in the mixture.
- Mass fraction is wi = mi / m_total, where mi is mass of component i and m_total is total mixture mass.
- For an ideal gas mixture, Dalton’s law gives P_total = sum Pi and Pi = yi P_total.
- For an ideal gas mixture, Amagat’s law gives V_total = sum Vi and Vi = yi V_total when all components are at the same T and P.
- The ideal gas equation for a mixture is P V = n_total R_u T, where R_u is the universal gas constant.
- Mixture molecular weight is M_mix = sum yi Mi, where Mi is the molecular weight of component i.
- The mixture gas constant is R_mix = R_u / M_mix when M_mix is expressed in mass per mole units consistent with R_u.
- Mass fraction and mole fraction are related by wi = yi Mi / M_mix and yi = (wi / Mi) / sum(wj / Mj).
Vocabulary
- Mole fraction
- The ratio of moles of one gas component to the total moles of all gases in the mixture.
- Mass fraction
- The ratio of the mass of one gas component to the total mass of the gas mixture.
- Partial pressure
- The pressure a gas component would exert if it alone occupied the mixture volume at the mixture temperature.
- Dalton’s law
- The rule that the total pressure of an ideal gas mixture equals the sum of the partial pressures of its components.
- Amagat’s law
- The rule that the total volume of an ideal gas mixture equals the sum of the component partial volumes at the same temperature and pressure.
- Mixture molecular weight
- The mole-fraction-weighted average molecular weight of all gas components in a mixture.
Common Mistakes to Avoid
- Using mass fraction in Pi = yi P_total is wrong because Dalton’s law uses mole fraction, not mass fraction.
- Forgetting to make fractions sum to 1 gives inconsistent mixture properties because mole fractions and mass fractions must each total exactly 1.
- Averaging molecular weights with mass fractions as M_mix = sum wi Mi is wrong because mixture molecular weight is mole-fraction-weighted, M_mix = sum yi Mi.
- Mixing unit systems for R_u, M_mix, and pressure leads to incorrect gas constants and state calculations because the ideal gas equation requires consistent units.
- Applying ideal gas partial pressure relations to highly nonideal gases without correction can be inaccurate because real gas mixtures may require compressibility factors or fugacity methods.
Practice Questions
- 1 A gas mixture contains 2.0 mol N2, 1.0 mol O2, and 1.0 mol CO2 at a total pressure of 400 kPa. Find the mole fraction and partial pressure of each gas.
- 2 A mixture has yN2 = 0.70, yO2 = 0.20, and yCO2 = 0.10. Using MN2 = 28.0 kg/kmol, MO2 = 32.0 kg/kmol, and MCO2 = 44.0 kg/kmol, calculate M_mix.
- 3 Air is approximated as 79 percent N2 and 21 percent O2 by mole at 101.3 kPa. Find the partial pressure of O2 and the mixture molecular weight using MN2 = 28.0 kg/kmol and MO2 = 32.0 kg/kmol.
- 4 Explain why partial pressure depends on mole fraction rather than mass fraction for an ideal gas mixture.