Ideal-Gas Mixtures, Partial Pressure, and Composition
Dalton's law states P = sum_i P_i with P_iV = n_iRT for a nonreacting ideal-gas mixture at common T and V; mole fraction gives P_i = x_iP.
Why this shows up in the exam
Finding mixture composition from mass and pressure · Comparing partial pressures and densities · Humidity and dry-gas pressure corrections
Learn the idea
Nonreacting ideal gases share volume and temperature while each contributes pressure according to its own particle count. Each species behaves as if it alone occupied the container, so composition questions combine one total state equation with mass or mole constraints.
🧠 Memory hook: Every species gets the whole volume but only its own mole share of pressure.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = sum_i P_i; P_i = x_i P — Dalton law for ideal nonreacting components at common T and V
- n_total = sum_i n_i — total amount conserved when components mix without reaction
- m_total = sum_i n_i M_i — mass-composition constraint using molar masses
How to approach it
- 1Introduce one mole variable per species
- 2Write total moles and total mass independently
- 3Solve and verify mole fractions sum to one
Common slip-ups that cost marks
- •Assigning each gas only part of the container volume
- •Averaging molar masses without mole weights
- •Using total pressure where dry-gas partial pressure is required
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
More from Kinetic Theory of Gases
Ideal gas law and gas laws
The ideal gas law and related gas laws describe the relationships between pressure, volume, temperature, and number of moles for ideal gases.
Degrees of freedom and thermal properties
Degrees of freedom determine the distribution of energy among molecules, affecting internal energy, specific heats, and the ratio of specific heats (γ).
Kinetic theory and molecular motion
The kinetic theory explains the behavior of gases in terms of the motion and collisions of their molecules, relating properties like pressure, temperature, and kinetic energy.
RMS speed and temperature dependence
The root mean square (rms) speed of gas molecules depends on temperature and molar mass, and is a key measure of molecular motion in gases.
Mean free path and collisions
Mean free path is the average distance a molecule travels between collisions, and depends on molecular size and number density.
Ideal-Gas Equation and Molecular Form
For a dilute ideal gas in thermal equilibrium, the state variables satisfy PV = nRT = Nk_B T, where intermolecular potential energy and molecular volume are neglected.