Gases & the Ideal Gas Law
- State the assumptions of kinetic molecular theory and how they define an ideal gas
- Apply PV = nRT to solve for any one variable, converting units to K and atm
- Use mole fractions to find partial pressures in a gas mixture
Kinetic molecular theory
Kinetic molecular theory (KMT) models an ideal gas as a huge number of tiny particles in constant, random motion. Its key assumptions: particle volume is negligible compared to the container, collisions are perfectly elastic (no energy lost), particles exert no intermolecular forces on each other, and the average kinetic energy is proportional to the absolute temperature (in kelvin). These assumptions are why a real gas behaves most ideally at high temperature and low pressure, where molecules are far apart and moving fast.
The ideal gas law
The four state variables of a gas — pressure, volume, moles, and temperature — are tied together by one equation, PV = nRT. The constant R depends only on your units; using pressure in atm and volume in liters, R = 0.08206 L·atm·mol⁻¹·K⁻¹. Temperature must always be in kelvin (K = °C + 273), because rate and energy scale with absolute temperature, not the arbitrary Celsius zero.
A 5.00 L vessel holds 2.00 mol of an ideal gas at 27 °C. What is the pressure in atm?
- 1.Convert temperature to kelvin: T = 27 + 273 = 300 K.
- 2.Solve PV = nRT for pressure: P = nRT ÷ V.
- 3.Substitute: P = (2.00 mol × 0.08206 L·atm·mol⁻¹·K⁻¹ × 300 K) ÷ 5.00 L.
- 4.Numerator: 2.00 × 0.08206 × 300 = 49.24 L·atm. Divide by 5.00 L.
Partial pressures
In a mixture, each gas exerts its own partial pressure as if it were alone, and by Dalton’s law the total pressure is their sum: P_total = P₁ + P₂ + …. Because each gas fills the same volume at the same temperature, a gas’s partial pressure is just its mole fraction (its share of the total moles) times the total pressure: Pᵢ = Xᵢ × P_total.
How many moles of an ideal gas occupy 11.2 L at 1.00 atm and 273 K? (R = 0.08206 L·atm·mol⁻¹·K⁻¹)
A sealed rigid container holds a gas at 1.00 atm and 273 K. If it is heated to 546 K with no change in volume or amount of gas, the new pressure is:
A container holds 2.0 mol N₂ and 3.0 mol O₂ at a total pressure of 5.0 atm. What is the partial pressure of O₂?
The single most common gas-law error is leaving temperature in °C. Always convert to kelvin first — a gas at 0 °C is at 273 K, not 0 K, and dividing by zero (or a tiny number) will wreck the arithmetic.
Answer the 3 checkpoints as you read.
Sign in to save your progress