Ideal Gas Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Pressure, volume, temperature and amount of an ideal gas are linked by PV = nRT (or PV = NkBT for N molecules). T must be in kelvins. When the amount of gas is fixed, use ratios: P1V1/T1 = P2V2/T2.
1. The equation
2. Read it as proportions
The type of gas doesn’t matter. A mole of helium and a mole of carbon dioxide at the same T and V have the same pressure.
For “by what factor” questions, cross out everything that stays the same and compare what’s left.
3. Example, then try it
2.0 mol of gas at 300 K fills a 0.050 m³ tank. What is the pressure?
P = nRT/V = (2.0)(8.3)(300) ÷ 0.050 ≈ 1.0 × 10⁵ Pa, about atmospheric pressure.
A sealed, rigid tank of gas at 27 °C has a pressure of 1.5 × 10⁵ Pa. It is heated to 127 °C. What is the new pressure? The gas is then moved to a cylinder and squeezed to half its volume at that same temperature. Now what is the pressure?
Kelvins: 27 °C = 300 K; 127 °C = 400 K.
Constant volume: P ∝ T, so P2 = (1.5 × 10⁵)(400/300) = 2.0 × 10⁵ Pa.
Constant temperature: P ∝ 1/V, so halving V doubles P: 4.0 × 10⁵ Pa.
Answer: 2.0 × 10⁵ Pa, then 4.0 × 10⁵ Pa.
4. Common mistakes
A gas in a rigid container is warmed from 20 °C to 40 °C. What happens to its pressure?
P ∝ T in kelvins: 293 K to 313 K is a factor of 313/293 ≈ 1.07, so the pressure rises by about 7%.
Ready to practice?
4 questions on Ideal Gas Law, each with a hint and an explanation for every wrong answer.