Module B.3 IBDP SL/HL Track

Gas Laws

Understand ideal gas behaviors, the kinetic model of matter, and state equations.

01. Observe 02. Think 03. Apply 04. Achieve Excellence

Gas Laws

Introduction

Gas laws connect visible laboratory measurements, such as pressure and volume, to the microscopic motion of huge numbers of molecules. The guide treats the ideal gas as a model: simple enough to calculate with, but powerful enough to explain pressure, temperature, and internal energy.

Guide Focus

  • Relate pressure, volume, temperature, and amount of gas using the ideal gas equations.
  • Explain macroscopic gas behaviour with the kinetic model.
  • Use pressure-volume graphs and identify when real gases approximate ideal gases.

Key Concepts

1. Pressure and amount of substance

Pressure is force per unit area: P = F / A. Amount of substance links particles to moles using n = N / NA, where NA is the Avogadro constant.

2. Ideal gas equations

The empirical gas laws combine to give PV / T = constant for a fixed amount of gas. The two main forms are PV = NkBT and PV = nRT.

3. Kinetic explanation of pressure

Gas pressure arises from molecules colliding with container walls and changing momentum. The guide uses P = (1/3) rho v_bar_squared to connect pressure with density and average molecular translational speed squared.

4. Temperature and internal energy

For a monatomic ideal gas, internal energy depends only on temperature: U = (3/2)NkBT = (3/2)nRT. Higher temperature means greater average random kinetic energy of molecules.

Common Mistakes

  • Using Celsius in PV = nRT or PV = NkBT. Temperature must be in kelvin.
  • Assuming every real gas is ideal under all conditions.
  • Confusing density rho with pressure P in the kinetic theory equation.

Exam Tips

  • Write down what is constant before choosing Boyle, Charles, pressure law, or the full ideal gas equation.
  • Use pressure-volume diagrams to track work and state changes visually.
  • Ideal behaviour is best at low pressure, high temperature, and low density.

Practice Questions

Question 1 (Multiple Choice)

A fixed mass of ideal gas is heated at constant volume. What happens to its pressure?

A. It increases. B. It decreases. C. It remains constant. D. It becomes zero.

Correct Answer: A

Solution Architecture

At constant volume and fixed amount of gas, P is proportional to absolute temperature, so heating increases pressure.

Question 2 (Structured Paper 2 Style)

A sealed container has volume 0.020 m3 and contains 1.5 mol of ideal gas at 300 K.

(a) Calculate the pressure of the gas. [2 marks]

(b) State what happens to the pressure if the temperature doubles at constant volume. [1 mark]

Paper 2 Structured Problem

Markscheme Breakdown

Part (a) Solution:

PV = nRT, so P = nRT / V = (1.5 x 8.31 x 300) / 0.020 = 1.9 x 10^5 Pa.

Part (b) Solution:

At constant volume, pressure doubles.