Mini-Lesson

Gas Laws & Kinetic Theory

This mini-lesson covers Theme B.3 — Gas laws: the ideal gas equation pV = nRT, the experimental gas laws (Boyle, Charles, pressure law), and the kinetic theory that explains them from molecular motion.

Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.

B.3 · ideal gas

The ideal gas equation

An ideal gas obeys the equation of state linking pressure, volume, amount and temperature:

pV = nRTp (Pa) · V (m³) · n (mol) · R = 8.31 J mol⁻¹ K⁻¹ · T (K, always!)

Temperature must be in kelvin in every gas calculation. The number of moles n = N ÷ N_A, where N is the number of molecules and N_A = 6.02 × 10²³ mol⁻¹.

Quick check

?A sealed rigid container of ideal gas is heated. Which of these must you convert before using pV = nRT?

Calculate

#Find the amount of gas (in mol) when p = 1.0 × 10⁵ Pa, V = 0.024 m³ and T = 290 K. Use R = 8.31.

mol

Hint: n = pV ÷ (RT) = (1.0e5 × 0.024) ÷ (8.31 × 290).

B.3 · gas laws

Boyle's and Charles's laws

Holding one quantity fixed gives the experimental gas laws:

Boyle's law (constant T): p ∝ 1/V, so p₁V₁ = p₂V₂.
Charles's law (constant p): V ∝ T, so V₁/T₁ = V₂/T₂.
Pressure law (constant V): p ∝ T, so p₁/T₁ = p₂/T₂.

Worked example — Boyle's law

Gas at 100 kPa fills 2.0 L. Compress it to 0.50 L at constant temperature.

p₂ = p₁V₁ ÷ V₂ = 100 × 2.0 ÷ 0.50 = 400 kPa

Calculate

#A gas at 100 kPa occupies 2.0 L. It is compressed at constant temperature to 0.50 L. Find the new pressure (kPa).

kPa

Hint: Boyle — p₂ = p₁V₁ ÷ V₂ = 100 × 2.0 ÷ 0.50.

Calculate

#A gas occupies 0.30 m³ at 300 K. It is heated at constant pressure to 400 K. Find the new volume (m³).

m³

Hint: Charles — V₂ = V₁ × T₂ ÷ T₁ = 0.30 × 400 ÷ 300.

Sort it

Which gas law is being used?

Tap an item, then tap the group it belongs to.

🔒 Boyle (const T)

🌡️ Charles (const p)

📦 Pressure law (const V)

B.3 · kinetic theory

Kinetic theory of gases

Kinetic theory models a gas as many tiny molecules in random motion. Pressure arises from countless collisions with the walls. The model assumes point molecules, no intermolecular forces, and perfectly elastic collisions.

average KE = (3/2)kTk = 1.38 × 10⁻²³ J K⁻¹ (Boltzmann constant); KE ∝ absolute temperature

This links the microscopic and macroscopic: the average translational kinetic energy of a molecule depends only on the absolute temperature — not on the type of gas.

Calculate

#Find the average translational kinetic energy of a molecule at 300 K, in units of 10⁻²¹ J. Use k = 1.38 × 10⁻²³ J K⁻¹.

× 10⁻²¹ J

Hint: KE = (3/2)kT = 1.5 × 1.38e-23 × 300 = 6.21e-21 J → 6.21.

Match it

Match the statement to its name

Tap a statement on the left, then its match on the right.

Statement

Answer

Recap

The big ideas to know

Ideal gas: pV = nRT; T always in kelvin; n = N ÷ N_A

Boyle: constant T: p₁V₁ = p₂V₂

Charles / pressure law: V ∝ T (const p) · p ∝ T (const V)

Kinetic theory: pressure from wall collisions; average KE = (3/2)kT

Key idea: average molecular KE depends only on absolute temperature

That completes Gas Laws & Kinetic Theory for IB Diploma Physics SL. Press Finish to see your score.

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