What does Gas Laws cover in IB Physics?

This topic covers the macroscopic and microscopic properties of gases, including pressure, temperature, and the ideal gas law. Pressure is defined as P = (F)/(A). The amount of substance is n = (N)/(N_A).

Is Gas Laws SL or HL?

Both. SL and HL students study Gas Laws to the same depth.

How does FourtyFive help me practise Gas Laws?

FourtyFive has 23 Gas Laws questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Gas Laws practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Gas Laws answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

Topic B.3 · SL and HL

Gas Laws: notes and practice questions

Q: How do I revise Gas Laws for IB Physics?

Start from the core idea: this topic covers the macroscopic and microscopic properties of gases, including pressure, temperature, and the ideal gas law. In the exam: both papers, and it is a favourite of Paper 1B because a gas experiment produces clean linear data once you plot the right pair of variables. May 2025 SL and HL Paper 1B TZ2 question 2 opened with "The equation PV = Nk_BT describes the behaviour of an ideal gas" and ran a full data analysis off it. Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

10 min read Jump to 20 practice questions

Summary

This topic covers the macroscopic and microscopic properties of gases, including pressure, temperature, and the ideal gas law.
Pressure is defined as $P = \frac{F}{A}$ .
The amount of substance is $n = \frac{N}{N_A}$ .
Ideal gases are described by the kinetic theory, approximating real gas behavior.
The ideal gas law is given by $\frac{PV}{T} = \text{constant}$ , $PV = Nk_BT$ , and $PV = nRT$ .
Pressure is related to the average (translational speed)² of molecules by $P = \frac{1}{3}\rho\overline{v^2}$ .
Internal energy of an ideal monatomic gas is $U = \frac{3}{2}Nk_BT$ or $U = \frac{3}{2}nRT$ .
Understand conditions for ideal gas approximation and differences from real gases.

How it is examined

Both papers, and it is a favourite of Paper 1B because a gas experiment produces clean linear data once you plot the right pair of variables. May 2025 SL and HL Paper 1B TZ2 question 2 opened with "The equation $PV = Nk_\text{B}T$ describes the behaviour of an ideal gas" and ran a full data analysis off it. In Paper 2 the common shapes are a two-state $P_1V_1/T_1 = P_2V_2/T_2$ calculation and an explain-in-molecular-terms question. Asking for a $PV$ diagram of an adiabatic process is HL B.4 territory, not B.3.

Given in the booklet

$P = F/A$ , $n = N/N_\text{A}$ , $PV/T = \text{constant}$ , $PV = Nk_\text{B}T$ , $PV = nRT$ , $P = \tfrac{1}{3}\rho \overline{v^2}$ , and both forms of the monatomic internal energy. $N_\text{A}$ , $R$ and $k_\text{B}$ are in the constants table. The assumptions of the kinetic model are prose and must be recalled.

Key ideas

pressure as given by $P = \dfrac{F}{A}$ , where F is the force exerted perpendicular to the surface
the amount of substance n as given by $n = \dfrac{N}{N_\text{A}}$ , where N is the number of molecules and $N_\text{A}$ the Avogadro constant
that ideal gases are described by kinetic theory and are a modelled system used to approximate real gases
that the ideal gas law can be derived from the empirical gas laws for constant pressure, constant volume and constant temperature, as given by $\dfrac{PV}{T} = \text{constant}$

Guiding questions

How are the macroscopic characteristics of a gas related to the behaviour of individual molecules?
What assumptions and observations lead to universal gas laws?
How can models be used to help explain observed phenomena?

Linking questions

How does the concept of force and momentum link mechanics and thermodynamics?
How does a consideration of the kinetic energy of molecules relate to the development of the gas laws?
How can gas particles of high kinetic energy be used to perform work?
What other simplified models are relied upon to communicate the understanding of complex phenomena? (NOS)

Practice questions

23 questions · 5 easy · 16 medium · 2 hard

Showing 20 of 20

Question 1

EasyPaper 1A · calculator1 mark

A chemical plant stores various industrial gases in identical containers, each designed to hold a specific volume. Four different pure gases are stored, each in a separate container. The gases are hydrogen ( $\text{H}_2$ ), oxygen ( $\text{O}_2$ ), nitrogen ( $\text{N}_2$ ), and carbon monoxide ( $\text{CO}$ ).

Each container has the same volume, and the gases are maintained at the same pressure and temperature.

Which sample has the smallest mass?

A. $\text{H}_2$

B. $\text{O}_2$

C. $\text{N}_2$

D. $\text{CO}$

Question 2

MediumPaper 1A · calculator1 mark

An ideal gas is a theoretical model used to describe the behavior of real gases. Which of the following statements about an ideal gas are correct?

I. The internal energy of the gas consists only of the kinetic energy of its particles.

II. For a fixed mass of the gas at constant temperature, its pressure is directly proportional to its volume.

III. The root mean square speed of the gas particles is proportional to the square root of the absolute temperature.

A. II and III only

B. I and II only

C. I and III only

D. I, II and III

Question 3

HardPaper 2 · calculator10 marks

(a)

A large weather balloon is filled with helium gas at ground level. The helium can be modelled as an ideal gas. The balloon is released and rises through the atmosphere.

(a) Explain, in terms of the kinetic model of an ideal gas, how the helium exerts a pressure on the inner surface of the balloon.

[4]

(b)

(b) As the balloon rises to a high altitude, the external atmospheric pressure decreases significantly. Assuming the temperature of the helium remains constant, explain why the volume of the balloon increases.

[3]

(c)

(c) In reality, if the balloon rises very quickly, the temperature of the helium gas inside is observed to decrease. Explain this observation in terms of the motion of the helium atoms and the walls of the balloon.

[3]

Question 4

EasyPaper 1A · calculator1 mark

A fixed mass of $n$ moles of an ideal gas is maintained at a constant pressure. The graph shows the variation of the volume $V$ of the gas with its absolute temperature $T$ .

Graph of Volume V versus Temperature T for an ideal gas at constant pressure

What is the pressure of the gas?

A. $\frac{nR(V_2-V_1)}{T_2-T_1}$

B. $\frac{nR(T_2-T_1)}{V_2-V_1}$

C. $nR\left(\frac{V_2}{T_2} - \frac{V_1}{T_1}\right)$

D. $nR\left(\frac{T_2}{V_2} - \frac{T_1}{V_1}\right)$

Question 5

MediumPaper 1A · calculator1 mark

A flexible weather balloon contains 0.75 mol of helium gas. At an altitude where the pressure is 90.0 kPa and the volume of the balloon is 0.020 m $^3$ , what is the temperature of the helium gas?

A. -12.0 ºC

B. 15.0 ºC

C. 288 ºC

D. 561 ºC

Question 6

HardPaper 2 · calculator11 marks

(a)

A fixed mass of an ideal monatomic gas is confined in a cylinder by a movable piston.

Explain, with reference to Newton's laws of motion, how the gas exerts a pressure on the piston.

[3]

(b)

The piston is slowly pulled outwards, increasing the volume of the gas at a constant temperature.

Explain, in terms of the motion of the particles, why the pressure of the gas decreases.

[3]

(c)(i)

The piston is now pushed inwards rapidly. No thermal energy is transferred between the gas and its surroundings.

Explain, in terms of the collisions between the particles and the piston, why the temperature of the gas increases.

[3]

(c)(ii)

The initial volume of the gas before the rapid compression was $3.60 \times 10^{-4} \text{ m}^3$ at a pressure of $1.05 \times 10^5 \text{ Pa}$ .

Calculate the internal energy of the gas before the compression.

[2]

Question 7

EasyPaper 1A · calculator1 mark

The internal energy of an ideal gas is equal to the total random kinetic energy of its particles. For a real gas, the internal energy is

A. also equal to the total random kinetic energy of its particles.

B. equal to the sum of the total random kinetic energy and the intermolecular potential energy of its particles.

C. equal only to the intermolecular potential energy of its particles.

D. zero.

Question 8

MediumPaper 1A · calculator1 mark

Two sealed gas cylinders, Cylinder P and Cylinder Q, contain ideal gases.

The volume of Cylinder P is half the volume of Cylinder Q. The pressure of the gas in Cylinder P is double the pressure of the gas in Cylinder Q.

The temperature of the gas in P is 27 °C and the temperature of the gas in Q is 127 °C.

What is the ratio $\frac{ \text{amount of substance in P} }{ \text{amount of substance in Q} }$ ?

A. $\frac{1}{3}$

B. $\frac{3}{4}$

C. $\frac{4}{3}$

D. $\frac{16}{3}$

Question 9

EasyPaper 1A · calculator1 mark

An ideal gas is held in a rigid container at an initial temperature of $47^\circ\text{C}$ . Thermal energy is transferred to the gas until its pressure is doubled. What is the final temperature of the gas?

A. $94^\circ\text{C}$

B. $367^\circ\text{C}$

C. $640^\circ\text{C}$

D. $913^\circ\text{C}$

Question 10

MediumPaper 2 · calculator8 marks

(a)

(a) A weather balloon is filled with hydrogen gas at a pressure of 1.0 x 10 $^5$ Pa and a temperature of 290 K. The volume of the balloon is 5.0 m $^3$ . Assume that this sample of hydrogen gas behaves as an ideal gas.

The molar mass of hydrogen (H $_2$ ) is 2.016 g mol $^{-1}$ . Show that the mass of a hydrogen molecule is approximately 3.35 x 10 $^{-27}$ kg.

[1]

(b)

(b) Estimate the average speed of the hydrogen molecules in the balloon.

[2]

(c)

[2]

(d)(i)

(d.i) A hydrogen molecule has an approximate volume of 2.0 x 10 $^{-30}$ m $^3$ . Calculate the ratio $\frac{\text{total volume of hydrogen molecules}}{\text{volume of hydrogen gas}}$ .

[1]

(d)(ii)

(d.ii) Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of hydrogen can be assumed to be an ideal gas.

[2]

Question 11

EasyPaper 2 · calculator2 marks

A sealed flask contains krypton gas maintained at a temperature of $310\text{ K}$ . The gas behaves as an ideal gas.

(a) Calculate the mean translational kinetic energy of a krypton atom in the flask.

Question 12

MediumPaper 2 · calculator13 marks

(a)

This question is about ideal gases and real gases.

(a) Explain what is meant by an ideal gas and state two ways in which a real gas differs from an ideal gas.

[3]

(b)

(b) State the conditions of temperature and pressure under which the behaviour of a real gas most closely approximates that of an ideal gas.

[2]

(c)

[3]

(d)

(d) Deduce why the internal energy of an ideal gas is considered to be solely its total random kinetic energy.

[2]

(e)

(e) A sealed cylinder contains a fixed mass of an ideal gas. Initially, the gas has a volume of $2.50 \text{ L}$ , a pressure of $1.05 \times 10^5 \text{ Pa}$ , and a temperature of $20.0 \text{ °C}$ . The gas is then compressed to a new volume of $1.80 \text{ L}$ and heated to a new temperature of $80.0 \text{ °C}$ . Calculate the final pressure of the gas.

[3]

Question 13

MediumPaper 1A · calculator1 mark

A sealed, rigid container is filled with a certain number of moles of helium (He) gas. An identical container is filled with the same number of moles of argon (Ar) gas. Both containers are maintained at the same temperature.

Which row correctly compares the density of the gas and the pressure in the two containers?

	Density	Pressure
A	same	same
B	same	different
C	different	same
D	different	different

Question 14

MediumPaper 1A · calculator1 mark

Two identical rigid containers, X and Y, are held at the same temperature. Container Y contains double the number of molecules of the same ideal gas as container X.

What is the ratio of the density in Y to the density in X, and the ratio of the pressure in Y to the pressure in X?

	Ratio of densities (Y/X)	Ratio of pressures (Y/X)
A.	1	1
B.	1	2
C.	2	1
D.	2	2

Question 15

MediumPaper 1A · calculator1 mark

A sample of an ideal monatomic gas has an internal energy of $1870 \text{ J}$ when its temperature is $27 \text{ \degree C}$ . The gas constant $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$ .

How many moles of the gas are in the sample?

A. $0.30 \text{ mol}$

B. $0.50 \text{ mol}$

C. $0.75 \text{ mol}$

D. $5.56 \text{ mol}$

Question 16

MediumPaper 1A · calculator1 mark

A fixed mass of an ideal gas, equivalent to $n$ moles, is contained in a cylinder fitted with a movable, frictionless piston, maintaining a constant pressure. The graph shows how the volume $V$ of the gas varies with absolute temperature $T$ .

Graph of volume V versus absolute temperature T for an ideal gas at constant pressure. It's a straight line passing through the origin and two points (T1, V1) and (T2, V2).

What is the pressure of the gas?

A. $nR \frac{T_2-T_1}{V_2-V_1}$

B. $nR \frac{V_2-V_1}{T_2-T_1}$

C. $nR \left( \frac{T_2}{V_2} - \frac{T_1}{V_1} \right)$

D. $nR \left( \frac{V_2}{T_2} - \frac{V_1}{T_1} \right)$

Question 17

MediumPaper 1A · calculator1 mark

Two identical sealed vessels contain monatomic ideal gases. One vessel contains argon (Ar) and the other contains neon (Ne).

The total mass of the gas in each vessel is the same, and both gases are at the same pressure.

The mass of an argon atom is approximately twice the mass of a neon atom.

What is $\frac{\text{internal energy of the argon gas}}{\text{internal energy of the neon gas}}$ ?

A. $\frac{1}{2}$

B. $1$

C. $\sqrt{2}$

D. $2$

Question 18

MediumPaper 1A · calculator1 mark

Two sealed laboratory flasks, A and B, contain samples of an ideal gas at the same pressure.

Flask A has a volume of $2.5 \text{ L}$ and is at a temperature of $27 \text{\textdegree C}$ . Flask B has a volume of $5.0 \text{ L}$ and is at a temperature of $127 \text{\textdegree C}$ .

What is $\frac{\text{amount of substance in A}}{\text{amount of substance in B}}$ ?

A. $\frac{1}{3}$

B. $\frac{2}{3}$

C. $\frac{3}{2}$

D. $3$

Question 19

MediumPaper 1A · calculator1 mark

An ideal gas and a real gas are at the same temperature and occupy the same volume. The number of particles in both gases is the same. How does the internal energy of the real gas, $U_{\text{real}}$ , compare to the internal energy of the ideal gas, $U_{\text{ideal}}$ ?

A. $U_{\text{real}} > U_{\text{ideal}}$ because real gas particles have volume.

B. $U_{\text{real}} < U_{\text{ideal}}$ because there are attractive forces between real gas particles.

C. $U_{\text{real}} = U_{\text{ideal}}$ because temperature is the same.

D. The relationship cannot be determined without knowing the pressure.

Question 20

MediumPaper 1A · calculator1 mark

Two sealed containers, P and Q, are filled with different samples of an ideal gas at the same pressure.

The volume of container P is twice the volume of container Q. The temperature of P is $27 \text{°C}$ and the temperature of Q is $327 \text{°C}$ .

What is $\frac{\text{amount of substance in P}}{\text{amount of substance in Q}}$ ?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. $2$

D. $4$

3 more Gas Laws questions in the app

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Gas Laws: notes and practice questions

How it is examined

Guiding questions

Linking questions

Practice questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

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Question 17

Question 18

Question 19

Question 20

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Where marks are lost

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How it is examined

Guiding questions

Linking questions

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Question 9

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Question 11

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Where marks are lost

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