B.3 Gas laws
Practice exam-style IB Physics questions for Gas laws, aligned with the syllabus and grouped by topic.
Question 1
A gas exerts a perpendicular force of 36 N on a plane surface of area 0.012 m². What is the pressure exerted on the surface?
A.
3.0 × 10³ Pa
B.
0.43 Pa
C.
4.3 × 10⁻¹ Pa
D.
0.00033 Pa
Question 2
A sample contains 1.20 × 10²⁴ molecules of a gas. What is the amount of substance in the sample?
A.
7.22 mol
B.
7.22 × 10⁴⁷ mol
C.
1.99 mol
D.
0.50 mol
Question 3
What is an assumption of the kinetic model of an ideal gas?
A.
The volume of the molecules is negligible compared with the gas volume.
B.
The collisions between molecules are inelastic.
C.
The molecules exert attractive forces except during collisions.
D.
The molecules all move with the same speed at a fixed temperature.
Question 4
A fixed mass of ideal gas expands at constant temperature. Its volume is doubled. What happens to its pressure?
A.
It becomes one half of its original value.
B.
It becomes one quarter of its original value.
C.
It remains unchanged.
D.
It doubles.
Question 5
A flat circular plate of area 4.0 × 10⁻³ m² is pushed by a gas at a pressure of 1.8 × 10⁵ Pa.
State the equation defining pressure.
[1]
Calculate the perpendicular force exerted by the gas on the plate.
[1]
Question 6
A gas cylinder contains 3.0 mol of helium atoms.
State what is meant by one mole of a substance.
[1]
Calculate the number of helium atoms in the cylinder.
[1]
Question 7
An ideal gas has pressure 1.0 × 10⁵ Pa and volume 2.5 × 10⁻³ m³ at 300 K. What is the amount of substance?
A.
1.0 mol
B.
0.10 mol
C.
7.5 × 10⁴ mol
D.
10 mol
Question 8
A fixed mass of ideal gas is represented on a pressure–volume diagram. Which type of change is shown by a vertical line?
A.
Constant pressure
B.
Constant amount of substance only
C.
Constant temperature
D.
Constant volume
Question 9
The pressure of a gas on a container wall is caused by molecules
A.
losing mass when they strike the wall.
B.
changing momentum during collisions with the wall.
C.
remaining stationary close to the wall.
D.
exerting a continuous gravitational force on the wall.
Question 10
A gas has density 1.2 kg m⁻³ and rms molecular speed 500 m s⁻¹. What is its pressure according to the kinetic model?
A.
2.0 × 10⁵ Pa
B.
6.0 × 10² Pa
C.
3.0 × 10⁵ Pa
D.
1.0 × 10⁵ Pa
Question 11
Two ideal gases are at the same thermodynamic temperature. The molecules of gas X have four times the mass of the molecules of gas Y. What is the ratio rms speed of X/rms speed of Y?
A.
1/4
B.
1
C.
1/2
D.
2
Question 12
What is the relationship between the molar gas constant R, the Boltzmann constant k_B and the Avogadro constant N_A?
A.
R = k_B/N_A
B.
R = N_A + k_B
C.
R = N_A/k_B
D.
R = N_A k_B
Question 13
Brownian motion is observed when tiny smoke particles are illuminated in air.
State what is meant by Brownian motion.
[1]
Explain how this observation supports the kinetic model of gases.
[1]
Question 14
A fixed mass of ideal gas has pressure 1.20 × 10⁵ Pa, volume 2.0 × 10⁻³ m³ and temperature 290 K. It is changed to a state with volume 3.0 × 10⁻³ m³ and temperature 350 K.
State the combined gas law for a fixed amount of gas.
[1]
Calculate the final pressure.
[1]
Question 15
A sealed flask of volume 1.50 × 10⁻² m³ contains 0.62 mol of ideal gas at 20 °C.
Convert the temperature to kelvin.
[1]
Calculate the pressure of the gas.
[1]
Question 16
A real gas is compressed at constant temperature until its density becomes high.
State one assumption about molecular volume in the ideal gas model.
[1]
Outline why the real gas may no longer behave ideally.
[1]
Question 17
A student investigates Boyle's law for a fixed mass of air in a syringe. The graph shows the measured pressure p against reciprocal volume 1/V.
Describe the relationship shown by the graph.
[1]
Use the graph to determine the value of pV for the gas.
[1]
State one condition that must be maintained for Boyle's law to apply.
[1]
Question 18
The graph compares the measured pressure of a real gas with the pressure predicted by the ideal gas equation as the gas is compressed at constant temperature.
State the range of volume over which the real gas is closest to ideal behaviour.
[1]
Describe how the deviation from ideal behaviour changes during compression.
[1]
Suggest a molecular reason for the deviation at small volume.
[1]
Question 19
The thermodynamic temperature of an ideal monatomic gas is doubled. What happens to the internal energy of a fixed amount of the gas?
A.
It increases by a factor of four.
B.
It doubles.
C.
It is unchanged.
D.
It halves.
Question 20
A sealed rigid container holds an ideal gas. The number of molecules is doubled and the thermodynamic temperature is halved. What is the new pressure?
A.
One quarter of the original pressure
B.
Twice the original pressure
C.
One half of the original pressure
D.
The same as the original pressure
Question 21
Under which conditions is a real gas most likely to approximate ideal gas behaviour?
A.
High temperature and low pressure
B.
Low temperature and low pressure
C.
High temperature and high pressure
D.
Low temperature and high pressure
Question 22
A graph of pressure p against reciprocal volume 1/V for a fixed amount of ideal gas is a straight line through the origin. What quantity is proportional to the gradient?
A.
Gas density only
B.
Celsius temperature only
C.
Molecular volume
D.
Thermodynamic temperature
Question 23
An ideal monatomic gas has amount 0.40 mol at 500 K. What is its internal energy?
A.
5.0 kJ
B.
2.5 kJ
C.
0.83 kJ
D.
1.7 kJ
Question 24
In the expression P = (1/3)ρv² for an ideal gas, the factor 1/3 arises because
A.
only one third of the molecular mass contributes to pressure.
B.
only one third of the molecules collide with walls.
C.
one third of collisions are inelastic.
D.
random motion is shared equally among three perpendicular directions.
Question 25
A fixed amount of gas is heated in a rigid container.
State what happens to the rms speed of the molecules.
[1]
Explain, in terms of molecular collisions, why the pressure increases.
[1]
Question 26
An ideal monatomic gas of amount 0.80 mol is heated from 300 K to 360 K.
State the equation for the change in internal energy of an ideal monatomic gas.
[1]
Calculate the change in internal energy.
[1]
Question 27
A gas has pressure 2.4 × 10⁵ Pa and density 1.6 kg m⁻³.
State the kinetic-theory relationship between pressure, density and rms speed.
[1]
Calculate the rms speed of the molecules.
[1]
Question 28
Two different ideal gases are at the same temperature.
State what can be concluded about the average translational kinetic energy of their molecules.
[1]
One gas has molecules of smaller mass. Explain why its rms speed is greater.
[1]
Question 29
A student plots volume against temperature in degrees Celsius for a fixed mass of gas at constant pressure.
State why the graph can be linear but should not be used directly in the ratio V/T with T in °C.
[1]
State the temperature scale required for gas-law ratios.
[1]
Question 30
In an experiment to verify Boyle's law using a gas syringe, the gas is compressed in several steps.
State the graph that should be plotted to test Boyle's law.
[1]
Suggest two reasons for waiting before recording each pressure reading after the volume is changed.
[1]
Question 31
The average translational kinetic energy of one molecule in an ideal gas is 6.2 × 10⁻²¹ J.
State the relation between average translational kinetic energy and temperature.
[1]
Calculate the temperature of the gas.
[1]
Question 32
A gas column of fixed amount is trapped in a capillary tube by a small oil drop. The capillary is heated in a water bath at atmospheric pressure. The graph shows gas-column length l against temperature θ in °C.
State why l can be used as a measure of the gas volume.
[1]
Use the graph to estimate the Celsius temperature at which the volume would be zero.
[1]
Explain one limitation of this estimate.
[1]
Question 33
A sealed flask contains a fixed amount of ideal gas. The table shows the pressure measured at different temperatures.
| Temperature / K | Pressure / kPa |
|---|---|
| 280 | 93.1 |
| 300 | 99.7 |
| 320 | 106 |
| 340 | 113 |
| 360 | 120 |
Identify the dependent variable in the investigation.
[1]
Use one row of the table to calculate the amount of gas in the flask.
[1]
Suggest why the pressure should be measured only after the flask has been in the water bath for several minutes.
[1]
Question 34
The diagram shows a pressure–volume path for a fixed amount of ideal gas.
Identify the section of the path that represents a constant-volume change.
[1]
State whether work is done by the gas during the constant-volume section.
[1]
Explain how the diagram shows that the gas does net work over the complete cycle.
[1]
Question 35
A container holds 4.0 × 10²² molecules of ideal gas at 310 K in a volume of 2.0 × 10⁻³ m³.
State the molecular form of the ideal gas equation.
[1]
Calculate the pressure of the gas.
[1]
Question 36
An ideal gas follows the rectangular path ABCD on a pressure–volume diagram. A→B is an expansion at constant pressure, B→C is at constant volume, C→D is a compression at lower constant pressure, and D→A is at constant volume.
Identify the two parts of the path during which the gas does work on the surroundings.
[1]
Outline how the net work done by the gas over one cycle is represented on the pressure–volume diagram.
[1]
State how the sign of the net work depends on the direction around the cycle.
[1]
Question 37
A gas near its condensation temperature is compressed slowly.
State two ideal-gas assumptions that may fail.
[1]
Explain why liquefaction cannot be predicted by the ideal gas model.
[1]
Question 38
The table gives the density ρ and rms speed v of different samples of the same ideal gas at the same temperature. The pressure p was measured for each sample.
| Density ρ / kg m⁻³ | rms speed v / m s⁻¹ | Pressure p / Pa |
|---|---|---|
| 0.60 | 520 | 5.37 × 10⁴ |
| 0.90 | 518 | 8.13 × 10⁴ |
| 1.20 | 521 | 1.07 × 10⁵ |
| 1.50 | 519 | 1.36 × 10⁵ |
| 1.80 | 520 | 1.61 × 10⁵ |
Calculate ρv² for one sample.
[1]
Use the table to test whether p is proportional to ρv².
[1]
Evaluate whether the data support P = (1/3)ρv².
[1]
Question 39
The graph shows the internal energy U of samples of an ideal monatomic gas plotted against amount of substance n at a fixed temperature.
State the relationship between U and n shown by the graph.
[1]
Use the gradient to determine the temperature of the gas.
[1]
Explain why the graph passes through the origin.
[1]
Question 40
The graph shows the compressibility behaviour of a real gas compared with an ideal gas at three temperatures. The ideal-gas line is also shown.
Identify the temperature at which the gas behaves most ideally over the pressure range.
[1]
Describe how increasing pressure affects the deviation from ideal behaviour.
[1]
Suggest two molecular explanations for the deviations at high pressure.
[1]
Question 41
The graph shows pressure p against number of molecules N for gas in a fixed-volume container at constant temperature.
Describe the relationship shown by the graph.
[1]
Use the gradient of the graph to determine the volume of the container.
[1]
Explain why doubling N at constant T and V doubles the pressure.
[1]
Question 42
A model is used to explain the behaviour of gases.
Outline three assumptions of the ideal gas kinetic model.
[1]
Explain how this model accounts for gas pressure and for the increase in pressure when a gas is heated at constant volume.
[1]
Question 43
A student designs an experiment to verify Charles's law using a trapped gas column in a capillary tube.
Describe how the experiment can be arranged so that gas volume is proportional to a measured length.
[1]
Discuss how the data should be collected and analysed to verify Charles's law, including one limitation of the method.
[1]
Question 44
An ideal gas is taken around a closed cycle on a pressure–volume diagram.
Describe how constant-pressure, constant-volume and constant-temperature changes are represented on a pressure–volume diagram.
[1]
Explain how a gas can do work during expansion and how this is represented on the diagram.
[1]
Question 45
A student tests the pressure law using a sealed metal sphere connected to a pressure sensor. The graph shows pressure p against temperature T in kelvin. Vertical error bars show pressure uncertainty.
State the expected form of the graph for an ideal gas at constant volume.
[1]
Use the graph to determine whether the data are consistent with the pressure law.
[1]
Evaluate one systematic error caused by the connecting tube between the sphere and pressure sensor.
[1]
Question 46
The ideal gas equation is often used for real gases.
State the ideal gas equation and define each symbol.
[1]
Evaluate the conditions under which this equation is a good approximation for a real gas and explain why the approximation fails under other conditions.
[1]
Question 47
The equation P = (1/3)ρv² relates gas pressure to molecular motion.
Define rms speed and state why the mean velocity of molecules in a gas at rest is zero.
[1]
Explain qualitatively how molecular collisions with a wall lead to the relationship between pressure, density and rms speed.
[1]
Question 48
The ideal gas equation can be written as PV = nRT or PV = Nk_BT.
Show how these two forms are related.
[1]
Compare and contrast the molar and molecular descriptions of an ideal gas, including when each form may be useful.
[1]
Question 49
Empirical gas laws can be combined to form the ideal gas equation.
State Boyle's law, Charles's law and the pressure law for a fixed amount of gas.
[1]
Discuss how these empirical laws are represented by PV/T = constant and how this leads to PV = nRT.
[1]
Question 50
A cylinder contains a fixed amount of ideal monatomic gas. The gas is heated and then expands, pushing a piston.
Calculate the increase in internal energy when 0.25 mol of the gas is heated from 290 K to 410 K.
[1]
Evaluate how the microscopic energy of the gas is related to the ability of the gas to do macroscopic work on the piston.
[1]
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