The shape of the lesson
By the end of the lesson, learners can
- Trade volume for pressure: Change the volume of a trapped gas at constant temperature and watch the pressure respond.
- The inverse relationship: Pressure and volume move in opposite directions so that their product stays fixed.
- Conditions: fixed mass of gas, constant temperature.
- Rearrange p1 V1 = p2 V2 for whichever quantity is unknown.
- Sense check: smaller volume must give larger pressure, and the reverse.
One picture every idea returns to
For a fixed mass of gas at constant temperature, the pressure multiplied by the volume is constant: pV = constant, so p1V1 = p2V2. Halving the volume doubles the pressure.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Squeeze it, and it pushes back.. Trap some air in a syringe, seal the end, and press. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Trade volume for pressure | Change the volume of a trapped gas at constant temperature and watch the pressure respond. Project tab 4 of the lab (Boyle's law) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: The inverse relationship | Pressure and volume move in opposite directions so that their product stays fixed. Model the worked example Worked example on the board, one line at a time. | Frayer Model |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 14 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in The inverse relationship, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Frayer Model
Pairs fill a four-box grid for the key term: definition, characteristics, examples and non-examples. The non-examples box is where the misconceptions surface, so give it the most time.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| At constant temperature the particles do not speed up when you compress the gas. | The pressure rises only because the same particles are packed into a smaller space, so they strike the walls more often per second. |
Boyle’s law (pV = constant): worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
State Boyle's Law, including the conditions under which it applies.
A gas has a volume of 2.0 litres at a pressure of 200 kPa. At constant temperature it is compressed to a volume of 0.5 litres. Calculate the new pressure.
A sealed syringe holds 100 cm³ of gas at a pressure of 300 kPa. The plunger is pulled out, at constant temperature, until the volume is 150 cm³. Calculate the new pressure.
Explain, in terms of particles, why reducing the volume of a fixed mass of gas at constant temperature increases its pressure.
Boyle's Law only holds if a particular quantity is kept constant. State this quantity, and explain why the average speed of the particles does not change when the gas is compressed under these conditions.
A student plots a graph of pressure (y-axis) against volume (x-axis) for a fixed mass of gas at constant temperature. Describe the shape of the graph, and state what the product of the two plotted quantities represents.
Answer key and marking notes
- For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume. ✓
- That is, pV = constant (so p1 V1 = p2 V2). ✓
- p₂ = p₁V₁ / V₂
p₂ = (200 × 2.0) / 0.5 = 400 / 0.5
p₂ = 800 kPa
Volume cut to a quarter, so pressure is four times bigger.
- p₂ = p₁V₁ / V₂
p₂ = (300 × 100) / 150 = 30000 / 150
p₂ = 200 kPa
Volume increased, so pressure dropped, as expected.
- In the smaller volume the particles travel a shorter distance between the walls. ✓
- So they collide with the walls more often, giving a greater force per unit area, which is a higher pressure. ✓
- The temperature must be kept constant. ✓
- The average speed of the particles depends on the temperature, so if the temperature is unchanged the particles keep the same average speed. ✓
- The graph is a curve that falls steeply at first and then levels off (a downward curve, never reaching the axes). ✓
- At every point the product pressure × volume is the same constant value. ✓
7 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A fixed mass of gas of volume 6.0 m³ at a pressure of 200 kPa is compressed at constant temperature to 2.0 m³. What is the new pressure?
- A67 kPa
- B600 kPa
- C1200 kPa
- D200 kPa
At constant temperature, a fixed mass of gas at 150 kPa occupies 8.0 L. The pressure is raised to 300 kPa. What is the new volume?
- A2.0 L
- B4.0 L
- C8.0 L
- D16 L
For a fixed mass of gas at constant temperature, how are the pressure and volume related?
- APressure is inversely proportional to volume.
- BPressure is directly proportional to volume.
- CPressure does not depend on volume.
- DPressure is proportional to the square of the volume.
A gas is compressed to a smaller volume at constant temperature. Using the particle model, why does the pressure rise?
- AThe particles travel shorter distances between the walls, so they strike the walls more often.
- BThe particles move faster.
- CThe particles grow larger.
- DThe particles gain mass.
A gas is sealed in a rigid container of fixed volume and then heated. Using the particle model, why does the pressure increase?
- AThe particles move faster, so they hit the walls harder and more often.
- BThe particles move closer together.
- CThe particles get bigger.
- DThe number of particles increases.
The graph shows how the pressure of a fixed mass of gas varies with its volume at constant temperature. What does the shape of the curve show?
- APressure is inversely proportional to volume.
- BPressure is directly proportional to volume.
- CPressure stays constant as volume changes.
- DPressure increases as volume increases.
A fixed mass of gas at constant temperature has a pressure of 100 kPa and a volume of 12 cm³. Which other pair of values is possible for the same gas?
- A200 kPa and 6.0 cm³
- B200 kPa and 24 cm³
- C50 kPa and 12 cm³
- D100 kPa and 24 cm³
Quiz key
p₂ = p₁V₁ ÷ V₂ = (200 × 6.0) ÷ 2.0 = 600 kPa. Option A divides the wrong way (200 × 2 ÷ 6); C multiplies pressure by the original volume.
V₂ = (150 × 8.0) ÷ 300 = 4.0 L. The pressure doubled, so the volume halves. Option D doubles the volume, treating pressure and volume as directly proportional.
Boyle's law states that pressure is inversely proportional to volume at constant temperature, so pV is constant. If pressure rose with volume (B), squeezing a gas would lower its pressure, which is not observed.
In a smaller volume the particles reach the walls sooner, so collisions are more frequent and the pressure rises. The temperature is constant, so the particle speed is unchanged (ruling out B).
Heating makes the particles move faster, so each collision is harder and collisions happen more often, raising the pressure. The volume is fixed and no gas is added, so B, C and D do not apply.
The curve falls as volume increases, and doubling the volume halves the pressure, which is the signature of an inverse proportion (Boyle's law). A straight rising line would be needed for direct proportion (B).
pV must stay constant at 100 × 12 = 1200. Only 200 × 6.0 = 1200 satisfies this. The other pairs give 4800, 600 and 2400, so they change the temperature or mass.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.