Teach lesson
Gas pressure and volume: small capsule, big pressure
Experiment with an ideal gas model to size a sealed sample chamber, then apply the relationship to a new case. Covers Boyle's law. Browser only: no lab or classroom materials.
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Learning Outcomes
Use an ideal gas model to predict how pressure changes when volume changes at fixed temperature.
Support a relationship between pressure and volume with chosen readings from the model.
Choose and justify a design that meets several numerical constraints.
Apply the relationship to a new starting point and say what a model cannot establish about real gases.
Student activity preview
Activity Content
Preview only. In a class session, students can fill in responses and submit their work to the teacher.
The mission
Text version of the investigation
A research drone must bring a sealed air sample home, but the chamber is too large for its return bay. Find the smallest whole-millilitre volume that meets the mission's pressure rules.
Every number in this lesson comes from an ideal gas model. Nothing here is measured from real apparatus. You can experiment with the model and use it to make a decision, but its values cannot show that real gases obey the rule the model is built on.
This version has the same questions as the interactive one and works without graphics. Answer each question before reading on: nothing on this page stops you from reading ahead, and your teacher can see that you used this version.
1. Predict before observing
3 min
The sealed chamber starts at 60 mL and 100 kPa absolute pressure. A thermal sleeve holds the gas at 293 K (about 20 °C).
First prediction
At 30 mL, what pressure do you predict? Why? Explain what halving the volume might change.
Fair-test setup
Which setup isolates the effect of volume?
Check your setup
Keep the seal closed and the temperature fixed. Opening the valve changes the amount of gas; heating changes the temperature. Either would stop you isolating the effect of volume.
2. Give your idea a fair test
4 min
Ideal model values, calculated and not measured
Choose at least four readings, including 60 mL and 30 mL, that give you two equal jumps of volume. Copy them into the table.
- 60 mL → 100.0 kPa
- 55 mL → 109.1 kPa
- 50 mL → 120.0 kPa
- 45 mL → 133.3 kPa
- 40 mL → 150.0 kPa
- 35 mL → 171.4 kPa
- 30 mL → 200.0 kPa
These are settled values for a fixed amount of gas at 293 K. In a fast real compression the gas can warm up for a moment; this model does not show that.
Your model readings (ideal model, not measured)
Record the readings you chose, one per row. Leave the other rows empty.
| Volume mL | Model pressure kPa |
|---|---|
Two equal jumps
When the volume drops in two equal jumps, how much does the pressure rise in each one? What does that say about your prediction?
3. From a pattern to a prediction
4 min
Proposed relationship
Which quantity do you think stays constant?
Your support for it
Support your relationship with two recorded observations.
Prediction at 24 mL
Use your relationship: what pressure do you predict at 24 mL, beyond the volumes you tested?
Particle explanation
Why does pressure rise at the same temperature?
Check your thinking
At 24 mL the model gives 250 kPa: P × V stays at 6000 kPa·mL for the same gas amount and temperature. P + V changes (100 + 60 = 160, 200 + 30 = 230), and so does P ÷ V.
The particles hit each area of wall more often. They do not shrink, and at a fixed temperature they keep the same average speed.
Pressure here is absolute: measured from vacuum, not from the surrounding air.
4. How small can you go?
4 min
Choose the smallest whole-number volume that meets all three rules. These limits belong to this fictional design challenge.
- The sample bay holds at most 40 mL.
- The absolute pressure limit is 180 kPa.
- Leave at least 10 kPa of headroom below that limit.
Calculate P = 6000 ÷ V, then headroom = 180 − P. Keep each attempt in your notes.
Your volume
What is the smallest whole-number volume that meets all three rules?
Why a smaller volume fails
Why would a smaller whole-mL volume fail? Use the numbers from this challenge.
Check your design
36 mL gives 166.7 kPa and 13.3 kPa of headroom. 35 mL gives 171.4 kPa and only 8.6 kPa of headroom. These are classroom design rules, not a safety certification for any apparatus.
5. What this model can and cannot tell you
2 min
You used an inverse relationship to make a decision. The model was built with P × V constant, so experimenting with it could not test that rule against real gas. A real syringe could. Your teacher may assign the LabsLand Boyle lesson, where you work with recorded measurements from real apparatus.
Reflection
What observation would make you doubt this model? (Optional)
One last question
3 min
This question is about a real syringe, not the model. It has no hints and no automatic feedback. Your teacher reads your reasoning.
A real syringe starts at 86 kPa with 60 mL of sealed air, at a fixed temperature.
Expected reading at 30 mL
What reading do you expect at 30 mL?
Expected reading at 45 mL
What reading do you expect at 45 mL?
Your reasoning
Explain how you got these readings.
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