👉 Volume gets smaller
The molecules are squeezed closer together. They hit the walls more often, so the pressure goes up.
Ideal Gas Molecules » Pressure and Volume of a Gas
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 5.20, 5.22
- Why squeezing a gas into a smaller volume raises its pressure, in terms of molecules
- That halving the volume of a gas doubles its pressure, if the temperature stays the same
- How to use p1 × V1 = p2 × V2 to find a new pressure or volume
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Unlock This CourseSqueezing a gas
Put your thumb over the end of a bicycle pump and push the handle in. The air inside gets squashed into a smaller space, and the handle pushes back harder and harder. The pressure of the air is going up.
In this lesson we always look at a fixed amount of gas. That means a fixed mass of gas in a sealed container, so no molecules can get in or out. We also keep the temperature constant, so only the volume and the pressure change.
In the lesson Gas Molecules and Pressure you saw that a gas makes pressure because its molecules keep hitting the walls of the container. Each hit is a tiny force. Millions of hits every second add up to a steady pressure. Now we use that idea to explain what happens when the volume changes.
Key terms:
- Fixed amount of gas: a sealed sample of gas with the same number of molecules all the time. It is the same as saying a fixed mass of gas.
- Constant temperature: the gas is kept at the same temperature, so its molecules keep the same average speed.
Explaining the pressure and volume link
Imagine a sealed syringe full of air with your finger over the end. Push the plunger in so that the volume is half what it was.
- The number of molecules has not changed, but they now have half the space.
- The molecules are closer together, so they travel a shorter distance between hits on the walls.
- So the molecules hit the walls more often.
- Each hit is a force on the wall. More hits every second means a larger total force on each square metre of wall.
- A larger force on the same area means a higher pressure.
The temperature has not changed, so the molecules are not moving any faster. The pressure goes up only because the hits are more frequent.
🎈 Volume gets bigger
The molecules have more room. They hit the walls less often, so the pressure goes down.
Learn this
For a fixed amount of gas at constant temperature: a smaller volume means a higher pressure. If you halve the volume, the pressure doubles. If you double the volume, the pressure halves.
You can describe the pattern in one more way. If you multiply the pressure by the volume, you always get the same answer, as long as the temperature and the amount of gas do not change.
The equation p1 × V1 = p2 × V2
Because pressure × volume stays the same, we can compare the gas before and after a change:
Pressure and volume of a fixed mass of gas
p1 × V1 = p2 × V2
p1 and V1 are the pressure and volume at the start. p2 and V2 are the pressure and volume at the end. This only works at constant temperature.
You do not need to memorise this equation. It is printed on the formulae page of the exam paper. You do need to know how to use it.
Units. The units must match on both sides. Pressure can be in pascals (Pa) or kilopascals (kPa), as long as you use the same one for p1 and p2. Volume can be in cm3 or m3, as long as you use the same one for V1 and V2. You do not need to convert to a special unit, because the same unit appears on both sides. The answer comes out in the unit you used.
Worked example 1: a syringe
A sealed syringe holds 60 cm3 of air at a pressure of 100 000 Pa. The plunger is pushed in until the volume is 20 cm3. The temperature stays the same. Calculate the new pressure.
Step 1: Write the equation: p1 × V1 = p2 × V2
Step 2: Substitute: 100 000 × 60 = p2 × 20
Step 3: Work out the left side: 6 000 000 = p2 × 20
Step 4: Divide by 20: p2 = 6 000 000 ÷ 20 = 300 000 Pa
Check: the volume went down to a third, so the pressure should go up three times. 3 × 100 000 = 300 000 Pa. ✅
Worked example 2: finding a volume
A gas has a volume of 500 cm3 at 100 kPa. Its pressure is raised to 250 kPa at constant temperature. Calculate the new volume.
Step 1: Substitute: 100 × 500 = 250 × V2
Step 2: 50 000 = 250 × V2
Step 3: V2 = 50 000 ÷ 250 = 200 cm3
Check: the pressure went up, so the volume should go down. 200 cm3 is smaller than 500 cm3. ✅
Worked example 3: a bubble rising in water
A diver breathes out a bubble of air at a depth where the pressure is 400 000 Pa. The bubble has a volume of 2.0 cm3. It rises to the surface, where the pressure is 100 000 Pa. Assume the temperature does not change. Calculate the volume of the bubble at the surface.
Step 1: Substitute: 400 000 × 2.0 = 100 000 × V2
Step 2: 800 000 = 100 000 × V2
Step 3: V2 = 800 000 ÷ 100 000 = 8.0 cm3
Answer: the bubble grows to 8.0 cm3. The water pressure around it falls as it rises, so the air inside spreads out into a bigger volume.
Worked example 4: a bicycle pump
A bicycle pump holds 400 cm3 of air at 100 kPa. The outlet is blocked and the handle is pushed in until the air is 100 cm3. Calculate the pressure of the air.
Step 1: Substitute: 100 × 400 = p2 × 100
Step 2: 40 000 = p2 × 100
Step 3: p2 = 40 000 ÷ 100 = 400 kPa
Answer: 400 kPa. The volume was quartered, so the pressure is four times bigger.
Suggested investigation (optional)
You can test the relationship with a sealed syringe joined to a pressure gauge. Read the volume from the scale on the syringe and the pressure from the gauge. Push the plunger in a little at a time, and record the volume and pressure each time. Push slowly and wait a moment before each reading, so that the gas stays at room temperature. If the relationship is right, pressure × volume comes out about the same every time. The main source of error is the gas warming up when it is squashed quickly. A column of trapped air in a tube can be used in the same way.
Common mistakes
- Using the equation when the temperature is changing. It only works at constant temperature.
- Mixing units, such as a pressure in kPa for p1 and in Pa for p2. Use the same unit on both sides.
- Saying the molecules move faster when the gas is squashed. At constant temperature their speed is the same. They hit the walls more often.
- Saying the molecules hit the walls harder. The key point is that they hit the walls more often.
- Adding p and V instead of multiplying them.
- Forgetting to check the answer: if the volume goes down, the pressure must go up.
Exam-style question
A sealed syringe contains 40 cm3 of air at a pressure of 100 kPa. The plunger is pushed in slowly until the volume is 25 cm3. The temperature of the air stays the same.
(a) Explain, in terms of the molecules of air, why the pressure increases. [3 marks]
(b) Calculate the new pressure of the air. [3 marks]
(c) State why the plunger was pushed in slowly. [1 mark]
Model answer
(a) The molecules are closer together in the smaller volume (1). So they hit the walls more often (1). This gives a bigger force on each unit area of the wall, so the pressure is higher (1).
(b) p1 × V1 = p2 × V2, so 100 × 40 = p2 × 25 (1). 4000 = p2 × 25 (1). p2 = 160 kPa (1).
(c) So that the temperature of the air stays constant (1).
Exam tip
In an "explain" question about pressure and volume, write "more often" and mention the walls. Answers that say only "the molecules are squashed" do not get the marks. For the calculation, write the equation, then the substitution, and finish with the unit.