P10: Particle Motion and Pressure
Particle motion in gases and gas pressure
Particle Motion And Pressure
📋 Key Definitions
Brownian motion: The random, zigzag motion of particles in a fluid (liquid or gas), caused by collisions with much smaller, fast-moving particles. This provides evidence for the particle model of matter.
Gas pressure: The force exerted by gas particles per unit area on the walls of a container, caused by particles colliding with the walls.
Absolute zero: The lowest possible temperature (−273°C or 0 K), at which particles have zero kinetic energy and stop moving.
Kelvin scale: A temperature scale that starts at absolute zero. An increase of 1 K is the same as an increase of 1°C.
🔬 Brownian Motion
In 1827, Robert Brown observed pollen grains in water moving in random, zigzag paths. This random motion is called Brownian motion.
The explanation: tiny, fast-moving water or air particles collide with larger, visible particles (like smoke or pollen). These collisions are uneven and random, causing the larger particles to move in unpredictable zigzag paths.
Brownian motion is evidence for the particle model — it shows that matter is made of particles in constant, random motion, and that smaller particles move faster than larger ones at the same temperature.
Worked Example 1: Explaining Brownian motion
Explain why smoke particles in air show Brownian motion.
Air particles are much smaller and move very rapidly. They collide with the larger smoke particles from all sides, but unevenly. At any instant, more air particles may hit one side of a smoke particle than the other, causing it to change direction randomly. This gives the smoke particle a random, zigzag path.
💨 Gas Pressure
Gas particles are in constant random motion. When they collide with the walls of their container, they exert a force on the wall. The pressure is this force per unit area.
p = F / A
p = pressure (Pa), F = force (N), A = area (m²)
How gas pressure arises: Gas particles collide with the walls of the container. Each collision exerts a tiny force. Billions of collisions per second add up to produce the overall gas pressure. The pressure depends on how hard and how often the particles hit the walls.
🌡️ Temperature and Pressure
If a gas is heated at constant volume, the temperature increases. This means:
- Particles have more kinetic energy → they move faster
- Faster particles collide with walls more frequently
- Each collision exerts a greater force
- Therefore, pressure increases
At constant volume: Increasing temperature increases the average kinetic energy of particles, so they move faster and collide with the walls more often and harder. This increases the pressure.
Worked Example 2: Temperature and pressure
A sealed gas cylinder is at 20°C and 200 kPa. It is heated to 40°C. Explain what happens to the pressure.
The temperature increases, so gas particles gain kinetic energy and move faster. They collide with the cylinder walls more frequently and with greater force. Since the volume is constant (sealed cylinder), the pressure increases. (Note: the pressure doesn't double because the temperature hasn't doubled in Kelvin — see the Kelvin scale section.)
📐 Volume and Pressure — Boyle's Law
If the temperature of a gas is kept constant and the volume is decreased:
- Particles are in a smaller space
- They collide with the walls more frequently
- Therefore, pressure increases
p₁V₁ = p₂V₂ (at constant temperature, for a fixed mass of gas)
p₁, p₂ = initial and final pressure; V₁, V₂ = initial and final volume
Boyle's Law: For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. If you double the volume, the pressure halves. If you halve the volume, the pressure doubles.
Worked Example 3: Boyle's Law calculation
A gas has a pressure of 100 kPa and a volume of 5.0 m³. If the volume is compressed to 2.0 m³ at constant temperature, what is the new pressure?
p₁V₁ = p₂V₂
100 × 5.0 = p₂ × 2.0
500 = 2.0 p₂
p₂ = 500 / 2.0 = 250 kPa
Worked Example 4: Finding new volume
A fixed mass of gas has a pressure of 200 kPa and a volume of 3.0 m³. The pressure is changed to 150 kPa at constant temperature. Calculate the new volume.
p₁V₁ = p₂V₂
200 × 3.0 = 150 × V₂
600 = 150 V₂
V₂ = 600 / 150 = 4.0 m³
❄️ Absolute Zero and the Kelvin Scale
If you cool a gas, the particles slow down. At some point they would stop moving completely — this is absolute zero.
K = °C + 273
To convert from Celsius to Kelvin: add 273
To convert from Kelvin to Celsius: subtract 273
| Celsius (°C) | Kelvin (K) | Description |
|---|---|---|
| −273 | 0 | Absolute zero — particles have minimum energy |
| 0 | 273 | Freezing point of water |
| 20 | 293 | Room temperature |
| 100 | 373 | Boiling point of water |
At absolute zero (0 K = −273°C), particles have zero kinetic energy and stop moving. This is the lowest possible temperature — you cannot cool anything below absolute zero.
Pressure and Kelvin temperature are directly proportional at constant volume. If you double the Kelvin temperature, you double the pressure. This is why you must convert to Kelvin before using proportional relationships with temperature.
Worked Example 5: Kelvin conversions
Convert: (a) 25°C to K, (b) 373 K to °C, (c) −196°C to K
(a) 25 + 273 = 298 K
(b) 373 − 273 = 100°C
(c) −196 + 273 = 77 K
❓ Practice Questions
Q1: Foundation Describe what causes gas pressure in a sealed container.
Q2: Foundation Explain how Brownian motion provides evidence for the particle model.
Q3: Higher A gas at 150 kPa has a volume of 4.0 m³. The volume is reduced to 1.5 m³ at constant temperature. Calculate the new pressure.
Q4: Higher Convert: (a) 37°C to K, (b) 300 K to °C.
Q5: Higher Explain, in terms of particles, why decreasing the volume of a gas increases its pressure at constant temperature.
✅ Answers
- Gas particles are in constant random motion. They collide with the walls of the container, exerting a force on them. The total force per unit area of the wall is the gas pressure.
- Brownian motion shows larger particles (e.g. smoke) moving in random zigzag paths. This is caused by collisions with smaller, invisible air or water particles. This random, uneven bombardment can only be explained if matter is made of tiny particles in constant motion — supporting the particle model.
- p₁V₁ = p₂V₂ → 150 × 4.0 = p₂ × 1.5 → 600 = 1.5 p₂ → p₂ = 400 kPa
- (a) 37 + 273 = 310 K (b) 300 − 273 = 27°C
- When the volume decreases, the particles are in a smaller space. They travel shorter distances between collisions with the walls, so they collide more frequently. More frequent collisions per second means a greater force per unit area, so pressure increases. The temperature is constant so the average speed of particles is unchanged.
🎯 Exam Tips
- When explaining gas pressure, always mention particles colliding with walls — not just "particles moving"
- Boyle's Law only works at constant temperature and for a fixed mass of gas — check these conditions before using p₁V₁ = p₂V₂
- Always convert temperatures to Kelvin before using proportional relationships — pressure is proportional to Kelvin temperature, not Celsius temperature
- In Brownian motion questions, make clear the distinction between the small, invisible particles (air/water) and the larger, visible particles (smoke/pollen)
- Remember: 1 kPa = 1000 Pa. Make sure all pressures are in the same units before calculating
- When asked to explain pressure changes, always link back to frequency of collisions and/or force of collisions
🔢 Maths Skills
Mathematical Skills
You must be able to use Boyle's Law (p₁V₁ = p₂V₂) by rearranging to find an unknown pressure or volume. You also need to convert between Celsius and Kelvin (K = °C + 273) and understand that pressure is directly proportional to Kelvin temperature at constant volume.
Maths Example
A gas at 300 K and 200 kPa is heated to 450 K at constant volume. Find the new pressure: p₂ = p₁ × T₂/T₁ = 200 × 450/300 = 300 kPa. A separate sample at 120 kPa and 0.5 m³ is compressed to 0.2 m³ at constant temperature: p₂ = p₁V₁/V₂ = 120 × 0.5 / 0.2 = 300 kPa.
⚠️ Common Misconceptions
Watch Out!
1. Wrong: Doubling the Celsius temperature doubles the pressure. Correct: Pressure is proportional to Kelvin temperature, not Celsius. 20°C (293 K) to 40°C (313 K) is not a doubling of temperature.
2. Wrong: Gas pressure is caused by particles pushing each other. Correct: Gas pressure is caused by particles colliding with the walls of the container and exerting a force on them.
3. Wrong: Absolute zero is when particles move very slowly. Correct: At absolute zero (0 K = −273°C), particles have zero kinetic energy and stop moving completely — it is the lowest possible temperature.
✍️ 6-Mark Question
Extended Answer
6 marks: A sealed balloon contains a fixed mass of gas at constant temperature. Describe and explain, in terms of particles, what happens to the pressure when the balloon is compressed to half its original volume.
When the balloon is compressed to half its volume, the same number of gas particles are now in a space half the size. The particles travel shorter distances between collisions with the walls, so they collide with the walls more frequently. Each collision still exerts the same force on average because the temperature is constant (so the average speed of particles is unchanged). The increased frequency of collisions means a greater force per unit area on the walls. Since pressure = force / area, and the area of the walls has also decreased, the pressure increases. Boyle's Law tells us that p₁V₁ = p₂V₂, so halving the volume doubles the pressure.
Mark scheme: 1 mark for same number of particles in smaller space; 1 mark for shorter distance between collisions; 1 mark for more frequent collisions with walls; 1 mark for same force per collision (constant temperature); 1 mark for greater force per unit area; 1 mark for pressure doubles (p₁V₁ = p₂V₂). (6 marks total)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student investigates Boyle's Law using a sealed syringe connected to a pressure gauge. They compress the syringe and record the volume and pressure. The theoretical values (calculated using p₁V₁ = p₂V₂) are shown alongside their measurements.
| Volume (cm³) | Measured pressure (kPa) | Theoretical pressure (kPa) |
|---|---|---|
| 20 | 101 | 101 |
| 15 | 130 | 135 |
| 10 | 186 | 202 |
| 5 | 340 | 404 |
(a) At 20 cm³ the measured and theoretical values agree. Explain why.
(b) As volume decreases, the measured values become increasingly lower than theoretical values. Suggest why.
(c) Explain why Boyle's Law assumes constant temperature and how failing to maintain this would affect the results.
Answers: (a) This is the starting measurement — no compression has occurred yet so there is no error. (b) Compressing the gas quickly does work on it, increasing its temperature. Higher temperature means higher pressure than predicted, but the measured values are lower, so friction in the syringe or slight air leaks may be responsible. More likely: the syringe plunger has friction so some force is lost, or the student did not wait for thermal equilibrium — actually the measured values being lower suggests slight air leakage at high pressures. (c) Boyle's Law requires constant temperature. If the gas warms up during compression, particles move faster and the pressure would be higher than predicted, making the law appear not to hold. The student should compress slowly and wait for the gas to cool back to room temperature before reading pressure.
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