This note covers the particle model of solids, liquids and gases, how moving particles create gas pressure, and how the pressure, volume and temperature of a fixed mass of gas are linked. These ideas explain everyday events such as a football pumped up hard, a tyre warming on a long drive and smoke drifting through a room.
Key ideas
The three states of matter. Everything is made of tiny particles (atoms, molecules or ions) that are always in motion. The state depends on how strongly the particles attract each other and how fast they move.
- Solid: particles are packed closely in a regular pattern. They vibrate about fixed positions. A solid has a fixed shape and a fixed volume.
- Liquid: particles are close together but in no regular pattern. They slide past one another. A liquid has a fixed volume but takes the shape of its container.
- Gas: particles are far apart and move quickly in random directions. There are almost no forces between them except during collisions. A gas fills its container, so it has no fixed shape or volume.
Solids and liquids are hard to compress because their particles are already touching. A gas is easy to compress because most of its volume is empty space.
Changes of state. Melting, freezing, boiling, evaporation and condensation change the arrangement of the particles, not the particles themselves. When a solid is heated, its particles vibrate more strongly until they break free of their fixed positions and the solid melts. Heating a liquid gives particles enough energy to escape from each other and form a gas.
Brownian motion. Pollen grains or smoke particles in air seen through a microscope jiggle about in a random, zigzag way. The visible particle is much larger than an air molecule. It is knocked unevenly by very many fast, invisible air molecules, so it is pushed first one way and then another. This is direct evidence that air molecules exist, are moving, and move randomly.
Temperature and particle motion. The temperature of a gas is linked to the average kinetic energy of its particles. A hotter gas means faster particles on average. The Kelvin scale starts at absolute zero, the lowest possible temperature (0 K = −273 °C), where particles have the least possible energy. To convert, add 273 to a Celsius temperature.
How a gas creates pressure. Gas particles hit the walls of the container. Each collision gives the wall a tiny push. Billions of collisions every second add up to a steady force on the wall. Pressure is this force on each unit of area.
- Heat the gas (fixed volume): particles move faster, hit the walls harder and more often, so pressure rises.
- Reduce the volume (fixed temperature): the same number of particles hit a smaller wall area. More collisions per unit area per second, so pressure rises.
- Add more gas (fixed volume and temperature): more particles means more collisions, so pressure rises.
Pressure and volume at constant temperature (Extended). For a fixed mass of gas at constant temperature, if the volume is halved the pressure doubles. The product of pressure and volume stays constant. This is called Boyle's law:
p1V1 = p2V2
Use any matching units for pressure and for volume, as long as both sides use the same ones. The temperature must stay the same and no gas may leak out.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Particle model | Matter is made of moving particles. The model explains states, changes of state and gas behaviour. |
| Brownian motion | Random zigzag movement of small visible particles caused by collisions with fast, invisible molecules. |
| Gas pressure | Force per unit area caused by particles colliding with the surface. |
| Absolute zero | 0 K or −273 °C, the lowest possible temperature. |
| T (K) = θ (°C) + 273 | Converts Celsius to Kelvin. Subtract 273 to go back. |
| p1V1 = p2V2 (Extended) | Fixed mass of gas at constant temperature. Gives the new pressure or volume. |
| pressure = force ÷ area | Links the push on a surface to its area. Units: N/m2 or pascals (Pa). |
Worked examples
Example 1 A bicycle pump holds 0.80 litres of air at a pressure of 1.5 × 105 Pa. The outlet is blocked and the piston is pushed in until the volume is 0.30 litres. The temperature does not change. Find the new pressure.
Fixed mass of gas at constant temperature, so use p1V1 = p2V2.
p2 = p1V1 ÷ V2
p2 = (1.5 × 105 × 0.80) ÷ 0.30
p2 = 1.2 × 105 ÷ 0.30 = 4.0 × 105 Pa
Answer: 4.00 × 105 Pa
Example 2 A scuba diver releases an air bubble of volume 4.0 cm3 at a depth where the pressure is 3.0 × 105 Pa. As it rises to the surface, where the pressure is 1.0 × 105 Pa, its temperature stays constant. Find the volume of the bubble at the surface.
The mass of air in the bubble is fixed and the temperature is constant, so p1V1 = p2V2.
V2 = p1V1 ÷ p2
V2 = (3.0 × 105 × 4.0) ÷ (1.0 × 105)
V2 = 12 cm3
Answer: 12 cm3 (the bubble expands as the pressure falls)
Example 3 A sealed metal can of gas is warmed from 25 °C to 100 °C. (a) Write both temperatures in kelvin. (b) Explain, using particles, why the pressure inside the can rises.
(a) Add 273 to each Celsius value.
25 + 273 = 298 K and 100 + 273 = 373 K.
(b) The can is sealed, so the number of particles and the volume stay the same. At higher temperature the particles move faster on average. They hit the walls more often and with greater force on each collision. The force on each unit area of wall is larger, so the pressure rises.
Answer: 298 K and 373 K; faster particles give more frequent, harder collisions, so the pressure increases.
Common errors
- Common error: saying particles themselves expand or melt when a substance is heated. The particles stay the same size. It is their spacing and movement that change.
- Common error: saying pressure rises because particles "collide with each other more". Gas pressure comes from collisions with the walls of the container.
- Common error: putting a Celsius temperature into a gas calculation or forgetting to convert. Gas temperatures must be in kelvin when they appear in a formula.
- Common error: using p1V1 = p2V2 when the temperature changes or gas escapes. It only works for a fixed mass of gas at constant temperature.
- Common error: saying the pollen grain in Brownian motion is hit by "air". It is hit by individual air molecules, which are far too small to see.
Exam tip: In particle explanations, name the property that changes (speed, spacing, number of particles) and then link it to the collisions with the wall in the order: how often, how hard, so pressure.
Check yourself
- Why can a gas be compressed much more easily than a liquid?
Answer
The particles in a gas are far apart, so there is a lot of empty space to squeeze into. In a liquid the particles are already touching, so there is almost no space to close up. - A gas of volume 600 cm3 at 2.0 × 105 Pa is expanded to 1500 cm3 at constant temperature. Find the new pressure.
Answer
p2 = p1V1 ÷ V2 = (2.0 × 105 × 600) ÷ 1500 = 8.0 × 104 Pa. - Convert 127 °C to kelvin and 250 K to degrees Celsius.
Answer
127 + 273 = 400 K. 250 − 273 = −23 °C. - Explain, using particles, why the pressure of a fixed mass of gas rises when its volume is reduced at constant temperature.
Answer
The particles move at the same average speed, but they now travel in a smaller space. They reach the walls more often, so there are more collisions per second on each unit of wall area. The force per unit area increases, so the pressure rises.