Lesson 1 of 3
The ideal model and real gases
Connect pressure to particle collisions and explain deviations.
A-Level 9476 (2026-2027)
I can state the ideal-gas kinetic-theory assumptions.Syllabus
Syllabus 9476, 3(a). State the ideal-gas kinetic-theory assumptions.
I can explain when the ideal approximation succeeds or fails.Syllabus
Syllabus 9476, 3(b). Explain when the ideal approximation succeeds or fails.
Pressure comes from collisions with the container
An ideal gas is a model with negligible particle volume and no intermolecular forces.
Gas particles move continually and randomly. When they collide with a wall, their momentum changes; the resulting force per unit area is the gas pressure. Increasing the number of particles per volume or their typical speed increases the rate or force of those impacts.
| Assumption | Meaning |
|---|---|
| Particles have negligible volume. | Their own volume is tiny compared with the container volume. |
| No intermolecular attractions or repulsions. | Particles move freely between collisions. |
| Continuous random straight-line motion between collisions. | There is no preferred direction in a gas at equilibrium. |
| Collisions are perfectly elastic. | Total kinetic energy is conserved in collisions; individual particles can exchange energy. |
| Mean kinetic energy depends on absolute temperature. | At the same temperature, different ideal gases have the same mean translational kinetic energy, not the same mean speed. |
Temperature must be measured in kelvin because the model relates mean kinetic energy to absolute temperature. At the same temperature lighter molecules typically move faster than heavier molecules. Heating a fixed amount in a rigid sealed container increases pressure because the particles strike the walls harder and more frequently.
Check your understanding
Hydrogen and oxygen are at the same temperature. Which is the same for both: molecular speed or mean kinetic energy?
Show the answer
Mean kinetic energy; the lighter H2 molecules move faster.
Temperature is proportional to mean kinetic energy, (1/2)mv2. With the same energy, a smaller mass means a higher speed.
Low pressure and high temperature favour ideal behaviour
Give both reasons: particle size matters less, and attractions matter less.
At low pressure the particles are far apart, so their own volume is a small fraction of the total and intermolecular attractions are less important. At high temperature their kinetic energies are large compared with the energies associated with attraction. These conditions make the ideal assumptions more reasonable.
At low temperature, attraction can significantly reduce the momentum transferred to the walls and can eventually cause condensation. At very high pressure, the particles are crowded: their finite volume reduces the free space available and short-range repulsion becomes important. Both ideal assumptions fail; a real gas is not just an ideal gas with slower particles.
Two different reasons for non-ideal behaviour
At fixed temperature a schematic real-gas curve of Z = pV/nRT begins near the ideal line Z = 1 at low pressure, dips below it when attractions dominate, and rises above it when finite particle volume and repulsion become important at high pressure. The curve is illustrative rather than data for a named gas.
Check your understanding
A student says, "A real gas always has a lower pressure than an ideal gas." Why is this wrong?
Show the answer
At high density, particle volume and repulsion can make the pressure higher instead.
Attractions lower the pressure compared with ideal. At very high pressure the particles' own volume matters more, raising it. Say which effect dominates under the given conditions.