B.3.3—Ideal gas model
- Syllabus
- First assessment 2025
- Objective
- —
- Level
- HL
Model an Ideal Gas
Ideal-gas model
An ideal gas is a kinetic-theory model: particles are in constant random motion, occupy negligible volume compared with the container, and interact negligibly except during collisions. Collisions are treated as elastic.
Connect microscopic and macroscopic quantities
Temperature is related to average translational kinetic energy. Pressure comes from momentum transfer when particles collide with the container walls. More energetic or more frequent collisions can increase pressure.
It is an approximation
Real gases have finite-size particles and intermolecular forces. The ideal model is most reliable when particles are far apart and interactions are relatively unimportant.
Common trap
The model does not say every particle has the same speed. It uses a distribution of speeds and averages over many particles.
B.3.3 Exam Analysis
Assessment in practice
1–2 marksHow it is assessed
The evidence uses a two-mark outline of the kinetic theory and a multiple-choice question about elastic collisions with container walls.
Command terms
Outline / State
What earns marks
Describe the kinetic-theory assumptions that connect observables to molecules: random motion, elastic wall collisions, momentum transfer causing pressure, and temperature related to average kinetic energy.
Watch for
Saying all particles have the same speed or that pressure is a static property unrelated to collisions.
Representative question
Question 1
[Maximum number: 2]
Outline how the kinetic theory of gases relates observable properties of a gas to the motion of the molecules.
«absolute» temperature is proportional to/related to the KE of the molecules. pressure is related to the «average» rate of momentum transfer due to the collisions of the molecules with the container
OR
average force molecules exert per unit area.
OR pressure is the result of molecular force on/collisions with the container walls.
Higher pressure is the result of higher KE of molecules « in constant random motion » or vice versa
OK to use atoms/molecules/particles
2 max
Synthesize B.3 Gas Laws
Macroscopic equations
Pressure is P=F⊥/A. For a fixed amount of gas, empirical laws combine to PV/T=constant, and the ideal-gas equations are PV=nRT=NkBT.
Microscopic model
Particles move randomly and collide elastically with walls. Momentum transfer produces pressure, with P=31ρv2. For a monatomic ideal gas, U=23NkBT=23nRT.
Bridge the descriptions
Use n=N/NA to move between moles and particles. Choose the equation from the data provided, convert temperature to kelvin, and keep SI units consistent.
Model boundary
The ideal approximation works best at high temperature and low pressure or density. At high density, high pressure or near condensation, finite particle size and intermolecular forces matter.