AP® Physics 2: Algebra-Based · Unit 9 · Topic 9.2
What Makes a Gas Ideal
An ideal gas is a model where molecules are treated as point particles with no size and no forces between them except during collisions, and real gases behave this way closely when they're dilute.
A real gas is made of a trillion trillion molecules bouncing around, each with its own size, speed, and pull on its neighbors. Tracking all of that is impossible, so the ideal-gas model throws most of it away. It assumes molecules take up zero volume, exert no forces on each other except when they collide, and that every collision is perfectly elastic, bouncing off like tiny billiard balls with no energy lost. Strip a gas down to those three assumptions and the chaos of a trillion atoms collapses into one clean relationship: PV = nRT.
This works because at ordinary densities, gas molecules really are tiny compared to the empty space between them, and they really do spend almost all their time far apart, not close enough to attract or repel each other. So treating them as sizeless, forceless points barely changes the answer. Squeeze the gas toward liquid density, though, and the cracks show. The molecules' own volume stops being negligible, since now it is a real fraction of the container's volume, and that is the first assumption to fail. Push density even higher and the attractive forces between molecules, ignored in the ideal model, start pulling pressure lower than PV = nRT predicts.
The elastic-collision assumption connects this model to conservation of momentum, the same principle behind every collision problem. Each molecule bouncing off the wall transfers momentum, and summing up billions of those tiny transfers is literally how pressure gets derived from the model. This sets up the next step in the unit: using those molecular collisions to connect temperature to average kinetic energy.
Key terms
- Ideal gas
- A theoretical gas whose molecules have zero volume and interact only through perfectly elastic collisions.
- Elastic collision
- A collision in which total kinetic energy and momentum are both conserved.
- Low density
- A state where molecules are spaced far apart on average, making their size and mutual forces negligible.
- PV = nRT
- The ideal gas law relating pressure, volume, moles, and temperature of a gas.
Watch it explained
- How it worksHow do a handful of simplifying assumptions collapse a trillion atoms into one short equation?
- Common mistakeWhy doesn't a real gas follow PV = nRT once you squeeze it near liquid density?
- Going furtherWhat changes about the model when the atoms start attracting each other at close range?
- Ties togetherHow does assuming elastic collisions tie the gas model back to conservation of momentum?
Check yourself
End of topic.