The kinetic molecular model explains an ideal gas as a large collection of tiny particles in constant random motion.

Its central idealizations are:

• the particles are far apart compared with their own size, so the volume occupied by the particles themselves is negligible compared with the container volume;
• particles move freely between collisions;
• intermolecular attractions and repulsions are neglected except during collisions;
• collisions between particles and with the container walls are elastic;
• the equilibrium motion is random and isotropic, with no preferred spatial direction.

These assumptions are not literally true for every gas. They define a simplified model whose predictions become accurate when molecules are sufficiently dilute and intermolecular forces are relatively unimportant.

Pressure as repeated momentum transfer

A gas molecule that collides elastically with a wall reverses the component of its momentum normal to that wall. The wall therefore receives an impulse.

A macroscopic sample contains an enormous number of molecules, so countless microscopic impulses occur every second. Their average force per unit area is the gas pressure.

This gives pressure a mechanical interpretation: it is not a static substance stored in the gas, but the averaged effect of molecular momentum transfer to boundaries.

Why compression raises pressure

At fixed molecular kinetic-energy scale, reducing the container volume shortens the typical distance between wall encounters. Molecules strike the walls more frequently, increasing the rate of momentum transfer and therefore the pressure.

This provides a microscopic interpretation of the inverse pressure-volume relation of an ideal gas at fixed temperature.

Why heating can raise pressure

If a gas in a fixed container is heated, its molecules typically move faster. Faster molecules transfer more momentum per collision and also reach the walls more frequently. The pressure therefore increases.

If the container can expand instead, the larger volume can reduce collision frequency, so the final pressure depends on which macroscopic variables are constrained.

Why different gases can share the same temperature

Temperature characterizes a statistical energy scale of the molecular motion, not the speed of one particular molecule. At the same temperature, molecules of different masses need not have the same typical speed: lighter molecules generally move faster than heavier ones.

The quantitative connection among pressure, molecular kinetic energy, temperature, and molecular speed follows by calculating the momentum transfer of many wall collisions.

Limits of the model

Real gases deviate from ideal behavior when molecular size or intermolecular forces become important, especially at high density and near condensation. Collisions also involve internal molecular structure that the simplest point-particle model ignores.

The kinetic molecular model is valuable because it connects macroscopic gas properties to microscopic mechanics while making its approximations explicit.