Particle motion in gases (Higher tier)

Gas pressure from particle collisions

Gas particles move randomly at high speed. Pressure is caused by the particles colliding with the walls of the container. Each collision exerts a tiny force; billions per second produce a measurable pressure.

Pressure = force ÷ area (units: Pa = N/m²).

Two factors determine the pressure:

• The rate of collisions (collisions per second).
• The average force of each collision (depends on particle speed).

Effect of temperature on pressure (constant volume)

When temperature increases, the particles move faster (more average kinetic energy).

• They hit the walls more often.
• They hit the walls harder.

Both effects increase the pressure. So at constant volume, pressure is proportional to absolute (kelvin) temperature:

P / T = constant (V constant)

Convert °C to K by adding 273. A balloon left in a hot car heats up and expands or could burst.

Effect of volume on pressure (constant temperature) — Boyle’s law

If the volume of a fixed mass of gas is decreased at constant temperature, particles travel a shorter distance between collisions and hit the walls more frequently → pressure increases.

P × V = constant (Boyle’s law, fixed mass, constant T)

Equivalently: P₁V₁ = P₂V₂.

A graph of P vs V is a curve (hyperbola); a graph of P vs 1/V is a straight line through the origin.

Doing work on a gas

Compressing a gas does work on it; if no heat escapes, the gas warms up (e.g. a bike pump warms when you pump fast). The energy transferred to the particles increases their kinetic energy and so the temperature.

Edexcel exam tip

When using P₁V₁ = P₂V₂, the units of P and V must match on both sides but do not have to be SI. So kPa × cm³ = kPa × cm³ is fine. Convert °C → K only when temperature appears in the equation (it does not, in Boyle’s law).