5.3.1 Kinetic Theory of Gases

• Gases consist of atoms or molecules randomly moving around at high speeds
• The kinetic theory of gases models the thermodynamic behaviour of gases by linking:
  • The microscopic properties of particles i.e. mass and speed
  • The macroscopic properties of particles i.e. pressure and volume

• The theory is based on a set of the following assumptions:
  • Molecules of a gas behave as identical (or all have the same mass)
  • Molecules of gas are hard, perfectly elastic spheres
  • The volume of the molecules is negligible compared to the volume of the container
  • The time of a collision is negligible compared to the time between collisions
  • There are no intermolecular forces between the molecules (except during impact)
  • The molecules move in continuous random motion
  • Newton's laws apply
  • There are a very large number of molecules

• The number of molecules of gas in a container is very large, therefore the average behaviour (eg. speed) is usually considered

Exam Tip

• A gas is made of a large number of particles
  • Gas particles have mass and move randomly at high speeds

• Pressure in a gas is due to the collisions of the gas particles with the walls of the container that holds the gas
• When a gas particle hits a wall of the container, it undergoes a change in momentum due to the force exerted by the wall on the particle (as stated by Newton's Second Law)
  
  • Final momentum = –mv
  • Initial momentum = mv
• Therefore, the change in momentum Δp can be written as:

Δp = final momentum – initial momentum

Δp = –mv – mv = –2mv

• According to Newton's Third Law, there is an equal and opposite force exerted by the particle on the wall (i.e. F = )

A particle hitting a wall of the container in which the gas is held experiences a force from the wall and a change in momentum. The particle exerts an equal and opposite force on the wall

• Since there is a large number of particles, their collisions with the walls of the container give rise to gas pressure, which is calculated as follows:

• Where:
  • p = pressure in pascals (Pa)
  • F = force in newtons (N)
  • A = area in metres squared (m²)

Exam Tip