Structure 1.5.1 – The Ideal Gas Model

An ideal gas is a theoretical model used to describe the behavior of gases under a set of simplified assumptions. It assumes particles behave in a perfectly predictable way and helps in deriving the ideal gas law.

Key Assumptions of the Ideal Gas Model:

1. Gas particles have negligible volume: The actual volume of the gas particles is so small compared to the volume of the container that it is considered zero. Thus, gases are mostly empty space.
2. No intermolecular forces: There are no attractive or repulsive forces between particles. They move independently of each other, only changing direction when colliding.
3. Random motion: Gas particles move in random directions with a range of speeds, constantly colliding with each other and the walls of the container.
4. Elastic collisions: When particles collide, no kinetic energy is lost. Total kinetic energy of the system remains constant, even though individual particles may gain or lose energy.
5. Temperature is proportional to average kinetic energy: The average kinetic energy \( E_k \) of gas particles is directly proportional to the absolute temperature (Kelvin), given by:
   \( E_k \propto T \)

Ideal Gas Equation:

The behavior of ideal gases is described by the ideal gas law:

\( PV = nRT \)

• \( P \) = pressure (Pa)
• \( V \) = volume (m³)
• \( n \) = number of moles (mol)
• \( R \) = ideal gas constant (8.31 J mol⁻¹ K⁻¹)
• \( T \) = temperature (K)

When does a real gas behave ideally?

• At high temperatures: particles have more kinetic energy, so intermolecular forces become negligible.
• At low pressures: particles are farther apart, so their own volume and attractions become insignificant.

When do real gases deviate from ideal behavior?

• At high pressures: particle volume is no longer negligible.
• At low temperatures: attractive forces between particles become significant.