Kinetic Molecular Theory of Gases and Gas Laws

Kinetic Molecular Theory of Gases (KMT) Assumptions for Ideal Gas Behavior

• Volume of Particles: The volume of individual gas particles is negligible compared to the total volume of the container.

• Particle Motion: Gas particles are in constant, random, straight-line motion.

• Collisions: Collisions between gas particles and with container walls are perfectly elastic, meaning total kinetic energy is conserved.

• Intermolecular Forces: Gas particles exert no attractive or repulsive forces on each other.

• Average Kinetic Energy: The average kinetic energy of gas particles is directly proportional to the absolute (Kelvin) temperature ($KE_{avg} = \frac{3}{2}RT$).

Real Gases vs. Ideal Gases

• Deviations: Real gases deviate from ideal behavior when particle volume is significant or when intermolecular forces exist.

• Ideal Conditions: Real gases behave most ideally under conditions of:

  • High Temperature: Particles move faster, reducing the effect of attractive forces.

  • Low Pressure: Particles are far apart, making their volume negligible and reducing intermolecular interactions.

• Molecular Properties: Real gases behave more ideally if they are:

  • Non-polar: Lack significant intermolecular forces (e.g., London dispersion forces are weakest).

  • Low Molar Mass/Small Size: Reduce particle volume and intermolecular forces (e.g., helium).

Average Kinetic Energy & Velocity

• Average Kinetic Energy:

  • Depends only on the absolute (Kelvin) temperature.

  • All gases at the same temperature have the same average kinetic energy.

• Average Velocity (Root Mean Square Velocity):

  • Formula: $u_{rms} = \sqrt{\frac{3RT}{M}}$ where $M$ is molar mass.

  • Increases with increasing temperature.

  • Decreases with increasing molar mass (lighter gases move faster).

Gas Laws Explained by KMT

• Boyle's Law ($P \propto \frac{1}{V}$): Decreasing volume increases particle collision frequency with walls, leading to increased pressure.

• Avogadro's Law ($V \propto n$): Increasing moles initially increases internal pressure. In a flexible container, this forces expansion until internal pressure equals external, resulting in increased volume.

• Gay-Lussac's Law ($P \propto T$): Increasing temperature increases average particle speed. In a rigid container, faster particles collide more frequently and forcefully with walls, increasing pressure.

• Charles's Law ($V \propto T$): Increasing temperature increases average particle speed and collision frequency, causing initial pressure increase. In a flexible container, this leads to expansion until internal pressure equals external, resulting in increased volume.