Lecture on Kinetic Molecular Theory of Gases

Introduction

• Kinetic Molecular Theory is a model explaining the behavior of ideal gases.
• Real gases differ from ideal gases and may deviate from these assumptions.

Key Assumptions of the Kinetic Molecular Theory

1. Negligible Volume of Particles

   • Volume of individual gas particles is negligible compared to the distance between them.
   • Significant in real gases, affecting pressure-volume relationship (e.g., larger particles deviate more from Boyle's Law).

2. Constant Random Motion

   • Gas particles are in constant motion as long as temperature > 0 Kelvin.
   • Particles move in straight lines but experience random motion due to collisions with other particles.

3. Elastic Collisions

   • Collisions between gas particles are elastic, conserving total kinetic energy.
   • Kinetic energy and momentum (mass x velocity) are conserved in elastic collisions.

4. No Interparticle Forces

   • Ideal gases exert no forces (attractive or repulsive) on each other.
   • Real gases (e.g., polar gases) do exert forces, deviating from ideal behavior.

5. Energy Proportional to Temperature

   • Average kinetic energy of gas particles is directly proportional to the Kelvin temperature.
   • Higher temperatures lead to faster-moving particles and increased kinetic energy.

Multiple Choice Practice

• Average Kinetic Energy: Dependent only on temperature, not pressure.
• Average Velocity at STP: Depends on molar mass; lighter gases move faster.
• Inconsistencies with Theory: Pressure not dependent on molar mass.

Conditions for Ideal Gas Behavior

• Ideal Conditions: Low pressure and high temperature favor ideal gas behavior.
• Real vs. Ideal Gases: Polar gases deviate more due to intermolecular forces.

Ideal Gas Comparisons

• Polar vs. Nonpolar Gases: Nonpolar gases behave more ideally.
• Intermolecular Forces: Minimal in gases with low molar mass and volume.

Gas Laws Explained

Boyle's Law

• Inverse relationship: Pressure increases with reduced volume due to more frequent collisions.

Avogadro’s Law

• Volume increases with the number of moles, as increased internal pressure causes expansion until equilibrium.

Gay-Lussac's Law

• Pressure increases with temperature; faster molecules collide more frequently.

Charles’s Law

• Volume expands with temperature in flexible containers; increased pressure initially leads to volume increase until equilibrium.

Pressure and Gas Variables

• Pressure and Moles: More moles result in higher pressure due to more collisions.
• Density and Temperature: Density inversely proportional to temperature; increases with pressure and molar mass.

Summary

• Understanding gas behavior through the kinetic molecular theory helps predict how gases respond to changes in temperature, pressure, and volume.
• Ideal gas laws provide a framework for understanding these relationships, though real gases often deviate due to molecular size and interparticle forces.