Chapter 18: Kinetic Theory of Gases

Chapter 18: Kinetic Theory of Gases

• Key Concepts:

  • Ideal Gas Law and Molecular Interpretation of Temperature
  • Distribution of Molecular Speeds
  • Real Gases and Phase Changes
  • Vapor Pressure and Humidity
  • Van der Waals Equation of State
  • Mean Free Path
  • Diffusion

• Assumptions of Kinetic Theory:

  • Large number of molecules, random motion and speeds.
  • Molecules are far apart and follow classical mechanics.
  • Collisions are perfectly elastic.

• Basic Assumptions:

  • Particles far apart compared to size.
  • Constant, rapid straight-line motion.
  • Negligible forces of attraction/repulsion between particles.
  • Each molecule has different velocity.

• Average Kinetic Energy:

  • Proportional to temperature of gas:
    KE \propto T

• Distribution of Molecular Speeds:

  • Described by Maxwell Distribution, depends on absolute temperature.

• Real Gases and Phase Diagrams:

  • Below critical temperature, gases can liquefy with sufficient pressure.
  • Triple point: all three phases (solid, liquid, gas) coexist in equilibrium.

• Vapor Pressure and Humidity:

  • Liquids boil when saturated vapor pressure equals external pressure.
  • Relative humidity = (actual vapor pressure/saturated vapor pressure) × 100.

• Van der Waals Equation:

  • Accounts for finite size of molecules and intermolecular forces:
    (P + a(n/V)^2)(V - nb) = nRT
    (where P=pressure, V=volume, n=moles, T=temperature, a,b=constants).

• Mean Free Path:

  • Average distance a molecule travels between collisions; depends on speed, density, and size of molecules.

• Diffusion:

  • Process where substances move from high concentration to low concentration; described by diffusion constant D.