Notes on Kinetic Molecular Theory and Gas Laws

Characteristics of Gases

  • Fill any container and exhibit random motion without attraction.
  • Display fluid properties similar to liquids.
  • Very low densities due to few particles occupying large amounts of empty space.

Key Concepts of Kinetic Molecular Theory (KMT)

  1. No Intermolecular Forces: Gas particles do not attract or repel each other, allowing free movement in containers.
  2. Volume: Gas particles are considered to have no volume; most of the space is empty.
  3. Constant Motion: Gas particles are in perpetual motion.
  4. Elastic Collisions: No kinetic energy is lost when gas particles collide with each other or the container walls.
  5. Average Kinetic Energy: All gases possess the same average kinetic energy at a given temperature.
    • Higher temperatures lead to increased energy.
    • Kinetic energy formula: KE = ( \frac{1}{2}mv^2 )

Ideal vs. Real Gases

  • Ideal Gases: Follow KMT assumptions closely and are represented by the ideal gas law.
    • Fugacity: A dimensionless number used to gauge ideality (fugacity = Pressure × Volume / (Moles × R × Temperature)).
  • Real Gases: Do not fully adhere to KMT.
    • Exhibit volume, leading to higher pressure.
    • Intermolecular forces affect behavior; typically behave like ideal gases under low pressure and high temperature.

Gas Laws

  • Pressure: Defined as Force/Area, resulting from collisions with container walls.
    • Units of pressure: atm, mm Hg, kPa (1 atm = 760 mm Hg = 101.3 kPa).
  • Ideal Gas Law: ( PV = nRT ) (P = Pressure, V = Volume, n = Moles, R = Ideal gas constant, T = Temperature).
  • Standard Temperature and Pressure (STP): P = 1 atm, T = 273.15 K.

Specific Gas Laws

  1. Boyle's Law: Pressure and volume are inversely related at constant temperature (P1V1 = P2V2).
  2. Avogadro's Law: Equal volumes of gases contain equal moles at constant temperature and pressure.
  3. Charles's Law: Volume is directly related to absolute temperature at constant mass and pressure (V1/T1 = V2/T2).
  4. Gay-Lussac's Law: Pressure is directly related to absolute temperature at constant mass and volume (P1/T1 = P2/T2).
  5. Dalton's Law of Partial Pressures: Total pressure is the sum of the partial pressures of individual gases in a mixture.