Gas Laws and Kinetic Molecular Theory

Kinetic Molecular Theory

  • Definition: Describes the behavior of gas particles.
    • Particles are in constant motion.
    • They collide with each other and the walls of the container.
    • Gas consists mostly of empty space, as particles are far apart.
    • Pressure is exerted when particles collide with container walls.
    • Interactions between particles are negligible.
    • The average kinetic energy of particles is related to the temperature of the gas.

Boyle’s Law

  • Formula: P1 V1 = P2 V2
  • Description: Relates pressure and volume at constant temperature and amount of gas.
    • As pressure increases, volume decreases (inversely proportional).

Charle’s Law

  • Formula: \frac{V1}{T1} = \frac{V2}{T2}
  • Description: Relates volume and temperature at constant pressure and amount of gas.
    • As temperature increases, volume increases (directly proportional).

Amontons’s Law

  • Formula: \frac{P1}{T1} = \frac{P2}{T2}
  • Description: Relates temperature and pressure at constant volume and amount of gas.
    • As temperature increases, pressure increases (directly proportional).

Ideal Gases

  • Definition: Phase of matter where particles are in constant motion and fill their container.

  • Characteristics of Ideal Gases:

    • Collisions between gas molecules are perfectly elastic.
    • No attractive or repulsive forces between particles.
    • Volume of particles is negligible, regarded as points.

  • Key Properties of Ideal Gases:

    • N = Number of particles
    • V = Volume of the container
    • T = Speed of the particles (related to temperature)
    • P = Frequency of collisions against container walls.

  • Ideal Gas Law:

    • PV = NRT
    • Where R (gas constant) = 0.08206

Dalton’s Law of Partial Pressure

  • Definition: The total pressure of a gas sample is the sum of the pressures of the individual gases.
  • Mole Fractions:
    • Mole fraction of a gas = \frac{moles \ of \ gas}{total \ moles}
    • Mole fraction can also be calculated using partial and total pressures:
    • Mole \ fraction = \frac{partial \ pressure}{total \ pressure}
    • Mole \ fraction \times total \ pressure = partial \ pressure

Graham's Law of Effusion

  • Definition: Relates the rate of effusion of gases to their molar masses.
  • Description: The rate of effusion is inversely proportional to the square root of the molar mass.
  • Equation: \frac{R2}{R1} = \sqrt{\frac{MOLAR \ MASS1}{MOLAR \ MASS2}}
    • Where R is the rate of effusion for each gas.