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.