Kinetic Molecular Theory and Gas Laws

Kinetic Molecular Theory

  • Model for Gases: The simplest model for gas behavior is the Kinetic Molecular Theory (KMT) which portrays a gas as a collection of particles in constant motion.

Basic Postulates of Kinetic Molecular Theory

  • Negligible Size: The size of gas molecules is negligibly small compared to the distances between them.

  • Average Kinetic Energy: The average kinetic energy (KE) of gas particles is proportional to the absolute temperature (in Kelvin).

  • Elastic Collisions: Collisions between gas particles and between particles and container walls are completely elastic, meaning no kinetic energy is lost in the collision.

Behavior of Gas Particles

  • Constant Motion: Gas particles (atoms or molecules) are endlessly moving.

  • Attraction Between Particles: The attraction between the gas particles is negligible, so they do not stick together upon collision.

  • Spacing: There is a significant amount of space between the gas particles relative to their size.

Temperature and Kinetic Energy

  • Temperature Effect: The average kinetic energy of gas particles increases with temperature, leading to increased particle speed.

  • Speed Variation: Particle speeds vary; not all particles in a gas sample move at the same velocity.

  • Energy Transfer: During collisions, energy may be exchanged but total energy remains constant.

Nature of Pressure

  • Pressure from Movement: Gas particles strike the walls of their container with force, creating pressure. The sum of forces from numerous particles results in a constant pressure.

Gas Laws

Boyle's Law

  • Definition: Volume of a gas is inversely proportional to its pressure when temperature and the number of particles are constant.

  • Implication: Reducing volume increases collision frequency, thereby increasing pressure.

Charles' Law

  • Definition: Volume of a gas is directly proportional to absolute temperature when pressure and quantity are constant.

  • Result of Heating: Increasing temperature results in increased average speed leading to a greater volume to maintain constant pressure.

Dalton's Law

  • Total Pressure: In a gas mixture, the total pressure is the sum of the partial pressures of individual gases.

  • Negligible Size and KE Equivalence: Gas particles have negligible size and different gases share the same average KE at a given temperature.

Avogadro's Law

  • Volume and Mole Relationship: Volume of a gas is directly proportional to the number of molecules at constant temperature and pressure.

  • Result of Increasing Molecules: More molecules mean more collisions with walls, necessitating an increase in volume to keep pressure constant.

Kinetic Molecular Theory and Ideal Gas Law

  • Equation: The relationship can be summarized with the ideal gas law: PV = nRT where P = pressure, V = volume, n = number of moles, R = ideal gas constant, T = temperature.

Temperature and Molecular Velocities

  • Molecular Movement: The average kinetic energy depends on mass and velocity. Gases at the same temperature have equal average kinetic energy.

  • Mass Effect: Heavier molecules move slower on average than lighter ones to maintain the same kinetic energy.

Diffusion and Effusion

  • Diffusion: Molecules spread from an area of high concentration to one of low concentration.

  • Effusion: Molecules escape through a small opening into a vacuum.

  • Rate Relation: Rates of diffusion and effusion correlate with root mean square average velocity, proportional to the inverse square root of molar mass.

Graham's Law of Effusion

  • Rate Comparison: The effusion rate ratio of two gases at the same temperature can be calculated using their molar masses.

Real Gases vs Ideal Gases

  • Non-Ideal Behavior: Real gases diverge from ideal behavior at high pressures or low temperatures due to intermolecular attractions and finite particle volume.

van der Waals Equation

  • Modifications: Johannes van der Waals modified the ideal gas law to account for both gas particle volume and intermolecular forces, introducing constants a and b for different gases,

  • Volume Adjustments: At high pressures, real gas volume exceeds ideal predictions due to molecular size. At low temperatures, real gas pressures fall below ideal predictions due to attraction forces affecting collisions.

To efficiently study these notes, focus on equations and definitions central to gas laws, the descriptions of gas behaviors through KMT, and recognize the distinctions between ideal and real gases regarding their conditions of behavior.