Kinetic Theory

Introduction

Kinetic theory explains the behavior of gases based on the movement of their molecules. It provides a microscopic understanding of how gases exert pressure, how temperature affects molecular motion, and how energy is distributed among gas particles. This theory forms the foundation of thermodynamics and helps explain real-world phenomena such as diffusion, gas pressure, and heat transfer.

Basic Assumptions of Kinetic Theory

The kinetic theory of gases is based on several fundamental assumptions:

• Gas molecules are in constant random motion. They move in all directions with different speeds.

• Molecular collisions are perfectly elastic. When gas particles collide with each other or with the walls of a container, no energy is lost.

• The volume of individual gas molecules is negligible. Compared to the total volume of the gas, the actual volume occupied by gas molecules is very small.

• There are no intermolecular forces. Gas molecules do not exert any attractive or repulsive forces on each other.

• The pressure of a gas is due to collisions. The force exerted by gas molecules when they collide with the walls of the container creates pressure.

These assumptions work well for ideal gases, but real gases deviate from these conditions under certain circumstances.

Kinetic Energy and Temperature

• The temperature of a gas is directly related to the average kinetic energy of its molecules.

• When temperature increases, gas molecules move faster, leading to higher kinetic energy.

• At absolute zero (-273.15°C or 0 K), molecular motion theoretically stops, meaning no kinetic energy is present.

Pressure of a Gas

• Gas pressure is caused by the continuous collision of gas molecules with the walls of the container.

• The higher the number of collisions, the greater the pressure.

• When the volume of a gas decreases, molecules collide more frequently, increasing pressure (Boyle’s Law).

• If the temperature increases, molecules move faster and hit the walls with greater force, leading to higher pressure.

Distribution of Molecular Speeds

The speeds of gas molecules in a sample vary, following the Maxwell-Boltzmann distribution:

• Most probable speed: The speed possessed by the largest number of molecules.

• Average speed: The mean speed of all gas molecules.

• Root mean square (rms) speed: A measure of the square root of the average of squared velocities of gas molecules.

This distribution explains why some gas molecules move faster than others at a given temperature.

Mean Free Path

• The mean free path is the average distance a gas molecule travels before colliding with another molecule.

• If the gas density increases, the mean free path decreases because there are more molecules in a given space, leading to frequent collisions.

• This concept is important in understanding diffusion and viscosity of gases.

Real Gases vs. Ideal Gases

Ideal gases follow the kinetic theory perfectly, but real gases show deviations under high pressure and low temperature. This happens because:

• Real gas molecules have a finite volume and cannot be ignored.

• Weak intermolecular attractions exist in real gases, especially at low temperatures.

To correct these deviations, Van der Waals' equation was introduced, which modifies the ideal gas law to account for molecular volume and intermolecular forces.

Applications of Kinetic Theory

• Explains gas laws like Boyle’s Law, Charles’s Law, and Avogadro’s Law.

• Helps in understanding diffusion—how gases mix due to molecular motion.

• Used in thermodynamics to describe heat transfer and energy distribution.

• Important in meteorology for studying atmospheric pressure and gas behavior in different layers of the atmosphere.

Conclusion

The kinetic theory provides a microscopic explanation of gas behavior, linking molecular motion to macroscopic properties such as temperature, pressure, and volume. It forms the basis for understanding gas laws, thermodynamics, and real-world applications, from weather patterns to industrial gas storage.