History and Assumptions of Kinetic Molecular Theory

Historical Framework of the Kinetic Molecular Theory of Gases

Gases represent some of the earliest substances documented in scientific study, with research and conceptual development beginning as early as the 1600s.
Early scientific observations established that all gases exhibit uniform physical behaviors. This consistency suggested that gaseous substances could be explained through a single, comprehensive theoretical framework.
By the late 19th century, the Kinetic Molecular Theory (KMT) became a widely accepted scientific standard.
Scientists utilize the Kinetic Molecular Theory as a primary framework for understanding the nature of gases and predicting their specific behaviors under various conditions.
The core function of the Kinetic Molecular Theory is to link the microscopic behaviors of ideal gas molecules to the macroscopic properties observed in gas samples.

The Five Fundamental Assumptions of Ideal Gases

As a foundational explanation for gas properties, the Kinetic Molecular Theory relies on five specific assumptions regarding the behavior of ideal gases:

Motion of Molecules: Gas samples consists of vast numbers of molecules that are in a state of constant, random, and linear motion.
Molecular Volume: The actual volume occupied by the individual gas molecules themselves is considered negligible in comparison to the total volume occupied by the gas.
Intermolecular Interaction: The intermolecular forces acting between gas particles are negligible, meaning there is effectively no attraction or repulsion between them.
Nature of Collisions: Collisions occurring between gas particles are completely elastic. In these interactions, the total kinetic energy of the system is conserved.
Relationship to Absolute Temperature: The average kinetic energy of gas molecules is directly proportional to absolute temperature only. This relationship implies that if temperature is reduced to absolute zero ( $0\,K$ ), all molecular motion ceases. This can be expressed as: $KE_{average} \propto T_{absolute}$

Indefinite Shape and Volume

Gases do not possess a definite shape or a definite volume.
The inherent randomness of gas molecule movements allows them to move with total freedom, enabling them to assume the volume of any container in which they are held.
Consequently, the volume of a gas is defined as the space within a container where molecules have the range to move freely.

Compressibility and Expandability

Gases exhibit low density, which facilitates compressibility. This is possible because gas molecules are typically positioned very far apart from one another.
Because gas molecules are randomly positioned at significant distances from each other, they exert negligible or no intermolecular force on one another.
The absence of these forces allows the gas to expand to fill spaces or be compressed into smaller volumes with ease.

The Process of Diffusion in Gases

Diffusion is defined as the rate at which the particles of a substance spread throughout a given area.
Gas molecules exist in state of perpetual motion and travel at very high velocities.
This velocity is proportional to the kinetic energy of the molecules, resulting in the creation of enormous amounts of intermolecular space between the particles.
These wide spaces and high velocities allow gas molecules to become completely and consistently mixed with one another, creating a homogeneous mixture.

Low Density and Fluidity of Gases

Density ( $\rho$ ) is defined as the ratio between the mass of a substance and the volume it occupies: $\rho = \frac{m}{V}$
Because gases are composed of molecules that are extremely scattered and far apart, very little mass is expected to occupy a specific volume.
This results in the characteristic low density of gaseous matter.
This low density is the primary factor that allows gases to move with fluidity.

Pressure and Molecular Collisions

Pressure ( $P$ ) is the measure of the amount of force ( $F$ ) a substance exerts per unit area ( $A$ ): $P = \frac{F}{A}$
Due to their constant motion, gas particles exert pressure in every direction against the interior surfaces of their container.
A higher amount of pressure corresponds to a higher probability of gas molecules colliding with one another.

Temperature and Kinetic Energy

Temperature is formally defined as the measurement of the average kinetic energy of the molecules in a substance.
Since gas molecules are in a state of constant motion and travel at exceptionally high speeds, their kinetic energy is high.
Following this relationship, gases are recognized for having high temperatures as a direct result of their high molecular kinetic energy.