5.6: Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.

The kinetic molecular theory is a microscopic model that helps understand what happens to gas particles at the molecular or atomic level when conditions such as pressure or temperature change. In 1857 Rudolf Clausius published a complete and satisfactory form of the theory, which effectively explains the different gas laws through the postulates that were developed based on hundreds of experimental observations of the behavior of gases.

The salient features of this theory are:

1. Gases are composed of particles (atoms or molecules) that are in continuous motion, traveling in straight lines and changing direction only when they collide with other molecules or with the walls of a container.
   Examine a sample of argon gas at standard temperature and pressure. It shows that only 0.01% of the volume is taken up by atoms with an average distance of 3.3 nm (atomic radius of argon is 0.097 nm) between two argon atoms. The distance is far greater than its own dimension.
2. The molecules composing the gas are negligibly small compared to the distances between them. Therefore, the combined volume of all gas particles is negligible relative to the total volume of the container. The particles are considered to be “points” that have mass but negligible volume.
3. The pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls.
4. Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic (do not involve a loss of energy).
   During elastic collisions, energy is transferred between the colliding particles. The average kinetic energy of the particles, therefore, stays constant and does not change with time.
5. The average kinetic energy of the gas molecules is proportional to the kelvin temperature of the gas.
   All gases, regardless of their molecular mass, have the same average kinetic energy at the same temperature.

This text is adapted from Openstax, Chemistry 2e, Chapter 9.5 The Kinetic-Molecular Theory.

While the gas laws summarize the relationships between different properties of ideal gases, the kinetic molecular theory explains why gases follow the laws. The theory is based on a few assumptions or postulates.

The first assumption is that gas particles are negligible in size. A gas is mostly empty space comprised of small particles that are separated at distances far greater than their own dimensions. Their combined volume is negligible relative to the total volume in which the gas is contained.

Contrary to solids and liquids, which are incompressible due to their close interparticle spacing, gases are highly compressible.

Gas particles are in a constant state of motion along straight lines in random directions. Their paths only change when they collide with other particles or with the walls of their container. 

The second assumption is that gas particles have perfectly elastic collisions. They collide and bounce off each other without sticking together. This can be compared to the collisions between billiard balls during a game of pool.

When gas particles collide, they exchange energy with each other, but there is no net loss of energy. In other words, the total energy of the system stays constant. 

Gas particles are constantly moving; therefore, they possess kinetic energy. Thus, the third assumption states that the average kinetic energy of a gas is proportional to its absolute temperature in kelvin. 

This means that kinetic energy increases with temperature, and consequently, the particles move faster. At higher temperatures, their velocity increases.

Conversely, as the temperature decreases, so does the kinetic energy of the particles, and they move more slowly.

At a given temperature, all gases, regardless of their molecular mass, have the same average kinetic energy. Kinetic energy is equal to ½ mass times velocity squared. Thus, for different gases to have the same average kinetic energy, their gas particles must travel at different average velocities. Therefore, heavier gases have lower average velocities, while lighter gases have higher average velocities. 

For example, helium and neon, when at the same temperature, have the same average kinetic energy. However, due to the difference in their masses, the neon atoms move much slower than the helium atoms.