# Kinetic Molecular Theory

## Basic Concepts

The gas laws developed by Boyle, Charles, and Gay-Lussac are based upon empirical observations and describe the behavior of a gas in macroscopic terms, that is, in terms of properties that a person can directly observe and experience, such as volume, temperature and pressure. An alternative approach to understanding the behavior of a gas is to begin with the atomic theory, which states that all substances are composed of a large number of very small particles (molecules or atoms). In principle, the observable properties of gas (pressure, volume, temperature) are the consequence of the actions of the molecules making up the gas.

The Kinetic Molecular Theory of Gases begins with five postulates that describe the behavior of molecules in a gas. Some of these postulates are based upon simple, basic scientific notions, while others provide simplying assumptions. In reading a postulate, do two things.

First, try to understand and appreciate the basic physical idea embodied in the postulate. This idea will ultimately be important in understanding the macroscopic properties of the gas in terms of the behavior of the microscopic molecules making up the gas.

Second, identify possible weakness or flaws in the postulates. Inaccurate predictions by a theory are often a consequence of flawed postulates used in the derivation of the theory.

## Postulates

1. A gas consists of a collection of small particles traveling in straight-line motion and obeying Newton's Laws.
2. The molecules in a gas occupy no volume (that is, they are points).
3. Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during the collision).
4. There are no attractive or repulsive forces between the molecules.
5. The average kinetic energy of a molecule is 32 k T. (T is the absolute temperature and k is the Boltzmann constant.)

## Behavior of Molecules in a Gas

To illustrate the significance of these postulates, consider the box containing a single molecule shown below. Start the animation and observe the molecule, represented by the blue ball, bouncing and traveling back and forth across the box. The collisions with the walls are perfectly elastic. Energy is neither gained nor lost from the collision. Because the walls do not move, the molecule's speed is unaffected by the collision. The graph plots the particle speed as a function of time. Observe that the speed has a constant value.

Molecule Speed vs Time

Now consider the box below, which contains more than one molecule. Start the animation and observe the blue molecule. Unlike the system above, in this system molecules will collide from time to time. Observe how the speed (and direction) of the blue molecule changes as a result of a collision. A consequence is that the speed of a given molecule is not constant. Each collision changes both direction and speed of the molecules. Sometimes a molecule moves slowly and sometimes it moves rapidly.

The graph shows how the speed of the blue molecule changes with time. Observe that the speed is approximately constant between collisions. At the moment of each collision there is an abrupt change in speed (and in direction).

Averaged over a long period of time, the average kinetic energy of a given molecule is 32 k T. Similarly, the average kinetic energy of a large number of molecules at a particular instant in time is also 32 k T.

Molecule Speed vs Time

## Molecular Dynamics Simulations

The above simulations implement a technique called molecular dynamics. The molecular dynamics simulations shown above do not perfectly implement the assumptions of the Kinetic Molecular Theory.

First, you will readily observe that the molecules are not points. Instead they have size. If the molecules get too close together, a large repulsive force pushes the molecules away from each other. The larger the molecules, the more frequently they will collide.

Second, there are intermolecular attractions. You may observe scenarios where two slow moving molecules pass close to each other. In this situation you may see the molecules being pulled towards each other.

If there were no intermolecular attractions, the speed of the blue molecule would be perfectly constant between collisions. Close inspection of the graph, however, shows that the speed of the blue molecule is not perfectly constant between collisions. This effect is the consequence of intermolecular attractions.

The Ideal Gas Law is a consequence of the postulates of the Kinetic Molecular Theory. Real gases, however, do not perfectly obey the Ideal Gas Law. Deviations are especially significant at high concentration and low temperature. Molecular Dynamics simulations provide a more accurate description of the behavior of real gases.

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© 2001, 2014, 2023 David N. Blauch