Part 5: The gas phase system will have an average kinetic energy that is proportional to temperature; the kinetic energy will be distributed among the particles according to a Boltzmann type of distribution.

Based on the earlier parts of the Kinetic Molecular Theory, the individual gas particles will exist with ever changing quantities of kinetic energy. If all the kinetic energy of all the particles were to be averaged, then the resulting value for that average will be directly representative of the temperature of the system. This is all based upon the temperature being determined in the absolute scale of temperature measurement called the Kelvin scale. As long as the temperature of the gas phase system remains constant, then there will not be a change in the average kinetic energy of the system. Yet, while the average is fixed, the individual objects in the system continue to collide and rearrange the distribution of the kinetic energy.

Years ago, a mathematician named Boltzmann figured out that the kinetic energy of a system such as this was distributed in a predictable way. Even though the individual objects continually exchanged kinetic energy with each other, there was a predictable result to how the kinetic energy was distributed.

He discovered that the varying values for kinetic energy occurred with predicable frequency. The distribution of the kinetic energy values based on his work is now known as the Boltzmann Distribution. When graphed, it produces a classic curve. This curve is in the form of a bell-shaped distribution.

The Boltzmann Distribution, as it applies to gases, shows the relationship between the many different values for kinetic energy carried by the particles in a system and the number of times a particular kinetic energy value is carried by those particles. In other words, if the graph was carefully drawn, it would show how many objects have 1 unit of KE, how many objects have 2 units of KE, how many objects have 3 units of KE, and so on.

Consider a gas phase system that contains many particles all moving randomly with randomly distributed kinetic energy.

Some of the particles will be moving very rapidly while others will be moving very slowly. Imagine being able to identify the objects by labels showing kinetic energy content. Using the data obtained from observation such as these it is possible to prepare a graph. For an example of a true Boltzmann Distribution, check this Java Applet.

Imagine this as the standard graph of a system at room temperature. As the system is heated the position of the average kinetic energy must shift to the right in order to reflect that change. The graph reflects that change. As the system cools, the average kinetic energy must respond by shifting position to the left. The graph reflects that change. Generally, as a system is heated the graph broadens and flattens. As it is cooled, the graph narrows and grows taller. At higher temperatures, the particles are more evenly distributed over a range of kinetic energy values.

This completes the discussion of the parts to the Kinetic Molecular Theory. Remember what it is trying to do. It is attempting to treat all real gases as if they were the same. Their differing behaviors are approximated as being described by the Ideal Gas. The Kinetic Molecular Theory is describing this imaginary, or Ideal, gas. These assumptions for behavior have some obvious errors associated with them. Yet, curiously enough, for the majority of circumstances, they will lead to very adequate descriptions of real gases.