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# Kinetic Molecular Theory for AP Chemistry

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By McGraw-Hill Professional
Updated on Feb 9, 2011

Practice problems for these concepts can be found at:

The Kinetic Molecular Theory attempts to represent the properties of gases by modeling the gas particles themselves at the microscopic level. There are five main postulates of the Kinetic Molecular Theory:

1. Gases are composed of very small particles, either molecules or atoms.
2. The gas particles are tiny in comparison to the distances between them, so we assume that the volume of the gas particles themselves is negligible.
3. These gas particles are in constant motion, moving in straight lines in a random fashion and colliding with each other and the inside walls of the container. The collisions with the inside container walls comprise the pressure of the gas.
4. The gas particles are assumed to neither attract nor repel each other. They may collide with each other, but if they do, the collisions are assumed to be elastic. No kinetic energy is lost, only transferred from one gas molecule to another.
5. The average kinetic energy of the gas is proportional to the Kelvin temperature.

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases: only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we'll show how to modify our equations to account for non-ideal behavior.

Before we leave the Kinetic Molecular Theory (KMT) and start examining the gas law relationships, let's quantify a couple of the postulates of the KMT. Postulate 3 qualitatively describes the motion of the gas particles. The average velocity of the gas particles is called the root mean square speed and is given the symbol urms. This is a special type of average speed.

It is the speed of a gas particle having the average kinetic energy of the gas particles. Mathematically it can be represented as:

where R is the molar gas constant (we'll talk more about it in the section dealing with the ideal gas equation), T is the Kelvin temperature and M is the molar mass of the gas. These root mean square speeds are very high. Hydrogen gas, H2, at 20°C has a value of approximately 2,000 m/s.

Postulate 5 relates the average kinetic energy of the gas particles to the Kelvin temperature. Mathematically we can represent the average kinetic energy per molecule as:

KE per molecule = 1/2 mv2

where m is the mass of the molecule and v is its velocity.

The average kinetic energy per mol of gas is represented by:

KE per mol = 3/2 RT

where R again is the ideal gas constant and T is the Kelvin temperature. This shows the direct relationship between the average kinetic energy of the gas particles and the Kelvin temperature.

Practice problems for these concepts can be found at:

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