## Kinetic Molecular Theory and Gas Laws

#### Learning Objective

• Express the five basic assumptions of the Kinetic Molecular Theory of Gases.

#### Key Points

• Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions.
• Kinetic Molecular Theory can be used to explain both Charles’ and Boyle’s Laws.
• The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only.

#### Terms

• macroscopic propertiesproperties that can be visualized or measured by the naked eye; examples include pressure, temperature, and volume
• ideal gasa hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and the walls of the container

## Basic Assumptions of the Kinetic Molecular Theory

By the late 19th century, scientists had begun accepting the atomic theory of matter started relating it to individual molecules. The Kinetic Molecular Theory of Gases comes from observations that scientists made about gases to explain their macroscopic properties. The following are the basic assumptions of the Kinetic Molecular Theory:

1. The volume occupied by the individual particles of a gas is negligible compared to the volume of the gas itself.
2. The particles of an ideal gas exert no attractive forces on each other or on their surroundings.
3. Gas particles are in a constant state of random motion and move in straight lines until they collide with another body.
4. The collisions exhibited by gas particles are completely elastic; when two molecules collide, total kinetic energy is conserved.
5. The average kinetic energy of gas molecules is directly proportional to absolute temperature only; this implies that all molecular motion ceases if the temperature is reduced to absolute zero.

## Applying Kinetic Theory to Gas Laws

Charles’ Law states that at constant pressure, the volume of a gas increases or decreases by the same factor as its temperature. This can be written as:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

According to Kinetic Molecular Theory, an increase in temperature will increase the average kinetic energy of the molecules. As the particles move faster, they will likely hit the edge of the container more often. If the reaction is kept at constant pressure, they must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.

Boyle’s Law states that at constant temperature, the absolute pressure and volume of a given mass of confined gas are inversely proportional. This relationship is shown by the following equation:

$P_1V_1=P_2V_2$

At a given temperature, the pressure of a container is determined by the number of times gas molecules strike the container walls. If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well. Increasing the kinetic energy of the particles will increase the pressure of the gas.