Gas Laws and Kinetic Molecular Theory

The Gas Laws are based on experiments, and they descibe how a gas behaves under certain conditions. However, the ideal Gas Law does not attempt to explain the behavoir of gases. A theory must be developed to explain the behavoir of gases.

The Kinetic Molecular Theory is a model that explains some of the behavior of gases. The Kinetic Molecular Theory relies on some assumptions that are shown to be reasonable through experimentation.

  1. The size of a gas particle is negligible as compares to the volume of the container in which the gas is placed.

    Gases are mostly empty space, and this is evident because gases can be easily compressed. It is easy to reduce the volume of a gas as compared to reducing the volume of a solid.

  2. Gases are in rapid motion, and they undergo elastic collisions with each other and the walls of the container; that is, momentum and energy is transfered not lost during collisions.

    Gases expand spontaneously to fill any container (rapid motion). Brownian motion of smoke particles (rapid motion). In an insulated container gases do not slow down and eventually condense (elastic collisions).

  3. The gas molecule do not interact with each other except for colliding with each other.

    Gases expand to completely fill a container; they would not if they were attracted to each other.

We will not derive the KMT. However, we could show that the following statement is reasonable.

The pressure exerted by a single particle in a container is

 

Because the velocity of all the gas particles is different, the pressure exerted by a bunch of molecules is

Since the mass of the gas particles does not change lets factor out the "1/3 m".

To make this expression applicable to a container filled with any number of gas particles we will find the average velocity squared and then multiply by the number of particles.

Substitute for the sum of the squared velocities.

remember N is just the number of particles

Remember that PR = nRT and substitute nRT for PV in the equation above.

Hey, something cool here...in a geeky sort of way.

T is proportional to . That is,
molecular motion increases with increasing temperature.

Using the equation above it is possible to relate the temperature of anideal gas to the average kinetic energy of a gas particle.

Since,

and

Since the number of particles can be expessed as number of moles times Avagadro's number, .