Gas Laws and Kinetic MolecularTheory
The Gas Laws are based on experiments, and they descibe how a gasbehaves under certain conditions. However, the ideal Gas Law does notattempt to explain the behavoir of gases. A theory must be developedto explain the behavoir of gases.
The Kinetic Molecular Theory is a model that explains some of thebehavior of gases. The Kinetic Molecular Theory relies on someassumptions that are shown to be reasonable throughexperimentation.
- 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.
- 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).
- 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 couldshow 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, thepressure exerted by a bunch of molecules is
Since the mass of the gas particles does not change lets factorout the "1/3 m".
To make this expression applicable to a container filled with anynumber of gas particles we will find the average velocity squared andthen multiply by the number of particles.
Substitute 
forthe sum of the squared velocities.
remember N is just the number ofparticles
Remember that PR = nRT and substitute nRT for PV in the equationabove.
T is proportional to 
.That is,
molecular motion increases with increasing temperature.
Since,
and
Since the number of particles can be expessed as number of molestimes Avagadro's number, 
.
