Kinetic Molecular Theory of Gases

Kinetic-molecular theory is a simple model to explain properties of gases. There are four basic postulates:

  1. A gas is composed of a large number of tiny particles (molecules, or atoms for the inert gases). These particles are so small that the sum of the particles volumes is negligible compared to the volume of their container - most of the container volume is empty space.

  2. The particles of a gas are in rapid, linear motion. They make frequent collisions with each other and the walls of any vessel containing them. All collisions between gas particles and between gas particles and container walls are elastic. (There is no net loss of kinetic energy in collision - energy can be exchanged between particles, but the total stays the same.)


    animation of translational motion in gasses

    public domain image via Wikipedia Creative Commons

  3. Except when they are colliding, the particles are completely independent of each other. That is, there are no forces of attraction or of repulsion between them.

  4. The particles in a gas have a wide range of velocities: some may be nearly still, while others move at great speed. Thus there is a wide range of kinetic energies in any gas. However, the average kinetic energy for any gas is the same at a given temperature. The average kinetic energy for the particles in a gas is proportional to the absolute temperature of the gas. (KE = 3/2 RT, R is still the Gas constant, but different units.)

 

 

 

 

 

 

 

 

 

 

 

 

 

Consequences/predictions:

  1. Gases are easy to compress - expected if there is lots of empty space between them.

  2. This explains why gases rapidly fill their containers. We also note that they don't condense out as a liquid or solid if they are left in an insulated container (they don't lose energy as they collide with walls.) Brownian motion is also a consequence of their rapid movement.

  3. Three is a bit more subtle, and we won't worry about it.

  4. From this postulate we expect a distribution of velocities. (Overhead 42, Zumdahl figure 5.20, p 219)

Plot of the Maxwell-Boltzman Distribution of gas particles at different temperatures

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Note that for kinetic energy, KE = 1/2 mV2, so V varies as the square root of the mass (m1/2). Notice also that the energy increases with the square of the velocity. (This is why an accident at 60 mph (88 ft/s) is much worse that one at 30 mph - four times as much energy is involved!)

© R A Paselk

Last modified 18 February 2011