Kinetic Molecular Theory — Overview & Importance

Have you ever played billiards? It's an older person's game. But, when I was young, I got into it. I even played in the state games. It was fun and challenging. At the time, I knew nothing about chemistry. Little did I know that billiards would be an excellent analogy for gas behavior.

Whenever we've talked about gases, we've made some assumptions. Those assumptions are the basis of the kinetic molecular theory. They explain the behavior of gases, the gas laws, and why a gas behaves like a real or ideal gas.

Kinetic Molecular Theory Assumptions

The kinetic molecular theory has five assumptions.

1. Gas particles have negligible volumes. The space between the gas molecules is much larger than the gas particle itself. Gases are expandable and compressible because of the empty space between them. This isn't true in solids and liquids because the atoms are more tightly packed.

2. Gases do not exert forces. There is a lot of space between gas molecules. So, we assume they don't have Van der Waal's forces.

3. Gases are constantly moving in a straight line. They only change direction when they collide. They can collide with another gas particle or the container.

4. Gas collisions are perfectly elastic. Elastic means that the total kinetic energy is the same. The particles may have more or less. But, between them, the total is the same. Inelastic collisions only conserve momentum.

5. A gas's average kinetic energy is proportional to its kelvin temperature. So, at absolute zero ($0K$), all motion stops. Of course, absolute zero is impossible. Do you remember quantum mechanics? At absolute zero, we would know a particle's position and momentum. But, the uncertainty principle tells us that's not possible. As a side note, did you know that Boulder, Colorado, is the coldest place on earth? Chemists at the University of Colorado at Boulder cooled an object to $0.00036 K$! That's a little too cold for me!

Let's return to the billiards table. When we strike the cue ball, it travels in a straight line. When it hits another ball, their trajectories change. Both balls have a new path. But, they are still moving in a straight line. Billiard balls are dense. So, we can assume their collisions are elastic. Of course, the balls are not in constant motion. So, it's not a perfect analogy. But, hopefully, it helped you to picture the kinetic molecular theory.

Kinetic Molecular Theory and the Gas Laws

Kinetic molecular theory helps us explain each of the gas laws. Let's take a look.

• Boyle's Law: Boyles law shows that gas pressure and volume are inversely related. Decreasing the container's volume creates less empty space between the gas molecules. So, we would expect more collisions. Volume dropped but, pressure increased. If we expand the system, there will be more space between particles. So, we have fewer collisions. Volume increased and, pressure decreased.

• Charles' Law: Charles law tells us that temperature and volume directly relate. We need an expandable container. If we increase the temperature, the gases' kinetic energies increase. They will collide more with the container. In a rigid container, the pressure would increase. But, an expandable container balances the new pressure by altering its volume. Now, even though our molecules are moving faster, they have more space to travel. So, the number of collisions remains constant.

• Gay-Lussac Law: The Gay-Lussac law reveals that temperature is proportional to pressure. Raising the temperature causes the kinetic energy to rise. So, the gas particles are moving faster. There will be more collisions and more pressure.

• Avagadro's Law: Avagadro's law relates the moles of gas to the volume. More molecules mean we have more collisions. So, as we increase moles, pressure follows. Again, we need an expandable container. Like Charle's law, the container's volume grows to counteract the new force.

• The Combined and Ideal Gas Laws: Both the combined and ideal gas laws merge the above relationships. The ideal gas law allows us to see each of the above associations. But, we have to keep two variables constant. For example, let's examine the relationship between pressure and temperature. Start by making the volume and moles constants. Then the pressure and temperature are on opposite sides of the equation. So, they are directly related.

Real and Ideal Gases

The kinetic molecular theory is the picture of an ideal gas. It is an excellent approximation and will obey the ideal gas law. But, we can think of many situations where each assumption stops working.

1. The kinetic molecular theory assumes that there is a lot of empty space between particles. So, the gas's volume is always negligible. But, if we have a lot of particles in a container, there is not much space between them. The gas particles' total volume fills a significant part of the container. So, at very high pressures or small volumes, the first assumption breaks down.

2. We also assume that gasses do not exert forces on each other. For nonpolar molecules, that's a fabulous assumption. They only experience weak dispersion forces. If two gases zoom past one another, it's unlikely they experience electrostatic attractions. But, for polar covalent molecules, it's a poor assumption. Dipole-dipole interactions and hydrogen bonding are strong enough to influence gases. For the intermolecular forces to not matter, we would need very high temperatures. The kinetic energy is much larger than the potential energy. So we assume the potential is unimportant. But, at meager temperatures, even dispersion forces become significant.

3. When assumption 2 breaks down, so does 3. If a gas particle is experiencing electrostatic interactions, its path will change. Attraction curves its route towards other molecules. But, repulsion arches its pathway away. Any curving increases the path's length. So, there will be fewer collisions because the particle travels further.

4. When gas molecules experience attraction, their collisions become inelastic. Their kinetic energy converts to potential energy. However, like all collisions, their momentum is still conserved.

5. Besides translational energy, molecules can also have vibrational and rotational. At high temperatures, the translational energy is much larger than vibration or rotation. So, we can assume they are unimportant. But, at smaller temperatures, rotation and vibration could cause energy transfer.

When kinetic molecular theory fails, we have real gases. To account for the breakdown, we use Van Der Waal's equation. It alters the ideal gas law with two new terms. The first term accounts for the particle's volume. Meanwhile, the second considers the intermolecular forces.

(Video) Kinetic Molecular Theory and its Postulates

by Professor Dave Explains

In this video, Professor Dave explains the Kinetic Molecular Theory. He starts by clarifying the difference between the gas laws and the theory. Next, he demonstrates each of the five postulates. Finally, you'll learn how the Kinetic Molecular Theory describes the gas laws. If you need help, this video is a great explanation!