0.14 The kinetic molecular theory  (Page 6/8)

It is helpful to think again about the analogy of people in a large open space. If the space is large enough and people wander randomly in the space, then they will almost never chance across each other and therefore almost never interact with each other. In this case, it would not matter to any individual in the space whether the other people in the room were friendly or unfriendly, passive or aggressive. Each person would move just as if she or he were the only person in the room.

Our conclusion, then, is that the particles in a gas are so far apart from one another that they move independently of each other, with no interactions or forces between them which might have created either attractions or repulsions. We say that there are no “intermolecular forces” or “intermolecular interactions.”

Postulates of the kinetic molecular theory

We are now ready to assemble a model to explain our observations in the Ideal Gas Law. Remember that we are trying to explain a macroscopic observation, in this case the pressure of a gas, using molecular properties or motions. So we capture the molecular concepts we developed in the three observations into a set of “postulates”:

• A gas consists of individual particles in constant and random motion.
• The distance (on average) between particles is very much larger than the sizes of individual particles.
• Because of the large distances between particles, the individual particles (on average) do not exert any forces on each other, so that they neither attract nor repel one another.
• The pressure of the gas is due entirely to the force of the collisions of the gas particles with the walls of the container.

Note that all of these postulates come from our analysis of experimental observations. And in turn, this model can be used to understand most of our observations of the properties of gases. With some extra work and additions, this model is also quite useful in understanding properties of liquids and solids as well.

The ideal gas law and the kinetic molecular theory

We know from our observations that the pressure of a gas decreases with volume, increases with temperature, and increases with the number of particles. To complete our connection between molecular properties and motions and experimental observations, we need to show that the postulates above lead us to the Ideal Gas Law. Notice that our postulates don’t say anything about temperature. We will have to deal with that later. First, we will show how the pressure of a gas is related to the number of particles and the volume.

A detailed derivation using Physics and Mathematics is possible, but for our purposes, we will focus on the concepts. First, we know that the pressure of the gas results from the force of collisions of the gas molecules with the walls of the container. Pressure is force divided by area, so we will focus only the force of the molecules hitting a small area, probably the surface of our pressure gauge. We can call that area A . The force F is the mass of the particles hitting the wall multiplied by the acceleration resulting from the particles hitting the wall. What is that acceleration? In the easiest case, we might imagine that a particle hitting the wall keeps all of its energy and simply changes its direction. Then the acceleration is simply the change from its speed v to the same speed in the reverse direction –v , so the acceleration is proportional to 2v and the force of each impact is proportional to 2mv . This makes sense: the faster the particles are moving, the greater their acceleration when they hit the wall, the greater the force they create. And the greater the mass of each particle, the greater the force of each impact.