The kinetic theory of gases

You will already know that the molecules in a gas are in a constant state of random motion. This feature of gases is one of the main foundations of the kinetic theory of gases. A statement of the main features of the kinetic theory of gases is given in box 1B. As far as w§ know, the kinetic theory of gases is an extremely well-supported theory. There is a great deal of evidence to show that, to all intents and purposes, the motion of gas molecules is random. This means that in any gas, on average, there will be as many molecules moving in one direction as in any other direction.

You might like to know that the average speed of gas molecules is of the order of 500 ms^-1 at room temperature. The lighter the molecule, the greater the average s reed (and vice versa). For example, hydrogen molecules have an average speed somewhat above 1500 ms-¹, and carbon dioxide molecules have an average speed nearer to 350 ms^-1.

There is a wide range of energies among the molecules in a gas. Some move very rapidly, and much faster than the average, and some move very much more slowly than the average. When a gas is heated, on average all the molecules increase their kinetic energies (i.e. move faster); but this does not mean that they all increase. Always, some will pick up more energy than others. Indeed, during a collision between two molecules, one of them may move off with a greater speed, and one with a lower speed than before. However, the majority move near to the average speed. The way the kinetic energy of the molecules varies with temperature. As the temperature goes up, the average energy of all the molecules increases, but the distribution of speeds, and therefore kinetic energies, spreads out. Especially, the proportion of molecules with high kinetic energies increases.

SAQ

Use ideas from the kinetic theory of gases to answer these two questions:

a What happens to the average kinetic energy of the molecules in a gas as the temperature increases?

b What might happen to the kinetic energy of any individual molecule in a gas as the temperature increases?

The pressure and volume of an ideal gas

The pressure of a gas is caused by the collisions of the molecules with the walls of its container. By doing some mathematics, it is possible to show that the pressure of an ideal gas depends on three factors:

1 the number of molecules per unit volume (i.e. the concentration of the gas);

2 the mass of the molecules;

3 their speed.

This should make sense to you because, if there are more molecules present in a given volume, there should be more collisions with the walls, so the pressure should increase. Likewise, if the molecules have a greater momentum (mass times speed), the harder they will bounce off the walls. Therefore, they exert a greater force on the walls, and cause the pressure to increase.

SAQ

Two identical cylinders A and В fitted with pistons are kept in different rooms. Both contain the same number of molecules of gas, but the volume of one (A) is less than that of the other (B). What is the most likely reason for the difference in volume?

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