Question

Apply the Kinetic Theory of gases to explain Boyle's law, Charles' law and Dalton's law ?

Answer 1

Boyles law :

When molecules collide they create pressure. When the molecules are closer together they collide more frequently. Hence less volume more collisions more pressure.

Explanation:

Kinetic theory is based on the kinetic energy of moving particles. The kinetic energy is directly related to the temperature.

In Boyle's Law the temperature is helped constant, so the kinetic energy of the molecules is a constant. The pressure and the volume are inversely related in Boyle's Law.

In Kinetic theory pressure is created by the collision of particles. ( atoms or molecules) with each other and the container. The more collisions the more pressure. An increase in temperature will cause an increase in the number of collisions as the molecules have more kinetic energy. This is not the case in Boyle's Law.

What happens in Boyle's Law is that the molecules are forced more closely together. The more densely packed the gas molecules are the more often they will collide creating more pressure. So if the volume is less the number of collisions and pressure will be greater. If the volume is greater the number of collisions and pressure will be less. So volume and pressure are inversely related if the temperature and total kinetic energy is kept constant.

Charles law:

Kinetic theory explains why the volume of a container must expand when the temperature of the gas inside increases in order for the pressure to remain constant.

Explanation:

Charles' law: for a fixed mass of gas at constant pressure the volume is directly proportional to the temperature.

Analysis of a gas when its temperature increases according to kinetic theory:

• The temperature has increased therefore the molecules have more kinetic energy, so they move with a greater velocity.

• If the container's dimensions do not change the molecules will travel across the container between the walls in less time (because they are moving faster and covering the same distance between the container walls). This will increase the rate of collisions, which would increase the pressure.

• But if the dimensions of the container increased then the molecules would cover a larger distance faster thereby maintaining a constant rate of collisions. This would maintain a constant pressure.

This is due to the relationship between temperature and mean molecular kinetic energy: E=3/2kT. Where E is the kinetic energy, k is the Boltzmann constant and T is the absolute temperature (i.e. temperature in kelvins).

The pressure on the container will also increase due to the greater change of momentum of the molecules when they collide with the wall. The increased temperature increased their kinetic energy, so when their momentum perpendicular to the wall is reversed it has a larger value.
To keep pressure constant due to this effect the volume would need to increase further to reduce the rate of collisions.

Dalton’s Law. :

Because of the large distances between them, the molecules of one gas in a mixture bombard the container walls with the same frequency whether other gases are present or not, and the total pressure of a gas mixture equals the sum of the (partial) pressures of the individual gases.