State the assumptions of kinetic theory of gases and derive the following expression for the pressure of a gas.

The assumptions of the kinetic theory of gases are:

1. Gas molecules are in constant, random motion: They move in straight lines until they collide with either other molecules or the walls of the container.
2. Gas molecules are considered as point particles: The volume of individual gas molecules is negligible compared to the container volume.
3. There are no attractive or repulsive forces between gas molecules: The collisions between gas molecules are perfectly elastic, meaning no energy is lost during the collision.
4. All gas molecules have the same average kinetic energy at a given temperature: The temperature of the gas is directly proportional to the average kinetic energy of the molecules.
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