Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure at constant temperature and number of moles, can be explained using the kinetic theory of gases. The kinetic theory makes the following assumptions:

• Gases consist of a large number of particles (atoms or molecules) that are in continuous, random motion.
• The volume of the particles is negligible compared to the total volume of the gas.
• The particles do not exert any attractive or repulsive forces on each other.
• Collisions between particles and the walls of the container are perfectly elastic (no energy is lost).
• The average kinetic energy of the particles is proportional to the absolute temperature of the gas.

Explanation of Boyle's Law based on Kinetic Theory:

1. Pressure and Molecular Collisions:

   Pressure exerted by a gas is due to the collisions of its particles with the walls of the container. Each collision exerts a small force on the wall. The total pressure is the sum of all these forces per unit area.

2. Changing the Volume:

   If the volume of the container is decreased while keeping the temperature constant, the particles have less space to move around in. This means they will collide with the walls more frequently.

3. Increased Collision Frequency:

   Because the particles are colliding with the walls more frequently, the force exerted on the walls per unit area (i.e., the pressure) increases.

4. Constant Kinetic Energy:

   Since the temperature is constant, the average kinetic energy of the particles remains the same. This means the average speed of the particles does not change. Therefore, each collision exerts roughly the same amount of force as before, but there are more collisions happening per unit time.

5. Inverse Relationship:

   The net effect is that decreasing the volume increases the frequency of collisions, which increases the pressure. Conversely, if the volume is increased, the particles have more space, collide with the walls less frequently, and the pressure decreases. This inverse relationship between volume and pressure at constant temperature is Boyle's Law.

In mathematical terms, Boyle's Law is expressed as: PV = k, where P is the pressure, V is the volume, and k is a constant for a given mass of gas at a constant temperature.

In summary, the kinetic theory explains Boyle's Law by linking the pressure of a gas to the frequency of collisions of its particles with the container walls. Decreasing the volume increases the collision frequency, thus increasing the pressure, and vice versa, assuming the temperature and number of particles remain constant.

More information may be found here:

• LibreTexts: Kinetic Theory of Gases
• Khan Academy: The Ideal Gas Law