Question

Explain Boyle's Law on the basis of the kinetic theory of matter.

Answer 1

Consider the box full of moving gas molecules. The particles have the same energy (temperature) throughout. As the box gets smaller, they have a smaller distance to travel before they collide with the walls, and thus the time between collisions gets increasingly smaller. In a given amount of time, the particles hit the walls more, which results in a greater amount of pressure. The amount of moles is clearly constant, as we are not adding or subtracting particles from the box. Another way of looking at this is that as the pressure increases, it drives the particles together. These compacted particles now occupy less volume. In order to compare a gas where either pressure or volume vary, we can combine the equations $P_1{V}_1=k$ and $P_2{V}_2=k$.

Because $k$ is constant for both values of pressure and volume, $P_1{V}_1=P_2{V}_2$