# How does kinetic molecular theory explain gas laws?

Jan 29, 2014

Kinetic molecular theory explains the gas laws in terms of the collisions of the molecules with the walls of the container.

#### Explanation:

BOYLE’S LAW: P ∝ 1/V

Compressing a gas makes the $V$ smaller but does not alter the average kinetic energy of the molecules, since $T$ is constant. Though the speed of the particles remains constant, the frequency of collisions increases because the container is smaller. Therefore, $P$ increases as $V$ decreases.

CHARLES' LAW: V ∝ T

The average kinetic energy $\left(\frac{1}{2} m {v}^{2}\right)$ of the gas particles is proportional to $T$. Since $m$ is constant, the velocity v must increase. As temperature increases, the particles exert greater force against the walls of the container. This increases the pressure. If the walls of the container are flexible, they will expand to balance the atmospheric pressure outside the container. Therefore, V ∝ T.

AMONTON’S LAW or Gay-Lussac’s Law: P ∝ T

As the temperature of a gas increases, so does the average kinetic energy of its particles. The particles collide with the container walls more frequently and with greater force. Therefore, the pressure increases as the temperature increases.