Question

Which assumptions of the kinetic–molecular theory explain the behavior of gases described by Gay-Lussac's law? Explain your answer.

Accepted Answer

Gay-Lussac's law states that the pressure of a gas is directly proportional to its temperature (in Kelvin) when the volume and the amount of gas are held constant. This can be expressed mathematically as: P&#x221D;T or PT=k, where k is a constant. The kinetic–molecular theory (KMT) provides a framework to explain this behavior. One key assumption of KMT is that the average kinetic energy of gas particles is directly proportional to the absolute temperature of the gas. As temperature increases, the particles move faster, leading to more frequent and forceful collisions with the walls of the container, which increases pressure. Another assumption of KMT is that gas particles are in constant, random motion and that their collisions with the container walls are perfectly elastic. This means that no energy is lost during collisions, so the increase in kinetic energy due to a temperature rise directly translates to an increase in pressure. KMT also assumes that the volume of individual gas particles is negligible compared to the volume of the container. This ensures that the behavior of the gas is primarily determined by the motion and collisions of the particles, which aligns with the direct relationship between pressure and temperature described by Gay-Lussac's law. Finally, KMT assumes that there are no intermolecular forces between gas particles. This allows the gas to behave ideally, meaning the pressure changes are solely due to changes in temperature, as described by Gay-Lussac's law.

Which assumptions of the kinetic–molecular theory explain the behavior of gases described by Gay-Lussac's law? Explain your answer.

Verified video answer for a similar problem:

Key Concepts

Kinetic-Molecular Theory

Gay-Lussac's Law

Assumptions of Ideal Gases