Chapter 12: Problem 25

Explain Gay-Lussac's law in terms of the kinetic-molecular theory.

Short Answer

Expert verified

Gay-Lussac's Law states the pressure of a gas is directly proportional to its temperature when volume is constant. This is in line with the Kinetic-Molecular Theory, which says gas molecules move faster and collide more forcefully with their container when temperature increases, thus increasing pressure. The reverse holds when temperature decreases.

Step by step solution

- Define Gay-Lussac's Law

Gay-Lussac's law states that the pressure of a gas is directly proportional to its absolute temperature, assuming volume is held constant. This means when the temperature of a gas is increased, its pressure increases, and when its temperature is decreased, its pressure decreases. This relationship can be represented as P/T = k, where P is the pressure, T is the temperature, and k is a constant. This law originates from the behavior of gas molecules as defined by the Kinetic-Molecular theory.

- Explain the Kinetic-Molecular Theory

The Kinetic-Molecular Theory describes the properties of ideal gases, though it can also be applied to real gases under many conditions. It states that gas molecules are always in constant, random motion, and their collisions with the walls of their container cause pressure. The speed of these molecules depends on their temperature—higher temperatures correspond to higher average kinetic energy for the gas molecules, and therefore to faster movements.

- Link the Kinetic-Molecular Theory to Gay-Lussac's Law

Knowing the principles of the Kinetic-Molecular Theory, we can now understand how temperature affects the pressure of a gas. As the temperature (and therefore the average kinetic energy of the molecules) increases, the molecules move faster and collide with the container walls more frequently and with greater force, increasing the pressure. Conversely, if the temperature decreases, the molecules slow down and the pressure reduces. This directly correlates with what Gay-Lussac's Law states.

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Explain Gay-Lussac's law in terms of the kinetic-molecular theory.

Short Answer

Step by step solution

- Define Gay-Lussac's Law

- Explain the Kinetic-Molecular Theory

- Link the Kinetic-Molecular Theory to Gay-Lussac's Law

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