Answer to Question #154840 in General Chemistry for Kiana

Question

Explain at least one gas law using the assumptions of the kinetic molecular theory.

Answer 1

Fundamentals of Kinetic Molecular Theory

${KE}=\frac{1}{2}m{u}^{2}$

Gas is composed of molecules, and the average distance between these molecules is much greater than the size of the molecules themselves. Compared with the volume of the gas itself, the volume occupied by gas molecules is negligible.

The molecules of the ideal gas have no attraction between each other or on the container wall.

These molecules are in constant random motion, and as entities, they obey Newton's law of motion. This means that the molecules move in a straight line (see the illustration on the left) until they collide with each other or the container wall.

Collision is completely elastic; when two molecules collide, they change direction and kinetic energy, but the total kinetic energy is retained. The collision is not "sticky".

The average kinetic energy of gas molecules is proportional to the absolute temperature. Note that the term "average" is very important here; the velocity and kinetic energy of a single molecule will cover a wide range of values, and some even have zero velocity at a given instant. This means that if the temperature drops to absolute zero, all molecular motion will stop.

Boyle's Law

The gas can be compressed because most gases have empty spaces. If we compress the gas without changing the temperature, the average kinetic energy of the gas particles remains the same. The speed at which the particles move does not change, but the container is smaller. Therefore, in a short period of time, the particles move from one end of the container to the other. This means they hit a wall more often. An increase in the frequency of collisions with walls will result in an increase in air pressure. Therefore, the pressure of the gas increases as the volume of the gas decreases.

Charle's Law

The average kinetic energy of particles in a gas is proportional to the temperature of the gas. Since the mass of these particles is constant, the particles need to move faster as the gas gets warmer. If they move faster, the particles exert a great force on the container each time they hit a wall, which leads to an increase in gas pressure. If the walls of the container are flexible, the gas pressure will expand again until it balances the atmospheric pressure. Therefore, as the temperature of the gas rises, the volume of the gas increases.