Question

Explain, in terms of the kinetic molecular theory, how an increase in the temperature of a gas confined to a rigid container causes an increase in the pressure of the gas.

Short answer

In terms of the kinetic molecular theory, an increase in the temperature of a gas confined in a rigid container leads to an increase in the average kinetic energy and, consequently, the average velocity of the gas molecules. This results in more frequent and forceful collisions with the container walls, which ultimately increases the pressure exerted by the gas.

Step-by-step solution

Understanding the Kinetic Molecular Theory

The kinetic molecular theory is a model used to explain the behavior of gases. According to this theory, a gas is made up of numerous tiny molecules that are in constant motion. These motions include both translation (moving through space) and random collisions with each other and with the walls of the container. The pressure that a confined gas exerts on the walls of its container is due to these collisions.

Connecting Temperature with Molecular Velocity

The temperature of a gas is related to the average kinetic energy of its molecules. Higher temperatures result in higher average kinetic energy. Since the kinetic energy of a molecule (KE) is given by KE = \(0.5 × m × v^2\), where m is the mass and v is the velocity of the molecule, an increase in the average kinetic energy means an increase in the average velocity of the gas molecules.

Effect of Increased Molecular Velocity on Pressure

When the average velocity of the gas molecules increases (due to an increase in temperature), the molecules will collide with the walls of the container more often and with greater force. As a result, the gas molecules transfer more momentum to the walls of the container, thereby increasing the pressure exerted by the gas.

Conclusion

In conclusion, according to the kinetic molecular theory, an increase in the temperature of a gas confined in a rigid container leads to an increase in the average velocity of the gas molecules. This, in turn, causes the molecules to collide with the walls of the container more frequently and with greater force. The increased momentum transfer to the walls results in a higher gas pressure.