Question

A fixed amount of O₂ gas is held in a container. If the volume of the gas is decreased at a constant temperature, describe how that would affect the average kinetic energy of the O₂ molecules, the root-mean-square speed of the O₂ molecules, and the pressure of O₂ gas in the container.

a) The average kinetic energy of the O₂ molecules increases/decreases/does not change.
b) The root-mean-square speed of the O₂ molecules increases/decreases/does not change.
c) The pressure of O₂ gas in the container increases/decreases/does not change.

Answer 1

Decreasing the volume of a container holding O₂ gas at constant temperature keeps the average kinetic energy and the root-mean-square speed of the molecules constant while increasing the pressure of the gas. a) The average kinetic energy of the O₂ molecules increases/decreases/does not change.

Step-by-step explanation:

A fixed amount of O₂ gas is held in a container where the volume is decreased at a constant temperature. The response to this scenario can be explained using the kinetic molecular theory of gases and ideal gas law principles.

• The average kinetic energy (KEavg) of the O₂ molecules remains constant because kinetic energy is dependent only on temperature, and the temperature is held constant.
• The root-mean-square speed (urms) of the O₂ molecules also remains constant for the same reason; it is directly related to the average kinetic energy and temperature.
• According to Boyle's law, the pressure of the gas in the container increases if the volume decreases while temperature is constant. This is due to gas molecules having less space to move around, thus colliding more frequently with the walls of the container.

In summary:

1. The average kinetic energy of the O₂ molecules does not change.
2. The root-mean-square speed of the O₂ molecules does not change.
3. The pressure of O₂ gas in the container increases.

Answer 2

When the volume of O₂ gas is decreased, the average kinetic energy of the O₂ molecules does not change. The root-mean-square speed decreases and the pressure of the O₂ gas increases.

Step-by-step explanation:

When the volume of a fixed amount of O₂ gas is decreased at a constant temperature, the average kinetic energy of the O₂ molecules does not change. The average kinetic energy of gas molecules is directly proportional to the temperature but not affected by the volume. Therefore, since the temperature remains constant, the average kinetic energy remains constant as well.

The root-mean-square speed of the O₂ molecules decreases. The root-mean-square speed is inversely proportional to the square root of the molar mass and directly proportional to the square root of the temperature. As the volume decreases, the density of the gas increases, and since the molar mass of O₂ is greater than zero, the root-mean-square speed decreases.

The pressure of O₂ gas in the container increases. According to Boyle's law, when the volume of a gas is decreased at a constant temperature, the pressure increases. This is because the number of molecules colliding with the container walls per unit area increases due to the decreased volume.