Final answer:
Decreasing the volume of O₂ gas at constant temperature increases the pressure but does not change the average kinetic energy or the root-mean-square speed of the molecules. Option 3 is the correct answer.
Step-by-step explanation:
When a fixed amount of O₂ gas is compressed in a container at a constant temperature, according to Boyle's law, the volume of the gas decreases while the pressure increases. The average kinetic energy of the O₂ molecules, however, does not change because it is only dependent on temperature, as per the kinetic molecular theory. As the volume decreases, the gas molecules have less space to move around in, resulting in more frequent collisions with the walls of the container. This leads to an increase in pressure.
The root-mean-square speed of the O₂ molecules also remains unchanged because it is a function of the temperature and the molar mass of the gas, which are both constants in this scenario. Therefore, the speed at which the molecules move on average does not increase or decrease as a result of the volume change.
To summarize, in a scenario where the volume is decreased at a constant temperature:
- The average kinetic energy of the O₂ molecules does not change.
- The root-mean-square speed of the O₂ molecules does not change.
- The pressure of the O₂ gas in the container increases.
The correct option is that the average kinetic energy of the O₂ molecules does not change.