According to the kinetic molecular theory, under which condition will molecules of all samples of ideal gases have the same average kinetic energy?

• A. When the samples have the same pressure
• B. When the samples contain the same number of molecules
• C. When the samples have the same volume
• D. When the samples are at the same temperature

Answer: (D)

Verified step by step guidance

1. Recall that according to the kinetic molecular theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. This relationship is given by the equation \(\overline{KE} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the temperature in kelvins.
2. Understand that average kinetic energy depends only on temperature and is independent of other factors such as pressure, volume, or the number of molecules in the sample.
3. Analyze each condition given: same pressure, same number of molecules, and same volume. None of these alone guarantee the same temperature, so they do not ensure the same average kinetic energy.
4. Recognize that when samples of ideal gases are at the same temperature, their molecules have the same average kinetic energy regardless of differences in pressure, volume, or quantity of gas.
5. Conclude that the condition for molecules of all samples of ideal gases to have the same average kinetic energy is that the samples must be at the same temperature.