Which of the following gas samples has the greatest average kinetic energy per molecule?

• A. Helium gas (He) at 250 K
• B. Carbon dioxide (CO_2) at 200 K
• C. Oxygen gas (O_2) at 400 K
• D. Nitrogen gas (N_2) at 300 K

Answer: (C)

Verified step by step guidance

1. Recall that the average kinetic energy per molecule of a gas depends only on the temperature and is given by the formula: \(\text{KE}_{avg} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvins.
2. Note that the type of gas (its molar mass or identity) does not affect the average kinetic energy per molecule; only the temperature matters.
3. Compare the temperatures of the given gas samples: Helium at 250 K, Carbon dioxide at 200 K, Oxygen at 400 K, and Nitrogen at 300 K.
4. Since average kinetic energy is directly proportional to temperature, the gas with the highest temperature will have the greatest average kinetic energy per molecule.
5. Identify the gas with the highest temperature, which is Oxygen at 400 K, and conclude that it has the greatest average kinetic energy per molecule.