According to the kinetic molecular theory, the molecules in which of the following samples have the greatest average molecular kinetic energy?

• A. CO2(g) at 273 K
• B. O2(g) at 400 K
• C. N2(g) at 300 K
• D. He(g) at 200 K

Answer: (B)

Verified step by step guidance

1. Recall that according to the kinetic molecular theory, the average kinetic energy of gas molecules depends only on the temperature of the gas, not on the type of gas or its molar mass.
2. Use the formula for average molecular kinetic energy: \(\text{KE}_{avg} = \frac{3}{2}RT\), where \(R\) is the gas constant and \(T\) is the temperature in Kelvin.
3. Compare the temperatures of the given gases: CO\(_2\) at 273 K, O\(_2\) at 400 K, N\(_2\) at 300 K, and He at 200 K.
4. Since the average kinetic energy is directly proportional to temperature, the gas sample with the highest temperature will have the greatest average molecular kinetic energy.
5. Identify that O\(_2\) at 400 K has the highest temperature among the options, and therefore its molecules have the greatest average molecular kinetic energy.