Which of the following statements about a sample of gas containing molecules of different masses is true according to the kinetic molecular theory?

• A. Lighter gas molecules have lower average kinetic energy than heavier molecules at the same temperature.
• B. All gas molecules, regardless of mass, have the same average kinetic energy at a given temperature.
• C. Heavier gas molecules move faster than lighter gas molecules at the same temperature.
• D. The pressure exerted by each type of molecule depends only on its mass.

Answer: (B)

Verified step by step guidance

1. Recall the key postulate of the kinetic molecular theory related to temperature and kinetic energy: At a given temperature, all gas molecules have the same average kinetic energy regardless of their mass.
2. Understand that the average kinetic energy (KE) of a gas molecule is given by the formula \( KE = \frac{1}{2} m v^2 \), where \(m\) is the mass of the molecule and \(v\) is its velocity.
3. Since the average kinetic energy is the same for all molecules at the same temperature, heavier molecules (larger \(m\)) must move slower (smaller \(v\)) to keep \(KE\) constant, while lighter molecules move faster.
4. Recognize that the statement 'Lighter gas molecules have lower average kinetic energy than heavier molecules at the same temperature' is false because kinetic energy depends on temperature, not mass.
5. Note that pressure exerted by gas molecules depends on factors like the number of collisions and their momentum, not solely on mass, so the statement about pressure depending only on mass is incorrect.