According to the kinetic molecular theory, if two different gases are at the same temperature, which of the following statements is true?

• A. The lighter gas molecules move slower than the heavier gas molecules.
• B. The average kinetic energy of the molecules in both gases is the same.
• C. The heavier gas molecules have greater average kinetic energy.
• D. Both gases have the same average speed of molecules.

Answer: (B)

Verified step by step guidance

1. Recall the kinetic molecular theory, which states that the average kinetic energy of gas molecules depends only on the temperature of the gas, not on the type or mass of the molecules.
2. Understand that the average kinetic energy (KE) of a gas molecule is given by the formula: \(\text{KE} = \frac{1}{2} m v^2\), where \(m\) is the mass of the molecule and \(v\) is its speed.
3. Since the temperature is the same for both gases, their average kinetic energies must be equal, meaning \(\frac{1}{2} m_1 v_1^2 = \frac{1}{2} m_2 v_2^2\).
4. Because the masses of the molecules differ, the speeds must adjust so that the kinetic energies remain equal; specifically, lighter molecules move faster on average than heavier molecules.
5. Therefore, the correct statement is that the average kinetic energy of the molecules in both gases is the same, while their average speeds differ inversely with their masses.