New Enroll in RBI Grade B New Batch - Starts on May 21

    Question

    For two different gases at the same temperature, the gas

    with the lighter molecules (lower molecular mass) will have, on average:
    A Lower molecular speeds Correct Answer Incorrect Answer
    B The same molecular speed Correct Answer Incorrect Answer
    C Higher molecular kinetic energy Correct Answer Incorrect Answer
    D Higher molecular speeds Correct Answer Incorrect Answer

    Solution

    In kinetic theory of gases, the average kinetic energy of a gas molecule depends only on temperature and is independent of the type of gas. The formula for average kinetic energy per molecule is: where:

    • m = mass of one molecule
    • M = molar mass
    From this, we can see:
    • Smaller the mass (lighter molecule) ➔ higher the rms speed.
    • Heavier molecule ➔ lower the rms speed.
    Thus, for a lighter gas at same temperature:
    • It has the same average kinetic energy as heavier gas.
    • But it has higher average speed.

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