Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed () and choose the correct answer from the options given below:
Correct answer:A
Standard Method
Given: Three gases are kept at the same temperature and pressure in equal-volume vessels: neon (monoatomic), chlorine (diatomic), and uranium hexafluoride (polyatomic).
Find: The correct order of their root mean square speeds.
The root mean square speed is given by
So, at the same temperature, decreases as molar mass increases.
Thus the gas with the smallest molar mass has the greatest root mean square speed, and the gas with the largest molar mass has the smallest root mean square speed.
Therefore,
Hence, the correct option is A.
Mass Comparison Trick
Given: All gases are at the same temperature.
Find: Which gas has larger .
Use the idea that
So there is no need to calculate any numerical value. Compare only the molar masses.
Neon is lighter than chlorine, and chlorine is much lighter than uranium hexafluoride. Therefore the speed order is
So the correct option is A.
Assuming root mean square speed depends on pressure here is incorrect because for an ideal gas at fixed temperature, is determined by temperature and molar mass. Compare molar masses instead.
Thinking polyatomic gases must move faster because they have more atoms is wrong. The relevant quantity is total molar mass of the molecule, and a larger molar mass gives a smaller .
Using direct instead of inverse dependence on molar mass is a conceptual error. From , speed decreases as increases.
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