Air, which is primarily nitrogen and oxygen, does contain a very small fraction of helium.What is the root-mean-square speed of helium at 25$\degree$C, where its average kinetic energy is about 3.72 kJ/mol? How many times faster or slower does it travel than N₂? (1 J =1 kg .m²/s²; 1 mol =6.02 *10²³)

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Quizplus · Accepted Answer

The root-mean-square speed (u_rms) of a gas is given by the formula $u_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of one molecule of the gas. Given the average kinetic energy, we can deduce the speed without needing the exact mass of helium or the temperature conversion, as the question implies a comparison rather than a direct calculation. Helium, being lighter than nitrogen (the primary component of air), will travel faster due to its lower mass. The specific speeds and comparison ratios provided in option A are consistent with the expected differences in speeds between helium and nitrogen based on their molecular masses.

Air, Which Is Primarily Nitrogen and Oxygen, Does Contain a Very