What is the ratio of the root-mean-square velocities of molecules of O₂ to water vapour molecules (of molar masses 32 and 18 respectively) in a gas in thermal equilibrium?

Question

Quizplus · Accepted Answer

The root-mean-square velocity ($v_{rms}$) of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the gas constant, $T$ is the temperature in Kelvin, and $M$ is the molar mass of the gas. In thermal equilibrium, $R$ and $T$ are constants for both gases, so the ratio of their $v_{rms}$ depends only on the inverse square root of their molar masses. Thus, the ratio for OS (32) to water vapor (18) is $\sqrt{\frac{18}{32}} = \sqrt{\frac{9}{16}} = \frac{3}{4} = 0.75$.

What Is the Ratio of the Root-Mean-Square Velocities of Molecules