How many times is the root-mean-square velocity of hydrogen molecules greater than

How many times is the root-mean-square velocity of hydrogen molecules greater than the root-mean-square velocity of water vapor molecules at the same temperature?

The mean square velocity of gas molecules is inversely proportional to the square root of the molar mass of the gas:

vcp = √ (3RT / M);

Let us find the ratio of the root-mean-square velocities of gas molecules as a root of the ratio of their molar masses:

vcp (H2) / vcp (H2O) = √ (M (H2O) / M (H2)) = √ (18/2) = 3.

Answer: the mean square velocity of hydrogen molecules is 3 times greater than the mean square velocity of water vapor molecules.