If the molecular mass of a gas increases by a factor of 4 at a constant temperature, what will its rms speed be?

Hello!

The absolute temperature (from the absolute zero) of a gas is directly proportional to the mean kinetic energy of its molecules. This energy is equal to `(M v_(rms)^2)/2,` where `M` is the molar mass of a gas (the mass of a mole of a gas). The molar mass is directly proportional to the molecule's mass, because each mole of a substance contains the same number of molecules.

The exact equation is  `v_(rms) = sqrt((3 R T)/M),` where `R` is the ideal gas constant which doesn't depend on gas properties.

Therefore if the molecule's mass increases by a factor of `4,` then the root-mean-square will decrease by the factor of `sqrt(4) = 2.`

That said, the only cause of such a change of a mass is a chemical reaction, but in that case the temperature will likely be changed too.