Arturo O. answered • 10/18/17
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H2 molecules are diatomic molecules. According to statistical thermodynamics, the RMS speed of a diatomic molecule is determined by
(1/2)mvrms2 = (5/2)kT
m = mass of a single H2 molecule
T = absolute temperature = (25 + 273) Kelvin
k = Boltzmann constant
vrms = √(5kT/m)
Plug in the numbers to get vrms.
Note: The factor of 5/2 assumes the diatomic molecules can translate in 3 directions and rotate around 2 axes (only 2 axes because rotation around the axis connecting the 2 atoms does not add kinetic energy in the ideal gas model). However, if the molecules can only translate in 3 directions with no rotational energy, then the expression for RMS speed becomes
(1/2)mvrms2 = (3/2)kT
vrms = √(3kT/m)
Perhaps this is the case they want you to consider in a basic chemistry course, if that is what you are taking now. But keep in mind it is a restricted case.
(I expect chemistry tutor J.R.S. to weigh in on this!)
J.R. S.
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For the record, I did not give a down vote, and I agree that your explanation is exactly correct. In most chemistry texts, they do, indeed, use the latter expression that you show but simplify it to rms velocity = √3RT/M where R is the molar gas constant (8.314 m2kg s-2 mol-1) and M is molar mass in kg/mole.
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10/19/17
Arturo O.
J.R.S.,
I know it was not you who cast the down vote. I can tell from your many fine answers that you would always include an explanation if you thought something was not correct.
Regarding whether to use the factors 5/2 or 3/2, it really comes down to the assumptions of the problem. If all of the kinetic energy is translational, then it is 3/2. But for a diatomic molecule, we usually include 2 additional degrees of freedom, for rotation in 2 perpendicular planes, with each rotational motion adding 1/2 to the factor, bringing it up to 5/2. But I do not know the justification to account for the just the 3 translational motions, which is what they are doing in those texts.
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10/19/17
Arturo O.
10/19/17