Molecular Weight Units for Mean Square Speed Calculation

[kd001]

I need to calculate the mean square speed of molecules in an ideal gas. Mean square speed is equal to 3RT/M, where M is the molecular weight. But what units do I use for the molecular weight if I use 0.08206 L.atm/(mol.K) as R?

Thanks a lot.

 

[Redbelly98]

The units for M would be something non-standard and awkward, if you are going to use L and atm as volume and pressure units. It would really be preferable to express R in m³ and Pa, then M can be in kg/mol.

That being said, if you are really curious about what the units would be, use the fact the volume is in liters and pressure is in atmospheres:

EDIT: see corrected version of the following, in next post

[STRIKE]1. Volume in liters implies that length units are ____?

2. And since pressure is in atm,[/STRIKE]

[STRIKE]1 atm = 1 m / d²

where "m" are the mass units you are looking for, and "d" is the length units found in step 1.[/STRIKE]​

[STRIKE]3. Solve that equation for "m", and then convert atm as necessary to get a value in kg.[/STRIKE]​

 

[Redbelly98]

Ah, I hate it when people confuse mass and force, and I've done exactly that!

Okay, if you're interested in what funky units we get for mass, when we are using atm for pressure units and liters for volume, then read on:

1. Volume in liters implies that length units are ____?

2. And since pressure is in atm,

1 atm = 1 F / d²

where "F" is the force unit, and "d" is the length units found in step 1.​

3. Replace F with

F = m·d/t²​

where "m" is the mass unit we are looking for, and "t" is the time unit. Let's assume we want to use seconds for the time units, so...

4. The equation from step 2 becomes

1 atm = (1 m·d/s²) / d²
1 atm = 1 m/(d·s²)​

5. Solve that equation for "m", and then convert atm as necessary to get a value in kg.​

It turns out that we get a mass unit equivalent to 10.1325 Megagrams. Not pretty.