TBR Question: Gas Motion

[Cosmic]

Q: What is the root mean square speed of neon atoms at 27 degrees C?

I get how to solve this question, but I'm a little confused as to what I should put for mass. The equation equals: rms = square root of 3RT/m. It's the "m" part of this equation that's confusing me.

Either I'm mistaken or I'm missing a really important fundamental concept here but is it true to say that the masses listed in the periodic table is both the molar mass for 1 mole of atoms AND the atomic mass of 1 element? This is apparently what TBR did in example 6.16 (page 25).
I would think the mass of 1 atom of Neon Gas equals the Molar Mass divided by Avogadro's #. In this case it would be: 20.2g/mol divided by 6.022x10^23atoms/mol which equals 3.3x10^23 grams. Converting this into kilograms so it could be used in the equation would require you divide this number by 1000 grams: 3.3x10^20 kg.

Perhaps they were just using the weight for 1 mole, but it doesn't make sense to me why they would use the mass of 1 mole of Neon atoms to calculate the rms for this question.

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[justhanging]

Q: What is the root mean square speed of neon atoms at 27 degrees C?

I get how to solve this question, but I'm a little confused as to what I should put for mass. The equation equals: rms = square root of 3RT/m. It's the "m" part of this equation that's confusing me.

Either I'm mistaken or I'm missing a really important fundamental concept here but is it true to say that the masses listed in the periodic table is both the molar mass for 1 mole of atoms AND the atomic mass of 1 element? This is apparently what TBR did in example 6.16 (page 25).
I would think the mass of 1 atom of Neon Gas equals the Molar Mass divided by Avogadro's #. In this case it would be: 20.2g/mol divided by 6.022x10^23atoms/mol which equals 3.3x10^23 grams. Converting this into kilograms so it could be used in the equation would require you divide this number by 1000 grams: 3.3x10^20 kg.

Perhaps they were just using the weight for 1 mole, but it doesn't make sense to me why they would use the mass of 1 mole of Neon atoms to calculate the rms for this question.

The rms will be different for every isotope of neon, but the difference will be small so they are not taking it into account. Just use dementional analysis and you can see that you get kg/molecule when you divide the molar mass and avogadro's number. Though this number is a wieghted average of the isotopes. The number listed in the periodic table are the weighted average of the masses in atomic mass units.

 

[Cosmic]

The rms will be different for every isotope of neon, but the difference will be small so they are not taking it into account. Just use dementional analysis and you can see that you get kg/molecule when you divide the molar mass and avogadro's number. Though this number is a wieghted average of the isotopes. The number listed in the periodic table are the weighted average of the masses in atomic mass units.

That's not what I'm asking though. The atomic weight is in atomic mass units. The gas constant wants amu's in kg's. If an amu = 1.6x10^-27 kg, how is it that neon atoms have an atomic weight of 20.2 kg. I think it's an error. Usually in other gas calculations like Graham's Law this conversion doesn't matter since you're dividing a ratio but here you're being asked specifically about the rms for one gas molecule.

 

[Swagster]

That's not what I'm asking though. The atomic weight is in atomic mass units. The gas constant wants amu's in kg's. If an amu = 1.6x10^-27 kg, how is it that neon atoms have an atomic weight of 20.2 kg. I think it's an error. Usually in other gas calculations like Graham's Law this conversion doesn't matter since you're dividing a ratio but here you're being asked specifically about the rms for one gas molecule.

It depends on the version of the constant you use in that equation. R is based on a mole, so you'd use molar mass. k is based on a single atom, and you'd use atomic mass. At least I think that's the difference in terms of mass. Do the units work out for you?

 

[Cosmic]

It depends on the version of the constant you use in that equation. R is based on a mole, so you'd use molar mass. k is based on a single atom, and you'd use atomic mass. At least I think that's the difference in terms of mass. Do the units work out for you?

Thanks, that makes sense. I forgot to consider the units of the gas constant, but yes it all works out now. 🙂