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KE and root mean speed


ChemSiddiqui
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hi,

 

i just wanted to confirm that in the formula that relates KE with root mean square speed;

 

KE= 1/2 mc^2

 

m is the mass of something rather than the molar mass? Say we have He(helium) which has the molar mass of 0.004 Kg/mol while its mass,m, is 4!. Slightly confused because in the root mean square speed formula I use the molar mass, M.

 

c = (3RT/M)^1/2

 

thanx in advance for any help!

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[Cue Obi-Wan voice] Follow the units, Luke [/Obi]

 

 

If you used molar mass, you'd get kinetic energy per mole. But as you demonstrate, some thermodynamics equations are normalized in that way — they use the gas constant constant ® rather than the Boltzmann constant (k), and R has units of J/K-mol (unlike k, which has units of J/K)

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right ok,

 

now here's an other question.

 

calculated the KE of He and SF6 from the equations from my last post at 500K and I get the same value for both. I am confused. SF6 is bigger and heavier molecule so must have a smaller value for rms speed which it has but why the same kinetic energy? I get 1.033 x 10^-20 in both cases. What is wrong here...am I on the right track?!

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right ok,

 

now here's an other question.

 

calculated the KE of He and SF6 from the equations from my last post at 500K and I get the same value for both. I am confused. SF6 is bigger and heavier molecule so must have a smaller value for rms speed which it has but why the same kinetic energy? I get 1.033 x 10^-20 in both cases. What is wrong here...am I on the right track?!

 

They will have the same average kinetic energy at the same temperature — that's exactly what temperature tells you. Larger mass means slower speed, but mv^2 will be the same.

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