## Physics Friday 70

We noted previously that for an ideal gas, the molecule speeds should follow the Maxwell speed distribution; from this, we predict a rms velocity . We can rewrite this in terms of the molar mass M and gas constant R: . Let us consider a “room” temperature of 290 K. The gas constant has value 8.3145 J K-1 mol-1, so this tells us that 3RT for our situation is 7234 J/mol. Let us then compute the vrms for several gasses:

Gas Molar Mass (kg/mol) vrms (m/s)
H2 0.00202 1.89×103
He 0.00400 1.34×103
CH4 0.0160 672
Ne 0.0202 599
N2 0.0280 508
C2H6 0.0301 490
O2 0.0320 475
Ar 0.0399 425
CO2 0.0440 405
C3H8 0.0441 405
Kr 0.0838 293
Xe 0.131 235