Calculate and compare the Urms for Helium and nitrogen at 20 degrees C.

Question

Calculate and compare the Urms for Helium and nitrogen at 20 degrees C.

Answer 1

You mean Vrms, the root mean square velocity.

V²rns = 3RT/M, where R is in J/K*mol, and M is molecular weight in kg/mole, becuase the defintion of the Joule is 1 kg m²/s².

For He,

V²rns = (3) (8.314 J/K*mol) (273 + 20 K) / (0.004 kg/mole);

Vrms = 1,352 m/s.

For N2,

V²rns = (3) (8.314 J/K*mol) (273 + 20 K) / (0.028 kg/mole);

Vrms = 511 m/s.

Obviously, the heaver the gas molecule, the slower the velocity.