What is the total random kinetic energy of all the molecules in 1 mole of hydrogen?

From gas kinetic theory, one has the result that the total internal energy of a mole of ideal gas particles is equal to the sum of the kinetic energies of each of the particles. For one mole of gas:

U = (3/2) * R*T

where R is the universal gas constant (8/314 J / (mol*K) and T is the thermodynamic temperature.

At 320K, a the total kinetic energy of the molecules in a mole of Kr is:

U = (3/2) * (8.314 J/mol*K) * (320K) = 2660 J

One mole of Kr gas has a mass of 83.80 gm, so the center-of-mass velocity of a mole of Kr that has a translational kinetic energy of 2660 J would be:

2660 J = (1/2) * (8.38*10^-2 kg) * v^2

6.35*10^4 (m/s) ^2 = v^2

252 m/s = v