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