Final answer:
The average kinetic energy per atom is 8.19 x 10^-21 J, the root-mean-square speed of atoms in the gas is 372.9 m/s, and the internal energy of the gas is 1.975 x 10^4 J.
Step-by-step explanation:
To find the average kinetic energy per atom, we use the formula KE_avg = (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K) and T is the temperature in Kelvin. Substituting the values, KE_avg = (3/2) x (1.38 x 10^-23 J/K) x 420 K = 8.19 x 10^-21 J.
To find the root-mean-square (rms) speed of atoms in the gas, we use the formula urms = sqrt((3kT)/m), where m is the molar mass of krypton (83.798 g/mol). Converting to kg/mol and substituting the values, urms = sqrt((3 x 1.38 x 10^-23 J/K x 420 K)/(83.798 g/mol x 0.001 kg/g)) = 372.9 m/s.
The internal energy of the gas can be found using the formula U = (3/2)nRT, where n is the number of moles of gas (4 mol), R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin. Substituting the values, U = (3/2) x 4 mol x 8.314 J/mol·K x 420 K = 19.75 kJ or 1.975 x 10^4 J.