Final answer:
The average kinetic energy per atom of krypton gas at 415 K is calculated using the Kinetic Molecular Theory formula. The root-mean-square speed can be found by using a formula that takes into account the temperature and mass of a krypton atom. The internal energy for two moles of gas is determined by multiplying the average kinetic energy per atom by the number of atoms in two moles.
Step-by-step explanation:
To find the average kinetic energy per atom of a krypton gas, we can use the equation that relates energy to the temperature of the gas in the Kinetic Molecular Theory (KMT). The formula for average kinetic energy (K) is:
K = (3/2)kBT
Where kB is the Boltzmann constant (1.38 x 10-23 J/K) and T is the temperature in kelvins. Plugging in the given temperature of 415 K, we find that the average kinetic energy per atom is:
K = (3/2)(1.38 x 10-23 J/K)(415 K) = 8.6 x 10-21 J/atom
The root-mean-square (rms) speed can be calculated using the formula:
urms = sqrt((3kBT)/m)
m is the mass of a krypton atom, which is the molar mass of krypton (83.8 g/mol) divided by Avogadro's number. After converting the mass to kilograms, you can find the rms speed.
The total internal energy of the gas for two moles can be found by multiplying the average kinetic energy per atom by the number of atoms in two moles, calculated using Avogadro's number (6.022 x 1023 atoms/mol).