Physics question please help

Question

Boltzmann’s constant is 1.38066×10−23 J/K, and the universal gas constant is 8.31451 J/K · mol. If 1.6 mol of a gas is confined to a 6 L vessel at a pressure of 6.7 atm, what is the average kinetic energy of a gas molecule? Answer in units of J.

Answer 1

To answer this, you must know the number of degrees of freedom of the molecules.  For example, a monoatomic ideal gas has 3 degrees of freedom, an ideal gas of diatomic molecules has 5 degrees of freedom, etc.  By the principle of equipartition of energy, if the molecules of the gas have j degrees of freedom, then the average kinetic energy of 1 molecule is

 

E = j(kT/2)

 

Monoatomic gas:  E = (3/2)kT

 

Diatomic gas:  E = (5/2)kT

 

etc.

 

Assuming an ideal gas, get the absolute temperature from the equation of state.

 

T = PV/(nR),

 

where n is the number of moles.  You have P, V, n, and R.  Work in appropriate units and get T in Kelvins.  You still need to determine the number of degrees of freedom j.  Then

 

E = (j/2)kT