Chem Kinetic real gases?

Question

a 100 L flask contains a mixture of CH4, and argon at 25 C, the mass of argon present is 228 g. and the mole fraction of methane in the mixture is 0.650. Calculate the total kinetic energy of the gaseous mixture.

How would you work this problem?

Answer 1

Do you remember that for each degree of freedom of a molecule, there is 0.5kT energy associated with it, where k the Boltzman constant 1.381×10−23 J/K, and T the temperature in Kelvin? Now, you also know that Ar is a monatomic gas, thus it only has 3 translational degrees of freedom (corresponds to a Cv = 3k/2 and a Cp = 5k/2). CH4 is a non-linear polyatomic gas, thus it has 3 translational as well as 3 rotational degrees of freedom (corresponds to a Cv = 3k and a Cp = 4k). Of course, especially for CH4, it is an approximation, since we omitted all the vibrational degrees of freedom, which is very well populated in the ground level.

Anyway, come to this problem.
228g Ar <==> 5.71 mol of Ar <==> 10.6 mol of CH4
So the total kinetic energy of the gaseous mixture is:
(5.71*3*8.314/2 + 10.6*3*8.314)*(273+25) (Joule)
You finish with the math.