Kinetic Theory — Practice

Question 1

Find the rms speed of oxygen (M = 32 g/mol) at 27 C (R = 8.314).

Accepted Answer

v_rms = sqrt(3RT/M) = sqrt(3 x 8.314 x 300 / 0.032) = sqrt(233831) = 483.6 m/s.

Question 2

Find the rms speed of hydrogen (M = 2 g/mol) at 27 C.

Accepted Answer

v_rms = sqrt(3 x 8.314 x 300 / 0.002) = sqrt(3741300) = 1934 m/s.

Question 3

Find Cv and Cp for argon (monatomic) (R = 8.314).

Accepted Answer

Cv = 3R/2 = 12.47 J/mol K; Cp = 5R/2 = 20.79 J/mol K; gamma = 5/3 = 1.67.

Question 4

Calculate the mean free path of air at STP (d = 3.5e-10 m, T = 273 K, P = 1.013e5 Pa).

Accepted Answer

lambda = kT/(sqrt(2) pi d^2 P) = (1.38e-23 x 273)/(1.414 x pi x (3.5e-10)^2 x 1.013e5) = approximately 6.8e-8 m.

Question 5

What are the degrees of freedom of a diatomic gas at room temperature?

Accepted Answer

Five: three translational and two rotational. Vibrational modes are frozen at room temperature.

Practice — Kinetic Theory