At what temperature do N2 momlecules have the same average speed as He atomes at 300.K?

Question

at what temperature do N2 molecules have the same average speed as He atoms at 300.K?

Answer 1

Don't gases have the same kinetic energy at a given temp. the average kinetic energy is 3kT/2. isn't it?

Answer 2

The average velocity of gas particles is a special kind of average. The room mean square velocity is the square root of the average of the squares of the particle velocities. The v(rms) velocity is inversely proportional to the molar mass (M).

v(rms) = [3RT/M]^0.5

v(rms N2) = [3RT(N2)/M(N2)]^0.5

v(rms He) = [3RT(He)/M(He)]^0.5

[3RT(N2)/M(N2)]^0.5 = [3RT(He)/M(He)]^0.5

Square both sides of this equation, then divide both sides by 3R. This leaves:

T(N2) / M(N2) = T(He) / M(He)

T(N2) / (28.0 g/mol) = 300. K / (4.00 g/mol)

T(N2) = 300. K x (28.0 g/mol) / (4.00 g/mol) = 2100 K