he average molecular speed in a sample of H2 gas

Question

The average molecular speed in a sample of CH2 gas at a certain temperature is 659 m/s.

The average molecular speed in a sample of H2 gas is __________ m/s at the same temperature.

Answer 1

This is a problem that utilizes Graham's Law of Effusion, namely: Rate α 1/M^1/2.

We use this to compare the rates of two gases with respect to one another. In this case, the rate of H₂ to that of CH₂ (which, btw, appears to be a misprint as CH₂ does not exist. I suspect it should be CH₄ but, for the sake of this question, will use CH₂.)

R_H2/R_CH2 = M^1/2_CH2/ M^1/2_H2

R_H2 = [(14 g/mol)^1/2/(2 g/mol)^1/2)] (659 m/sec) = (7)^1/2 (659 m/sec) = ~ 1744 m/sec