Gas A has a density that is 1.20 times that of gas B. If gas A effuses through an orifice at a rate of 3.41g/L, at what rate will gas B effuse?

Question

Hint: Ratio the molecular masses to the densities. Use this information with Graham's law of diffusion. Note that 3.41g/L is a rate. (3.11)

The part that confuses me is how to ratio the molecular masses after that I could use some steps just to make sure I get it right. thank you in advance.

Answer 1

The rate of effusion is inversely proportional to the square root of the molecular mass.
Let the rates be Ra, Rb.
Let the densities be Da, Db
Da / Db = 1/1.2
Based on the Law of effusion,
Ra/Rb = sqrt(Db) / sqrt(Da).
Db/Da = sqrt(1.2)/sqrt(1)
(3.41g/L) / Rb = sqrt(1/1.2)
(3.41g/L) / Rb = sqrt(1)/sqrt(1.2)
Solve for Rb

Answer 2

I think something is amiss here. If A has a higher density than B, then A must effuse slower than B (the answer GK gives of 3.73 supports that), but the answer of 3.11 doesn't support that. The only way I can come up with 3.11 is for the density of B to be 1.2 times that of A. Have I missed something? Perhaps I'm having trouble envisioning 3.41 g/L as a rate; g/L sounds like a density to me.

Answer 3

Now I am beginning to worry. I missed the units given. Could it be grams/minute instead of g/L?

Answer 4

Capacino, the ball is in your court.