Question
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?
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.
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.
Answers
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
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
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.
Now I am beginning to worry. I missed the units given. Could it be grams/minute instead of g/L?
Capacino, the ball is in your court.
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