Chemistry Equilibrium of Methanol Vapor Decomposition

AI Thread Summary
The discussion centers on the equilibrium of methanol vapor decomposition, specifically the mole ratio of hydrogen (H2) to methanol (CH3OH). It highlights that the effusion rate of H2 is faster than that of CH3OH, resulting in an effused mixture with a higher H2 concentration than the equilibrium mole ratio of 33:1. The confusion arises from incorrectly setting the equilibrium mole ratio equal to the effusion ratio, which does not account for the differing effusion rates. Graham's law of diffusion is relevant here, as it explains the relationship between gas effusion rates and molecular weights. Understanding these principles clarifies why the initial assumption about the mole ratio was incorrect.
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Homework Statement
A 4.72-g sample of methanol (CH3OH) was placed in an otherwise empty 1.00-L flask and heated to 250°􏰀C to vaporize the methanol. Over time the methanol vapor decomposed by the following reaction:
CH3OH(g) <-> 34 CO(g) 􏰁+ 2H2(g)
After the system has reached equilibrium, a tiny hole is drilled in the side of the flask allowing gaseous compounds to effuse out of the flask. Measurements of the effusing gas show that it contains 33.0 times as much H2(g) as CH3OH(g). Calculate K for this reaction at 250°C.
Relevant Equations
equilibrium
graham's law of effusion
The solution says that when the effusion rate ratio is multiplied by the equilibrium mole ratio of H2 to CH3OH, the effused mixture will have 33.0 times as much H2 as CH3OH. I don't understand why.

I just set the equilibrium mole ratio of H2 to CH3OH as equal to 33.0 times, Why is this incorrect?

Thanks.
 
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i_love_science said:
I just set the equilibrium mole ratio of H2 to CH3OH as equal to 33.0 times, Why is this incorrect?

If the mole ratio of H2 to CH3OH inside of the flask is 33:1, then the gasses effusing from the flask will have a H2:CH3OH ratio greater than 33:1 because H2 effuses from the flask at a faster rate than CH3OH.
 
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You actually stated Graham's law of diffusion as relevant but you didn't use it.
 
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