TBR Vapor Pressure Question

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narinari

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46) If the vapor above a 50% mixture of methanol with butanol at 22 degrees C were collected and placed into a flask where it condenses, what is the mole percent of methanol in vapor above the new (second) flask?

[Pure methanol has a vapor pressure of 87 torr and pure butanol has a vapor pressure of 29 torr a 22 deg C.]

A. Less than 25%
B. Between 25 and50%
C. Between 50 and 75%
D. Greater than 75%

Book Explanation:
Choice D is correct. From a 50% by moles mixture of the two liquids, the vapor due to methanol above the flask is 87 /(87 + 29). When the vapor is condensed, collected, and placed into the second flask, the condensed solution is 75% methanol by moles. The vapor pressure of methanol above the second flask is greater than 75% because methanol evaporates more readily than butanol evaporates.


Ok, what I'm confused about this question is given the information that the mixture is 50%, wouldn't that mean that it would be like 50 g/100g for each, & then that way I could see that the number of moles of methanol are greater than ethanol? I'm basically just confused as to how the vapor pressure due to methanol above the flask is 87/(87+29). Why can you take the pure pressure of methanol & divide it by its pure pressure + ethanol's? I don't see how this can be derived from Raolt's law of Ptotal = mole fraction of A * Pa + mole fraction of b * Pb. Maybe I'm just missing something really obvious.

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Hmmm I see that:

Ptotal = .5 *(87) + .5 (29)
P total = 58

If the partial pressure of methanol is 43.5

then its contribution to the total pressure is 43.5/58.

43.5/58 = 75%

When you put the vapor that is 75% methane & 25% ethane into the new beaker, the solution has a greater ratio of methane to ethane.

Therefore Ptotal = .75*87 + .25 * 29

because methane has both a greater pure vapor pressure, & a greater ratio in the new beaker, then its molar ratio in the vapor is going to be pretty high.

If it wasn't then I'm guessing you would have had to do the math out which would be tedious.

My way is more complex, but I'm still having difficulty figuring out how they book was able to quickly figure out that 87/(87+29) would give you the mole percent of methane in the original beaker above the solution

Edit: NVM, I figured it out. So stupid.

Pt = .5*87 + .5*29

Therefore: .5*87 / .5 (87 + 29) -> 87/(87+29)

Need to drink coffee, & why didn't TBR put this down? Sheesh.
 
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This can also be done qualitatively - the first sample is naturally going to be richer in the MORE volatile component because it vaporizes at a lower temperature. Thus, the first sample is going to be a LOT more % methanol than butanol in any case because:

1. The sample is already richer in methanol than butanol.
2. Methanol is more volatile than butanol, so that adds to the effect of vapor pressure in the sample.
 
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This can also be done qualitatively - the first sample is naturally going to be richer in the MORE volatile component because it vaporizes at a lower temperature. Thus, the first sample is going to be a LOT more % methanol than butanol in any case because:

1. The sample is already richer in methanol than butanol.
2. Methanol is more volatile than butanol, so that adds to the effect of vapor pressure in the sample.


I think the biggest hurdle for me was realizing that when they said the mixture's was 50% that they meant it was 50% BY MOLE.

What is a 50% mixture? Is it 50% by mass, 50% by volume, or 50% by moles? Dunno if TBR was being vague on this question or that I should have immediately known that a 50% mixture is by mole.
 
I think the biggest hurdle for me was realizing that when they said the mixture's was 50% that they meant it was 50% BY MOLE.

What is a 50% mixture? Is it 50% by mass, 50% by volume, or 50% by moles? Dunno if TBR was being vague on this question or that I should have immediately known that a 50% mixture is by mole.

Looking back on the question (I remember doing this passage 1.5 months ago-ish), I intuitively assumed they meant by mole simply because the question stated "what is the mole percent". Volume would be out because they didn't give us the density or concentration or whatnot of the compounds in question, and it would be downright cruel for them to take that leap and make it by mass. Common sense would dictate that you can extrapolate backwards using that logic, but..

That being said, I haven't encountered a situation in a FL where I've been beset by this kind of ambiguity, but the MCAT is so annoyingly ambiguous sometimes. :bullcrap:
 
more shady and easier way is to notice that VPs are 90 and 30 respectively which is means that Mole fraction of methanol is greater than butanol (3 times greater). So you have 3 part methanol 1 part butanol.....soooooooooooooo that means you have 75% more methanol. :naughty:
 
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