TBR GChem Ch7, Passage 5, #29

[EZR]

Vapor Pressure.

There are three separate beakers:

#1: 50g methanol + 50g ethanol
#2: 50ml methanol + 50ml ethanol
#3: 1mol methanol + 1mol ethanol

Question: Above which breaker is the vapor pressure of methanol the GREATEST?

I chose beaker 1. The book says answer is number 2:
"The mole fraction of methanol in Beaker II is even greater than the mole fraction of ethanol in Beaker I."How is this true?!


Density of methanol: 0.7914 g/mL
Density of ethanol: 0.7893 g/mL

Using those ^ given densities, I get 39.57g methanol and 39.47g ethanol for Beaker #2. This is obviously less than the 50g compounds in Beaker #1.

Mole fraction of methanol:
Beaker 1 = 0.93
Beaker 2 = 0.59


What am I missing?

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[MedPR]

Vapor Pressure.

There are three separate beakers:

#1: 50g methanol + 50g ethanol
#2: 50ml methanol + 50ml ethanol
#3: 1mol methanol + 1mol ethanol

Question: Above which breaker is the vapor pressure of methanol the GREATEST?

I chose beaker 1. The book says answer is number 2:
"The mole fraction of methanol in Beaker II is even greater than the mole fraction of ethanol in Beaker I."How is this true?!


Density of methanol: 0.7914 g/mL
Density of ethanol: 0.7893 g/mL

Using those ^ given densities, I get 39.57g methanol and 39.47g ethanol for Beaker #2. This is obviously less than the 50g compounds in Beaker #1.

Mole fraction of methanol:
Beaker 1 = 0.93
Beaker 2 = 0.59


What am I missing?

You're missing that vapor pressure is dependent on mol fraction, not total mass.

In beaker 1 you have equal masses. So your mass ratio is 1methanol:1ethanol

In beaker 2 you have a greater mass of methanol since you have equal volumes but methanol has a higher density. So your mass ratio is 1.xmethanol:1ethanol

Without even calculating mol fraction (too much work for this problem in MCAT) you should be able to see that 50mL of each will yield you a bit more grams of methanol than grams of ethanol. Since their molar masses don't change, a greater mass to mass ratio will lead to a greater mol fraction.

I'm not sure where you are getting 0.93 for your mol fraction...

MM Methanol = 32.
MM Ethanol = 46

50/32= 1.6
50/46 = 1.1
1.6/(1.1+1.6)=.59

Unless you do very exact calculations, you will end up calculating that the mol fraction for beaker 1 and 2 are equal. To answer this question quickly you need to make the connection that lower density and equal volume = higher mass.

 

[BerkReviewTeach]

To answer this question quickly you need to make the connection that lower density and equal volume = higher mass.

Great point MedPR. It's not only important to get the question right, but to also do it quickly. I have a feeling you are going to get a high score.

 

[gettheleadout]

To answer this question quickly you need to make the connection that lower density and equal volume = higher mass.

You mean lower mass.

d = M/V

If d decreases and V is constant, then M must decrease. But yes, because ethanol has a lower density it will have a lower mass with equal volume compared to methanol.

 

[411309]

Unless you do very exact calculations, you will end up calculating that the mol fraction for beaker 1 and 2 are equal. To answer this question quickly you need to make the connection that lower density and equal volume = higher mass.

Isn't it higher density and equal volume= more mass? Density is g/ml in this case and volume is ml so multiplying density by volume gives grams, so a higher density with equal volumes would give more mass.

But what medpr said pretty much sums it up. On the mcat you can't spend too much time getting bogged down on math, what I liked about tbr is they gave you ways to avoid math. Which is why i loved their system for optics, their five case system pretty much makes it where you rarely need the the thin lens equation.

Edit- dang you patrick star avatar guy you beat me yet again : O

 

[MedPR]

Great point MedPR. It's not only important to get the question right, but to also do it quickly. I have a feeling you are going to get a high score.

Idk if you were making fun of me because I confused high mass/low mass, but if that was sincere I really appreciate it

You mean lower mass.

d = M/V

If d decreases and V is constant, then M must decrease. But yes, because ethanol has a lower density it will have a lower mass with equal volume compared to methanol.

Isn't it higher density and equal volume= more mass? Density is g/ml in this case and volume is ml so multiplying density by volume gives grams, so a higher density with equal volumes would give more mass.

But what medpr said pretty much sums it up. On the mcat you can't spend too much time getting bogged down on math, what I liked about tbr is they gave you ways to avoid math. Which is why i loved their system for optics, their five case system pretty much makes it where you rarely need the the thin lens equation.

Edit- dang you patrick star avatar guy you beat me yet again : O

Yea, I started to type out the sentence with ethanol in mind, then I finished it with while thinking about methanol. The answer is the same, just fix the typo!

 

[gettheleadout]

Idk if you were making fun of me because I confused high mass/low mass, but if that was sincere I really appreciate it






Yea, I started to type out the sentence with ethanol in mind, then I finished it with while thinking about methanol. The answer is the same, just fix the typo!

Haha for the record I wasn't trying to put you down for the typo, and I'm 99.9% certain BRT meant it sincerely.

 

[Arcadia06]

Hi! If your still check SDN. I had a question with this problem tooo! I thought that the greatest vapor pressure would be seen with the solution having the lowest solute concentration? Any clarity would help

 

[SSerenity]

Yes, you can quickly look at the density and determine #2 will have more than 50% (by weight) methanol, ruling out #1.

However, you still have to convert to moles in order to rule out #3, am I correct? Is there another quick trick to avoid calculating this part?

 

[richkaj]

Methanol is lighter than ethanol due to it's molecular weight. Having more of methanol leads to a higher vapor pressure. You are right, the solution with the lowest ethanol will have the greatest vapor pressure. The more ethanol that blocks methanol from leaving leads to a lower vapor pressure. Vapor pressure is just the ability of a substance to evaporate... Hope this helps...

 

[richkaj]

Great question about #3. Converting moles to grams should suffice. There would be more ethanol (2COH) than methanol (1COH) when multiplying by their molecular weight. More ethanol, less vapor pressure for methanol.