Phase Diagram/Gibbs Free Energy question??

[Hshephe2]

On a Kaplan question, I was given a phase diagram and told that compound A was in a liquid state. Then it asks which process would have the most negative value of G (most spontaneous):
A. Sublimation
B. Vaporization
C. Condensation
D. Deposition

I thought it would be (B). Vaporization, because less order = more spontaneous. However, it says that (C). Condensation is the correct answer because "any process that favors the pro- duction of a liquid will be the most spontaneous".

I am confused.. is it because it takes less energy to condense a liquid than to vaporize it?

Thanks!

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[Trayshawn]

Bullsh*t. You can't tell if you don't know the temperature.

Fusion and Vaporization are exergonic at high temperatures. Condensation and Freezing are exergonic at low temperatures.

ΔG = ΔH - TΔS easily proves this. There are two opposing effects here, entropy and enthalpy. Vaporization increases entropy (as you said) but also requires heat input (endothermic). Condensation releases heat (exothermic) which is good, but decreases entropy. In such a case, temperature determines which process is favorable.

Same rationale applies to sublimation and deposition.


Of course, I'm only going off of what you put here. It is also possible that there is extra information in the original question that you are missing that makes this question less ambiguous. But, as you have stated it here, there is no way to provide an answer.

 

[Hshephe2]

I failed to mention that the temperature was 375 K..

According to your explanation, this is a lower temperature.
What would qualify as a "high temperature"?

 

[mehc012]

I guess my only input would be that, since the substance is IN a liquid state, then whichever reaction would FORM a liquid must be the most spontaneous, or else the substance would be in a different phase.

In other words, if vaporization was the most spontaneous reaction for these conditions, Substance A would have all gone from liquid to a gas. Therefore, we know that condensation must be more spontaneous than vaporization since it actually looks more like this:
liquid ↔ gas

 

[Trayshawn]

I failed to mention that the temperature was 375 K..

According to your explanation, this is a lower temperature.
What would qualify as a "high temperature"?

Without a sense of the magnitude of change in enthalpy and entropy, you cant say what is considered high or low temperature. That depends on the compound in question.

It seems the best way to answer this is what the guy above me suggested. Since its already in liquid state, that must be the most stable condition. So anything going to it would be favorable. Good catch!

 

[mehc012]

Without a sense of the magnitude of change in enthalpy and entropy, you cant say what is considered high or low temperature. That depends on the compound in question.

It seems the best way to answer this is what the guy above me suggested. Since its already in liquid state, that must be the most stable condition. So anything going to it would be favorable. Good catch!

Thanks! It's good that these review books try to throw in the tricky "oh wow, I didn't consider that" questions, but it's even more important to make sure that the answer explanation is REALLY CLEAR on how you should get to that answer, and that that logic is not generalizable to all cases...for example, the answer explanation on this one seemed to imply that forming a liquid was always favorable, which is not good.

So thank you for explaining the actual concept at hand here!