Aamc 7 #20

[Jwinsler7]

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Quick conceptual question,

A gas that occupies 10L at 1 atm and 25 degree celsius will occupy what volume at 500atm and 25 degree celsius?

A. exactly 0.020L
B. Somewhat more than 0.02L because of the space occupied by the individual gas molecules
C. Somewhat more than 0.02L because of the repulsions between the individual gas molecules
D. Somewhat more than 0.02L because of increased number of collisions with the side of the containers

I chose C, but the correct answer is B.
I could see why B is logical, yet I fail to see why C can't be the correct answer.

At such high pressure, repulsion between gas molecules would be far more predominant than attraction, so the volume would be greater than idea volume.

Could anyone explain why B is a better choice than C?
Thanks

 

[LianaStan]

I'm not exactly sure where you are drawing the conclusion that the force will be repulsive given that the question does not state the gas is composed of like charged ions. To assume that at a high pressure gases repel each other is also wrong. Think about the phase change diagrams you have seen. At a high pressure the gas will actually condense completely to form a liquid.

 

[Jwinsler7]

I'm not exactly sure where you are drawing the conclusion that the force will be repulsive given that the question does not state the gas is composed of like charged ions. To assume that at a high pressure gases repel each other is also wrong. Think about the phase change diagrams you have seen. At a high pressure the gas will actually condense completely to form a liquid.

From what I understand, you don't necessarily need charged ions for attraction/repulsion of gas molecules...And using your logic of phase diagram, volume of liquid would be less than volume of gas. That definitely does not make any sense. Look at the answer choices. This question is obviously not assuming any phase changes. Thanks for your attempt though.

Ideal gas law is only valid when pressure is not too high or temperature is not too low. At such high pressure (500 atm), ideal gas law is no longer valid, so from my understanding, real gas law needs to be used (van der waal's equation). That's where one needs to consider attraction and repulsion between gas molecules. Like I said, at such high pressure, repulsion would be more predominant than attraction. That's why I chose C.

Anyone else would like to enlighten me why B is a better choice than C?

 

[LoLCareerGoals]

Van der Waals equation: P = nRT/(V-nb) - n^2*a/V^2.
First modifying term ("-nb") is due to volume of the molecules (if you solve for V you will get "+nb" increase in volume), so far points to answer B.
Second modifying term "-n^2*a/V^2" is the correction for molecular attraction. Ideal gas equation assumes there are no intermolecular forces (like in a liquid), but there are some.
Not pointing to C as far as I can tell.

Also B is more directly linked to volume. Not sure why you assume there would be repulsion between gas particles either.

 

[Jwinsler7]

Van der Waals equation: P = nRT/(V-nb) - n^2*a/V^2.
First modifying term ("-nb") is due to volume of the molecules (if you solve for V you will get "+nb" increase in volume), so far points to answer B.
Second modifying term "-n^2*a/V^2" is the correction for molecular attraction. Ideal gas equation assumes there are no intermolecular forces (like in a liquid), but there are some.
Not pointing to C as far as I can tell.

Also B is more directly linked to volume. Not sure why you assume there would be repulsion between gas particles either.

Hmm, I was taught "-nb" term is the correction for molecular repulsion..

 

[LoLCareerGoals]

There are two assumptions that make ideal gas ideal:
1) Zero volume molecules (-nb term corrects for that in a "real" equation)
2) Zero intermolecular forces (-n^2*a/V^2 term corrects for that in a "real" equation).

In a gas molecules constantly collide/bounce off each other. I don't understand where you are getting the repulsion from.
I am guessing you are getting an intuition that since a gas "wants" to occupy as large of a volume as possible when given a chance, there must be some intermolecular repulsion at work? This happens because it is entropically favourable (entropy grows) for a gas to occupy a larger volume:
deltaS = nr*ln(V2/V1).

 

[Jay2910]

Is there a way to work this out without using the van der waal's equation?

 

[Saint Fu]

The way I reasoned this out is that electromagnetic forces, like gravitational forces, are generally weak at a distance. In either case, the force drops with the square of the distance, so unless they're right up next to each other, other factors (such as the size of the particles themselves) are more likely to dominate.