Ideal Gas Law Discrepancy? AAMC 7 #20

[ssjsike]

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

A) exactly .02L
B) Somewhat more than .02L because of the space occupied by the individual gas molecules
C) Somewhat more than .02L because of the repulsions between the individual gas molecules
D) Somewhat more than .02L because of the increased number of collisions with the sides of the container


-The answer is B. I got the question right by process of elimination, but this information seems to go against what TPR physics says:

The book states:

1) The molecules of an ideal gas are so small compared to the average spacing between them that the molecules themselves take up essentially no volume
2) The molecule of an ideal gas experience no intermolecular forces.

Under some conditions, these assumptions don't hold up very well, and the laws for ideal gases don't apply to real gases. In particular, high pressures and low temperatures cause real gases to deviate the most from ideal gas behavior. In reality, the actual volume and pressure for a real gas are less than those values obtained from applying the ideal gas law to that gas. That is, Preal<Pideal because the real gases do experience intermolecular forces, reducing collisions with the walls of the container. And Vreal<Videal because molecules of real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).


*What am I missing here? Can someone give me their input on this matter? Thank You.

 

[muhali3]

At very high pressures, the ideal gas law predicts a certain volume, however, since the volume of the gas molecules are being neglected, the calculated volume is lower than what it actually is, since each individual gas molecule is taking up space.

Under the ideal gas law, those wouldn't be taking up any space and the volume would be less.

 

[vin5cent0]

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

A) exactly .02L
B) Somewhat more than .02L because of the space occupied by the individual gas molecules
C) Somewhat more than .02L because of the repulsions between the individual gas molecules
D) Somewhat more than .02L because of the increased number of collisions with the sides of the container


-The answer is B. I got the question right by process of elimination, but this information seems to go against what TPR physics says:

The book states:

1) The molecules of an ideal gas are so small compared to the average spacing between them that the molecules themselves take up essentially no volume
2) The molecule of an ideal gas experience no intermolecular forces.

Under some conditions, these assumptions don't hold up very well, and the laws for ideal gases don't apply to real gases. In particular, high pressures and low temperatures cause real gases to deviate the most from ideal gas behavior. In reality, the actual volume and pressure for a real gas are less than those values obtained from applying the ideal gas law to that gas. That is, Preal<Pideal because the real gases do experience intermolecular forces, reducing collisions with the walls of the container. And Vreal<Videal because molecules of real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).


*What am I missing here? Can someone give me their input on this matter? Thank You.

The answer is right there in your description.

"...the laws for ideal gases don't apply to real gases. In particular, high pressures and low temperatures"

With an ideal gas at certain pressures/temp, the volume of a gas molecule is so small that it's negligible. In this problem, though, it's asking you about the molecules at a very high pressure. The pressure is so high, that at that point you can't assume the volume of the molecules is negligible without throwing off your answer by a greater magnitude.

 

[ssjsike]

I think I should clarify what exactly I'm confused about.

The answer states:


B) Somewhat more than .02L because of the space occupied by the individual gas molecules


However, the book states:

And Vreal<Videal because molecules of real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).


The reason that I got this question right is because there was no answer choice that said "Somewhat less than .02L because of the space occupied by the individual gas molecules"

By the TPR book, Vreal<Videal, so why does the answer for AAMC imply that Vreal>Videal? Or am I missing something all together?

 

[muhali3]

Your TPR book is only right at medium pressure. At high pressure, the effect of molecular volume is greater than the effect of intermolecular forces.

Here's an answer to your question: http://forums.studentdoctor.net/showpost.php?p=2827924&postcount=8

For the MCAT, it's easier to just associate increased pressure with positive deviations due to molecular volume, and reduced temperature with negative deviation due to intermolecular forces.

 

[MT Headed]

The book states:

Vreal<Videal because molecules of real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).

It looks like TPR confused themselves about what is measured when we measure volume, and therefore they got the inequality sign wrong.

Vreal>Videal, because real gases also have molecular volume.

Besides, if you look at the van der Waals equation there is a plus sign next to the P term, and a minus sign next to the V term, so the inequalities must go in opposite directions. Preal<Pideal, and Vreal>Videal

 

[mitchlucker]

I'm not sure about this. I'm glad I didn't buy AAMC 7 haha.

In my MCAT notes I have

"at very high pressures, actual volume is LESS than predicted than an ideal gas due interactions between molecules, and at very, very high pressures, actual volume is MORE than predicted by an ideal gas due the occupation of space by the individual molecules."

What the difference is between very high, and very, very high pressures is unknown to me, I usually just assume the pressure is "very, very high" and that actual volume is more. The only answer that makes sense is B.

 

[paul411]

What the difference is between very high, and very, very high pressures is unknown to me, I usually just assume the pressure is "very, very high" and that actual volume is more.

1 atm is normal atmospheric pressure at sea level. 500 atm (from the question) which is 500X more pressure than normal is considered "very, very high".

To make it easier to intuit, consider this:
1 atm = 14.7 pounds per square inch
500 atm = 7348 pounds per square inch

But you are right, the distinction is hard to make without being given additional data. However,

The reason that I got this question right is because there was no answer choice that said "Somewhat less than .02L because of the space occupied by the individual gas molecules"

The question is purposely constructed like that. If the option you mentioned ("Somewhat less than 0.02L...") was provided, they would have to give you additional data (real gas law, a, b) for you to determine the right answer with certitude.

From a test-taking perspective: This question requires you to determine (a) whether the volume would be exactly .02L or slightly more and (b) the correct reasoning for the answer from (a).

 

[neurodoc]

The "ideal" situation involves molecules that are "points" without "volume" and which do not exert intermolecular forces (except those perhaps due to eleastic molecular collisions which are usually ignored). The non-ideal situation involves: 1) the space (volume) occupied by the molecules and, 2) the forces (attractive or repulsive) due to molecular interactions that are more pronounced the closer the molecules are to each other.

The actual volume of gaseous molecules is considered to be negligible, but if the molecules are packed very closely (in a liquid or solid phase under very low temp or high pressure) molecular volume is indeed important and would tend to make the "real" volume greater than the "ideal" volume, since the molecules themselves take up space and they cannot be packed infinitely closer to each other.

Similarly, when molecules are packed closer together (by low T or high P), they can exert intermolecular forces. These forces can be repulsive or attractive, depending on what forces we are discussing (electrostatic, gravitational, etc). In general. for identical molecules, repulsive forces predominate. This would, in general, again have the effect of making "real" volume greater than "ideal" volume at low T or high P. I know that the so-called Van Der Waal's force is considered to be "attractive," so maybe they want you to say that this would decrease the "real" volume.

This strikes me as a poorly asked question. But I've explained the way I'd look at it.🙂

 

[Xivilus1231]

I am looking at this question from an empirical perspective.

The volume IN the container is less than ideal volume because the molecules will take up some volume right?

In order to factor in the volume of the molecules in the container, the volume of the container will have to be greater than the ideal volume.

Otherwise the gases won't fit in the container. You must read the question carefully, it is asking what volume can the gas occupy (what container can the gas fit in, and why?)

Therefore, there is no discrepancy or errors on the part of TPR (Vreal < Videal) or the AAMC question.