Understanding the variables in the ideal gas law

[September24]

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I know that the ideal gas law is

Pv=nrt

Pressure, I believe, is the pressure exerted by the gas against the walls of a container. However, is the volume here the volume of the gas itself or the volume of the container.

I ask because this concept applies to the van der waals equation. At low temperature, gases are more "vulnerable" to intermolecular forces so they will be attracted to one another resulting in less collisions with the walls of container and lower pressure than expected. If this is the case,

(P+a)(V-nb)=nrt

A is added here because once rearranged:
P=nrt - (A)

I left out the volume term but I see that pressure is actually reduced. Am I understanding this correctly?


My biggest confusion is volume. At high pressures, the volume of the molecules of gas are not negligible as assumed by the ideal gas law. The volume of the container is smaller than expected since gases take up volume.

(P+a)(v-nb)=nrt

V=nrt+b

Rearranged, it looks like the real volume is higher than expected which doesn't make sense to me. Shouldn't the real volume be smaller?

I'm sorry, this is just a bit confusing. Conceptually, the concept makes sense but the VDW equation is a bit weird.

 

[cjcarter]

V real > V ideal. According to the kinetic molecular theory, one of the characteristics of an idea gas is that gas molecules have zero volume. Which for real gases, is obviously not true. Molecules of a real gas DO have volume, so their volume has to be added to the ideal volume in PV=nRT. Don't think in terms of the container. Think about the gas molecules themselves.

P real < P ideal. Again, molecules in a real gas do exhibit forces on each other, and the main intermolecular forces in a gas are attractive, the gas molecules are pulled inward toward the center of the gas, which ends up slowing them down and causing them to hit the container with less force than PV=nRT predicts. So it is subtracted.

 

[Blueprint MCAT Tutor]

V real > V ideal.
P real < P ideal.

Careful here - phrasing it that way can potentially be confusing.

You can get deviations down or deviations up based on how "extreme" the conditions are:

At low pressures, under "normal" conditions, the main thing to consider is the attractive force between the molecules. Electrostatic forces can work over a distance, so the molecules can be attracted to each other, making the gas "clump up" so to speak.

Meaning if you measure pressure, it'll be lower than you're expecting, since the gas isn't pressing out against the walls of the container as much as you were expecting (the gas is clumping up in the middle of the container with the molecules sticking to each other).

Alternatively, if you hold pressure constant and measure volume, the volume will be smaller than you're expecting since, again, the gas molecules are attracted to each other and aren't pushing out against the sides of the container making it expand to the volume you were expecting.

At really high pressures, under "extreme" conditions, the size of the molecules themselves is now the dominant factor. So you were expecting a volume of 0.5000 L but the molecules themselves take up some space, so when you measured volume, you got 0.5001 L. Thus the overall volume was bigger than you were expecting.

Pressure can actually be higher or lower than ideal, based on what factor is more important.

In the equation above, if "b" is the more important factor (how big the molecules are), then the denominator of that fraction gets smaller, the overall value goes up. P real > P ideal

However, if "a" is the more important factor (how sticky the molecules are to each other), then that whole second term gets bigger. Because you're subtracting it, the overall value goes down. P real < P ideal

Hope this helps! 🙂

-Bryan

 

[cjcarter]

That's too many things to know. They would have to explain in the passage about which factor is more important. We don't even have to know the equation for the test. TPR and EK both say to know the inequalities.

 

[cjcarter]

I could totally see them giving the PV/RT graph and know the negative deviation is due mainly to attractive intermolecular forces, and the positive deviation is due mainly to molecular volume.

 

[September24]

Thanks for the help guys! And yes, PV/RT graphs are definitely a possibility. At least EK 1001 has them.

I'm still confused on volume. You guys said Vreal>Videal. I read that the volume in the ideal gas law is THE VOLUME OF THE CONTAINER ITSELF. If the gas molecules have volume themselves, shouldn't they be reducing the overall volume. In other words, gases take up space so there is less "space left over" in the container thus reducing overall volume for the gases to move around in?

 

[cjcarter]

http://www.chemguide.co.uk/physical/kt/realgases.html

Check out this link. It explains it pretty well.

 

[cjcarter]

It basically boils down to the ideal gas equation doesn't account for the volume the molecules themselves take up. So the volume of the container + the volume of the molecules has to be greater than predicted in PV=nRT. The VDW equation accounts for the volume of the container AND the molecules.

Like Bryan said, this becomes even more prominent the more the gas is compressed (at high P)

 

[Blueprint MCAT Tutor]

You guys said Vreal>Videal.

No no be careful.

Under "normal" conditions V real < V ideal. The link cjcarter posted shows you this with this table where the volume is less than ideal:

Under "extreme" conditions V real > V ideal because the volume of the molecules themselves is creating deviation.

 

[Sergiy MSc]

Hi, to help to better grasp the idea of Van der Waals "Real" gas versus "Ideal", there exists Android app visualising some Ag and He molecules movement in a container with a Piston, at a big scale. You can turn on/off intermolecular forces on fly, build graph P(V), apply heating etc.