Berkeley Review Question - Real Gases

[iamgroot2]

The question states:

For an inert real gas, if you were to reduce the pressure to half of its original value, then what would the final volume (Vf) relative to the initial volume (Vi) be?
A. 1/2 Vi - a little bit
B. 1/2 Vi + a little bit
C. 2 Vi - a little bit
D. 2 Vi + a little bit

The answer is C.

So, I understand that A and B are first eliminated, because of the inverse relationship between pressure and volume, as derived by the ideal gas law. I think I understand the rationale for C, which is that in an ideal situation if you were to compare to ideal gases, then 1/2 the pressure, should double the volume. The second part would be to then factor in the volume that the gas particles occupy, would lead to a final volume = 2 Vi - a little bit.

Here are my two questions:

1. If we are compareing the final volume (Vf) relative to the initial volume (Vi), since we are dealing with a real gas in both the initial and final volumes, wouldn't the ratio be...

Volume initial = Videal - a little bit (the volume occupied by the gas particles) : Volume final = Videal - a little bit (the volume occupied by the gas particles) ?

Wouldn't that mean that, Vf = 2 Vo, since we factored in the volume occupied by the gas particles in both scenarios?

2. The final few sentences in the rationale state, "If the pressure were double [instead], the volume wouldn't be reduced by exactly one-half, either. The new volume would be 1/2 Vi + a little bit."

I thought we always subtracted the ideal gas volume - the volume occupied by the gas. Could someone explain the plus sign?

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[iamgroot2]

Bump

 

[JimKimSlim]

I think you’re focusing too much on the van dear waals equation. Think more broadly with respect to your questions. When you reduce the pressure, the volume occipied by the particles becomes more negligible, so you need to subtract that volume a little bit. You have to remember that the real gas law is usually used when you're dealing with very high-pressure, low volume system.

 

[iamgroot2]

I think you’re focusing too much on the van dear waals equation. Think more broadly with respect to your questions. When you reduce the pressure, the volume occipied by the particles becomes more negligible, so you need to subtract that volume a little bit. You have to remember that the real gas law is usually used when you're dealing with very high-pressure, low volume system.

I get that part where because you have a set ideal volume (2 * Vo) that needs to be subtracted by the volume of the molecules to account for their volume, as the pressure is reduced by half.

Why do we add a little bit when we double the pressure, if under ideal conditions, this would just be 1/2 Vo?

 

[JimKimSlim]

Under high pressure, low volume, the volume of the particles is no longer negligible so you have to add a small factor.

 

[PlsLetMeIn21]

I so remember this question. It's a tricky concept they're asking about. Just remember that the space can get bigger or smaller, but the atoms and molecules can't change size.

If the pressure is cut in half, the space will double, but the size of the atoms does not double. Not everything has doubled, so the volume (the space plus the molecules) has not quite doubled.

 

[BerkReviewTeach]

Excellent way to look at it PlsLetMeIn. That is exactly how to think about the variations between real and ideal gases when they expand and contact.