Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Topic started by: Procrastinate on August 06, 2010, 09:01:16 AM
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Hi, I was wondering whether anyone could give me some explanations on the constants of the Van der Waals equation. I have done some extensive research but most websites and books don't give much information about the Van der Waals constants.
I was wondering if anyone could provide me with more background knowledge about these constants:
I know that:
- a has something to do with intermolecular forces. Apparently if particles are too close together they repel and if they are far away they attract. Does anyone what the number represents?
- I know that b has something to do with volume. Apparently, the greater the b constant, the greater the volume, but could someone confirm and specify that for me?
Any extra information would be extremely helpful. Thank you.
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I'm pretty sure you could find the actual value of the constants in the Internet. I think in order to understand constants in the Van Der Waals equation, you should know the limits of the ideal gas (and I'm also pretty sure you already know that).
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First, in an ideal gas we neglect the molecular interaction between molecules. However, we should also consider interactions in real gases. Therefore, the pressure of the real gas will be larger than that of the ideal gas. Therefore, there is the constant a added to the pressure.
Second, in an ideal gas we also neglect the volume of the molecules. However, in a real gas we can't do that. Real gas molecules also have volume and they take space. Therefore, the volume of the real gas will be smaller than that of the ideal gas. Therefore, we have constant b subtracted from the volume.
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First, in an ideal gas we neglect the molecular interaction between molecules. However, we should also consider interactions in real gases. Therefore, the pressure of the real gas will be larger than that of the ideal gas. Therefore, there is the constant a added to the pressure.
I'm really sorry if I wasn't supposed to revive this, but I have a question. If the interactions were attractive forces, how would the pressure of the real gas be larger than that of the ideal gas? I was taught that the parameter a respents the role of attractions, and I don't see how attraction between molecules would increase the pressure.
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My theory is that as attractive force exists in real gases, the volume will also decrease. The effect of the increase in volume will be dominant than the attractive force making the molecules close together.
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First, in an ideal gas we neglect the molecular interaction between molecules. However, we should also consider interactions in real gases. Therefore, the pressure of the real gas will be larger than that of the ideal gas. Therefore, there is the constant a added to the pressure.
I'm really sorry if I wasn't supposed to revive this, but I have a question. If the interactions were attractive forces, how would the pressure of the real gas be larger than that of the ideal gas? I was taught that the parameter a respents the role of attractions, and I don't see how attraction between molecules would increase the pressure.
In fact it doesn't ;D
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3F%7B+p_%7Bideal%7DV_%7Bideal%7D%3DnRT+%5C%5C%3Cbr+%2F%3E%5Cleft%28p_%7Breal%7D%2Ba%5Cfrac%7Bn%5E2%7D%7Bv%5E2%7D%5Cright%29%5Cleft%28V_%7Breal%7D-nb%5Cright%29%3DnRT+%7D&hash=c708b80eb819a799f04f04c4745af2549be37dd3)
so:
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Bonus
Seeing the starting post seems like Procrastinate wanted to know where does this equation comes from, here's a brief overview on the subject:
1) In the ideal gas equation molecules are considered adimensional entities so their volume doesn't matter. Here the volume occupied by the gas molecules (the so-called covolume), which is more or less 4 times the real volume of molecules is taken into account (b), so n moles of gas need a volume correction of nb:
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3F%7B+V_%7Breal%7D%3DV_%7Bideal%7D%2Bnb+%7D&hash=566177d6de7f61034fb34ad2604f3146b5185ad0)
2) In the ideal gas intermolecular forces are neglected, but a precise account of the real gas behaviour forces us to keep in mind that, even if really weak, such forces shouldn't be forgotten in our analysis. You can easily demonstrate that the intermolecular distance for a gas of n moles in a container of volume V is:
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where k is a constant value which changes from species to species. Now, imagine our molecules are apolar (this equation doesn't take into account polarity or other attractive forces): the only interactions present are London Forces (instantaneous dipole-instantaneous dipole) and (this has been proven experimentally) they are inversely proprtional to the sixth power of the intermolecular distance:
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Now, these forces cause a decrease in the number of collisions with the surfaces of the container and this means a decrease in pressure too. Using a new constant, we'll call "a" the final expression pops out:
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≈•≈
Substituting the corrected forms of volume and pressure in the ideal gas equation you get the final expression:
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