Pressure

[chiddler]

1 liter container with 1 mol H2, and another with UF6. With which one is pressure greater?

the Vrms of the H2 is greater for sure, but the UF6 is carrying so much more momentum. But I think I remember reading that UF6 will be only slightly slower so the huge mass is a greater contributor to pressure. Is it UF6?

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[folktale]

I'd say UF6 as well. The pressure depends more heavily on the volume that the molecules take up. 1mol UF6 takes up WAAY more than 1 mole H2.

 

[cloak25]

I thought that collision frequency is the greater contributor to pressure in a container. Since H2 has higher Vrms, it would collide with walls of the container more often = greater pressure? ..

 

[milski]

At the same temperature, I assume? If we were talking about ideal gases, the pressure would be the same. Since they're not, UF6 has significantly larger molecules and as such will have a higher pressure.

 

[syoung]

yeah PV = nRT, if ideal gas, and they say same n and same V...

 

[piojita63]

at

I thought that collision frequency is the greater contributor to pressure in a container. Since H2 has higher Vrms, it would collide with walls of the container more often = greater pressure? ..

th

I agree with this. I thought that ideal gases were assumed to have no volume, thus pressure is directly proportional to collision frequency. Aren't we supposed assume all gases on the MCAT are ideal unless stated otherwise? I would answer H2 here...what is the answer supposed to be?

 

[chiddler]

yeah PV = nRT, if ideal gas, and they say same n and same V...

atth

I agree with this. I thought that ideal gases were assumed to have no volume, thus pressure is directly proportional to collision frequency. Aren't we supposed assume all gases on the MCAT are ideal unless stated otherwise? I would answer H2 here...what is the answer supposed to be?

come on people! how can I be referring to an ideal gas when i compare H2 (m.m 2) and UF6 (m.m 352!!!)

thank you milski.

 

[piojita63]

Yes, you are right that the large molecular weight would certainly make this gas deviate from "ideality", so in this case (for MCAT purposes), we can assume it's "real" even though they didn't specifically say? I'm sorry for continuing to be confused. I just thought that we always had to assume it was ideal (even if that was counterintuitive to the situation), unless otherwise stated. The real vs. ideal is a good MCAT trap, so I just want to make sure I'm clear.

 

[chiddler]

Yes, you are right that the large molecular weight would certainly make this gas deviate from "ideality", so in this case (for MCAT purposes), we can assume it's "real" even though they didn't specifically say? I'm sorry for continuing to be confused. I just thought that we always had to assume it was ideal (even if that was counterintuitive to the situation), unless otherwise stated. The real vs. ideal is a good MCAT trap, so I just want to make sure I'm clear.

you're absolutely right to assume. my question just wasn't in the context of an mcat question, but rather a general question that's all.

thanks for the responses.

 

[milski]

Yes, you are right that the large molecular weight would certainly make this gas deviate from "ideality", so in this case (for MCAT purposes), we can assume it's "real" even though they didn't specifically say? I'm sorry for continuing to be confused. I just thought that we always had to assume it was ideal (even if that was counterintuitive to the situation), unless otherwise stated. The real vs. ideal is a good MCAT trap, so I just want to make sure I'm clear.

In general, yes, you can assume that the gas is ideal. But then the comparison between the two gases given in the question becomes rather meaningless - what would be the point of giving you specific gases and asking about the differences if they behave the same anyway?

If they were asking about properties of idea gas which depend on the type of molecule (like specific heat capacity), then it might make sense to treat them as ideal gas. But then, they would not mess with anything more complicated than an diatomic gas on the MCAT.

 

[EnginrTheFuture]

Another nice thing to note... any mention of UF6 is usually a hint towards comparison of real gasses. This is the compound formed in order to enrich different isotopes of Uranium for nuclear power plants. p-chem classes and mcat prep books love using this molecule for Vrms questions for some reason.

 

[syoung]

so larger V (UF6 >>H2) leads to higher pressures in real life then?

 

[milski]

so larger V (UF6 >>H2) leads to higher pressures in real life then?

Yes, larger size of the molecule leads to higher pressure. The modified version of the ideal gas law is:

(P+ aN^2/V^2)(V-Nb)=NkT, where b is proportional to the size of the molecule (or more precisely to the distance between two molecules when they are pressed against each other).

As b goes up, V-Nb will go down and the pressure will have to go up.

 

[Dasypus]

Okay, I did the math. For one mole in 22.2 L of space (about what the ideal would be), pressure of H2 is 1.01 atm, and pressure of UF6 is 0.986 atm.

This is because while b for H2 is 0.026 and b for UF6 is 0.113, a for H2 is 0.2453 and a for UF6 is 16.01. Thus, at normal-ish volumes, the effect of a is stronger than the effect of b. (To translate, the relatively strong attractions between molecules make more difference than the space that each molecule takes up, given such a large volume.)

If you're interested, for one mole in 1L, pressure of H2 is 22.8 atm, and for UF6 is 9 atm.

 

[milski]

Interesting. From where did you get the a|b values?

 

[Dasypus]

http://www2.ucdsb.on.ca/tiss/stretton/database/van_der_waals_constants.html

 

[chiddler]

can i please have a more layman explanation of what this means, please.

 

[Dasypus]

Um... lemme try? But no promises.

The average kinetic energy of a gas molecule, any gas molecule, is a direct function of temperature. Now, kinetic energy is directly proportional to PV. So at a fixed volume and temperature, the pressure is the same no matter the mass of the gas particles. It doesn't matter what the mass of that gas molecule is, since every increase in impulse as a bigger molecule hits the side of the container is matched (cancelled out) by a decrease in number of hits to the side, because it's moving slower (so as to have the same kinetic energy as a lighter, faster molecule).

So, upshot: the mass of the UF6 isn't what makes a difference in pressure.

What does make a difference? Two things:

a) according to the ideal gas assumptions, the atoms/molecules should have no interaction with each other. This is false for every real gas. The van der Waals equation constant 'a' is a measure of just how bad an assumption it is for a given gas.

b) according to the ideal gas assumptions, the atoms/molecules should take up no space. This, too, is false for every real gas.

At all but the highest pressures/smallest volumes, it is factor 'a' that makes the big difference. This is why, for 22.2 L of space, or 1 L of space, UF6 has a much lower gas pressure than H2: it has far more intermolecular attraction forces.

 

[chiddler]

thanks, then the correlation is not as simple as we initially thought. i suppose we would be given such information were it in a passage.

 

[Dasypus]

I find that staring for a while at graphs like the ones on this page http://www.chem.ufl.edu/~itl/4411/lectures/lec_e.html really helped me. Note that at (relatively) low pressures, PV is *lower* than you'd expect. A corrolary of this is that at a fixed volume, the pressure is lower than you'd expect for an ideal gas, unless you really shrink that volume down.

 

[milski]

Cool, that makes a lot of sense. For some reason I did underestimate the importance of a in the corrected formula.

 

[Tatiana3325]

Another nice thing to note... any mention of UF6 is usually a hint towards comparison of real gasses. This is the compound formed in order to enrich different isotopes of Uranium for nuclear power plants. p-chem classes and mcat prep books love using this molecule for Vrms questions for some reason.

.