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[RedKing]

Tried to suss this out by looking at the Wiki entry on partial pressure, but the math is too much to wrap my head around without sitting down and really giving it a go.

So my question is this:

If I have a mixture of gases (say, N₂, O₂, and Ar) and I increase the pressure of that mixture, does the pressure increase proportionally or does it depend on the specific gas? And does the mechanism by which the pressure is increased matter (say, mechanical compression vs. heating)?

Example: Let's say I have 70% N2, 20% O2, 10% Ar, at a total pressure of 1 bar. If I increase that by 10% to 1.1 bar total, is the pressure increase distributed so that the N2 partial pressure increases 0.07 bar, O2 0.02 bar, and Ar 0.01 bar?

And if not, what's the math to figure it out?

[GreatJustice]

IIRC Dalton's law of pressures states that the pressure increase is just added from one gas to the next.

So if Gas 1 has a pressure of 101.3 kPa and Gas 2 has a pressure of 50 kPa, and both make up 50% of the compound, the combined is 151.3 kPa. So yeah, the pressure increases proportionally regardless of element.

[RedKing]

Well, I guess what I'm asking is, are the *changes* distributed proportionally? Because I know that proportion by volume and proportion by pressure aren't necessarily the same thing...I think.

[Sheb]

Well, within good approximation, all those laws holds. If a gas is making up 30% of a mix's volume, it'll make up 30% of the pressure and 30% of the molarity.

Now, for some gas there are small change, due to the fact that you need to correct all those laws (Basically add a factor that account for the atoms size (Laws of perfect gases assume infinitely small atoms) and another for particle itneractions that slightly diminishes pressure. But at normal temperature and pressure, it's no problem.

[RedKing]

Hmm...what about at extremely low pressures and low temperatures? (I'm doing this for some scenarios of terraforming using sulfur hexafluoride)

[Siquo]

(I'm doing this for some scenarios of terraforming using sulfur hexafluoride)

Only on B12.

Well, if you mean what will the pressure be after adding a certain number of Joules, you'd have to calculate the increase in temperature according to the (technical term here for the energy-per-temperature constant per material) for each material and then you'll have the new temperature, and then apply http://en.wikipedia.org/wiki/Charles%27s_law.

I think Source: one year of university physics

[RedKing]

Hrm....wonder if I could work up an equation for that. Trying to figure out an elegant way to chart out the temperature increase in a gaseous mixture as SF₆ is added to the mixture, which would significantly increase the thermal capacity of the atmosphere, which would increase the pressure.

This is why it kinda of sucks not taking any maths in college. And the last hard-science I took was a summer course of Introduction to Earth Science that even the professor told me "Look, you don't need to be here. Just show up for the exams."

So much forgotten since high school....

[GreatJustice]

Well, I did my exam on this a few days ago, though I'm unsure as to useful this is.

Combined gas law is V2 / V1 = T2 / T1 * P1 / P2, so if you're working with volume, temperature, and pressure with set changes, you'd use that.

[10ebbor10]

Well, I did my exam on this a few days ago, though I'm unsure as to useful this is.

Combined gas law is V2 / V1 = T2 / T1 * P1 / P2, so if you're working with volume, temperature, and pressure with set changes, you'd use that.

Problem is that one assumes an ideal gas, which neither of the 3 are. Even worse, they ain't even the same gas, and for this topic the important part is in the discrepancy.

Not sure if I can help. What exactly and why do you need to know?

[Virex]

Hmm...what about at extremely low pressures and low temperatures? (I'm doing this for some scenarios of terraforming using sulfur hexafluoride)

At extremely low temperatures and especially for stuff like SF₆, the ideal gas law no longer holds. Instead you'll need to start working with the virial expansion. Luckily, someone has done the heavy lifting for us and provided us with this paper, which contains a load of information on SF₆. Unfortunately it's behind a paywall, but my uni has a subscription to all of ACS, so I'll get you a copy if you need it.


If you want to know more difficult things I'll happily bring my copy of Atkins' Physical Chemistry, though it's  been years since I've done any intensive thermodynamics.

[Starver]

Somewhere along the line you might want to repeat after me: "P-one V-one over T-one equals P-two V-two over T-two".

Or,

P1.V1		P2.V2
-----	=	-----
T1		T1

(Grrr... inserting [hr]-tags into the middle makes the forum parser insert spurious [table] tags in unexpected places.  And I mean unexpected, because they weren't where I'd expect them to be if it was putting them in on the assumption that an HR was the end of one tagging and the start of another...)

Here P|V|Ts 1 and 2 are the "before" and "after".  You might have to deal with components P_1a, P_1b, etc for the partiality of pressure, but maybe can assume the T_1xs are the same (or at least vary the same, unless you have stratification of both temperature and composition across the sample column of atmosphere), and the respective Vs of course are remarkably similar (again, unless stratification occurs)...  But it allows you scope to add in the new gasses at any temperature you wish (or, more likely, having injected them under pressure[1], 'contribute' a now lower temperature for that proportion of the gas, which combined with the atmosphere you're injecting into means a new combined mean temperature can be applied to each component.


(Ninjaed twice thrice, and I see that GJ has given an alternate form of the above formula.  As to the idealisation, I think there's enough other complications to make non-idealness a minor stumbling block on the way to exactitude.  Assuming I read the problem correctly.)

[1] With it being at a certain temperature under pressure, which becomes less as the volume decreases.  The alternative being releasing them in a massive exothermic reaction, I suppose, in which case you can somewhat work out the net rise in atmospheric temperature.

[Zrk2]

Starver, the second T₁ should be a T₂. Other than that all is good, and holds with what I remember from high school.

[Starver]

Starver, the second T₁ should be a T₂. Other than that all is good, and holds with what I remember from high school.

Yup, sorry, that was obviously a result of my having to 'repair' the table, after the preview (twice!) messed up what I thought was basically sound hand-coded BBCode and changed what came back into the message-editing box...

(Also tried it with underlined top-side, but it just didn't look right, hence the compromise "-----"s.  Anyway, that's off-topic.)

[Leafsnail]

And does the mechanism by which the pressure is increased matter (say, mechanical compression vs. heating)?

The answer to this one is no providing the gas ends up in the same state (same temperature and volume).

I think you can at least approximately use the rule you're suggesting.  I know that sometimes when you mix gases together the total pressure of the two of them reduces or increases (depending on whether the particles attract or repel each other) but that shouldn't matter here since the mixture is staying the same.  The only thing to bear in mind is that gases behave less and less ideally as you go to higher pressures and lower volumes.

[misko27]

Oh wait I was just doing this.
 
That's awesome. I JUST had tests on all the Dalton's law, Charles law, Gay-lussac's law and the like. I neve rthought I'd ever be asked anythign like that again.