SD on partial pressures

I tried asking this in this thread, which inspired it. However, it seems to have been soundly ignored there.

In a situation with two different mixtures of gasses with different total pressures separated by a (slightly) permeable membrane, some people are invoking “partial pressures” to argue that the concentrations of gasses will balance out. What I’m wondering is whether partial pressures “really” exist, or are they just statistical artifacts from the probabilities of one gas molecule or another getting through the membrane.

Well, in any situation, gas pressure is just an average of probabilities of individual molecules. I don’t know why that makes it any less ‘real’, though.

I suspect maybe I’m not quite understanding your question, so if you want to go into a little more detail, go ahead.

What do you mean by that? Many-particle systems aren’t amenable to rigorous solution, so you have to look at them statistically. That said, gas molecules interect with one another through a variety of forces. You can’t just treat them as ball bearings in a shaken jar, except as a first approximation. When they start passing through narrow channels in membranes, they interact with the walls.

This doesn’t directly answer your question, but may be illuminating:

A Servelle (sp?) refrigerator, as used in small RVs (the big ones are different) operates at nearly constant total pressure through the entire refrigeration loop. The only pressure change is a few inches of water head pressure in the boiler and adsorber sections.

Refrigeration is accomplished because the partial pressure of the refrigerant (ammonia) varys thoroughout the loop. The remainder of the total pressure is made up by hydrogen.
Hydrogen and ammonia partial pressures are traded back and forth around the loop. Because the total pressure is constant, the loop can be driven entirely by convection and gravity.

In this example, the concept of partial pressure has real, physical, and useful ramifications…it is not simply an artifact of “book keeping” tools used to analyze the situation.

Link, see diagram 101C about midway down page.

A partial pressure is a mathematical artefact in the sense that it can’t be measured independently. It’s a defined quantity:

partial pressure (component A) = (fraction of A in mixture) (total pressure of mixture) – [for an ideal gas]

I can’t stick a probe in a container of mixed gasses and measure the partial pressure of A directly. I can (in theory) measure the concentration of A and the total pressure of the canister, and calculate the partial pressure.

Just because it’s only a calculable quantity doesn’t mean it’s not useful. See also enthalpy, potential energy, entropy, exergy etc.

This sounds like a somewhat philosophical question. Partial pressures have real, measurable effects; does that make them real? They also fall out somewhat naturally from statistical-mechanics treatments of ideal-gas mixtures, so it seems reasonable to consider them as “real” as other somewhat complicated thermodynamic quantities, such as temperature.

But on the other hand (as you suspected), on a microscopic level all that’s going on is detailed balance. Every particle incident on the left side of the barrier has some probability-rate p of diffusing across it to the right side, and every particle incident on the right side has the same probability-rate p of diffusing across it to the left side. (These rates could differ for different species, but the left->right and right->left rates cannot differ without allowing entropy reductions, so that would require an external entropy sink.) So, clearly, the net macroscopic diffusion rate for particles of a given species is proportional to the difference in the rate of particles of that species incident on the barrier from the left side and from the right side: i.e., to the difference in partial pressures.

I didn’t say it wasn’t useful. I don’t hold physical scientists in that low esteem.

What I mean (to answer other posts) is that total pressure is real in the sense that a molecule of one type feels a net push one way or the other. Does it feel any different a push than a molecule of another type?

But partial pressures “really exist” in the same way that total, absolute pressures “really exist.”

For example, suppose you have some total pressure – let’s say 1 psi – of nitrogen on one side of a permeable membrane, and vacuum on the other. The pressure on the membrane is caused by billyuns and billyuns of nitrogen molecules doinking against the membrane, right?

Now, of those billyuns and billyuns of molecules doinking against the membrane, a few of them wriggle their way through to the other side (the membrane being permeable, after all). The number of molecules that wriggle their way through depends on the number of molecules that doink the membrane in the first place. If you double the the pressure to 2 psi, you double the number of molecules doinking the membrane, and double the number of molecules that wriggle their way through. If you halve the the pressure to 0.5 psi, you halve the number of molecules doinking the membrane, and halve the number of molecules that wriggle their way through. Which is a long-winded way of saying permeation scales with pressure, right?

OK, now let’s get fancy. Instead of 1 psi nitrogen, I have 1 psi of a 50/50 mixture of nitrogen and argon. Same pressure, same number of molecules doinking the membrane. However – and here’s the key – there’s only half as many molecules of nitrogen doinking the membrane. Same total pressure as in the first case, but the partial pressure of the nitrogen is only half of what it was. So you would expect only half the number of nitrogen molecules to permeate through the membrane (as well as some argon).

OK, fancier yet. Same membrane, but with 1 psi of a 50/50 mixture of nitrogen and argon on one side and 1 psi of pure nitrogen on the other side. Now there’s the same total pressure on each side, but the partial pressures of nitrogen on each side is different. So you would expect twice as much nitrogen to wriggle through the membrane in one direction as the other, resulting in a net flow of nitrogen from the pure N2 side to the mixture side (as well as a flow af argon in the other direction).

So the permeation scales with the partial pressure, which is simply a measure of how many molecules of a certain type of gas are doinking the membrane, in the same way that total presesure is simply a measure of how many molecules total are doinking the membrane.

Does that answer your question?

Partial pressure is not a statistical anomaly or a philosophical dead end, but a very real thing.

My copy of Umiversity Chemistry by Bruce Mahan says this:

The absolute pressure of the mixture is the sum of the partial pressures in the mixture.

This comes into play every time you take a breath; in your lungs, the partial pressure of oxygen in your blood is lower than it is is the inhaled air, so Oxygen flows through the membranes of the capillaries into the blood. Similarly, the partial pressure of carbon dioxide is greater in the blood, so it is exhaled. Note that this whole process occurs at a constant atmospheric pressure.

Sorry if I ignored your question in the other thread.

So what if I have a membrane that’s permeable to (say) helium, but not permeable to ethane or some other largish gas. On one side, I have 1 atm He, and on the other side 1 atm Et. Will the helium end up diffusing across the membrane to achieve the same partial pressure, even though it results in higher pressure (and thus lower entropy) on one side, when it ends up with 1.5 atm total gas?

Yes. Wacky, eh?

Why do you say that higher pressure=lower entropy?

Hmm, I think I was mistaken here. It does seem now that the total entropy of the system doesn’t decrease in that process. My (limited) memory of high school chem taught me that compressing gases reduces their entropy, as each particle has a smaller area in which it could possibly be found. I think I overextrapolated that just now to “higher pressure=less entropy.”

The misconception here is that pressure will prevent the molecules from passing through the membrane. Remember that pressure is caused by the molecules striking the container they’re in. The atoms will strike the membrane too, but some pass through holes in it (if they’re not too large). The only way they could be pushed back is if there happens to be a molecule right at the other end of the passage through the membrane, but that’s unlikely since gas molecules are very spread out. So you’re going to have molecules passing through the membrane in each direction. It’ll flow faster in one direction if the passable molecules on one side are more dense, but will eventually even out. Any molecules that are too large to fit through can’t really do anything to stop the smaller ones from flowing either way. Hopefully that makes better sense of it.