Total pressure v/s Partial pressure

If I have 2 containers, something like in the diagram. One has gas A, while other has gas B. Both containers have equal volume and at same temp. Then when I remove the corks, and let the gases flow, until when will they flow, and will I finally have a half of Gas A in one container and rest half in the other, and similarly for gas B, or will only one of them flow until total pressure in the 2 containers is same?

In other words, what is the necessary condition for flow of gas - Difference in its partial pressure, or difference in total pressure? • Be careful with tags. Now you can make new ones so you should read about tagging. – Mithoron Jul 31 '16 at 17:16
• Are the number of moles of each gas in each of the two containers initially the same also? – Chet Miller Aug 1 '16 at 1:23
• Sorry I forgot to mention that. Please consider both cases, one when both have same number of moles, other when they don't. – Shodai Aug 1 '16 at 14:24

If the membrane is permeable to both gases, then both gases will become uniformly distributed between the two containers, and the final pressure will be uniform. So, if the initial pressures in the two containers are $p_1$ and $p_2$, the initial number of moles in the two containers are $$n_1=\frac{p_1V}{RT}$$ and $$n_2=\frac{p_2V}{RT}$$ The total number of moles does not change, so the final pressure is $$p=\frac{(n_1+n_2)RT}{2V}=\frac{p_1+p_2}{2}$$The final mole fractions in the combined container are $p_1/(p_1+p_2)$, and $p_2/(p_1+p_2)$. The final partial pressures are $p_1/2$ and $p_2/2$.

• I see, that's what I thought - Both the gases will finally have equal partial pressure and so they'll be symmetrically distributed. Can you please confirm this - Do gases flow if there is a pressure difference overall, or if there is a difference in partial pressure? Please give example if possible, using Semi-permeable membrane or something. – Shodai Aug 2 '16 at 4:12
• Is it possible to have a situation where I have a container, equally divided by a container having an SPM that allows only one gas to pass through, then in equilibrium, will the total pressure across the SPM be equal, or only the partial pressure of one of the gases? In other words, do ideal gases behave independently, as if the other doesn't exist? I believe they do, and then we should be able to superimpose their situations. – Shodai Aug 2 '16 at 8:56
• Regarding your first question post, they will not have equal partial pressures if the initial pressures in the two chambers are not equal. I think what you are missing in your thinking is that the gases can also diffuse into one another. So it is not valid to talk solely about transport as a result of flow; you must also include transport as a result of diffusion. If they are ideal gases, the final state will be the same as if they behaved independently. But, the path to the final state will not be the same. – Chet Miller Aug 2 '16 at 11:34
• Of course you can have situations where there is a semipermeable membrane which allows one gas to pass, but not the other. In the end, the partial pressure of gas that can pass through will be the same in both chambers. – Chet Miller Aug 2 '16 at 11:36

It depends on what you mean by flow - the movement of the gas (as shown by a flag waving in the air) or simply the movement/homogenization of the contents of both inside the chambers.

In the case of visible rushing of gas from one chamber into another, it's the total pressure gradient that matters, in the case of homogenizing contents, it's the partial pressure. Let's explain by example:

If Gas A and Gas B are at equal pressure on the left and right side, if you have a flag in the middle when you remove the obstruction you won't expect it to flap into either side. It would probably stay centered, but you would notice that some of Gas A starts to move towards Gas B's chamber and vice versa. Depending on the temperature and other factors, this may be a fast or slow process.

Now, if Gas A was at a lower pressure at the time of opening (because there was less gas A), you would see the flag flap to indicate that gas B was rushing into Gas A's chamber. The magnitude of the flow being proportional to what the absolute pressure difference was.

A good way to see this is to actually use water with two different colored dyes.

• I see that, but then once gas B has rushed enough to the other side, and then there is equal pressure across the flag, will we still have a dynamic equilibrium with some of gas A going to the right and some more of gas B coming to left, until both have same equal partial pressure on both sides? – Shodai Aug 1 '16 at 14:26
• @Shodai that's right – IT Tsoi Aug 1 '16 at 14:49
• Okay, but if we consider only the beginning, then will we assume neglegible flow of gas A to the other side? – Shodai Aug 1 '16 at 14:51
• Hard to say "negligible" without knowing the exact numbers and how big the hole/passage is but I suppose you could say that since what will be observed on the macro level is Gas B rushing into Gas A's chamber – IT Tsoi Aug 1 '16 at 14:53