# A Gas diffusion through a semi permeable membrane

1. Jun 20, 2017

### Zamw

Say I have a small solid polymer container filled with gas A. The walls of the container are semi-permeable, so gas A on inside can't get through/out. On the outside, gas B at atmospheric pressure, which can migrate through the membranes of container. Pressure inside the container is 0,6 bar. Will gas diffusion of gas B from the outside to the inside bring the container up to 1,6 bar? Is the driving "force" here the partial pressure difference of gas B in- and outside or will gas B migrate inwards untill total pressure inside equals the total pressure outside and stop at 1 bar? And what if the solid container exerts a counter pressure because it wants to go back to its original state?

Last edited: Jun 20, 2017
2. Jun 20, 2017

From what I could find (in a google) on osmotic pressure, it would suggest that the equilibrium point would be one atmosphere of any gas on either side of the membrane. However, from what I know about diffusion and Fick's law, the flow would continue until the pressure of gas B was one atmosphere on both sides. It's an interesting question, and I think the correct answer is the one atmosphere of gas B answer. $\\$ In the case of osmotic pressure, I think the analysis there might not apply because it is working with the flow of liquids, and the conclusion is that there is no liquid flow when hydrostatic equilibrium is achieved by balancing the osmotic pressure.

Last edited: Jun 20, 2017
3. Jun 21, 2017

### Zamw

So that would mean if I blew a balloon with helium and left it for a period of time, the balloon would start swelling because of the O2 and N2 migrating inwards?

4. Jun 21, 2017

No it would shrink because the helium is a smaller atom and is likely to be get through the barrier more easily than the $N_2$ and $O_2$. You would also find if you did a very careful analysis of the gas about a week later that some $N_2$ and $O_2$ would get into the balloon. $\\$ One thing to remember with this diffusion is that it can be a very slow process=the computation determines the equilibrium condition, but it doesn't compute how long it might take for that state to be achieved. In the case of the helium, most of the helium has diffused out of the balloon long before the $N_2$ and $O_2$ pressure becomes appreciable inside. For the helium case, the more interesting experiment would be to fill a balloon with $O_2$ and $N_2$ and have it inside a container of helium, and see how quickly the helium gets into the balloon, especially if you used a thinner type of balloon that allowed the diffusion process to occur more quickly.

Last edited: Jun 21, 2017
5. Jun 22, 2017

### Zamw

So even if the pressure of the balloon and the atmosphere in the helium room are at 1 bar, the helium would continue to migrate in until the partial helium pressure is equalized? Doesn't the total pressure in the balloon, rising above the room pressure, prevent this from actually happening? Helium particels will still colide with O2 and N2 particels and diffuse outwards as fast as inwards?

6. Jun 22, 2017

The rate of diffusion is determined by the difference in the particle densities (or partial pressures) of a specific type on both sides of the membrane. In the case of helium, it is likely to have a higher diffusion constant then nitrogen or oxygen. You could write a simplified diffusion equation : $\frac{dN_{in}}{dt}=DA(P_{out}-P_{in})$ where $D$ is the diffusion constant for a particular gas for the membrane material that is being used, $A$ is the area of the interface, and $PV=NkT$ is how the number of atoms $N$ relates to $P$. From this, you can see that equilibrium will be achieved when $P_{out}=P_{in}$. ($P$ here is the partial pressure for the specific gas.) The unknown here though is the diffusion constant $D$. If it is very small, it could take a long time to reach the equilibrium state=the diffusion process could be very slow. It could also be much different for nitrogen and oxygen than for helium.