Does a gas move from a region of high to low pressure according to it's own partial pressure rather than the total gas pressure? I have a plastic bottle that is impermeable to ${\rm CO}_2$ but slightly permeable to $\rm O_2$.
If I fill up the bottle with pure $\rm CO_2$ at $3$ atmospheres and expose it to $\rm O_2$ at $1$ atmosphere, will $\rm O_2$ enter the bottle? My understanding is that gases move from high to low partial pressure independent of other gases. Is this true?
 A: In an ideal case in which particles don't interact, or in the limit of dilute gas, yes. Because the bottle contains no $O_2$ then the gas is more likely to enter the bottle than to leave it (because... there is no $O_2$ inside) so you have a net diffusive flow inside the bottle. That is, until the bottle reaches a (partial) pressure so high that the outgoing flow of $O_2$ (the molecules that was outside, randomly entered the bottle, and now randomly leaves) balances the incoming one.
In a more complex but more general case, where particles interact (either same-gas particles interact with each other or $O_2$ interacting with $CO_2$ (not always the case for these two gases, but for two other gases it could happen) and/or gas particles occupy a volume, then higher order effects might play a role (in the limit, if the bottle has no free space because the $CO_2$ is filling it completely then of course $O_2$ won't enter. But if you put in the numbers you see that for that to happen you need huge amounts of gas).
Imagine you have 100 moles of $CO_2$ in that bottle. Then, if you approximate a $CO_2$ molecule as a sphere of radius $0.15 nm$ then you get that 100 moles completely fill out a 1L bottle, there is literally no "empty" space left. In that case, $O_2$ would not enter - but this is far from ideal/dilute conditions (and would also need a bottle with very strong pressure resistance)!
As a first approximation, you can use a Van der Waals gas model, where particles have an interaction and a volume, and then when the gas is not in dilute conditions anymore, the partial pressure concept fails.
But in the ideal case / dilute case, partial pressure law holds and $O_2$ would diffuse inside the bottle.
A: This is the gaseaous analogue of osmotic pressure with the plastic bottle playing the role of the semipermeable membrane. In equilibrium the ${\rm O}_2$ pressure will be the same within as without, and inside    there will be ${\rm CO}_2$ pressure as well. The total pressure inside will therefore be be higher and may even burst the bottle.
