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Imagine a container containing a solution with a solute, X, evenly distributed within it. Say we could engineer a membrane to split the container that only allows particles of X from say, left to right; would the concentration of X on right side of the membrane increase beyond the left side?

From a thermodynamic perspective, it seems pretty certain that this would not happen because the entropy of the system would reduce if a net movement of X to one side of the container occurs; and there is no energy input that would explain this.

But from the perspective of the particles themselves, this doesn't really make sense (to me anyways). If particles move according to Brownian motion, then surely particles of X on the left side would randomly collide into our membrane and pass through to the right side; whereas on the right particles of X cannot pass through to the left side. How do individual particles of X 'know' (forgive the personification!) that moving from left to right is thermodynamically unfavourable? Is there some other mediating factor that stops particles of X moving through the membrane at all?

Just to clear up a few things:

I realise that if there was a net movement of X to the right then an osmotic pressure would also build up. Let's say that either the membrane we make is highly compliant or is permeable to water so this is not an issue.

My other suspicion was that making a unidirectional membrane like this is impossible; but as far as I can tell they already exist in nature - carrier proteins that are used to transport solutes down concentration gradients are unidirectional (atleast from what I know; if this is a misconception please tell).

Sorry if this question has already been asked in some other form, I suspect it probably has been but in rather mathematical language which would have gone over my head; I don't have much of a physics/maths background!

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    $\begingroup$ Sounds like you're basically describing a "Maxwell's Demon". Have you looked up information on that? For example, pitt.edu/~jdnorton/Goodies/exorcism_phase_vol/… $\endgroup$ – Samuel Weir Apr 19 '18 at 19:53
  • $\begingroup$ @Samuel thank you, that page really clears things up:) $\endgroup$ – ogu01 Apr 22 '18 at 14:35
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My other suspicion was that making a unidirectional membrane like this is impossible; but as far as I can tell they already exist in nature - carrier proteins that are used to transport solutes down concentration gradients are unidirectional (atleast from what I know; if this is a misconception please tell).

Making a passive transporter that does this would be impossible. You'd be able to extract energy from the concentration gradient that it created.

But membranes like your example are possible, they simply use active transport mechanisms. Protein pumps can create concentration gradients, but consume energy to do so.

https://en.wikipedia.org/wiki/Active_transport

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