# How can semi-permeable membrane be so smart?

According to the definition, a semi-permeable membrane is a membrane that allows only solvent molecules to pass through it; solute molecules are blocked. Solvent molecules flow from the membrane side that has low solute concentration (i.e. high solvent concentration) to high solute concentration (i.e. low solvent concentration).

Lets take a case:

1. I take oil as a solvent in one side and water as a solvent in other side. I take the same solute in both sides.
2. Initially, the water side is filled to height $h$ and the oil side to height $2h$. The amount of solute is same in both the sides. So the solute concentration is more in water than in the oil. Accordingly, oil will flow from the oil side to water side. Now, I add more water on the water side to reduce the solute concentration on the oil side. Accordingly, water should now flow towards the oil side.

So what will happen? Will this happen? What makes the semi-permeable membrane so smart or intelligent?

• Water and oil? Do you understand how solubilities work? – Mithoron Feb 13 '16 at 15:38
• @Mithoron I know water and oil are immiscible.. If that was what you meant... I was just trying to give an example .. Please correct or edit my question if you can to explain it better :) – brainst Feb 13 '16 at 17:16

Most of the time what you say about semi-permeable membranes is correct.

a semi-permeable membrane is a membrane that allows only solvent molecules to pass between the membrane; solute molecules are blocked. Solvent molecules flow from the membrane side that has from low solute concentration (i.e. high solvent concentration) to high solute concentration (i.e. low solvent concentration).

However, you have to keep in mind several assumptions that are inherent in the definition as you have given it. The most important of these is that thermodynamic activity differences in the membrane-permeable solvents determine the membrane behavior. When phases are immiscible, such as the water/oil system in your example, it is essential to think in terms of activities, not in terms of concentration.

I take oil as a solvent in one side and water as a solvent in other side. I take the same solute in both sides.

So we are imagining a solute that can be dissolved by both water and by oil. What do we know about the solubility of the solute in these two solvents? What is the partition coefficient? And what can we say about the thermodynamic activity difference across the membrane for the three species? Let's go step by step:

1. Water. Water is not soluble in oil to an appreciable degree. In equilibrated phases, the thermodynamic activity of each chemical species is the same in each phase. Therefore in an oil-water mixture, the thermodynamic activity of water in the aqueous phase is the same as the thermodynamic activity of water in the oil phase. The extremely low solubility of water in oil means that if there were to be a difference in thermodynamic activities across the membrane, only a few molecules would need to cross over for the condition of equal water activities to be satisfied.

2. Oil. Oil is not soluble in water to any appreciable agree. Therefore the same argument applies.

3. Solute. The solute could have a different concentration on each side of the membrane, but because we don't know the partition coefficient, we don't know what the equilibrium state is. Suppose the solute were membrane permeable. Even if it was twice as concentrated in water than in oil, if it's partition coefficient favored an equilibrium where the oil-to-water concentration ratio was 10, then it would flow from the water to the oil. But, in your example the solute is not permeable to the membrane.

Initially, the water side is filled to height $h$ and the oil side to height $2h$. The amount of solute is same in both the sides. So the solute concentration is more in water than in the oil.

Now hopefully the discussion above makes you realize that there aren't many chemiosmotic forces in your example. The only driving force left is hydrostatic pressure. So the oil will cross the membrane, not the water, just because of hydrostatic pressure differences. This is regardless of the solute concentration.

Now, I add more water on the water side to reduce the solute concentration on the oil side. Accordingly, water should now flow towards the oil side.

Well adding more water raises the height $h$ to some higher height and thus increases the hydrostatic pressure. So the increased pressure forces water back through the membrane.

A semi-permeable membrane is not ‘smart’. If you wish, it is actually rather dumb. All it can do is perform a simple selection of ‘I’m letting you through’ versus ‘I’m not letting you through.’ Most membranes will work along the lines of size, polarisability or both.

Size is easily explained: The membrane’s pores have a certain size and what is larger than that cannot diffuse through. Most classical solvents are rather small molecules — water molecules are very small. So it is easy to conceive a membrane that can let water through but has pores too small for large biomolecules or maybe even ions. Remember that dissolved ions are usually surrounded by a solvation sphere, so their size is substantially larger that it may look.

Polarisability is also a rather simple concept but it requires a certain structure of the membrane. The membrane could, for example, consist of a very hydrophobic surface. In that case, ions would likely not want to go near it. It’s a little bit harder to explain, but it may also allow the solvent molecules to go through while the solutes cannot.

Of course, as I said, the membrane is dumb and cannot distinguish solvent from solute. Say you had one that can let water through but not glycerin; maybe due to glycerin’s size. And say you have a $1~\%$ solution of water in glycerin, so $1~\mathrm{g}$ water in $99~\mathrm{g}$ glycerin. The latter is clearly the solvent. However, the membrane would still only let water pass since it is ‘dumb’.

‘Smart’ and ‘dumb’ are bad words altogether, though, since this all is based on physical properties which have nothing to do with smartness (even though smart is a rather frequent keyword in many scientific papers).

Semi-permeable membranes such as cell membranes use active transport to move things AGAINST a concentration gradient (Or through a membrane that would otherwise be impermeable), using energy to do so. You are right, for many materials, things simply balance out like your example. However, in active transport, only some materials are taken in. Here's an article about active transport: https://en.wikipedia.org/wiki/Active_transport