# 18.29 Reverse osmosis

The picture above is almost the same as the second picture in post 18.27; a membrane (green) separates water molecules (blue) from a solution of big molecules (red) in water. The big molecules are too big to pass through the pores of the membrane. The only difference between the pictures is that there is now a piston in contact with the solution. If the cross-sectional area of the piston is A, and a force F is applied to the piston, the solution is subjected to a pressure F/A (I am assuming that friction is negligible).

If F/A is less than the osmotic pressure, π, of the solution, water molecules will flow through the pores in the membrane until the solution is diluted to a solution whose osmotic pressure is F/A. The system will then be in equilibrium. All this is explained in post 18.27.

If F/A = π, there will be no flow through the membrane because osmosis cannot occur (post 18.27).

What happens if F/A is greater than π? In other words, what happens when F is greater than πA? The piston moves towards the membrane, because the applied force, F, is greater than the force, πA, exerted by the tendency of water molecules to pass through the membrane (post 18.27). As the piston moves towards the membrane, the volume of liquid on the left-hand side of the membrane decreases. Since the big molecules cannot pass through the pores of the membrane, water molecules must flow out of the solution, from left to right in the picture.

So, when F, is greater than πA, the solution becomes more concentrated and the mass of pure water (on the right-hand side of the membrane) increases – this process is called reverse osmosis. Reverse osmosis is used to recover pure water from solutions – it is often used to produce drinking water from sea water.

If you now know everything you want about “reverse osmosis” – stop reading. If you would like to understand more about how reverse osmosis relates to the concepts of work (post 16.20), entropy (posts 16.35 and 16.38) and free energy (post 18.27) – continue reading.

When F, is less than πA, water flows across the membrane, from right to left, and dilutes the solution. This process is called osmosis and occurs spontaneously to increase the entropy of the system (post 18.27). A spontaneous process is one that occurs naturally with no external influence; in a spontaneous process, the entropy of the system increases (post 16.38). Examples include the flow of heat from hot things to cold things (post 16.35) and diffusion (post 18.26).

If we now increase F to πA, we are doing work on the system. This work pushes water out of solution (from the left-hand side of the picture), through the membrane to its right-hand side. By doing work on the system, we reduce some of its ability to increase its entropy. When F, is greater than πA, we reduce this ability even further.

So, doing work on a system reduces its ability to increase its entropy. Now look at the picture above, copied from post 18.27. Despite the level of water on the left-hand side being higher than on the right, the potential energy of the column of water (in B) is not converted into kinetic energy (no water flows through the membrane) because the free energy of the system is zero (post 18.27). If we push the top of the column down, using a piston, water starts to flow. By pushing the piston down, we are doing work on the system. Since this causes water to flow, we must be increasing the free energy of the system.

If you have continued reading to this point, there are two important points to note:

1. we can reverse the direction of a spontaneous change in a system by doing work on the system.
2. doing work on a system increases its free energy – that part of its internal energy that is free to do work.

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