8: Where does it all end?

So, a quick recap. We can figure out which way water is flowing. Also, using the iteration technique at the end of the section on diffusion through a membrane, we can figure out how much water is flowing at each time step (Δ t).

However, there is still one more property of the system that we can figure out — what happens at the end of that slower and slower process — in other words, what are the equilibrium concentrations, and how much water is on either side of the membrane. We can do this without endlessly pushing buttons on a calculator.

Let’s use sugar as an example. Say we started with 0.2 mole of sugar in 1 litre of water on one side, and 0.8 mole of sugar in 1 litre of water on the other side and the two compartments are the same size. The water is free to move back and forth across the membrane, but the sugar’s not going anywhere, and no extra sugar or water can move in or out of the 2-compartment system. So at the end of the day:

  • there will still be 0.2 mole of sugar on one side and 0.8 on the other side, 
  • there will still be 2 litres of water, and
  • the concentrations on either side will be equal, 
  • but the water will not be equally distributed.

How can you find the final water volumes using intuition?

How can you find the final water levels (W1 and W2) using formal equations? (W1 and W2 are the water volumes on each side of the membrane.)