## Osmosis

Osmosis is a critical phenomena related to the movement of solvent across semi-permeable membranes. A semi-permeable membrane is one through which solvent molecules can pass, but solute molecules cannot. This may seem like a very odd material (and in some ways it is), but biological cells are composed of such membranes. Thus the importance of osmosis in biology, as it has a strong effect on how solvent is shuttled in and out of cells.

First, what is osmosis? Osmosis is the spontaneous movement of solvent through a semi-permeable membrane. It occurs when two solutions of different concentrations are separated by such a membrane. Remember, the free energy of a solution depends on its concentration. Higher concentration solutions have lower free energy. That is higher concentration solution are thermodynamically more stable. When two solutions of different concentrations are placed on opposite sides of a membrane, there is a free energy difference between the two sides. As a result, the solvent will move in such a way as to lower its free energy. This means it will pass through the membrane from the low concentration side to the higher concentration side. This movement of solvent is called osomsis. The solvent is said to "osmose". The osmosis will continue until both side of the membrane have the same concentration (same free energy). This is the equilibrium state. Take the example shown below.

A tube has a semi-permeable membrane at the center with two solutions on either side. The solution on the left has a higher concentration than the one on the right. Thus the solvent will move from the righthand side to the lefthand side to get to the solution of lower free energy. This will lead to a dilution of the solution that was initially more concentrated and a concentration of the solution that was initially more dilute. The flow will continue until the two sides are equal in free energy. The movement of solvent from one side to the other, will lead to a height difference between the two sides. This height can be converted into a pressure. The pressure is given as

$\Pi = \rho g h$

Where Π is the pressure and is related to the density of the solution, $$\rho$$, the acceleration due to gravity, $$g$$, and the height of the solution, $$h$$. It is important to take care with units with this formula. In general, it is best to use densities in kg m-3, g = 9.8 m s-2, and heights in meters. This will yield pressures in Pascals. This pressure is also related to the concentration difference between the two solutions. It is given as

$\Pi = iMRT$

Where again Π is the osmostic pressure, M is the difference in concentration of the solutions, R is the ideal gas constant, and T is the temperature is in Kelvin. Again, units are critical. If the concentration is in molarity (moles per liter), then using R in L-atm will give pressures in atm. Remember the concentration that matters is the total concentration of all solutes. Any ions that dissociate you need to account for the van't Hoff factor, i. If you are calculating the "osmotic pressure" of a solution. It is assumed this is a comparison to a pure solvent. Thus the difference in concentration is simply the concentration of the solution.

Unlike boiling point elevation and freezing point depression, the effects of osmosis can be large. For a 1 M NaCl solution the osmotic pressure is 48.9 atm (i = 2, Π = iMRT = (2)(1 mol L-1)(0.08206 L-atm K-1 mol-1)(298 K) = 48.9 atm. This is a substantial pressure.

Another way to think about the osmotic pressure is that it is the pressure that needs to be applied to stop the osmotic flow. This leads to another important concept: reverse osmosis. This the non-spontaneous transport of the solvent through the semipermeable membrane from concentrated solutions to dilute. This is a process that can be used to purify water. How can the solvent flow be reversed? By greatly increasing the free energy of the concentrated solution by adding pressure. Applying a pressure equal to the osmotic pressure will stop the osmosis. Applying a pressure greater than the osmotic pressure will reverse the osmosis. As we apply pressure to the concentrated side, the solvent will flow the other direction through the membrane resulting in pure solvent. One challenge with reverse osmosis is that as you produce pure solvent, the solution gets more and more concentrated. The means the osmotic pressure is increasing and a ever higher pressure is required to continue the process. A major problem with reverse osmosis for water purification is that the membranes can burst at such high applied pressures.

A couple of other thoughts. You might wonder how it is possible to construct a semi-permeable membrane that can pass the solvent but not solute. In general these are simply barriers with very small holes. If the solvent is small and the solute is big, the semi-permeable membrane acts essentially as a filter. But how does the membrane work when the solvent is water and the solute is an ion like Na+? Isn't Na+ much smaller than a water molecule? Yes and no. A Na+ in the gas phase is much smaller than a water molecule. But we are looking at a Na+ in solution. More correctly we are interested in Na+(aq). In aqueous solution, the Na+ is strongly interacting with a number of water molecules. Thus it is not smaller than a water molecule, but instead it is the size of 6-8 water molecules. Now we can construct a barrier that will let the water pass and hold back the ions. In addition, the ions are charged and the water is neutral. Thus we have additional means of "filtering" out the solute.

Finally, osmosis is very important for biological cells. If we place cells into solutions in which the concentration of the solution outside the cell is much lower than inside the cell, water will spontaneously move through the cell membrane into the higher concentration inside. If the concentration difference is sufficiently high this process will continue until the cell wall burst. Conversely, if we place the cells into a solution in which the concentration outside the cell is higher than inside, the water in the cells will spontaneous move out of the cells into the outer solution. This will effectively remove water from the cells. But if we ensure the concentration inside and outside is identical, then there will be no free energy difference between the inside and the outside and the rate or water leaving the cell will be identical to the rate of water entering the cell. These three conditions are depicted below. When the outer solution has a higher concentration than inside the cell, called hypertonic, the cells shrivel. When the concentration outside is lower than inside, called hypotonic, the water moves in and the cells burst. When the concentrations are the same, isotonic, the cells free exchange water with the solution without resulting in a concentration change.

Osmotic Pressure