0.17 Phase equilibrium in solutions  (Page 9/9)

The process by which a pure solvent passes through a semi-permeable membrane into a solution of the same solvent is called “osmosis.” Our task is to develop a model which accounts for osmosis. We once again turn to the concept of dynamic equilibrium.

Before the solute is added and the two flasks contain only pure water, the rate of flow of water from the left to the right must be exactly the same as the rate of flow of water from the right to the left. If this were not true, the water levels would be constantly changing. So, before adding the solute, we start with dynamic equilibrium. Adding the solute disrupts this equilibrium, since the water levels start to change once the solute is added. Since we only add the solute to the flask on the right, the solvent on the left is unchanged and the flow of water from left to right does not change. To account for the net flow of water from left to right, the flow of water from right to left must decrease when we add the solute. This once again sounds familiar. The presence of the solute must inhibit the flow of water through the membrane. Either the solute particles block some of the passages in the membrane, or some of the water molecules are bound up in solvating the solute particles and therefore cannot pass through the membrane. Viewed either way, the solute slows the flow of water from right to left, so there is a net flow of water from left to right. That is why we observe osmosis.

The left flask will always contain pure water in this set-up, since solute never travels from right to left. This would suggest that the osmosis should continue until there is no water remaining in the left flask. But that is not what we observe. Instead, after a while, the net flow stops and dynamic equilibrium is re-established. This is not expected. How can the rate of flow of water from right to left ever rise to meet the rate of flow of water from left to right? The clue to the answer is found by looking at the taller column of water in the neck of the flask on the right. The water piling up in the column on the right generates an extra pressure on the water near the membrane, increasing the rate of flow from right to left. Once the pressure is high enough, the rate of flow from right to left matches the rate of flow from left to right and equilibrium is achieved. The pressure required to achieve equilibrium to counter osmosis is called the “osmotic pressure.” Experimental data show that the osmotic pressure, usually labeled as Π, is proportional to the molarity of the solute in the solution:

Π = MRT

Osmotic pressures can be quite high, several times more than the atmospheric pressure. This means that osmotic pressure can be a significant driving force in nature. For example, a biological cell wall is a semipermeable membrane, permitting the passage of water and some smaller molecules like O ₂ or CO ₂ , but not the passage of larger molecules like proteins. As a result, osmosis is the process by which the roots of plants extract water from the surrounding soil.

Review and discussion questions

1. The observed data in Figure 2 show us that the vapor pressure of the solution is proportional to the fraction of the molecules which are solvent molecules:

   P _vap =P ^* _vap *X _water

   Using dynamic equilibrium arguments, explain why the vapor pressure is proportional to the mole fraction of the solvent.
2. This same equation shows that the vapor pressure of the solution depends on the identity of the solvent, since P vap * depends on what the solvent is. But it does not depend on the identity of the solute. Using dynamic equilibrium arguments, explain both of these facts.
3. For a solution of two volatile liquids, Raoult’s Law works very well in predicting the vapor pressure if the molecules of the two liquids are somewhat similar. For molecules which are quite different, Raoult’s Law is not as accurate. Explain these observations using the dynamic equilibrium model.
4. The vapor above a solution of two volatile liquids is richer in the more volatile liquid than is the solution. Explain why this is true. Devise a way to use this observation to create a liquid solution which is significantly richer in the more volatile component than the original liquid solution.
5. In an old-fashioned homemade ice cream freezer, the ice cream mixture is placed in a container which is immersed in a slurry of ice and water. The slurry itself is contained in an insulated container. NaCl is usually added to the slurry. When the salt is added, the temperature of the slurry is observed to drop significantly by as much as 20 °C. Explain why the temperature drops when the salt is added. Hint: since temperature measures kinetic energy, the temperature drop signals a drop in kinetic energy. Think about where this energy goes.
6. To observe osmotic pressure, we must separate the solutions with a semi-permeable membrane. What would be observed if we were to replace the semi-permeable membrane with a permeable one? How would this affect the dynamic equilibrium?