OSMOSIS and ESCAPING TENDENCY
by
Gary L. Bertrand
Professor Emeritus of Chemistry
Missouri University of Science and Technology
   The two cells to the right each contain a pure solvent (blue color) in the outer compartment and the solvent with a non-volatile solute (red color) in the inner compartment.  The white area in the compartments represents a vapor space which initially contains air  and solvent vapor.  The cells are designed with a stopper which allows a glass tube to be lowered from the outside to join the inner tube, which will prevent movement between the vapor in the inner and outer compartments.
   The inner compartment of the cell on the right is sealed (black area) so that there is no contact between the liquids in the inner and outer compartments.  The cell on the left has a semi-permeable membrane separating the inner and outer compartments, so that the solvent can move between the compartments but the solute cannot.

  Both cells are cooled and attached to a vacuum to remove the air that is dissolved in the liquids and from the vapor spaces.  The glass tubes at the top of the cells are sealed, and the tube on the left is lowered to mate with the inner compartment of the cell on the right, as is shown below.  The cells are then allowed to come to room temperature.  The levels of the liquids may change during this process, but that will not affect the final result.
   A situation has been created in which the solvent in the cell on the left is free to move between the inner and outer compartments through the semi-permeable membrane.  In the cell on the right, the solvent is free to move between the compartments through the vapor space.

   The solute is not free to move in either cell.

   In both cells, the solvent is free to move between the compartments in either direction.  The arrows indicate that the net effect in both cases is from the pure solvent in the outer compartment to the solution in the inner compartment.
   In most cases, movement of solvent through the membrane (osmosis) will be more rapid than movement through the vapor space (distillation), but the rates depend on the porosity of the membrane and the vapor pressure of the solvent.


NOTE:  If the air has not been removed from the cell on the left, the pressure inside the inner tube will build up as the liquid rises.  This will slow down the osmotic flow such that the liquid in the inner compartment will at some point rise higher in the right cell than  in the left.  However, eventually the air in the inner compartment will diffuse through the liquids and the membrane to equalize the pressure in the two compartments, and the inner liquid on the left will rise to the same level as on the right.
   After sufficient time, the result will be identical in both cells:  the difference in liquid levels will be the same in each cell, and the concentration of solute will be the same in the inner compartments of the two cells. This is the state of equilibrium in which the solvent molecules are still free to move between the two compartments.  However, the forward and reverse movements are occurring at the same rate so that there is no net change in the situation.

    The difference in height of the liquids in the inner and outer compartments is a measure of the osmotic pressure of the solution in the inner compartment.  The movement of solvent can be reversed in the cell on the left by applying pressure on the inner compartment.

    The osmotic pressure is defined as the pressure difference between the solvent and the solution which will prevent solvent from entering the solute compartment.  There are commercial instruments for this type of measurement.  

     In this example, the solute is confined to the liquid in the inner compartment by barriers: the impermeable seal  on the right, the semi-permeable membrane on the left, and by the vapor space in both cases.  It cannot escape from the liquid phase in the inner compartment.

    On the other hand, the solvent is free to move between the two liquid phases and the vapor phase(s).  At the start of  the experiment, the solvent "escapes" from the outer compartment (pure liquid state) more rapidly than from the inner compartment where it is less concentrated.    However, the rise of liquid in the inner compartments has two effects: (1)  the concentration of solvent in the solution increases, speeding up the escape from the inner compartment; and (2) the higher inner liquid level exerts a greater pressure on the liquid at the membrane, further speeding up the escape there.  

    The process continues until the solvent molecules in the inner compartment has the same escape rate as the solvent molecules in the outer compartment, and equilibrium is established.


 
  Some of my students have questioned this description of the "distillation process" in the cell on the right, since the system comes to equilibrium with a finite concentration of solute, such that the partial pressure of the solvent must be less at the top of the inner column than the vapor pressure of the pure solvent in the outer compartment.   This is true because the pure solvent is at a lower level than the liquid at the top of the inner compartment, and the pressure of a gas decreases with altitude by the barometric pressure law.

    In any chemical system, every component has a tendency to escape.
  The "escape" may be from one physical phase to another, or from one chemical form to another (a chemical reaction) in the same phase or a different phase.  However, there may be barriers on both the microscopic and macroscopic levels which prevent that escape.  The tendency to escape increases with concentration and pressure.  Temperature also has an effect, but that effect is more complicated.  In thermodynamics, the tendency to escape has been given the name fugacity (derived from the Latin for "fleetness").

    The concept of "escaping tendency" is very important in the application of Thermodynamics to chemical systems.  Osmosis and the lowering of vapor pressure of a solvent by the presence of a solute are two of the simplest situations for this application.  These are two of the colligative properties of a solvent, which depend only on the concentration of solute particles (molecules, ions, etc.) in dilute solutions, and not on the chemical nature of the solute.  Other colligative properties include freezing point depression and boiling point elevation.