I04 OSMOSIS AND OSMOTIC PRESSURE 



substance is i.86° C, and the theoretical osmotic pressure of such a solution 

 is 22.4 atmos., an equation relating freezing point depressions and osmotic 

 pressures is easily derived. If we let A represent the freezing point depression 

 of a solution, its osmotic pressure (O.P.) may be calculated as follows: 



O.P. : 22.4 = A : 1.86 

 1.86 O.P. = 22.4 A 



O.P. = 12.04 A ^ 



For example, a solution for which the determined freezing point depres- 

 sion is 0.930 would have an osmotic pressure of i i.io atmos. ( 12.04 X O.930). 

 This equation appears to be approximately correct over a wide range of con- 

 centrations since deviations from the theoretical osmotic pressures of solutions 

 are accompanied by almost strictly proportional deviations from their theo- 

 retical freezing point depression values. This method is often called the 

 cryoscopic method of determining osmotic pressures. The osmotic pressures 

 as determined by this method are as at the freezing point temperature of the 

 solution. 



Electro-osmosis. — Under certain conditions pure water will diffuse from 

 one side of a membrane to the other under the influence of a difference of 



GLASS WALL -x 



Fig. 21. Diagram to illustrate electro-osmosis. 



electrical potential, a process which is called elcctro-ostnosis. When water 

 is confined in a capillary glass tube adsorption of OH~ (or HCOs") ions 

 imparts a negative charge to the walls of the tube . Adjoining them is a layer 

 of H+ ions equal in number to the adsorbed anions. In other words ions 

 become distributed as an electrical double layer just as they do around a col- 

 loidal particle (Fig. 21). 



If a difference of electrical potential is present between the two ends 

 of the tube, water will travel towards the negative electrode. The anions 

 are firmly adsorbed by the walls of the tube and cannot move. The hydrogen 

 ions, however, are free to move and migrate toward the cathode carrying the 

 water, of which they are a part, along with them. In other words the moving 



* A slightly more accurate form of this equation has been derived by Lewis 

 (1908). The tables of Harris and Gortner (iQH. 191 5), based on the Lewis 

 equation, are very useful for converting freezing point depressions Into osmotic 

 pressures. 



