204 



For thermodynamical reasons, it was known that the product 

 of the concentration of the diffusible ions of a pair on one side of 

 the membrane equals the product of these same ions on the other 

 side, or 



[Na+]2 X [Cl-]2 = [Na+]i X [Clii 



(Brackets signify molar concentrations.) This equation expresses 

 mathematically the equilibrium that bears Donnan's name. 

 The law was known (it is the basis of much modern physical 

 chemistry) ; Donnan applied it to the situation involving a mem- 

 brane. Were the membrane permeable to all ions, the law of 

 diffusion would demand that the sum of the ions on the one side 

 of the membrane should equal thai on the other, but this cannot 

 be true because of the inability of the large albumin ion to pene- 

 trate the membrane. There are thus set up two forces, or pres- 

 sures, opposing each other— osmotic, demanding equal sums of 

 ions; and electrical, demanding equal products of ions, on the 

 two sides of the membrane. Obviously, equal sums and equal 

 products cannot exist simultaneously. Donnan assumed that at 

 equilibrium electrical forces dominate when [Na]i+ > [Na]2+ and 

 [Cl]r > [Cl]2~. That this is actually the case may not neces- 

 sarily (experimentally) be true; for example, were sugar added 

 to one side of the membrane, the osmotic pressure thus intro- 

 duced would certainly overcome the electrical pressure and 

 change the ratio of the concentrations on the two sides of the 

 membrane. In any case, there is, at equilibrium, a balance 

 between osmotic and electrical forces, which presumably leaves 

 an excess osmotic pressure on one side of the membrane. 



If instead of a membrane separating an albumin solution from a 

 salt solution, a block of gelatin is immersed in a salt solution, 

 the same conditions exist, except that the force of cohesion 

 between the gelatin ions of the sohd block is substituted for the 

 membrane. The osmotic pressure developed causes swelling of 

 the gelatin. According to Proctor and Wilson gelatin immersed 

 in hydrochloric acid forms gelatin chloride, which ionizes into 

 gelatin cations and chlorine anions. (The situation is the same as 



