124 THEORY OF COLLOIDAL BEHAVIOR 



the following equation, which was used by Procter and Wilson 

 for the distribution of free HC1 between a jelly of solid gelatin 

 chloride and surrounding water, but which holds also for the 

 case where the gelatin chloride is in solution and separated from 

 the outside solution by a collodion membrane impermeable for 

 gelatin ions, 



x 2 = y(y + z) (1) 



where x is the concentration of H and Cl ions in the outside 

 solution, y the concentration of the H and Cl ions of the free 

 acid inside the gelatin solution, and .z the concentration of the 

 Cl ions in combination with the gelatin. (For the sake of 

 simplification complete electrolytic dissociation of HC1 and 

 gelatin chloride is assumed.) Since all the quantities in Equa- 

 tion (1) are positive, the concentration x of the hydrogen ions 

 in the outside solution must be greater than the concentration y 

 of the hydrogen ions in the inside solution; and the total con- 

 centration of the chlorine ions in the inside solution, y + z, 

 must be greater than the concentration of the Cl ions in the out- 

 side solution, x. This difference in the distribution of the 

 crystalloidal ions on the opposite sides of the membrane is 

 caused by the fact that one type of ions (the protein ions) cannot 

 diffuse through the membrane. 



We now come to the most important point for the foundation 

 of the theory of colloidal behavior. If it is true that the Donnan 

 equilibrium is the cause of the P.D. between a gelatin chloride 

 solution and the outside solution, the Donnan equilibrium is 

 likely to be also the cause of the influence of the mysterious 

 influence of electrolytes on the other properties of proteins, since 

 the curves for P.D. are similar to the curves of osmotic pressure, 

 viscosity, and swelling. In order to prove that the P.D. is due 

 to the Donnan equilibrium, we must be able to show that the 

 unequal distribution of the H and Cl ions on the opposite sides 

 of the collodion membrane allows us to account quantitatively 

 for the P.D. on the basis of Nernst's well known logarithmic 

 formula for concentration cells. 



We have seen in Chap. IV that we can determine the con- 

 centration of the Cl ions of the gelatin chloride solution by titra- 

 tion; and we can, of course, also determine the Cl of the outside 

 watery solution by titration. Let x be the concentration of Cl 



