130 THEORY OF COLLOIDAL BEHAVIOR 



the hydrogen ion concentration. This is the characteristic pH 

 effect already discussed in connection with viscosity, osmotic 

 pressure, etc. Pauli explained this behavior of the viscosity 

 curves on the basis of ionization and hy drat ion. The hydration 

 can have no connection with the P.D., but the ionization un- 

 questionably has. Pauli assumes that the viscosity rises with 

 increasing ionization of a protein salt and explains the maximum 

 and drop by the repression of ionization of the protein salt by the 

 anion of the acid added. This latter explanation is plainly 

 inadequate in our case, since it would mean that the electrolytic 

 dissociation of gelatin chloride is markedly diminished by a 

 N/10,000 HC1 solution. We can show that the Donnan theory 

 accounts mathematically for the influence of pH on the P.D. of 

 gelatin chloride solutions as expressed in Fig. 41. 



Donnan had arrived at his equilibrium equation on the basis 

 of thermodynamical considerations, but Proctor and Wilson 

 have pointed out 1 that it can be derived more simply from the 

 ordinary laws of ionization, 



"since the nonionized portion of hydrochloric acid which, although small, 

 must exist takes no direct part in the equilibrium and must be equal in 

 both places. " 



Hence when a solution of gelatin chloride is separated by a 

 collodion membrane from a solution of HC1 (without gelatin), 

 if x is the concentration of H and Cl ions in the outside solu- 

 tion and [HC1] the concentration of non-ionized HC1, 



x 2 = K [HC1] 



If y is the concentration of hydrogen ions inside the solution, 

 y is the corresponding concentration of Cl ions; and if z is the 

 concentration of Cl ions in combination with gelatin 



y(y + z) = K [HC1] 

 hence 



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



x = V y(y + z) 



PROCTER, H. R., and WILSON, J. A., J. Chem. Soc., vol. 109, p. 309, 1916. 



