H. ECKWEILER, H. M. NOYES, AND K. G. FALK 305 



of an electric current has been used to determine the isoelectric points 

 of a number of proteins and other complex bodies.^''' ^^ 



The equation for calculating the isoelectric point of an amphoteric 

 electrolyte 



V 



kb 



was deduced by Michaelis and Mostynski.^^ Their deduction does 

 not appear to be altogether clear in so far as the assumptions involved 

 are concerned. The following deduction brings out perhaps more sat- 

 isfactorily these assumptions. It includes the view that the concen- 

 tration of the unionized molecule in each case is given by the total 

 number of molecules, not separate molecular species as indicated 

 above. 



ha (HAOH) = (H+) (AOH-) 



h (HAOH) = (0H-) (HA+) 



ka _ (H+)(AOH-) 

 h ~ (OH-)(HA+) 



^ (H+)' ^ (AOH-) 

 K ' (HA+) 



If 



(AOH-) = (HA+) 



(H+)=J^ (1) 



This derivation assumes the equalities of (HAOH) in the two ioniza- 

 tion equations and of (AOH~) and (HA+). In the Michaelis and 

 Mostynski original deduction, the assumptions were stated to be the 

 equality of the complex anion and cation concentrations and a mini- 

 mum total ionization of the ampholyte. 



The following deduction involves the view of different molecular 

 species ionizing as acid and as basic salts. 



"Hardy, W. B., /. Physiol, 1898, xxiv, 288. Cohn, Gross, and Johnson," 

 p. 149. 



23 Michaelis, L., and Mostynski, B., Biochem. Z., 1910, xxiv, 79. 



