66 HYDROGEN ION CONCENTRATION 



we obtain 



[A-] = [U] . , '^^ and [A+] = [U] 



kb 



€^' Vf: 



or 



[A-] = [U] y^^ and [A+] = [U] ^^^^ 



Therefore 



[A-] = [A+] 



In the above derivations it is assumed that the electrically un- 

 charged part of the ampholyte is present in one chemical modifica- 

 tion only. But the following case is also conceivable. The ampho- 

 lyte may exist in two forms, Ai and A2 (such as lactam and lactim 

 forms), so that the cations have only that conJSguration which corre- 

 sponds to Ai and the anions only that which correspond to A2. 



The idea would suggest itself then that in equation (1), page 61, 

 Ui should be substituted for U, and in (2) U2 for U, where Ui is 

 the concentration of the undissociated Ai form and U2 that of the 

 undissociated A2 form. The author stated this idea first^^ and sub- 

 sequently it was developed by Eckweiller, Noyes and Falk.^^ These 

 latter authors modified the equation for the isoelectric point in the 

 manner shown 



= V^ 



J ^,_„ , [A+] [A=] 



[Ai] [A2-] 



in which A and Ai are the two tautomeric modifications of the 

 ampholyte. This newer interpretation is, however, not quite cor- 

 rect. For in our experiments we determined not the equilibrium 

 between the ampholyte ions and of any tautomeric form of the un- 

 charged ampholyte molecule, but only the equilibrium between the 

 ions and the undissociated ampholyte molecules in toto. Or, in 

 other words, our experimentally determined values of ka and kb 



"Michaelis and Davidsohn, Biochem. Zeitschr. 30, 143 (1910); see p. 149, 

 concerning theobromin. 



38 H. Eckweiller, H. M. Noyes and K. G. Falk, Journ. of Gen. Physiol. 3, 

 291 (1921). 



