738 



ACTIVITY COEFFICIENT OF THE HYDROGEN ION 



curve of gelatin (taken from the titration curve for gelatin deter- 

 mined by Loeb), expressed as the per cent of uncombined gelatin 

 present. It is apparent that the two curves are strikingly similar. 

 Both are parallel to the X axis below pH 2 and then rise to a maxi- 

 mum, one at pH 5.0 and one at pH 6.0. Both then drop rapidly 

 and again become parallel to the X axis beyond pH 11.0. This ren- 

 ders it probable that the rate of hydrolysis is some function of the 

 amount of uncombined gelatin present. It will be noted from the 

 table that the value of the "constant" at pH 5.0 (where the gelatin 

 is completely uncombined) is about 200 times that of its value in 

 the range where the gelatin is all present in the form of salt. If we 

 assume then as a first approximation that the uncombined gelatin 



o g 



i 



c 



c 

 ;3 100 



(0 



S. 80 



60 

 40 

 20 





 pH 



1 2 3 4 5 6 7 8 9 10 11 12 13 



Fig. 6. Influence of the hydrogen ion concentration on percentage of uncom- 



elocity 



bined gelatin and on the value of A'l = 



Ch+30Coh 



hydrolyzes 200 times as rapidly as the combined and that the rel- 

 ative efhciency of the H and OH ions remains the same we get for 

 the velocity of the reaction 



Velocity = A'2 (Ch + 30 Coh) (Ccombined + 200 Cfree) (2) 



where Ccombined ^^^ Cfree Tcfer to the concentration of free and 

 combined gelatin as detemiined from the titration curve. The sum 

 of these two quantities is taken as 1. The values for K2 are given 

 in the last column (Table VIII). It is evident that although they 

 can hardly be considered as constant thej^ are very much more so than 

 the values for Ku The rates calculated from (2) are plotted in Fig. 

 5. They may be considered satisfactory as a rough approximation. 



