KINETICS OF HYDROLYSIS 



377 



in which x is the amount transformed after time t, a is the initial 

 quantity of substrate and k is the velocity-constant of the reaction. 

 When integrated this yields the equation : 



log 



a 



a — X 



kt. 



(i) 



In the derivation of this equation it is to be noted that the 

 velocity of the reverse reaction is regarded as being negligible, 

 so that no station of equilibrium is reached until the transfor- 

 mation is practically complete. This condition is tolerably well 

 fulfilled in the reaction under consideration, for the hydrolysis 

 of the polypeptid does not cease until the quantity of unde- 

 composed polypeptid is practically unappreciable. In the fol- 

 lowing table are given the values of the constant k for the 

 hydrolysis of d-alanyl-d-alanin by liver extract at 37 degrees 

 calculated by Abderhalden and Michaelis from the experimental 

 values oi a — X and t obtained by Abderhalden and Koelker. 

 In every case the initial concentration of the dipeptid was such 

 that 1.45 grams of the substance were dissolved in 6 cc. of the 

 digest. 



It is evident that, within the experimental error, k calculated from 

 formula (i) is tolerably constant for the higher concentrations of 

 ferment solution (6 cc. of ferment solution); for lower ferment- 

 concentrations, however, the value of k does not even approxi- 

 mate to constancy, but rises markedly as hydrolysis proceeds; 

 in other words the velocity of the transformation does not fall 



