QUANTITATIVE RELATIONSHIPS IN HYDROLYSIS 211 



which is known as the Schiitz-Borissoff Rule. The rule only holds good, 

 however, during the earlier stages of the hydrolysis and before about 

 fifty per cent, of the substrate has been hydrolyzed. Arrhenius has 

 found that an exactly similar relationship obtains between the time 

 and the extent of the transformation in the hydrolysis of Ethyl Acetate 

 by ammonia. He accounts for it by the fact that in this instance, and 

 presumably also in pepsin-digests, the catalyzer is bound and inactiv- 

 ated by one of the products of the hydrolysis; thus ammonia combines 

 with the acetic acid which is liberated by the hydrolysis of ethyl acetate, 

 forming ammonium acetate which exerts no catalytic action. 



If we differentiate the above algebraical expression of the Schiitz- 

 Borissoff rule we obtain: 



dx k 2 aF 



= velocity of hydrolysis = 

 dt 2 x 



from which it is evident that the velocity of hydrolysis is inversely 

 proportional to its extent. We can account for this by supposing that 

 the enzyme combines with a product of the hydrolysis to form an 

 inactive compound according to the equation: 



Free enzyme + product = inactive compound 



and that the concentration of enzyme is so small compared with that of 

 the substrate that in the first few moments after digestion has begun 

 the concentration of the inactive compound is nearly equal to the 

 whole of the initial concentration of the enzyme. 1 The trace of free 

 and active enzyme which then remains will be given by: 



initial concentration of enzyme 



Concentration of free enzyme = constant X - 7: 7 1 



concentration of product 



or, expressed algebraically: 



kF 



Concentration of free enzyme = 



The actual velocity of hydrolysis must be proportional to the con- 

 centration of active catalyst and also to the concentration of uncon- 

 sumed substrate; hence we have: 



kF 

 Velocity of hydrolysis = -- k*(a x) 



where "k 1 " is a proportionality-factor which differs in meaning and 

 magnitude from "k." 



1 These conditions obviously do not hold in a mixture of ethyl acetate and ammonia, 

 but the progressive modification of the electrolytic dissociation of the residual ammonia 

 by the ammonium acetate which is formed during the reaction brings about very similar 

 quantitative relationships. The conditions depicted, however, correspond much more 

 closely to those which we may reasonably expect to obtain in a mixture such as that 

 furnished by a pepsin-digest than to those which actually obtain in a mixture of ammonia 

 and ethyl acetate. 



