KINETICS OF HYDROLYSIS 381 



According to Henri, the velocity of hydrolysis might con- 

 ceivably be directly proportional to the mass of the ferment- 

 substrate compound (= Fg) or to the mass of the free ferment 

 and that of the substrate. In the former case we obtain: 



dx _ kmF {a — x) . . 



dt 1 + m (a — x) + nx ' 



in which k is the velocity-constant of the reaction. In the latter 

 case we have: 



dx kF (a — x) 



dt 1 -\- m (a — x) -\- nx 



(xi) 



Obviously both equations are identical in form; the former 

 when integrated, leads to the equation : 



(1 + no) log \- (m — n)x = kzt, (xii) 



(J/ wC 



in which k^ is a constant which is directly proportional to the 

 total concentration of ferment, and n and m are independent 

 of the mass of ferment or substrate, but are obviously dependent 

 upon the temperature and the conditions (reaction, etc.) of the 

 experiment. Putting 



m — n _ 

 1 + na~ ^' 



we obviously regain the equation of Abderhalden and Michaelis. 

 The condition that m and n should be independent of the mass 

 of ferment, however, is obviously not fulfilled by Abderhalden 

 and Michaelis' results, since e varies notably with the concen- 

 tration of the ferment; while ks does not approximate to direct 

 proportionality to the mass of ferment. 



In the derivation of Henri's equation it will be evident that 

 many simplifying assumptions are made which are not justified 

 by anything save the fact that they afford the simplest con- 

 ception of the relations. Thus it is assumed that the active 

 mass of the ferment in so far as hydrolysis is concerned is directly 

 proportional to its actual mass, that one molecule of ferment 

 reacts with one molecule of substrate, that one molecule of fer- 

 ment reacts with one molecule of the products of hydrolysis, 

 that the concentration of the ferment-substrate compound is 



