446 CHEMICAL DYNAMICS 



measured from left to right were great compared with that of 

 either of the reactions (A) and (B) measured from right to left, 

 and provided, also, the quantity of enzyme combined at any 

 instant with the substrate were unappreciable we would obtain, 

 for the kinetics of the reaction of hydrolysis, the monomolecular 

 equation, in which the velocity constant of hydrolysis would 

 be proportional to the ferment-mass. If these conditions were 

 not fulfilled we would obtain, provided the proportion of the 

 dehydrated to the hydrated enzyme did not alter very appre- 

 ciably during the reaction, the differential equation 



dx ^ kiF {A — x) 



dt~ \^a{A-x)-&x'^' ^^ 



or its integrated form : 



(Cf. Chap. XVI.) For the reversion we would obviously obtain 

 the differential equation : 



dt \-a{A-x)+fix^' ^^^ 



From equations (A) to (D), applying the mass-law, it will be 

 obvious that the quantity of enzyme dehydrated by unit mass 

 of substrate will be dependent upon the mass of the hydrated form 

 which is present, consequently, the constant a (and similarly the 

 constant /3) will be dependent upon the mass of ferment present, 

 and will also, if an appreciable shift in equilibrium represented by 

 equation (D) occurs as a result of the hydrolysis, alter somewhat 

 in value as hydrolysis proceeds*; hence the final position of equi- 

 librium, when the velocity of reversion is equal to the velocity of 

 hydrolysis, must be dependent upon the mass of ferment. 



Quite independently of the mathematical formulation of the 

 time-relations involved in this process, it will be clearly seen that 

 the presence of the enzyme must result in a greater or smaller 

 shifting of the point of equilibrium between the protein and its 

 products when we reflect that the hydrated form HFFOH, accord- 

 ing to the above scheme, only accelerates the hydrolysis, while 

 the anhydrous form FF only accelerates the synthesis, and since 



* It is for this reason that we cannot employ equations (i) and (iii) to deter- 

 mine the station of equilibrium in these systems. 



