426 CHEMICAL DYNAMICS 



The condition of "balance" at equilibrium is therefore rep- 

 resented by the equation: 



(C) Ci2H220ii + H2O <=± 2 C6H12O6. 



If mi be the mass of maltose, nii that of glucose and W that of 

 water, then at equilibrium we shall have, in accordance with the 

 mass-law : 



miW = 77 m^, (i) 



/Ci 



in which k and ^2 are the velocity-constants of the forward and 

 the reverse reactions, respectively. If maltase is indeed a 

 "typical" catalysor, then we must assume that although ki 

 and k^ are each multiplied by the presence of the catalysor their 

 ratio remains unaffected and, consequently, the relative pro- 

 portions between mi and m2 and W at equilibrium are not affected 

 by the presence of maltase.* 



k-y 

 Now the value of the ratio 7^ for this reaction is such that in 



ki 



dilute solutions (i.e., when W in equation (i) is large) the point 

 of equilibrium in equation (C) lies so far over towards the right 

 that hydrolysis of the maltose, at the end of the reaction, is 

 practically complete, no appreciable quantity of unhydrolysed 

 maltose remaining in the system. This being the case we cannot 

 expect, through the agency of any "typical" catalysor, to secure 

 the synthesis of maltose in a dilute solution of glucose. A con- 

 siderable increase in the concentration of the system, however, 

 although it does not bring about any appreciable alteration 

 either in ki or in k^, nevertheless alters the proportion of maltose 

 to glucose at equilibrium very profoundly. The reason for this 

 is apparent upon inspection of equation (i). Increasing the 

 concentration of the system is equivalent to reducing the mag- 

 nitude of W and hence inducing a compensating increase in mi 

 (the mass of maltose) at equilibrium. In a concentrated system 

 we find, accordingly, that the hydrolysis of maltose is never 

 complete, whether maltase or any other catalysor be employed 

 to accelerate the process. A concentrated solution of glucose is 

 therefore not in a condition of equilibrium until a proportion 

 of maltose has been restored to the system by the occurrence of 



* It should be clearly borne in mind that the verity of this statement has 

 never been proven. 



