178 VELOCITY OF REACTION, AND 



the constants are the reciprocals of the resistances to the reaction 

 running in the two opposed directions, and hence this means that the 

 resistance to such a reaction running from left to right is small com- 

 pared to the resistance for it running from right to left. 



It must be pointed out, however, that in the later stages of the 

 reaction running from left to right, when a - x has become very small 

 compared to x, although ^ is large compared to & 2 , the second ex- 

 pression may cease to be negligible, and hence, although the equation 

 obtained by neglect of the second expression may truly represent the 

 course of the reaction throughout the greater part of its length, there 

 may be a difference between observed and calculated results at the later 

 stages of the experiment. 



The discrepancy will be less the lower is the initial concentra- 

 tion of the substratum, and, as we have seen in speaking of equili- 

 brium in dilute solutions of type 2, where one substance is resolved 

 into two others, the equilibrium point lies close up to complete 

 resolution into the two substances. Accordingly for this type of 

 reaction in dilute solution, which includes all the digestive processes, 

 the second expression can be allowed to drop without sensible 

 error. 



In concentrated solutions, for this type of reaction, as the reaction 

 approaches completion, and the tendency to reversion begins to 

 become potent, the velocity of reaction must, however, fall off, and 

 the velocity constant calculated by neglecting the reversibility ex- 

 pression (Jc 2 x 2 ) must fall off in value, as it is actually found to do by 

 experiment. 



This important fact has been neglected by most experimenters, 

 and the drop in velocity has been attributed to combination between 

 the catalyst and the products of reaction. This explanation of the 

 effect of products of reaction in slowing the reaction is no doubt ex- 

 perimentally correct, for the enzyme does combine with the products 

 or one of them. But such combination is also the preliminary stage 

 in the process of reversal, and the ferment must equally combine with 

 the substratum when the reaction is running from left to right. The 

 subject will be returned to when the results of experiment upon strong 

 solutions of carbohydrates are considered; for the present, with this 

 word of warning as to the danger of neglecting the reversal factor in 

 such experiments, we may proceed to the derivation of the equations, 

 connecting x the quantity converted in time t, and the velocity constant, 

 when the second expression is neglected as small in value. Since the 

 second constant falls away in this process, we can replace ^ by Jc, 

 when the typical equations become : 



