58 VELOCITY OF REACTION, AND 



experimentally correct, for the enzyme does combine with the 

 products or one of them. But such combination is also the pre- 

 liminary 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 k by k, 

 when the typical equations become : 



Nos. 1 and 2. Where a single substance undergoes change into 

 either one or two others : l 



dx . . 



In words, this means that the velocity of reaction is proportional 

 to the molecular concentration, at the moment, of the substance 

 undergoing change. 



The above equation can be written 



dx 



= k dt, 



a x 



this when integrated gives log nat. (a x) = kt + const., and since 

 when x is 0, t is 0, the constant is - log nat. a = const. Subtracting, 

 we get log nat. a log nat. (a x) kt, 



or 



a-x 

 and, for the value of the constant of reaction, 



The curve showing the quantity of substance changed in different 

 times, for such reactions in which only one substance undergoes 

 change, is accordingly a logarithmic curve. 



1 Or indeed any number of others ; the same equation would hold, for example, 

 for a triglyceride, breaking up into three molecules of fatty acid and one of 

 glycerine. This arises because there is only one substance changing on the 

 left-hand side, and the back action of those on the right side is negligible. 



