176 VELOCITY OF REACTION, AND 



It follows from this that the resistances k ana k 2 bear the same 

 values in whichever way the reaction is going, and that anything which 

 slows or hastens the reaction in the direction A + B >C + 1) must also 

 equally hasten or slow it in the direction A + B< C + D. 



Hence a catalyst or enzyme which at one set of concentrations increases 

 the velocity of a reaction in one direction must equally hasten it at another 

 set of concentrations in the opposite direction. In other words, all cata- 

 lytic action must be reversible, although in most instances the equilibrium 

 point lies so near one end that the action of the enzyme on the velocity of 

 reaction in one of the directions cannot be demonstrated experimentally. 



The equation for the velocity of reaction between two pairs of 

 substances A, B and C, D, given above, can be much simplified, if 

 A and B be present in the proper molecular concentration for reacting 

 upon each other at the commencement and C and D be initially absent. 

 For then the initial molecular concentration of A and B will be the same ; 

 let it be represented by a and let x be the change in molecular concen- 

 tration at time t after the commencement of the reaction. Then the 

 equation for the velocity of change in x at time t, by using equation 

 (2) and remembering that a = b, and c = d = becomes 



~ t =k^(a-xY-lc^ (3) 



Similar equations for the velocity of reaction can be deduced, 

 by using the same processes of reasoning, for the other types of 

 reaction which have been discussed under the heading of equilibrium. 



For example 



1. For a single substance undergoing conversion by molecular 

 rearrangement into another single substance such, for example, as an 

 isomeric change: 



dx 



dt =^i (a-x)-k 2 (b + x), 



where a and b are the original molecular concentrations of the sub- 

 stances A and B, and x the change in molecular concentration at time t. 

 This equation obviously takes the form 



2. For a single substance A undergoing conversion into two 

 substances B and C, the common type of action of enzymes and 

 many other catalysts: 



dt =k l (a-x)-k z (b + x) (c + x), 



