ACTION OF ENZYMES 55 



or 



/. , 



6 A . 6 



but in the equation of equilibrium 



therefore K = * 



A^ 



It follows from this that the resistances & x and k 2 are the same re- 

 spectively in whichever way the reaction is going, and that anything 

 which slows or hastens respectively the reaction in the direction 

 A + B -> C + D must also equally slow or hasten it in the direction 



Hence a catalyst or enzyme ivhich 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 concentration at time t after the commence- 

 ment 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 



J-Va-^-Vrf [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 : 



--. = J^ (a-x)- k 2 (b + x), 



