404 



Thermodynamics of Enzyme Reactions /22 : I 



Kinetic theory shows that this fraction is e~ E " IRT . If Z is the collision 

 rate, in the standard state, then the collision theory outlined above 

 predicts that the reaction rate k for 



should be 



A + B^C 



k = Ze~ E a IRT 



(1) 



This formula can be somewhat 

 refined in that all colliding pairs may 

 not react even though they have 

 enough energy to come close enough 

 together. Some may fly apart rather 

 than reacting; others may be oriented 

 unsuitably relative to one another. 

 The absence of reaction in some of 

 the collisions for which E T is greater 

 than E a may be included in Equation 

 1 by introducing a probability factor 

 a (less than one). Thus, one has 



Figure 3. Arrhenius plots. Curves 

 expected for different reactions when 

 the log of the rate constant is plotted 

 against \/RT. On the basis of this 

 plot, one determines a slope /jl called 

 the Arrhenius constant. As discussed 

 later, low values of /x for reactions in 

 liquids (that is, curve Number 1 

 above) suggest the reaction may be 

 diffusion controlled. However, high 

 values of fx (curves Number 2 and 

 Number 3 above) probably reflect the 

 intrinsic properties of the reacting 

 molecules. 



k = aZe' E a' RT 



(2) 



One test of this collision theory of 



reactions is to plot log k against l/RT. 



A straight line should result if the 



preceding theory is correct,and if the 



activation energy E a is constant. 



Figure 3 shows typical lines of this 



nature. This theory, even in cases 



where one cannot estimate either a or 



Z, still forms the basis for our concepts 



of how reactions occur on a molecular 



scale. For gases, it is possible to 



compute Z, and hence, to find a from 



Equation 2. 



The problem of applying Equation 2 to liquids poses many difficulties. 



There are even a number of questions which one may raise about its 



application to gaseous reactions. Most fundamental of these is why the 



activation energy E a should remain constant with temperature. 2 Per- 



2 A constant value of E a implies, for example, that the intramolecular bonds 

 of the reacting molecules do not change size with temperature changes, and that 

 the shape of the active sites on enzymes is temperature independent. 



