200 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



More Factors of the Specific Rate Constant 



Various interpretations have been given to the pre-exponential term, A. 

 The most successful has come from the theory of absolute reaction rates, 

 which was pioneered by H. Eyring mainly in 1935, and expounded in detail 

 in 1941 in the famous book by Glasstone, Laidler, and Eyring 6 , and since 

 then in most books on physical biochemistry. 



Essentially the reacting molecules are pictured (refer to Figure 8-4) as 

 proceeding through a state in which they are in a metastable state called the 

 "activated complex," which is more or less in equilibrium with reactants in 

 the initial state, 1. While in this complex, the molecules can either proceed 

 to form product, the final state, or return to reactants, the initial state. 



If equilibrium can exist between reactants and complex, the thermody- 

 namic functions can apply to this part of the reaction: thus H i - //, = 

 A//*; S x - S x = AS*; and F* - F, = AF*. 



From statistical mechanical arguments the pre-exponential term by this 

 theory reduces to" 



k T 



h 



where t is a "transmission coefficient," which expresses the fraction of com- 

 plexes which proceed to products (often assumed to be 1.0); k g is the ideal 

 gas constant per molecule (R/6 x 10 23 = 1.38 x 10" 16 erg per deg C per 

 molecule), and h is Planck's constant (6.63 x 10~ 27 erg sec). 



The over-all rate, then, for a reaction such as that considered on p. 194, is: 



v = [A) a [B] b T^— g*sv* e-W/xr 



h 



It can be seen that a measured value of rate, v, at known concentrations of A 

 and B, plus a measured value of the activation energy, AH*, permits the 

 value of AS X to be obtained. 



Especially in biological processes has the evaluation of the entropy of ac- 

 tivation been important. Remember, the entropy change tells us whether 

 the heat capacity of the system has increased or decreased during the reac- 

 tion, and since the heat energy contained within molecules increases with 

 the complexity of the molecule, it is often possible to infer certain physical 

 properties of the activated state, and hence of the molecular movements dur- 

 ing reaction. This technique has proved useful in learning about the mech- 

 anism of muscle contraction, for example, certain details of which are con- 

 sidered in Chapter 10. 



In short, the rate of a process depends upon the concentrations and the 

 temperature, and on the free energy change accompanying the formation of 

 the activated complex from reactants. 



