22 : 1/ Thermodynamics of Enzyme Reactions 405 



haps the enthalpy, or some other similar function, really should remain 

 constant. If one of the latter were true, the interpretation of a would 

 be more complex, but one would still find a straight line by plotting 

 log k against l/RT. To avoid this question, some people call the slope 

 of the lines in Figure 3 the Arrhenius constant p. (The graph itself is often 

 called an Arrhenius plot.) 



Another moot point involves the concepts of entropy and Gibbs' 

 free energy. From the point of view of kinetic theory, entropy is a 

 measure of the randomness of the system. If A and B are initially 

 separate molecules and become pairs during the reaction, the total 

 entropy has decreased. Where on the potential curve should one first 

 consider A and B as one molecule C? The answer is not obvious. If 

 one starts at point r l5 say in Figures 1 and 2, then it is really the Gibbs' 

 free energy which must exceed some minimum value AG*. By defini- 

 tion, one may write 



AG* = A//* - TAS* 

 for an isothermal change. In this case, Equation 2 should have been 



k = aZe~ AHi ' RT e + Ast ' R (3) 



If AH* and A.S* are independent of temperature, then A//* will be the 

 slope of the Arrhenius plot. If one also may write 



A//* = A£* + PAV 



for an isobaric reaction, and if AV is proportional to the absolute 

 temperature, then A£* will be the slope of the Arrhenius plot. (It is 

 easiest to read the "J" as activation.) In almost all cases, the constant 

 a cannot be obtained by any other means than from the Arrhenius plot. 

 Accordingly, the exact interpretation of /jl, the slope of the Arrhenius 

 plot, cannot be definitely determined. 



All of the foregoing schemes predict qualitatively that the reaction 

 rate should vary exponentially with the temperature. The temperature 

 dependence of the collision frequency Z is so small as compared to the 

 exponential variation that it cannot be detected in most cases. The 

 preceding theory also indicates that there should be no obvious connec- 

 tion between the net energy obtained from the reaction E° (or AG ), 

 and the activation energy AG* which determines the stability of the 

 reacting molecules. 



The height of the potential energy barrier AG* determines the ease 

 with which a reaction can occur. The action of a catalyst, such as an 

 enzyme, may be thought of as distorting the shape of one or both 

 reactants so that the effective value of AG* is lowered without changing 

 in any way the value of AG . 



