EFFECTS OF THE DIELECTRIC CONSTANT 807 



of an electrostatic nature in the over-all reaction must be considered. In the 

 determination of succinic dehydrogenase activity, one must also take into 

 account the effect of the dielectric constant on the acceptor reaction. 



Effect of the Dielectric Constant on the Rates of Inhibition 



The rate of a reaction is dependent on the activation energy and this 

 in turn is frequently dependent on electrostatic forces between the inter- 

 acting molecules. Thus the activation energy can be modified by a change 

 in the dielectric constant. One may visualize these effects simply as the 

 affects of the dielectric constant on the forces between molecules as they 

 approach one another to a distance required for reaction. Reactions between 

 oppositely charged substances should proceed more rapidly as the dielectric 

 constant is decreased, whereas reactions between similarly charged sub- 

 stances should go more slowly. This has been found to be true for many 

 chemical reactions. Rates of inhibition should follow the same laws. 



Expressions relating rate constants with the dielectric constant may be 

 derived in several different ways (Laidler and Eyring, 1940; Scatchard, 

 1932, 1939; Laidler, 1958, p. 205; Amis, 1952; Laidler and Ethier, 1953). 

 We shall consider the dependency of the electrostatic fraction of the free 

 energy of activation on the dielectric constant. The total energy of acti- 

 vation may be divided into electrostatic and nonelectrostatic parts. The 

 energy that is involved in the formation of the activated complex is 



AF* = JFl + Ji^*„ (15-61) 



usually made up of several contributions; not only the different forces 

 operating between the molecules during their approach to one another but 

 also energy terms relating to the structural and electronic alterations nec- 

 essary for the formation of the complex. In the general case, the electrostatic 

 portion would consist of all ionic and dipolar interactions, but if we consider 

 a simple reaction of ionic groups alone, the treatment is straightforward. 

 The rate constant for the formation of the EI complex may be written as: 



k = ^ e-^^'F'/RT) (15.62) 



JSh 



according to transition state kinetics. Taking the logarithm of each side 

 and substituting from Eq. 15-61: 



, , , RT AFt.s ^Ft _ ^„, 



log k = log — — ~ — (15-63 



Nh 2.303RT 2.303RT 



The energy required in bringing the ionic groups to within a distance d, 

 their separation in the activated complex, is given by (Eq. 6-54): 



AFt = 305 ^ (15-64) 



aJJ 



