SALT CONCENTRATION AND IONIC STRENGTH 825 



with AB and thus K"^ = (AB)/(X). The thermodynamic equilibrium con- 

 stant is, however, written in term of the activities: 



K.* = ^=S^l^ ,15-87) 



a^ (X) y. 



The rate is then given by: 



K (AB) -^^ = A;o(AB) ^^ (15-88) 



-"■0 7x 



where the unimolecular rate constant h^ = Ic^i^o- The observed unimolecular 

 rate constant may be written as: 



h = A-o ^^ (15-89) 



Therefore: ^' 



log k = log h - 0.509 V s"(2^^ - zD (15-90) 



using the uncorrected Debye-Hiickel expression for the activity coefficients. 

 It is evident that when the charges on AB and the activated complex X 

 are the same, k = ^'q, and there would be no effect of changing the ionic 

 strength. The charges on AB and X, however, may not be the same, the 

 formation of the activated complex perhaps involving the dissociation or 

 association of a proton. It is likely that in any case there will be no more 

 than a unit charge difference so that when AB is neutral, log klk^ will equal 

 it 0.509 \ s . Thus the rate of dissociation of a complex may be increased, 

 decreased, or unaffected by a change of the ionic strength. 



It is probable that in many enzyme reactions, the situation is not quite 

 as simple as this and the decomposition of the ES complex to form products 

 must be written in several steps, such as: 



ES ^ Xi ;i± EP ^ X2 ^ E + P (1.5-91) 



so that the effect of ionic strength upon the enzyme rate may be complex 

 if one step is not limiting the rate. The dissociation of an EI complex is 

 probably straightforward on the other hand. There is also some justifiable 

 doubt as to the validity of using the ordinary Debye-Hiickel equations for 

 expressing the activity coefficients applicable to the equilibrium between 

 any complex AB and its activated counterpart X, especially in enzyme 

 reactions in which the activation process may well occur in a region shielded 

 from the medium. 



If the interaction is not between two ionic groups but between an ionic 

 group and a neutral group, Eq. 15-84 would predict that no ionic strength 

 effects would be observed, as pointed out by Laidler (1950, p. 131). In 

 this case the additional term, K^^s, is important and: 



log y = K,,s (15-92) 



