INHIBITIOX CONSTANTS AND INTERACTION ENERGY 265 



Determination of Enthalpy and Entropy Changes 

 Substitution of AF from Eq. 6-91 in: 



^^^ "^ AS (6-94) 



dT 

 leads to the following expression for the change in enthalpy: 



AH = 2.303 RT' ^^^f' = 441.8 -^tjt^ kcal/mole (at 37.5°) (6-95) 

 dl dl 



Thus the slope of the plot of p^^ against temx)erature will provide the 

 change in enthalpy and the entropy change may then be estimated from 

 Eq. 6-93 which may be written for 37. 5^ as: 



AS = 1422 -^^ + 4.58 vK, (6-96) 



dl 



where AS is given in cal/mole/degree as is customary. 



For interactions involving ionic groups the following method leads to 

 the entropy change directly (Laidler and Ethier, 1953). If the electrostatic 

 ion-ion interaction energy is given by AF = 305 z^z^jdgD from Eq. 6-56, 

 substitution of this in Eq. 6-94 leads to: 



eD' [dT j. 



AS = 305 1^, I 4^ I (6-97) 



From Eq. 6-73, (dD^dT)^ is found to be - 0.338 at 37.5o, and if D is 

 taken as 74.1: 



AS = - 18.8 ^ cal/mole/degree (6-98) 



However, if D varies with the interaction distance and Eq. 6-74 is used, 

 it is seen that the entropy change will depend on d/, for separations of 5-7 

 A, AS would be 8.7-4.4-fold greater than in Eq. 6-98, which is more in 

 accord with experimental values in ionic reactions. If we now assume that 

 the total free energy change is made up of electrostatic and nonelectro- 

 static contributions: 



AF = AF„,, + AF,, (6-99) 



one may write: 



In K, = ^^"" + _?2^^^ (6-100) 



RT RTd^D 



and from a plot of In K^ against IjD the value of z^z.^jd^ may be obtained. 



