Apparent Heat of Activation at the Reversible Potential

Derivation of the Apparent Heat of Activation at the Reversible Potential 

Normally, as may be seen from Eq. (11), evaluation of AH can be made from plots of In kvsA/T or, taking account of any doublelayer effects, from nioVs, /T, This gives the apparent heat of activation at the reversible potential. The real but experimentally undeterminable AH at 17 = 0 differs from the apparent value by 

As is well known, the apparent heat of activation evaluated experimentally is dependent on 17, as follows from Eq. (11). Following the form of that equation, the exchange current density i o can be written in an abbreviated practical form as 

For processes that obey the conventional form of the Tafel equation with b = RT/aF, the AH° evaluated at various 17 is simply given by 

It is useful to show the results of their illustrative calculations of the consequences of b not being simply RT/aF, with a constant, by evaluating AH° for various cases corresponding to the several forms of b as f(T) encountered experimentally. For this purpose, AH° is taken arbitrarily as 41.8kJmor and corresponding I o values can be calculated for various temperatures. Corresponding i values at various 17 and for various temperatures can be evaluated from the Tafel equation in the form log i = log io + 17/2.36, where b is taken as one of the four possible forms encountered experimentally  

---

Traditionally, the quantity given by-/ (3 In i0/31 /T) is tenned the apparent heat of activation at the reversible potential. The word apparent is a code word for the fact that the quantity delivered by (7.92) has a mixed meaning (because it is partly concerned with the energy barrier to the reaction and partly with the thermodynamics of the reaction occurring reversibly). 

---