i found several definitions of the activation energy in electrochemistry, but i dont know why they are different. For example in Atkins "Physical Chemistry" the activation gibbs energy is defined as:

$\Delta^‡G_c=\Delta^‡G_c(0)+\alpha F\Delta\phi$

and he assumed that $\Delta\phi$ is equal to $E^{eq}$ when no current flows through the battery.

In the Book "Electrochemical Methods" of Bard and Faulkner another definition ist used: $\Delta G_c^‡=\Delta G_{0c}^‡+\alpha F(E-E^{0'})$

$E^{0'}$ is the formal potential.

I have also found a possible explanation in the Book "Electrochemical Dictionary" , but I do not quite understand. The following sentence is in the book:

"If a reference electrode is used the Galvani potential difference can be replaced by $(E-E^{0'})$, i.e., with the difference of the electrode potential related to a reference electrode and the formal potential" . But Why we need the reference to the formal potential?

I would be glad if someone can explain me why the used different definitions?


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