Complex reactions activation energy for

The overall rate equation based on a complex mechanism often has an overall rate constant made up of the several individual constants for the set of reactions. The observed activation energy is then made up of those of the individual reactions and may be able to be predicted, or used as a consistency check of the mechanism. 

For example, the Rice-Herzfeld mechanism for hydrocarbon pyrolysis has overall rate expressions such as Eq. 1.4-18  

An order of magnitude estimate of the overall activation energy is given by using typical values for the initiation, hydrogen abstraction, radical decomposition, and termination steps  

This is the size of overall activation energy that is observed. Note that it is much lower than the very high value for the difficult initiation step, and is thus less than the nominal values for breaking carbon-carbon bonds. 

For the specific Example 1.4-5 of ethane pyrolysis, Eq. i of that example shows that the overall rate constant is  

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