Relationship to the Arrhenius Rate Law

There is another analysis often used to experimentally determine energies for the reaction barrier. This is the Arrhenius rate law (Eq. 7.17). This law was derived empirically by Arrhenius long before the development of TST. Arrhenius observed that the rates of reactions increased exponentially as the absolute temperature increased, producing the simple relationship of Eq. 7.17. There are two parameters associated with this law, the preexponential factor (A) and the activation energy (EJ. In this method the barrier to the reaction is associated with the activation energy. 

Both the Arrhenius rate law and the Eyring equation tell us that rate constants are temperature dependent. However, the potential energy surface is generally treated as being temperature independent. The barrier heights and the heat of reaction are determined solely by the structures of the molecules undergoing reaction. Sometimes, a heat capacity difference between individual species on the surface can lead to a temperature dependence of the surface (see Chapter 3 for a discussion of heat capacity). However, this is rare, and we will not consider this possibility further here. 

Diagram showing the Boltzmann distribution of molecules as a function of kinetic energy for two different temperatures. Ti is the lower temperature and T2 is a higher temperatu re. 

4 Revisiting What is the Nature of the Activated Complex and Why Does TST Work  

Diagram showing multiple hypothetical trajectories that take the molecules over the region of the energy surface near the transition state. The insert shows the distribution of molecules passing over the col as a function of distance from the transition state. 

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