Activation Energy and Reaction Rate Constant

There are two types of molecular theories on reaction rates collision theory and transitimr state theory. According to the coUision theory, the upper limit of a bimolecular rate constant of a gaseous reaction is the molecular collision frequency obtained by gas kinetics. The molecular coUtsimr frequency Zab between molecules, A and B, is given by 

Source NASA/JPL Panel Evaluation No. 17 unless otherwise noted UPAC Subcommittee Report Vol. I 

On the other hand, for the transition state theory reaction formula is expressed as 

Experimentally, in most of the cases bimolecular reaction rate constants are known to be expressed by 

This equation is called the Arrhenius expression and is the fundamental equation representing the temperature dependence of reaction rate constants. Comparing the Arrhenius expression Eq. (2.39), with rate constant Eq. (2.33) by the collision theory and (2.38) by the transition state theory, the temperature dependence of the exponential factor is exactly the same as derived by these theories, and Ea of the Arrhenius expression corresponds to the activation energy Ea of the transition state theory. A plot of the logarithm of a reaction rate constant, In k against MRT, is called an Arrhenius plot, and the experimental value of activation energy can be obtained from the slope of the Arrhenius plot. This linear relationship is known to hold experimentally for numerous reactions, and the activation energy for each reaction has been obtained. 

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