Transition state theory

Kinetics and thermodynamics are related to one another

Transition state theory is a kinetic theory based on the hypothesis that the intermediate state in a kinetic process is in equilibrium with the reactants (and therefore also the products). Despite the fact that we cannot actually see the intermediate and its existence may be extremely short lived, we assume that the energetic relationship between the transition state and the reactant state obeys the same kinetics of thermodynamic principles. Thus, there is an activation enthalpy and entropy. We can understand those aspects based on a microscopic model that takes the vibrations and rotations of the molecule into account as the reaction takes place. However, in any model of the rate constant there must also be frequency factor. We can see the model for the rate constant as an attempt frequency that describes the number of times per second that the molecule advances towards the transition state combined with a barrier height due to the enthalpy that describes the probability of making a crossing to the products on each attempt. Modern transition state theory has a strong similarity with a simpler theory advanced by Arrhenius more than 100 years ago. The Arrhenius theory hypothesizes that there is an attempt frequency and a barrier that determines the probability of reaching the product state. The Arrhenius barrier is known as the actiation energy. The temperature dependence of the rate constant in Arrhenius theory is similar to the temperature dependence of free energy, which permits the study of the magnitude of the activation energy based on temperature depenedent measurements of the rate constant.

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Transition state theory

Transition state theory is a detailed molecular theory that provides a role for both the enthalpy and entropy in the rate constant. Transition state theory is based on the assumption that the transition state is in equilibrium with the reactant state. This is difficult to prove since we do not observe the transition state directly. However, isotope effects and experiments with transition state analogs provides strong evidence to support the theory. The transition state enthalpy is relatively easy to understand since it plays the same role as the activation energy. The transition state entropy is part of the prefactor, which is the temperature-independent part of the rate constant.

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Catalysis results from a lowering of the energy barrier. This leads to an acceleration of both the forward and reverse reactions without any effect on the thermodynamics of the reaction.

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Practice Problems in Transition State Theory