In Eq. (2.6), [Xt] is the concentration ofXt andfD, fA, and fxt are the activity coefficients of D, A, and Xt, respectively. The rate constant, k, can be described by the following equation, based on transition-state theory:
where AG*, ASt, and AHt are the free energy, entropy, and enthalpy of activation, respectively. AG* is the difference in free energy between the reactant state and the activated complex, as shown in Fig. 5. The term K is the Boltzmann constant, h is the Planck constant, and Tis the temperature in degrees kelvin.
In descriptive terms, Eq. (2.7) essentially suggests that for chemical reaction to occur, molecules must first collide. The term KT/h represents a so-called universal collision number. Not only must the molecules collide, but they must collide with sufficient overall free energy for rearrangement of the molecules to occur. The term e ---AGt/RT represents the fraction of molecules colliding with sufficient energy to overcome the free-energy barrier to reaction. This free-energy barrier is made up of both an enthalpic term (AHt) and an entropic term (ASt).
Other kinetic theories, such as the collision theory, were proposed earlier. In the collision theory, proposed by Lewis, the reaction rate, v, was given by
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