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Unformatted text preview: On Rate Constants: Simple Collision Theory, Arrhenius Behavior, and Activated Complex Theory 17th February 2010 0.1 Introduction Up to now, we haven’t said much regarding the rate constant k . It should be apparent from the discussions, however, that: • k is constant at a specific temperature, T and pressure, P • thus, k = k(T,P) (rate constant is temperature and pressure depen dent) • bear in mind that the rate constant is independent of concentrations, as the reaction rate, or velocity itself is treated explicity to be concen tration dependent In the following, we will consider how the physical, microscopic detaails of reactions can be reasoned to be embodied in the rate constant, k. 1 Simple Collision Theory Let’s consider the following gasphase elementary reaction : A + B → Products The reaction rate is straightforwardly: 1 Rate = k [ A ] α [ B ] β = k [ A ] 1 [ B ] 1 α = 1 β = 1 = k N A V N B V V = volume Recall previous discussions of the total collisional frequency for heteroge neous reactions: Z AB = σ AB s 8 kT πμ n * A n B * where the n * A = N A V , n B * = N B V are number of molecules/particles per unit volume. We can see the following: Z AB = σ AB s 8 kT πμ  {z } k N A V N B V Here we see that the concepts of collisions from simple kinetic theory can be fundamentally related to ideas of reactions, particularly when we consider that elementary reactions (only for which we can write rate expressions based on molecularity and order mapping) can be thought of proceeding due to collisions (or interactions of some sort) of monomers (unimolecular), dimers(bimolecular), trimers (trimolecular), etc. If we are to naively say that reactions occur due only to collisions of parti cles (keep in mind the nature of the system – gasphase,elementary reaction), then we can at the zero’th order equate the maximum reaction rate to the total collisional frequency for heterogeneous pairs: R max = Z AB k max [ A ] 1 [ B ] 1 = σ AB s 8 kT πμ  {z } k N A V N B V k max ≡ σ AB s 8 kT πμ 2 1.1 Simple Collision Theory: Caveats Simple collision theory (SCT), we see from above, remarkably predicts an expression for the microscopic rate constant that relates to the dimensions of...
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This note was uploaded on 02/02/2012 for the course CHEM 444 taught by Professor Dybowski,c during the Fall '08 term at University of Delaware.
 Fall '08
 Dybowski,C
 Physical chemistry, pH, Kinetics

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