Rate constant hard sphere approximation

The strong collision assumption is often invoked to equate ks with the hard-sphere rate constant kns This approximation assumes that every collision of C (n) with another molecule M will completely stabilize (deactivate) the excited molecule. It fact different collision partners are more or less effective in such deactivation. A collision efficiency fi is introduced to account for this effect ... 

The diffusional rate constant kD is calculated on the basis of the Debye-Hiickel theory (Equation 6.107), where the distance tr is the sum of A and B radii in the hard-sphere approximation. 

To a first approximation, the activation energy can be obtained by subtracting the energies of the reactants and transition structure. The hard-sphere theory gives an intuitive description of reaction mechanisms however, the predicted rate constants are quite poor for many reactions. 

The important theoretical expressions for fcc above have been derived from a model of hard-sphere molecules in a continuous medium. Intermolecular forces between reactant molecules have been neglected. When the reactants are ionic or polar, there will be long-range Coulombic interactions between them. For reactions between ions, we stated in Chapter 2 (Section 2.5.3) an expression for the value of the rate constant at low concentrations, and noted some reactions between oppositely-charged ions that have rate constants in approximate agreement with it. We also noted that for several such reactions the effect of added inert ions follows approximately the Debye-Hiickel limiting law. 

The goal of extending classical thermostatics to irreversible problems with reference to the rates of the physical processes is as old as thermodynamics itself. This task has been attempted at different levels. Description of nonequilibrium systems at the hydrodynamic level provides essentially a macroscopic picture. Thus, these approaches are unable to predict thermophysical constants from the properties of individual particles in fact, these theories must be provided with the transport coefficients in order to be implemented. Microscopic kinetic theories beginning with the Boltzmann equation attempt to explain the observed macroscopic properties in terms of the dynamics of simplified particles (typically hard spheres). For higher densities kinetic theories acquire enormous complexity which largely restricts them to only qualitative and approximate results. For realistic cases one must turn to atomistic computer simulations. This is particularly useful for complicated molecular systems such as polymer melts where there is little hope that simple statistical mechanical theories can provide accurate, quantitative descriptions of their behavior. 

E i stands for the activation energy which is the molar equivalent of the barrier height designated Vab in this discussion. The value A in Equation 6.40 is sometimes called a frequency or pre-exponential factor. It is somewhat dependent on temperature, var3dng as >/T in the hard-sphere picture because of the collision rate s dependence on temperature. This factor can often be approximated as a constant over limited ranges of temperature. 

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