Activation energy collision theory

An estimate of the enthalpy change which conesponds to the activation energy of the collision theory analysis of 167kJmoP may be made by assuming that the formation of tire dimer from two molecules of the monomer is energetically equivalent to tire dipole-dipole and dispersion interactions of two HI molecules. These exothermic sources of interaction are counterbalanced... 

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

Collision theory leads to this equation for the rate constant k = A exp (-EIRT) = A T exp (,—EIRT). Show how the energy E is related to the Arrhenius activation energy E (presuming the Arrhenius preexponential factor is temperature independent). 

FIGURE 13.25 (a) In the collision theory of chemical reactions, reaction may take place only when two molecules collide with a kinetic energy at least equal to a minimum value, /rmn (which later we identify with the activation energy), (b) Otherwise, they simply bounce apart. 

According to the collision theory of gas-phase reactions, a reaction takes place only if the reactant molecules collide with a kinetic energy of at least the activation energy, and they do so in the correct orientation. 

A gas composed of molecules of diameter 0.5 nm takes part in a chemical reaction at 300. K and 1.0 atm with another gas (present in large excess) consisting of molecules of about the same size and mass to form a gas-phase product at 300. K. The activation energy for the reaction is 25 kj-mol. Use collision theory to calculate the ratio of the reaction rate at 320. K relative to that at 300. K. 

In experimental practice, we usually ignore the temperature dependence of the prefactor and extract the activation energy by making an Arrhenius plot, as discussed in Chapter 2. The consequence of collision theory, however, is that a curved plot, rather than a straight line, will result if the activation energy is of the same order of k T. 

A pre-exponential factor and activation energy for each rate constant must be established. All forward rate constants involving alkyne adsorption (ki, k2, and ks) are assumed to have equal pre-exponential factors specified by the collision limit (assuming a sticking coefficient of one). All adsorption steps are assumed to be non-activated. Both desorption constants (k.i and k ) are assumed to have preexponential factors equal to 10 3 sec, as expected from transition-state theory [28]. Both desorption activation energies (26.1 kcal/mol for methyl acetylene and 25.3 kcal/mol for trimethylbenzene) were derived from TPD results [1]. 

The term A in Equation (2.6) is a constant known as the Arrhenius constant and E is the energy of activation derived from collision theory (Atkins, 1978). The enthalpy of activation can be calculated from transition state theory (Jencks, 1969) as... 

Consideration of a variety of other systems leads to the conclusion that very rarely does the collision theory predict rate( constants that will be comparable in magnitude to experimental values. Although it is not adequate for predictions of reaction rate constants, it nonetheless provides a convenient physical picture of the reaction act and a useful interpretation of the concept of activation energy. The major short-... 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

Transition state theory complements collision theory. When particles collide with enough energy to react, called the activation energy, Ea, the reactants form a short-lived, high energy activated complex, or transition state, before forming the products. The transition state also could revert back to the reactants. 

If hu0 is small compared with kT, the partition function becomes kT/hv0. The function kT/h which pre-multiplies the collision number in the transition state theory of the bimolecular collision reaction can therefore be described as resulting from vibration of frequency vq along the transition bond between the A and B atoms, and measures the time between each potential transition from reactants to product which will only occur provided that the activation energy, AE°0 is available. 

Thus, El is higher than the experimental activation energy and can give much higher rates of activation and, therefore, much higher value of k lk[ than simple collision theory. 

Considering again Eq. (2.6) and referring to E as an activation energy, attention is focused on the collision rate Zab> which from simple kinetic theory can be represented by... 

Effect of Solvent on Arrhenius Plots. If water is a substrate, then the presence of an organic solvent, which may disrupt the structure and/or orientation of water, may alter the Arrhenius plot. For example, a linear plot is seen with fumarate hydratase in the presence of 10% methanol. However, the plot is biphasic in the presence of 10% ethanol . See Boltzmann Distribution Collision Theory Temperature Dependency, Transition-State Theory Energy of Activation On... 

Chemistry (collision theory or transition state theory) has developed the equations for reaction rates and activation energies in terms of concentration. 

By comparison of (M) and (F), it can be seen that the preexponential factor A in the Arrhenius equation can be identified with PaA]i(8kT/Tr/ji,y/2 and the activation energy, a, with the threshold energy Eu. It is important to note that collision theory predicts that the preexponential factor should indeed be dependent on temperature (Tl/2). The reason so many reactions appear to follow the Arrhenius equation with A being temperature independent is that the temperature dependence contained in the exponential term normally swamps the smaller Tl/Z dependence. However, for reactions where E.t approaches zero, the temperature dependence of the preexponential factor can be significant. 

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