Chemical reaction rates, collision assumptions

In order to understand how the constant k depends on temperature, it was assumed that the chemical reactions may take place only when the molecules collide. Following this collision, an intermediate state called an activated complex is formed. The reaction rate will depend on the difference between the energy of the reactants and the energy of the activated complex. This energy E is called activation energy (other notation E ). The reaction rate will also depend on the frequency of collisions. Based on these assumptions it was shown (e.g. [3]) that k has the following expression (Arrhenius reaction rate equation) ... 

In the reaction B + M C + M, species-M is any species, which in this binary gas system formally means B or C. The gas reaction is interpreted as thermal decomposition of species-B by high-energy collision with either itself or species-C. Reaction is initiated by collision between two molecules that are relatively unreactive chemically (compared to radicals) only a tiny fraction (exp(- )) of the collisions that occur lead to reaction, those involving the most thermally energetic molecules. This is consistent with the assumption of the reaction rate being second order overall, but first order with respect to reactant species-B. The mass fraction of the other collision partner, species-M, which does not appear in the reaction rate expression, is implicitly taken to be constant at a value of unity. 

In ordinary unimolecular reaction rate theory, the usual assumptions of strong collisions and random distribution of the internal energy simply serve to wash out precisely those features of the molecular dynamics that become of primary importance in the cases of photochemical, chemical, and electron impact excitation. Whereas evaluation of all the consequences is incomplete at present, it is already clear that the representation of an excited molecule in terms of the properties of resonant scattering states holds promise for the elucidation of those aspects of the internal dynamics that are important in photochemistry. 

The chemical collision theory has been able to explain many of the observations related to chemical kinetics. The assumption made for this theory is that particles must physically collide for a chemical reaction to occur. In addition, these collisions must be effective without sufficient force, the electrons surrounding the nuclei of the atoms involved would just repel each other and the atoms would not combine. Thus, the rate of any step in a reaction is directly proportional to (1) the number of collisions per unit time and (2) the fraction of these collisions that are effective. 

The assumption that before (and after) the collision, the system exsists in a well-defined stationary state gives us reason to make another fundamental assumption that the reactants are in thermal equilibrium which is not disturbed during the reaction. This implies that the reaction rate is not so very high that the equilibrium energy distribution of reactants is maintained by the collisions between them. This is certainly the case in most chemical reactions. 

Bimolecular elementary processes involve the collisions of two molecules, which we discussed in Chapter 9. We now show that such a process obeys a second-order rate law. The collision rate in a gas is very large, typically several billion collisions per second for each molecule. If every collision in a reactive mixture led to chemical reaction, gas-phase reactions would be complete in nanoseconds. Since gas-phase reactions are almost never this rapid, it is apparent that only a small fraction of all collisions lead to chemical reaction. We make the important assumption The fraction of binary collisions... 

Transition-state theory is based on the assumption of chemical equilibrium between the reactants and an activated complex, which will only be true in the limit of high pressure. At high pressure there are many collisions available to equilibrate the populations of reactants and the reactive intermediate species, namely, the activated complex. When this assumption is true, CTST uses rigorous statistical thermodynamic expressions derived in Chapter 8 to calculate the rate expression. This theory thus has the correct limiting high-pressure behavior. However, it cannot account for the complex pressure dependence of unimolecular and bimolecular (chemical activation) reactions discussed in Sections 10.4 and 10.5. 

---