Collision number, significance reaction rates

Most chemical reactions occur much more rapidly at higher temperatures. The increase in reaction rate for ivi2 reactions relates to the fact that at higher temperamres the number of collisions between reactants with sufficient energy to surmount the activation energy (AG ) increases significantly (see Fig. 6.3). 

Applications to date of reactive molecular dynamics methods demonstrate feasibility for the study of hundreds or thousands of particles involved in chemical reactions for which reactive probabilities do not vary too widely. The latter condition is essential if statistically significant numbers of all possible events are to occur within a practical computation period. Even if the requirement for a large excess of elastic collisions is relaxed, however, reaction rates typical of experimental chemical systems demand simulation run times which approach the feasible limit except for quite small numbers of particles. Turning therefore to a higher level method for this type of system, one may treat numbers of particles in a small cell or volume element rather than individual particles, and invoke a Monte Carlo procedure for determining which reactive event will occur, how much time will elapse between events, and in which "cell" of the system the... 

In the absence of flow, and in the initial stages of the reaction (p < 0.3) the molecular weight distribution closely follows the Flory distribution [6], though at later times there is a significant deviations with <7<( + p). Thus a narrower distribution is obtained relative to the Flory distribution [6], which is in agreement with experimental results. Application of a shear flow results in acceleration of the reaction (Figure 8), and this results because of orientation of the molecules by the flow rather than an increased number of shear induced collisions. There is a nearly linear increase in degree of polymerization with shear rate, at a fixed time, of reaction which is in concurrence with experiments [32]. 

According to Equation 6.3, this factor is equivalent to the Arrhenius A-factor. In the collision model it is a measure of the standard rate at which reactant species collide that is it is a measure of the number of collisions per second when the concentrations of the reactant species are both 1 mol dm"-. It is necessary to specify standard conditions since, in general, the collision rate depends on the concentrations of the species present (cf. Section 4.1). The value of Atheory a given bimolecular reaction depends on the hard-sphere radii and masses of the reactant species. Calculations show that it does not vary significantly from reaction to reaction with values usually of the order of 10 dm mol s . Table 7.1 compares the calculated values of Atheory for gas-phase bimolecular reactions with those derived from experiment. 

A similar line of reasoning can be followed for substances reacting in solution. The number of collisions between species other than the solvent in a solution is only slightly greater than in the gas phase. Thus, for the same concentration and temperature, reactions in solution should occur at approximately the same rate as in the gas phase. However, reacting species, especially ionic species, frequently interact with the solvent, and this can significantly affect the rate at which collisions occur. 

The capture hypothesis forms the basis for the LGS model for ion-neutral reactions and many exothermic reactions appear to proceed at the collision frequency. Despite the appeal and widespread validity of the LGS model, a number of ion-neutral reactions have rates significantly... 

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