The Collision Model

Why does the light stick glow with less light in cold water than in hot water  

Would you expect this curve to eventually go back down to lower values Why or why not  

For a reaction to occur, though, more is required than simply a collision—it must be the right kind of collision. For most reactions, in fact, only a tiny fraction of collisions leads to a reaction. For example, in a mixture of H2 and I2 at ordinary temperatures and pressures, each molecule undergoes about 10 ° collisions per second. If every collision between H2 and I2 resulted in the formation of HI, the reaction would be over in much less than a second. Instead, at room temperature the reaction proceeds very slowly because only about one in every 10 collisions produces a reaction. What keeps the reaction from occurring more rapidly  

T FIGURE 14.15 Molecular collisions may or may not lead to a chemical reaction between Cl and NOCI. 

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It is clear by comparing the uansition state theory with the collision model that the conesponding entropy of activation can be calculated from the value... 

The collision model of reaction rates just developed can be made quantitative. We can say that the rate constant for a reaction, k, is a product of three factors ... 

Substituting this expression for f into the equation written above for k, we obtain the basic equation for the collision model ... 

The transition-state model is generally somewhat more accurate than the collision model (at least with p = 1). Another advantage is that it explains why the activation energy is ordinarily much smaller than the bond enthalpies in the reactant molecules. Consider, for example, the reaction... 

You will recall from Section 11.4 that the collision model yields the following expression for the rate constant ... 

Now that we have a model, we must check its consistency with various experiments. Sometimes such inconsistencies result in the complete rejection of a model. More often, they indicate that we need to refine the model. In the present case, the results of careful experiments show that the collision model of reactions is not complete, because the experimental rate constant is normally smaller than predicted by collision theory. We can improve the model by realizing that the relative direction in which the molecules are moving when they collide also might matter. That is, they need to be oriented a certain way relative to each other. For example, the results of experiments of the kind described in Box 13.2 have shown that, in the gas-phase reaction of chlorine atoms with HI molecules, HI + Cl — HC1 I, the Cl atom reacts with the HI molecule only if it approaches from a favorable direction (Fig. 13.28). A dependence on direction is called the steric requirement of the reaction. It is normally taken into account by introducing an empirical factor, P, called the steric factor, and changing Eq. 17 to... 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Thus, the lines generated by the autocorrelator (341b) and by the collision models described above radically differ from the lines generated by relations of the type (383) and (384). The difference between the two above-mentioned methods is summarized as follows. 

In the condensed phase the AC permanently interacts with its neighbors, therefore a change in the local phase composition (as were demonstrated on Figs. 8.1 and 8.2) affects the activation barrier level (Fig. 8.6). Historically the first model used for surface processes is the analogy of the collision model (CM) [23,48,57]. This model uses the molecular-kinetic gas theory [54]. It will be necessary to count the number of the active collisions between the reagents on the assumption that the molecules represent solid spheres with no interaction potential between them. Then the rate constant can be written down as follows (instead of Eq. (6)) ... 

Fig. 8.6. Potential curves of Vvs. h in the transitive state model (a) and the collision model (b), where EA and Ed are the adsorption and desorption activation energies, respectively Q is the heat of adsorption, h the distance from the surface (horizontal axis of the figure).

For the first time, the collision model including the lateral interaction between adspecies was used by Roberts [105] for adsorption-desorption... 

The stage of adsorption is the simplest elementary process among the other surface processes. It can be both a main process in adsorption and one of the stages of complex interface process. At least one of the adsorption or desorption stage is always presented in any surface process. In the theory of desorption process, the AC was introduced independently for the mono-and bimolecular desorption processes by different authors [107,108] in 1974. In both papers the quasi-chemical approximation has been used. Flowever, actual computations [107] have been performed at e — 0 (the collision model). They have shown that TDS slitting is caused even by a slight repulsion e <0.05 des. The expressions obtained for the desorption rates have been applied to TDS computations for H2/W(100), CO/W(210), and N2/W(100) [109,110]. 

For the first time the reaction of CO oxidation was considered in Refs. [137,138], However, the equations for two-site processes differ from corrected Eq. (62b) due to using in these works a different definition for the bimolecular reaction activation energy the term with Ey was absent in the reaction activation energy. Actually calculations were performed with simplified assumption about s = 0 (the collision model). The theoretical curves have given a qualitative agreement with experiment data. 

In the review information only about the first steps of MC simulation is given as today this method is dominant by comparison with the kinetic theory. The calculations based on the dynamic MC methods for the lattice-gas model are carried out using the master equation (24). The calculation results depend appreciably on the way of assigning the probabilities of transitions Wa. This was repeatedly pointed out in applying both the cluster methods (Section 3) and the MC method (see, e.g. Ref. [269]). Nevertheless, practically in all the papers of Section 7 the expressions (29) and (30) do not take into account the interaction between AC and its neighbors (i.e., the collision model was used). It means s (r) = 0, whereas analysis of the cluster simulations demonstrated important influence of the parameter s (r) (that restricts obtained MC results). 

Consider a basic distinction between the transitive state model and the collision model for the adsorption rate Cad(/1). What types of curves could be obtained taking into account the interaction between nearest neighbors and additional contributions from the second neighbors. 

P. Fede, O. Simonin, and L. Zaichik. Pdf approach for the collision modelling in binary mixture of particles. In Symp. on Fluid-particle Interactions in Turbulence. ASME-FED, 2006. 

A simple relation between the steric factor of the collision model and the partition functions used in the transition-state theory may be made by employing the relation derived in Eq. (XII.3.14) between frequency... 

In this section we will introduce a model that can be used to account for the observed characteristics of reaction rates. This model, the collision model, is built around the central idea that molecules must collide to react. We have already seen that this assumption can explain the concentration dependence of reaction rates. Now we need to consider whether this model can also account for the observed temperature dependence of reaction rates. 

The kinetic molecular theory of gases predicts that an increase in temperature increases molecular velocities and so increases the frequency of in-termolecular collisions. This agrees with the observation that reaction rates are greater at higher temperatures. Thus there is qualitative agreement between the collision model and experimental observations. However, it is found that the rate of reaction is much smaller than the calculated collision frequency in a given collection of gas particles. This must mean that only a small fraction of the collisions produces a reaction. Why ... 

Equation (15.10) is a linear equation of the type y = mx + b, where y = ln( ), m = —EJR = slope, x = 1/T, and b = ln(A) = intercept. Thus, for a reaction where the rate constant obeys the Arrhenius equation, a plot of n(k) versus 1/T gives a straight line. The slope and intercept can be used to determine the values of a and A characteristic of that reaction. The fact that most rate constants obey the Arrhenius equation to a good approximation indicates that the collision model for chemical reactions is physically reasonable. 

Temperature Dependence of Rate Constants and the Collision Model... 

How does the collision model explain the effect of concentration on the reaction rate ... 

According to the collision model of chemical reactions, how is it possible that two molecules may collide but not react (Chapter 17)... 

The collision model of reactions provides an enlightening method for visualizing chemical reactions. In order for a chemical reaction to occur, the reacting molecules must collide. However, for most reactions, the. rate of a given reaction is found to be much lower than the frequency of collisions. This indicates that most collisions do not result in a reaction. 

Notice that the rate may be increased by increasing the concentration of the reactants. If we consider the collision model, this makes sense. The greater the concentration of a species, the more likely are collisions. 

The term reaction mechanism specifies the sequence of chemical steps through which reactants are transformed into products. In the collision model of homogeneous reactions the steps are described in terms of their molecularity. However, the sequence of bond redistributions and other processes (diffusion, recrystallization, etc.) by which a solid reactant is converted into products will generally be far more complex (see Chapter 18) and the information required to characterize contributing steps is far less accessible. Description of these steps. 

In this section we will briefly review the collision model for binary hard-sphere collisions using the notation in Fox Vedula (2010). The change in the number-density function due to elastic hard-sphere collisions (Boltzmann, 1872 Cercignani, 1988 Chapman Cowling, 1961 Enksog, 1921) obeys an (unclosed) integral expression of the form ... 

Owing to the presence of the pair correlation function, the collision model in Eq. (6.2) is unclosed. Thus, in order to close the kinetic equation (Eq. 6.1), we must provide a closure for written in terms of /. The simplest closure is the Boltzmann Stofizahlansatz (Boltzmann, 1872) ... 

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. 

The idea that reactions occur during molecular collisions, which is called the collision model, explains many characteristics of chemical reactions. 

For example, it explains why a reaction proceeds faster if the concentrations of the reacting molecules are increased (higher concentrations lead to more collisions and therefore to more reaction events). The collision model also explains why reactions go faster at higher temperatures. 

How does the collision model account for the fact that a reaction proceeds faster when the concentrations of the reactants are increased ... 

What is the premise underlying the collision model How is the rate affected by each of the following ... 

The central idea of the collision model is that molecules must collide in order to react. Give two reasons why not all collisions of reactant molecules result in product formation. 

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