Parallel reactions activation energy

Although it is not universally true that the activation energies of reactions parallel their heats of reaction, this is approximately true for the kind of addition reaction we are discussing. Accordingly, we can estimate E = k AH, with k an appropriate proportionality constant. If we consider the difference between two activation energies by combining this idea with Eq. (7.21), the contribution of the nonstabilized reference reaction drops out of Eq. (7.21) and we obtain... 

Step 4 of the thermal treatment process (see Fig. 2) involves desorption, pyrolysis, and char formation. Much Hterature exists on the pyrolysis of coal (qv) and on different pyrolysis models for coal. These models are useful starting points for describing pyrolysis in kilns. For example, the devolatilization of coal is frequently modeled as competing chemical reactions (24). Another approach for modeling devolatilization uses a set of independent, first-order parallel reactions represented by a Gaussian distribution of activation energies (25). 

In the case of parallel reactions, the fastest reaction will set or control the overall change. In all rate determining cases, the relative speed of the reactions will change with the temperature. This is caused by different energies of activation among the steps in the sequence. This is just one more reason for limiting rate predictions from measurements within the studied domain to avoid extrapolation. 

Change of reaction conditions to minimize kinetic complications. For example, if two parallel reactions have substantially different activation energies, their relative rates will depend upon the temperature. The reaction solvent, pH, and concentrations are other experimental variables that may be manipulated for this purpose. 

Calculate activation energies for the three Diels-Alder reactions (energy of transition state - sum of energies of reactants). Which reaction has the smallest energy barrier Which has the largest energy barrier Do your results parallel the measured relative rates of the same reactions (see table at left) ... 

Relative reactivity wiU vary with the temperature chosen for comparison unless the temperature coefficients are identical. For example, the rate ratio of ethoxy-dechlorination of 4-chloro- vs. 2-chloro-pyridine is 2.9 at the experimental temperature (120°) but is 40 at the reference temperature (20°) used for comparing the calculated values. The ratio of the rate of reaction of 2-chloro-pyridine with ethoxide ion to that of its reaction with 2-chloronitro-benzene is 35 at 90° and 90 at 20°. The activation energy determines the temperature coefficient which is the slope of the line relating the reaction rate and teniperature. Comparisons of reactivity will of course vary with temperature if the activation energies are different and the lines are not parallel. The increase in the reaction rate with temperature will be greater the higher the activation energy. 

The measured [ OH]/[ OH] branching ratio versus inverse temperature is plotted in Fig. 4. If the two species are produced by two parallel pathways, the total reaction rate is a simple sum of the two pathway-resolved rates. In this case, the data points in an Arrhenius plot should fall on a straight line with a slope proportional to the difference in activation energies for the two competing pathways. A fit to the data in Fig. 4 yields the result that the barrier to O atom abstraction is 1.0 0.4kcal mol larger than for H atom abstraction. Although... 

Such a pre-equilibrium closely parallels that suggested by Dewar et for the manganic acetate oxidations of several aromatic ethers and amines (p. 405). Other features of the reaction are a p value of —0.7 and identical activation energies of 25.3 kcal.mole for oxidation of toluene, ethylbenzene, cumene, diphenylmethane and triphenylmethane. 

Figure 1. Selectivity is determined by the relative difference in activation energy between two possible products, while the rates of reaction to product 1 or 2 are determined by the absolute activation barriers, AgJ and AG. Curve calculated assuming AG = 18 kcal moF and a temperature of 300 K. Inset is a simplified potential energy diagram for the conversion of a reactant into two parallel products [10]. (Reprinted from Ref [10], 2002, with permission from American Chemical Society.)...

In Fig. 8 we show a set of energy levels for the adiabatic case, where we assume that, in going from R to the transition state, there is no exchange between the different levels. The third level in R must go through the third level in the transition state. The overall rate is then made up of a series of parallel reactions, each with its own individual energy of activation. So we can write (12), where [RJ is given by (13). Substitution of (13) into (12)... 

It has been shown [90] that the homogeneous dissociation of methane is the only primary source of free radicals and it controls the rate of the overall process. This reaction is followed by a series of consecutive and parallel reactions with much lower activation energies. After the formation of acetylene (C2H2), a sequence of very fast reactions occurs, leading to the production of higher unsaturated and aromatic hydrocarbons and finally carbon ... 

An evident parallel variation of the increment in re and in the bond length rX is observed. On the other hand, the influence of the strengths of the X—Y bonds on the activation energies in these reactions were taken into account. The electronegativities of C and Si, Ge, Sn atoms are close. The empirical dependence of the parameter re (in m) on DXy and rXY in the interaction of radicals carrying a free valence on the C and O atoms with the C—H, Si—H, Sn—H, Ge—H, and P—H bonds is presented on Figure 6.5. 

Table XV lists the isokinetic temperatures of several reactions representing a wide variety of mechanisms, these examples having been chosen because the isokinetic temperature happened to fall in the popular experimental range between 0 and 100°. There are many other polar reactions that have isokinetic temperatures well outside of the accessible temperature range there are many whose variations in activation energy and entropy are not parallel and these, of course, do not have an isokinetic temperature even approximately. When one of a series of reactions deviates markedly from a parallel trend in activation energy and entropy established by the others, it is probable that it differs in mechanism from the others. This is a better indication of a change in mechanism than either marked differences in rate or in activation energy.

The antiaromatic region is not important for the reactivity of the parent enediyne because the activation energy is determined only by the energy difference between the reactant and the TS. However, for the cyclic enediynes in Fig. 7 in which the C1-C6 distances are 3.39 and 2.92 A, respectively, antiaromaticity of the reactant should be relevant to the reaction kinetics. In addition, the role of repulsion between the in-plane filled orbitals is accentuated by a parallel decrease in the attractive two-electron interaction between the re and re orbitals which vanishes at the 3.2 A distance between the terminal carbon atoms. 

The expedience of the reverse reaction, proceeding almost without any activation energy, depends on the value of affinity of molecule B to cation A+. The higher this value is, the more favorable is the reaction. Field [12] supposed that cation affinity should vary in parallel with proton affinity. Thus, the probability of fragmentation of various ions AB+, with formation of identical ion A+, will be inversely proportional... 

In classical kinetic theory the activity of a catalyst is explained by the reduction in the energy barrier of the intermediate, formed on the surface of the catalyst. The rate constant of the formation of that complex is written as k = k0 cxp(-AG/RT). Photocatalysts can also be used in order to selectively promote one of many possible parallel reactions. One example of photocatalysis is the photochemical synthesis in which a semiconductor surface mediates the photoinduced electron transfer. The surface of the semiconductor is restored to the initial state, provided it resists decomposition. Nanoparticles have been successfully used as photocatalysts, and the selectivity of these reactions can be further influenced by the applied electrical potential. Absorption chemistry and the current flow play an important role as well. The kinetics of photocatalysis are dominated by the Langmuir-Hinshelwood adsorption curve [4], where the surface coverage PHY = KC/( 1 + PC) (K is the adsorption coefficient and C the initial reactant concentration). Diffusion and mass transfer to and from the photocatalyst are important and are influenced by the substrate surface preparation. 

Problem 3.4 For a first order parallel reaction, the Arrhenius factor for formation of two products are 1010 and 108 sec-1 and their energy of activation are 150 and 75 kJ mol-1, respectively. At what temperature the two products will be formed at the same rate ... 

However, we have to reflect on one of our model assumptions (Table 5.1). It is certainly not justified to assume a completely uniform oxide surface. The dissolution is favored at a few localized (active) sites where the reactions have lower activation energy. The overall reaction rate is the sum of the rates of the various types of sites. The reactions occurring at differently active sites are parallel reaction steps occurring at different rates (Table 5.1). In parallel reactions the fast reaction is rate determining. We can assume that the ratio (mol fraction, %a) of active sites to total (active plus less active) sites remains constant during the dissolution that is the active sites are continuously regenerated after AI(III) detachment and thus steady state conditions are maintained, i.e., a mean field rate law can generalize the dissolution rate. The reaction constant k in Eq. (5.9) includes %a, which is a function of the particular material used (see remark 4 in Table 5.1). In the activated complex theory the surface complex is the precursor of the activated complex (Fig. 5.4) and is in local equilibrium with it. The detachment corresponds to the desorption of the activated surface complex. 

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