Non-Arrhenius steps

Such behavior is exceptional and appears to be restricted to reactions of free radicals at low temperatures. The rules for temperature dependence of multistep reactions in the following assume that no such non-Arrhenius steps are involved. 

Barring participation of anomalous non-Arrhenius steps, the rate coefficients of all individual steps increase with temperature. A decrease of the reaction rate with increasing temperature then can only be produced by reverse steps whose coefficients increase more sharply than do those of the forward ones ... 

This is a necessary condition (in the absence of non-Arrhenius steps), but not a sufficient one Even if it is met, the rate may increase with increasing temperature because the activation energy of the first denominator term in eqn 12.2 is lower than that of the numerator and may exert the stronger influence. 

This ensures that at least one denominator term, the j th, in the rate equation increases with temperature by a larger factor than does the numerator, and is a necessary condition, but not a sufficient one (again granted absence of non-Arrhenius steps). 

The complex K3 is non-Arrhenius and is the sum of three products. The reason for this is that the brutto-equation involves three molecules of H2, and the three steps of the detailed mechanism must be subject to the same type of kinetic law. It is due to this fact that such spanning trees appear. 

Apparent activation energies of reactions may be negative, corresponding to a decrease in rate with increase in temperature, if the pathway contains at least one reverse step with an activation energy that is high compared with those of the forward steps. Also, the rates of a few reaction steps of free radicals decrease with increasing temperature in a non-Arrhenius fashion. 

Figure 11 shows a typical example of the temperature-dependent behavior for the reactions of OH radical with aromatic compounds. The measured bimolecular rate constants of OH radical with nitrobenzene showed distinctly non-Arrhenius behavior below 350°C, but increased in the slightly subcritical and supercritical region. Feng a succeeded in modeling these data with a three-step reaction mechanism originally proposed by Ashton et while Ghandi etal. claimed to have developed a so-called multiple collisions model to predict the rates for the reactions of OH radical in sub- and super-critical water. 

Another, very rare anomaly is that single reaction steps of radicals at very low temperatures may not obey the Arrhenius equation at all. Normal Arrhenius behavior arises from an activation barrier which the reaction must surmount. In many exothermic reactions of radicals with one another or with small molecules, there is no such barrier to speak of (see Section 10.4), and a hindrance from other effects, say, molecular rotation, may increase as the temperature is raised. This makes the rate decrease in a non-Arrhenius fashion with increasing temperature. Examples include reactions of CN- with 02, ethene, ethyne, and ammonia and of OH- with O , butenes, and HBr. This interesting anomaly has recently been reviewed by Sims [11], The discussion here and in other part of this book assumes no such steps are involved. 

Few reactions have been studied over the enormous range indicated in Figure 5.1. Even so, they will often show curvature in an Arrhenius plot of n k) versus T. The usual reason for curvature is that the reaction is complex with several elementary steps and with different values of E for each step. The overall temperature behavior may be quite different from the simple Arrhenius behavior expected for an elementary reaction. However, a linear Arrhenius plot is neither necessary nor sufficient to prove that a reaction is elementary. It is not sufficient because complex reactions may have one dominant activation energy or several steps with similar activation energies that lead to an overall temperature dependence of the Arrhenius sort. Arrhenius behavior is not necessary since some low-pressure, gas phase, bimolecular reactions exhibit distinctly non-Arrhenius behavior even though the reactions are believed to... 

Isoconversional kinetics is an efficient compromise between the common single-step Arrhenius treatment and the predominantly encoxmtered processes whose kinetics are multi-step and/or non-Arrhenius. Isoconversional methods are capable of detecting and handling such processes in the form of a... 

Before concluding with step 1, we should reflect on the rather high value for n in the rate expression of the reference reaction (n — 2.51). This indicates strong non-Arrhenius behavior. Our attempt to describe the intramolecular H migration in form of a simple Arrhenius rate equation is therefore only valid within the small temperature range around—in this example—1000 K. 

In Chap. 3, Hua Guo et al. stress the importance of tunneling in both unimolecular and bimolecular reactions. They have calculated the thermal rate constant, k T), for the exothermic HO + CO H + CO2 reaction [190]. In combustion, this reaction is the main source of heat as the last step of hydrocarbon oxidation. They explain that it proceeds via the HOCO intermediate. In the last step of the reaction, the system has to surmount a transition state. There the reaction coordinate is essentially the H-O stretch and tunneling can dominate. This gives rise to a strong non-Arrhenius... 

E a > Ea a + E (Fig. 7.10b). An important consequence of this discussion is that we have to be very cautious about making predictions about the effect of temperature on reactions that are the outcome of severed steps. Enzyme-catalyzed reactions may also exhibit strongly non-Arrhenius temperature dependence if the enzyme denatures at high temperatures md ceases to fimction. 

Thiocyanate ion frequently reacts in oxidation with a rate-determining step reminiscent of those with the halides, and this oxidation is no exception. A study based on measurements of the limiting polarographic currents for thiocyanate in the presence of hydrochloric acid and bromate gives clear evidence of first-order dependence on bromate and on thiocyanate ion concentrations and of second-order dependence on hydrogen ion concentration. The authors report the Arrhenius parameters as, AH = 11.4 kcal.mole and AS = 28.0 caLmole . deg . One strange, and unexplained, anomaly is present. The experimental first-order coefficient for bromate reaction appears to be constant over about one half-life for equimolar initial thiocyanate and bromate concentrations. Yet these rate coefficients depend linearly on thiocyanate ion concentration for [SCN ] > [BrOj ], but non-linearly below. It seems improbable that the postulated mechanism with first steps (1 )-(3), is capable of explaining this, viz. 

Non-isothermal kinetic studies [69] of the decomposition of samples of nickel oxalate dihydrate doped with Li and Cr showed no regular pattern of behaviour in the values of the Arrhenius parameters reported for the dehydration. There was evidence that lithium promoted the subsequent decomposition step, but no description of the role of the additive was given. 

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