Searching for a Mechanism

Any given reaction is much more temperature-sensitive at a low temperature than at a high temperature. 

From the Arrhenius law, the value of the frequency factor does not affect the temperature sensitivity. 

EXAMPLE 23 SEARCH FOR THE ACTIVATION ENERGY OF A pasteurization PROCESS 

Milk is pasteurized if it is heated to 63°C for 30 min, but if it is heated to 74°C it only needs 15 s for the same result. Find the activation energy of this sterilization process. 

To ask for the activation energy of a process means assuming an Arrhenius temperature dependency for the process. Here we are told that 

In many instances the rale data are cmrelated before a mechanism is found. It is a normal procedure to reduce the additive constant in the denominator to 1. We therefore divide the numerate and denominator of Equation (9-9) by kj, to obtain 

General Considerations. The rules of thumb listed in Table 9-2 may be of some help in the development of a mechanism that is consistent with the experimental rate law. 

Species having the concentralion(s) appearing in the denominator of the rate law probably collide with the active intermediate, for example. 

If a constant appears in the denominator, one of the reaction steps is probably the spontaneous decomposition of the active intermediate, for example, 

Species having the concentrationfs) appearing in the numerator of the rate law probably produce the active intermediate in one of the reaction steps, for example, 

The active intermediate. AZO. collides with azomethane, AZO [Reaction 2], resulting in the concentration of AZO in the denominator, 

AZO decomposes spontaneously [Reaction 3], resulting in a constant in the denominator of the rate expression. 

The appearance of AZO in the numerator suggests that the active intermediate AZO is formed from AZO. Referring to Reaction 1, we see that this case is indeed true. 

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The fit with H= 1.53 is quite good. The results for the fits with n = 1 andn = 2 show systematic deviations between the data and the fitted model. The reaction order is approximately 1.5, and this value could be used instead of n= 1.53 with nearly the same goodness of fit, a = 0.00654 versus 0.00646. This result should motivate a search for a mechanism that predicts an order of 1.5. Absent such a mechanism, the best-fit value of 1.53 may as well be retained. 

Interaction of dioxygen species with Fe aq and with Fe " aq has been very briefly reviewed. In relation to 0x0-, peroxo-, and superoxo-complexes as models for intermediates in oxygenase activity, a brief report on a 2000 symposium on activation of oxygen summarizes the then-current situation in the search for a mechanism common to mono- and dinuclear iron sites, mono- and dinuclear copper sites, and copper-iron sites. The outline proposals comprise ... 

The trial-and-error procedure involved in searching for a mechanism is illustrated in the following two examples. 

EXAMPLE 2a SEARCH FOR A MECHANISM FOR THE ENZYME------------ SUBSTRATE REACTION... 

To design a chemical reactor the rate expression must be known. Assuming the reaction is known not to be elementary, we must search for a mechanism that describes the reaction taking place or use experimental data directly. Mechanisms can be hypothesized as the sum of a series of elementary reactions with intermediates. Using methods developed by physical chemists, we can hypothesize whether the proposed mechanism fits the actual experimental evidence. If no inconsistencies are found, the hypothesized mechanism is possibly the actual mechanism. However, agreement of the mechanism with the experimental data does not necessarily mean that the proposed mechanism is correct, since many mechanisms can be hypothesized to fit such data. 

In a search for a mechanism of the inhibitory action exerted by chlorpromazine on some enzymatic processes, the interaction of this substance with oxidized flavines and xanthines was investigated, and the formation of charge-transfer complexes was observed. There are many indications that the phenothiazine-melanine interaction, which is probably involved in the retinotoxicity of some phenothiazine drugs, is also of the donor-acceptor type, as suggested... 

Searching for a mechanism that could justify these high pressures, we have suggested that ... 

As seen in Table 2.1, the overall order of an elementary step and the order or orders with respect to its reactant or reactants are given by the molecularity and stoichiometry and are always integers and constant. For a multistep reaction, in contrast, the reaction order as the exponent of a concentration, or the sum of the exponents of all concentrations, in an empirical power-law rate equation may well be fractional and vary with composition. Such apparent reaction orders are useful for characterization of reactions and as a first step in the search for a mechanism (see Chapter 7). However, no mechanism produces as its rate equation a power law with fractional exponents (except orders of one half or integer multiples of one half in some specific instances, see Sections 5.6, 9.3, 10.3, and 10.4). Within a limited range of conditions in which it was fitted to available experimental results, an empirical rate equation with fractional exponents may provide a good approximation to actual kinetics, but it cannot be relied upon for any extrapolation or in scale-up. In essence, fractional reaction orders are an admission of ignorance. 

The last two columns of Table 7.2 show a comparison of observed rates with those calculated with eqn 7.7 and these coefficients. The agreement is excellent. Even so, eqn 7.7 should not be viewed as established beyond doubt until a plausible mechanism leading to it has been found and predictions made with it have proved correct. The search for a mechanism will be described in Example 7.4 in the next section. 

Certainly, solving this problem deserves further studies. If they are successful, the dynamic programming method can prove to be an important tool for the analysis of mechanisms. DP application seems to be most effective to search for a mechanism satisfying some subjective criterion of extremality. Such application can be exemplified by the considered algorithm of optimal circuit synthesis that can be treated as a procedure of simultaneous determination of economic and physical components of the whole mechanism of pipeline system construction. In the context of physicochemical problems the optimality criteria may be the maximum yield of useful products of the modeled process or its minimum harmful impact on the environment. 

Addition of adenosine to isolated rat hepatocytes, as well as to other liver preparations, provokes marked increases in the intracellular concentration of ATP and total adenine nucleotides (Chagoya de Sanchez et al., 1972 Lund et al., 1975 Wilkening et al., 1975), that are explained by the utilisation of adenosine by adenosine kinase- The present work was initiated as a search for a mechanism whereby the rate of degradation of the adenine nucleotide pool would adapt to an increased rate of synthesis- It led to the unexpected ascertainment that, under normal conditions, there is a continuous foriaation of adenosine by the hepatocytes. This production does, however, not contribute to the formation of allantoin but is part of a futile cycle operating between AMP and adenosine. 

In spite of these rules, the search for a mechanism is very difficult and the experiment plays an important role. It is, however, possible to build skeletons of models valid for a family of reactions and this is what we will attempt in Chapter 12 and the following chapters. 

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