Mechanism with the Rate Law

The mechanism must correlate with the rate law. Most importantly, a mechanism must support the experimental facts shown by the rate law, not the other way around. 

Let s see how the mechanisms of several reactions conform to these criteria and how the elementary steps fit together. 

Mechanisms with a Slow Initial Step We ve already seen one mechanism with a rate-determining first step—that for the reaction of NO2 and CO. Another example is the reaction between nitrogen dioxide and fluorine gas  

Molecules of reactant and product appear in both elementary steps. The free fluorine atom is a reaction intermediate. 

Does this mechanism meet the three crucial criteria  

Conjuring up a reasonable reaction mechanism can be a classic example of the use of the scientific method. We use observations and data from rate experiments to hypothesize what the individual steps might be and then test our hypothesis by gathering further evidence. If the evidence supports it, we continue to apply that mechanism if not, we propose a new one. However, we can never prove, just from data, that a particular mechanism represents the actual chemical change, only that it is consistent with it. 

Regardless of the elementary steps proposed for a mechanism, they must meet three criteria  

The elementary steps must add up to the overall balanced equation. We cannot wind up with more (or fewer) reactants or products than are present in the balanced equation. 

The elementary steps must be physically reasonable. As we noted, most steps should involve one reactant particle (unimolecular) or two (bimolecular). Steps with three reactant particles (termolecular) are very unlikely. 

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Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

The reader can show that a third scheme also gives the same answer. In it the two cations first associate (however unlikely), and this dinuclear complex reacts with Cl-. To summarize any reaction scheme consistent with the rate law is characterized by the same ionic strength effects. In other words, it is useless to study salt effects in the hopes of resolving one kinetically indistinguishable mechanism from another. 

Kinetically indistinguishable chain mechanisms can be characterized by different ionic strength profiles, as was apparently first demonstrated in a study this author conducted with D. A. Ryan on the reaction of (aqua)-2-propylchromium cation with oxygen.17 This reaction was presented in Chapter 7. Two schemes that are consistent with the rate law are as follows ... 

How does one know when the complete roster of reaction schemes that are consistent with the rate law has been obtained One method is based on an analogy between electrical circuits and reaction mechanisms.13 One constructs an electrical circuit analogous to the reaction scheme. Resistors correspond to transition states, junctions to intermediates, and terminals to reactants and products. The precepts are these (1) any other electrical circuit with the same conductance corresponds to a different but kinetically equivalent reaction scheme, and (2) these circuits correspond to all of the fundamentally different schemes. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

The first step in Mechanism I is the unimolecular decomposition of NO2. Our molecular analysis shows that the rate of a unimolecular reaction is constant on a per molecule basis. Thus, if the concentration of NO2 is doubled, twice as many molecules decompose in any given time. In quantitative terms, if NO2 decomposes by Mechanism I, the rate law will be Predicted rate (Mechanism I) = [N02 ] Once an NO2 molecule decomposes, the O atom that results from decomposition very quickly reacts with another NO2 molecule. 

Every rate law must be determined experimentally. A chemist may imagine a reasonable mechanism for a reaction, but that mechanism must be tested by comparing the actual rate law for the reaction with the rate law predicted by the mechanism. To determine a rate law, chemists observe how the rate of a reaction changes with concentration. The graph of the data for the NO2 decomposition reaction shown in Figure 15-6 is an example of such observations. 

Experiments show that this reaction is second order in NO2, as predicted by the second proposed mechanism. The one-step mechanism can be ruled out because it is not consistent with the experimental rate law. Agreement with the rate law does not prove that the second mechanism is the correct one, however, because other mechanisms may predict the same rate law. It is one strong piece of evidence that supports this particular two-step process. 

The proposed mechanism must agree with the rate law. We expect the ratedetermining step to determine the reaction rate Rate = k2 [N02F2]. To... 

True/False. The mechanism for a reaction with the rate law, Rate = k[A]2[B], will have a step where two molecules of A collide with a molecule of B. 

Boreskov assumed the power law dependence for reaction rate, which is mathematically incorrect. Thus, strictly speaking, he did not prove Equations (13) and (14). Authors performed the analysis of the model corresponding to the single-route reaction mechanism with the rate-limiting step and proved these relations rigorously (see Lazman and Yablonskii, 1988 Lazman and Yablonskii, 1991). Mathematically, expression (12) is the first term of infinite power series by powers kinetic parameters of rate-limiting step. 

The electrode mechanisms treated, along with the rate laws and the appropriate digital simulation parameters, are shown in Table 16. The symbols for mechanisms 5 and 6, RS-2 and RS-3, indicate that these reactions represent cases of radical (primary intermediate B) reacting with substrate (A). Mechanism 5 foDows second-order kinetics while third-order kinetics characterize mechanism 6. The theoretical data for the mechanisms are summarized in Tables 17—23. The calculations are for EX — f revI equal to 300 mV. Data are also available for EX — Eiev — 100 mV. In the following paragraph, the data are explained with reference to the eC mechanism, i.e. Table 17. 

Write a mechanism that is consistent with the rate law. 

The term k3/K in equation (36) may be equated with the rate law v" = At3 [allyl Sn] [I2][I ] and hence a mechanism involving nucleophilic assistance by the iodide ion is indicated, whilst the term k2b corresponds to the rate law v" = k2b[allyI4Sn][I3 ] and hence to a mechanism in which a direct attack of I3 on... 

A complete mechanism for the chlorite-iodide system entails many steps. In addition to those consistent with the rate laws for processes (VII) (A) and (B), the elementary steps of the Dushman reaction need to be included. A set of relevant steps for these processes in collected in Table 7. 

Although certain mechanisms for a reaction can be eliminated on the basis of experimental evidence, it is never possible to prove that the reaction follows a particular mechanism. It can only be demonstrated that all the experimental facts are consistent with that mechanism. One piece of experimental information that is of primary importance is the rate law that the reaction follows. The rate law predicted by a possible mechanism must be consistent with the rate law determined in the laboratory. If the two are not consistent, that mechanism can be ruled out. In the case of these nucleophilic substitution reactions, experimental studies have shown that two different rate laws are followed, depending on the substrate (R—L), the nucleophile, and the reaction conditions. This means that there must be two different mechanisms for the reaction. Let s look at each. 

It is interesting to compare the expected rates of Mn oxidation via abiotic mechanisms with the rates expected from the biological kinetic rate law described above. Abiotic Mn oxidation rates at pH 8.03 were measured in seawater by von Langen et al. (1997) who reported a first-order rate constant of l.lxlO-6 (normalized for Po2 = 1 atm and T = 25°C). At this pH and for similar conditions, the cell concentration of L. discophora required to obtain the same rate would be only 0.30 pg/1 (Zhang et al., 2002) (i.e., approximately 3x10s cells/1). It is reasonable to assume that cell populations of Mn-oxidizing bacteria far greater than this would be possible in natural environments. Even smaller population sizes would be required to match abiotic rates (if they could be measured) at lower pH values. 

A number of questions might be addressed in the discussion of the results. How reproducible are the initial rate measurements (Note that runs D5 and E3 are duplicates also, runs El and the standard assay for enzyme activity have identical initial concentrations.) Are the enzyme-catalyzed data compatible with the Michaelis-Menten mechanism Do the data from both runs C and D follow apparent zero-order kinetics, and how does this agree with expectations based on comparing (S) with KJ Which of the two types of analysis, Lineweaver-Burk or Eadie-Hofstee, seems to give the better results and why How does 2 agree with the estimate of the turnover number based on the specific activity Are the acid-catalyzed data consistent with the rate law given in Eq. (10) ... 

This mechanism agrees with the rate law found by Martinsen ... 

This would be followed by th( rapid dissociation of HD-S by reaction with S or by the back reaction with NIb-S. This does not seem as likely a mechanism although compatible with the rate law. 

Suggest a reaction mechanism and rate-limiting step consistent with the rate. law. (Hint Some species might be weakly adsorbed.)... 

In general, many kinetics data are accumulated prior to proposing a reaction mechanism. In our case, we will simply use the stoichiometry information obtained in Experiment 5.4 along with intuition based on past work in the field. The following is an interactive pre-lab exercise for proposing the rate law for the electron transfer between [Co(en)3)]2+ and [Co(ox)2(en)]. The kinetics will then be investigated using conventional visible spectroscopy. Experimental data, in combination with the rate law, will be used to determine the outer-sphere electron rate constant. 

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