Rate-determining step concept

A judicious combination of the stationary-state, preliminary-equilibrium, and rate-determining step concepts will often yield the rate equation for more complex reaction schemes. An example is given in Problem 6. 

Figure 3.7. Illustration of quasi-equilibrium and rate determining step concepts.

A special type of substituent effect which has proved veiy valuable in the study of reaction mechanisms is the replacement of an atom by one of its isotopes. Isotopic substitution most often involves replacing protium by deuterium (or tritium) but is applicable to nuclei other than hydrogen. The quantitative differences are largest, however, for hydrogen, because its isotopes have the largest relative mass differences. Isotopic substitution usually has no effect on the qualitative chemical reactivity of the substrate, but often has an easily measured effect on the rate at which reaction occurs. Let us consider how this modification of the rate arises. Initially, the discussion will concern primary kinetic isotope effects, those in which a bond to the isotopically substituted atom is broken in the rate-determining step. We will use C—H bonds as the specific topic of discussion, but the same concepts apply for other elements. 

Consider the series reaction A—>B—>C. If the first step is very much slower than the second step, the rate of formation of C is controlled by the rate of the first step, which is called the rate-determining step (rds), or rate-limiting step, of the reaction. Similarly, if the second step is the slower one, the rate of production of C is controlled by the second step. The slower of these two steps is the bottleneck in the overall reaction. This flow analogy, in which the rate constants of the separate steps are analogous to the diameters of necks in a series of funnels, is widely used in illustration of the concept of the rds. 

Ingold and co-workers champion the concept that nitration is primarily ionic in character and its rate-determining step (at least in a coned nitrating acid medium) involves the nitronium ion, thus ... 

Examples (10.1) and (10.2) used the fact that Steps 4, 5, and 6 must all proceed at the same rate. This matching of rates must always be true, and, as illustrated in the foregoing examples, can be used to derive expressions for the intrinsic reaction kinetics. There is another concept with a time-honored tradition in chemical engineering that should be recognized. It is the concept of rate-determining step or rate-controlling step. 

AU of the remarks above also apply to the case where a given reaction occurs along several parallel pathways. As a result of the principle of independence, the concept of a rate-determining step of the overall reaction becomes meaningless for such a reaction. 

This great variety of pathways makes it difficult to decide which of the steps is the rate-determining step. It is most likely that at intermediate current densities the overall reaction rate is determined by the special kinetic features of step (15.24) producing the oxygen-containing species. The slopes of = 0.12 V observed experimentally are readily explained with the aid of this concept. Under different conditions, one of the steps in which these species react further may be the slow step, or several of the consecutive steps may occur with similar kinetic parameters. 

Using the concept of the rate-determining step significantly simplifies the overall rate expression. Therefore, it is widely used in the analysis of kinetie data, especially in the field of heterogeneous catalysis. 

Applying the concept of the rate-determining step (see Section 5.4.2) one can derive the following kinetic equations for adsorption of A, surface reaction, and desorption of R or S, respectively, as rate-limiting processes ... 

If it is known which of the reactions determine the rate of the overall complex electrode process, then the concept of the stoichiometric number of the electrode process v is often introduced. This number is equal to the number of identical partial reactions required to realize the overall electrode process, as written in an equation of type (5.2.2).t If the rate constant of this partial rate-determining reaction is ka, then ka = /ca/v. Thus, for example, if the first of reactions (5.1.7) is the rate-determining step in the overall electrode process (5.1.4) then the stoichiometric number has the value v = 2. 

Gomez-Sainero et al. (11) reported X-ray photoelectron spectroscopy results on their Pd/C catalysts prepared by an incipient wetness method. XPS showed that Pd° (metallic) and Pdn+ (electron-deficient) species are present on the catalyst surface and the properties depend on the reduction temperature and nature of the palladium precursor. With this understanding of the dual sites nature of Pd, it is believed that organic species S and A are chemisorbed on to Pdn+ (SI) and H2 is chemisorbed dissociatively on to Pd°(S2) in a noncompetitive manner. In the catalytic cycle, quasi-equilibrium ( ) was assumed for adsorption of reactants, SM and hydrogen in liquid phase and the product A (12). Applying Horiuti s concept of rate determining step (13,14), the surface reaction between the adsorbed SM on site SI and adsorbed hydrogen on S2 is the key step in the rate equation. 

This mechanism also illustrates the concept of a rate-determining Step (rds) to designate a slow step (relatively low value of rate constant as opposed to a fast step), which then controls the overall rate for the purpose of constructing the rate law. 

At low cM, the rate-determining step is the second-order rate of activation by collision, since there is sufficient time between collisions that virtually every activated molecule reacts only the rate constant K appears in the rate law (equation 6.4-22). At high cM, the rate-determining step is the first-order disruption of A molecules, since both activation and deactivation are relatively rapid and at virtual equilibrium. Hence, we have the additional concept of a rapidly established equilibrium in which an elementary process and its reverse are assumed to be at equilibrium, enabling the introduction of an equilibrium constant to replace the ratio of two rate constants. 

Many ion-transfer reactions involve two or more steps. Often one of these steps proceeds more slowly than the others, and if the reaction proceeds under stationary conditions, this step determines the overall rate. We will elaborate this concept of a rate-determining step further. For this purpose consider a reaction taking place according to the general scheme ... 

In the past two chapters we have already encountered examples of reactions involving several steps, and introduced the notion of rate-determining step. Here we will elaborate on the subject of complex reactions, introduce another concept the electrochemical reaction order, and consider a few other examples. 

Kinetics is one of the key issues of catalysis together with selectivity and catalyst stability. Chemical kinetics has been discussed in several dedicated works [1] and the readers will be aware of its basics [2], In the following sections several commonly used concepts are mentioned such as steady state approximation, rate-determining step, determination of selectivity, and a few points of particular interest to catalysis will be high-lighted such as incubation. 

The concept of categorizing carcinogens into threshold carcinogens and non-threshold carcinogens is a pragmatic approach that simplifies the reality of dose-response relationships. The observed dose-response curve for tumor formation in some cases represents a single rate-determining step however, in many cases it may be more complex and represent a superposition of a number of dose-response curves for the various steps involved in the mmor formation. It is therefore more realistic to assume that there is a continuum of shapes of dose-response relationships which cannot be easily differentiated by data and information usually available. 

In the above chain reaction, the first step is the slow step and the second is the rapid step. The equilibrium constant for Reaction 2-8 is iCs = 0.00287, and the forward rate constant is lcgf = 0.043 s. The equilibrium constant for Reaction 2-132 is iCi32 = 10 and the rate constant is Ci32f = 10 s. Hence, the first step is the rate-determining step. Using the steady-state concept, the reaction rate law is (ignoring the backward reaction of Reaction 2-132) ... 

In these later sections, interpretations of quantitative data for product mixtures are emphasised, and the relationship between kinetics and product analysis will be developed. Mechanistic applications of kinetic data are limited to steps of reactions prior to and including the rate-determining step. As separate later steps often determine the reaction products, detailed product studies and investigations of reactive intermediates are important supplements to kinetic studies. Examples of solvolytic and related (SN) reactions have been chosen first because they provide a consistent theme, and second because SN reactions provide an opportunity to assess critically many of the mechanistic concepts of organic chemistry. Product composition in solvolytic reactions will be discussed next followed by product selectivities (Section 2.7.2) and rate-product correlations (Section 2.7.3). 

For this case the Horiuti-Boreskov concept is always valid and does not require an assumption about the rate-determining step. 

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