Chemical reaction rate-determining step

Reaction kinetics, particularly for many solid-state endothermic and reversible rate processes, are sensitive to reaction conditions [the procedural variables (1)]. Because of the participation of secondary controls, the reaction rate measured is not necessarily that of the limiting chemical (or rate-determining) step. 

Transition-state theory may be useful in testing the dissolution mechanisms presented above. According to TST, for any elementary chemical reaction the reactants should pass through a free-energy maximum, labeled the activated complex , before they are converted to products. It is assumed that the reaction rate-determining step is related to the decomposition of this activated complex ... 

Since the rate of a chemical reaction only depends on the slowest, or rate-determining step, and any preceding steps, species B will not show up in the rate law. 

An important consequence of the isotope-dependence of Dq is that, if a chemical reaction involves bond dissociation in a rate-determining step, the rate of reaction is decreased by substitution of a heavier isotope at either end of the bond. Because of the relatively large effect on Dq, substitution of for H is particularly effective in reducing the reaction rate. 

In tills chapter a number of reactions are discussed in which die rate-determining step occurs in die solid state, and die solid is chemically changed by die reaction. 

These examples illustrate the relationship between kinetic results and the determination of reaction mechanism. Kinetic results can exclude from consideration all mechanisms that require a rate law different from the observed one. It is often true, however, that related mechanisms give rise to identical predicted rate expressions. In this case, the mechanisms are kinetically equivalent, and a choice between them is not possible on the basis of kinetic data. A further limitation on the information that kinetic studies provide should also be recognized. Although the data can give the composition of the activated complex for the rate-determining step and preceding steps, it provides no information about the structure of the intermediate. Sometimes the structure can be inferred from related chemical experience, but it is never established by kinetic data alone. 

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. 

Mass-transfer rates have been determined by measuring the absorption rate of a pure gas or of a component of a gas mixture as a function of the several operating variables involved. The basic requirement of the evaluation method is that the rate step for the physical absorption should be controlling, not the chemical reaction rate. The experimental method that has gained the widest acceptance involves the oxidation of sodium sulfite, although in some of the more recent work, the rate of carbon dioxide absorption in various media has been used to determine mass-transfer rates and interfacial areas. 

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. 

The first step (loss of the leaving group) is the rate-determining step, much Uke we saw for SnI processes. The base does not participate in this step, and therefore, the concentration of the base does not affect the rate. Because this step involves only one chemical entity, it is said to be uiumolecular. Unimolecular elimination reactions are called El reactions, where the 1 stands for unimolecular. ... 

Each elementary reaction in a mechanism proceeds at its own unique rate. Consequently, every mechanism has one step that proceeds more slowly than any of the other steps. The slowest elementary step in a mechanism is called the rate-determining step. The rate-determining step governs the rate of the overall chemical reaction because no net chemical reaction can go faster than its slowest step. The idea of the rate-determining step is central to the study of reaction mechanisms. 

Process (3.8) is a total 2e per cadmium atom and indicates that CdS formation occurs via a sulfur atom abstraction from 8203 . This reaction was called for in order to suggest that the reduction of Cd " is the only electrochemical step, whereby charge is consumed, followed by a subsequent chemical step comprising sulfur association to reduced cadmium. Sulfur is generated by the decomposition of thiosulfate. On the other hand, reaction (3.9) corresponds to an overall 4e /Cd process where reduction of S2O3 itself must occur as well as that of Cd ", the former comprising actually the rate-determining step. This route becomes more favorable as pH decreases for it requires additional protons. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

Chemical reactivity differences may be calculated if for the transition state of a rate-determining step of a reaction a structural model can be given which is describable by a force field with known constants. We give only two examples. Schleyer and coworkers were able to interpret quantitatively a multitude of carbonium-ion reactivities (63, 111) in this way. Adams and Kovacic studied the pyrolysis of 3-homoadamantylacetate (I) at 550 °C and considered as transition state models the two bridgehead olefins II and III (112). From kinetic data they estimated II to be about 2 kcal mole-1 more favourable than III. 

Nevertheless, chemical methods have not been used for determining ionization equilibrium constants. The analytical reaction would have to be almost instantaneous and the formation of the ions relatively slow. Also the analytical reagent must not react directly with the unionized molecule. In contrast to their disuse in studies of ionic equilibrium, fast chemical reactions of the ion have been used extensively in measuring the rate of ionization, especially in circumstances where unavoidable irreversible reactions make it impossible to study the equilibrium. The only requirement for the use of chemical methods in ionization kinetics is that the overall rate be independent of the concentration of the added reagent, i.e., that simple ionization be the slow and rate-determining step. 

Because solvent viscosity experiments indicated that the rate-determining step in the PLCBc reaction was likely to be a chemical one, deuterium isotope effects were measured to probe whether proton transfer might be occurring in this step. Toward this end, the kinetic parameters for the PLCBc catalyzed hydrolysis of the soluble substrate C6PC were determined in D20, and a normal primary deuterium isotope effect of 1.9 on kcat/Km was observed for the reaction [34]. A primary isotope effect of magnitude of 1.9 is commonly seen in enzymatic reactions in which proton transfer is rate-limiting, although effects of up to 4.0 have been recorded [107-110]. 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

Warning if a chemical process comprises several reaction steps, only the progress of the slowest step can be followed kinetically. These graphical methods of determining k are only useful for obtaining the rate-determining step (RDS) of such reactions. Although the reaction may appear kinetically simple, it is wisest to assume otherwise. 

Given a reaction mechanism, the order with respect to each reactant is its coefficient in the chemical equation for that step. The slowest step is the rate-determining step, so... 

There are many possible reaction pathways between acrylonitrile and adiponitrile and, in each, there are several possible rate-determining steps. None of the reaction intermediates has yet been detected electrochemically or spectroscopically thus indicating very fast chemical processes with intermediates of half-lives of < 10-5 s. Bard and Feiming Zhou [104a] have recently detected the CH2 = CHCNT radical by Scanning Electrochemical Microscopy (SCEM) using a 2.5 fim radius Au electrode (1.5 mol CH2 = CHCN in MeCN/TBAPF6). The dimerization rate has been determined to 6.107 M-1 S l. 

The protonation constant for reaction (33) has been determined from 183W chemical shifts at 20°C as log K = 4.59 0.03. The protonation is complex and a rearrangement of all the protons probably takes place. A possible explanation for the observed kinetics involved is that one of the [H3Wi2042]9 isomers bears three internal protons and the other has one external and two internal protons. The exchange of a proton between the internal and external sites would then be the rate-determining step (141). 

For very fast chemical reactions and/or moderately fast electron transfers, the latter become the rate-determining steps. On the cathodic side, the current is controlled by forward electron transfer A —> B. On the anodic side, the current is controlled by forward electron transfer D —> C. This applies whether the rate law for electron transfer is of the Butler-Volmer type or of any other type (e.g., a MHL law). 

When the molar volume of product, i.e. solid (AB) is less than that of solid (A), the product layer will be porous and the rate determining step is the chemical process occurring at the interface of solid (A). Such reactions are also known as topochemical reactions. The rate of reaction may be determined by the available surface area of A. For example, if reaction involves spherical particle, the rate of reaction (i.e. - dV/dt, where V is the volume of particle at time t) is given as... 

The rates of many chemical reactions does not appear to depend on the solvent. This is because the activation energy for the process of diffusion in a liquid is nearly 20 kJ mol1 whereas for chemical reactions it is quite large. Thus, step (i) is usually not rate determining step in reactions in solutions. When the reaction takes place in solution, it is step (ii) that determines the rate of a bimolecular reaction. This conclusion is supported by the fact that the rates of these reactions do not depend upon the viscosity of the solvent. The rate should be effected by the solvent if diffusion of reactant is the rate determining step. 

The Dotz reaction mechanism has received further support from kinetic and theoretical studies. An early kinetic investigation [37] and the observation that the reaction of the metal carbene with the alkyne is supressed in the presence of external carbon monoxide [38] indicated that the rate-determining step is a reversible decarbonylation of the original carbene complex. Additional evidence for the Dotz mechanistic hyphotesis has been provided by extended Hiickel molecular orbital [23, 24] and quantum chemical calculations [25],... 

A distinction between "molecularity" and "kinetic order" was deliberately made, "Mechanism" of reaction was said to be a matter at the molecular level. In contrast, kinetic order is calculated from macroscopic quantities "which depend in part on mechanism and in part on circumstances other than mechanism."81 The kinetic rate of a first-order reaction is proportional to the concentration of just one reactant the rate of a second-order reaction is proportional to the product of two concentrations. In a substitution of RY by X, if the reagent X is in constant excess, the reaction is (pseudo) unimolecular with respect to its kinetic order but bimolecular with respect to mechanism, since two distinct chemical entities form new bonds or break old bonds during the rate-determining step. 

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