Elementary and Overall Reactions

In kinetics a fundamental distinction is made between elementary and overall reactions. An elementary reaction describes an exact reaction mechanism or pathway. Three example elementary reactions are 

The reactants and products of elementary reactions may be solids, ions, or molecular species, including gases, radicals, or free atoms. For example, the breakdown of ozone to oxygen, which is described by the overall reaction 2O3 — 3O2, probably involves the elementary reactions 

As written, an overall reaction does not indicate the reaction mechanism or pathway. An example of an overall reaction is 

Rates of overall reactions can be predicted only if the rates of component elementary reactions are known. Rates of elementary reactions are proportional to the concentrations of reactants. This may or may not be the case for overall reactions. 

For a reaction to occur the reacting molecules must come into contact or, in other words, collide. We can visualize A colliding with B to give C  

We regard such elementary reactions as real events. 

It is improbable that an elementary reaction will require the collision of four, five, or more molecules at one instant with the correct orientation to produce product. Reactions of the type 

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The importance of distinguishing between elementary and overall reactions comes in formulating rate laws. For elementary reactions only, the rate law may be written directly from the stoichiometric equation. Thus for the general elementary gas-phase reaction... 

Contrast elementary and overall reactions with some examples. What is a rate-limiting step ... 

The GA method serves as a fast and accurate estimation technique for many scientists and engineers whose work involves thermodynamic characterization of elementary and overall reaction processes. One convenient way to perform Group additivity calculations is by using the THERM code for hydrocarbons distributed by Bozzelli [81, 82]. 

Although elementary reactions and overall reactions can only be distinguished in the laboratory, a few simple guidelines can be used to guess. If the number of particles of the reaction is 4 or more, it is an overall reaction. If the number of particles is 3, then most likely the reaction is an overall reaction because there are only a limited number of trimolecular reactions. Almost all elementary reactions have molecularities of 1 or 2. However, the reverse is not true. For example. Reaction 1-5, 203(gas) 302(gas), has a "molecularity" of 2 but is not an elementary reaction. 

Most chemical reactions are complex in nature. They proceed through a so-called reaction mechanism or, equivalently, detailed mechanism, or just mechanism that consists of a number of steps, referred to as elementary steps. Each elementary step comprises a forward and a reverse elementary reaction. Rigorously, every step and every overall reaction is reversible but in reality many steps and overall reactions can be considered to be irreversible. An elementary reaction takes place exactly as written and elementary reaction is characterized by one energetic barrier. The rate of an elementary reaction can be defined as the number of elementary acts of chemical transformation per unit volume of the reaction mixture (or per unit catalyst surface area, etc.) per unit time. 

Explain the important distinctions between eadi pair of terms (a) first-order and second-order reactions (b) rate law and integrated rate law (c) activation energy and enthalpy of reaction (d) elementary process and overall reaction (e) enzyme and substrate. 

An important point about kinetics of cyclic reactions is tliat if an overall reaction proceeds via a sequence of elementary steps in a cycle (e.g., figure C2.7.2), some of tliese steps may be equilibrium limited so tliat tliey can proceed at most to only minute conversions. Nevertlieless, if a step subsequent to one tliat is so limited is characterized by a large enough rate constant, tlien tire equilibrium-limited step may still be fast enough for tire overall cycle to proceed rapidly. Thus, tire step following an equilibrium-limited step in tire cycle pulls tire cycle along—it drains tire intennediate tliat can fonn in only a low concentration because of an equilibrium limitation and allows tire overall reaction (tire cycle) to proceed rapidly. A good catalyst accelerates tire steps tliat most need a boost. 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

For a proposed reaction mechanism to be valid the sum of its elementary steps must equal the equation for the overall reaction and the mechanism must be consistent with all experimental observations The S l mechanism set forth m Figure 4 6 satisfies the first criterion What about the second d... 

The many methods used in kinetic studies can be classified in two major approaches. The classical study is based on clarification of the reaction mechanism and derivation of the kinetics from the mechanism. This method, if successful, can supply valuable information, by connecting experimental results to basic information about fundamental steps. During the study of reaction mechanisms many considerations are involved. The first of these is thermodynamics, not only for overall reactions, but also on so-called elementary steps. 

The overall reaction stoichiometry having been established by conventional methods, the first task of chemical kinetics is essentially the qualitative one of establishing the kinetic scheme in other words, the overall reaction is to be decomposed into its elementary reactions. This is not a trivial problem, nor is there a general solution to it. Much of Chapter 3 deals with this issue. At this point it is sufficient to note that evidence of the presence of an intermediate is often critical to an efficient solution. Modem analytical techniques have greatly assisted in the detection of reactive intermediates. A nice example is provided by a study of the pyridine-catalyzed hydrolysis of acetic anhydride. Other kinetic evidence supported the existence of an intermediate, presumably the acetylpyridinium ion, in this reaction, but it had not been detected directly. Fersht and Jencks observed (on a time scale of tenths of a second) the rise and then fall in absorbance of a solution of acetic anhydride upon treatment with pyridine. This requires that the overall reaction be composed of at least two steps, and the accepted kinetic scheme is as follows. 

The most widely accepted mechanism of reaction is shown in the catalytic cycle (Scheme 1.4.3). The overall reaction can be broken down into three elementary steps the oxidation step (Step A), the first C-O bond forming step (Step B), and the second C-O bond forming step (Step C). Step A is the rate-determining step kinetic studies show that the reaction is first order in both catalyst and oxidant, and zero order in olefin. The rate of reaction is directly affected by choice of oxidant, catalyst loadings, and the presence of additives such as A -oxides. Under certain conditions, A -oxides have been shown to increase the rate of reaction by acting as phase transfer catalysts. ... 

Derive the expression for v (= —d[0 j/df), making steady-state and long-chain approximations. How is Ea for the overall reaction related to the activation energies of the elementary reaction steps ... 

The extent to which such reactions take place in parallel with the dominant reaction (4.1) is, in general, difficult to quantify as the overall reaction (4.3a) may consist of the elementary step (4.1) followed by reaction between adsorbed CO and adsorbed oxygen on the metal surface ... 

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. 

At equilibrium, the rates of the forward and reverse reactions are equal. Because the rates depend on rate constants and concentrations, we ought to be able to find a relation between rate constants for elementary reactions and the equilibrium constant for the overall reaction. 

That is, the equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse elementary reactions that contribute to the overall reaction. We can now see in kinetic terms rather than thermodynamic (Gibbs free energy) terms when to expect a large equilibrium constant K 1 (and products are favored) when k for the forward direction is much larger than k for the reverse direction. In this case, the fast forward reaction builds up a high concentration of products before reaching equilibrium (Fig. 13.21). In contrast, K 1 (and reactants are favored) when k is much smaller than k. Now the reverse reaction destroys the products rapidly, and so their concentrations are very low. 

Show how the equilibrium constant is related to the forward and reverse rate constants of the elementary reactions contributing to an overall reaction (Section 13.10). 

This reaction cannot be elementary. We can hardly expect three nitric acid molecules to react at all three toluene sites (these are the ortho and para sites meta substitution is not favored) in a glorious, four-body collision. Thus, the fourth-order rate expression 01 = kab is implausible. Instead, the mechanism of the TNT reaction involves at least seven steps (two reactions leading to ortho- or /mra-nitrotoluene, three reactions leading to 2,4- or 2,6-dinitrotoluene, and two reactions leading to 2,4,6-trinitrotoluene). Each step would require only a two-body collision, could be elementary, and could be governed by a second-order rate equation. Chapter 2 shows how the component balance equations can be solved for multiple reactions so that an assumed mechanism can be tested experimentally. For the toluene nitration, even the set of seven series and parallel reactions may not constitute an adequate mechanism since an experimental study found the reaction to be 1.3 order in toluene and 1.2 order in nitric acid for an overall order of 2.5 rather than the expected value of 2. 

The overall reaction between CO2 and GMA was assumed to consist of two elementary reactions such as a reversible reaction of GMA and catalyst to form an intermediate and an irreversible reaction of this intermediate and carbon dioxide to form five-membered cyclic carbonate. Absorption data for CO2 in the solution at 101.3 N/m were interpreted to obtain pseudo-first-order reaction rate constant, which was used to obtain the elementary reaction rate constants. The effects of the solubility parameter of solvent on lc2/k and IC3 were explained using the solvent polarity. 

A mechanism is a description of the actual molecular events that occur during a chemical reaction. Each such event is an elementary reaction. Elementary reactions involve one, two, or occasionally three reactant molecules or atoms. In other words, elementary reactions can be unimolecular, bimolecular, or termolecular. A typical mechanism consists of a sequence of elementary reactions. Although an overall reaction describes the starting materials and final products, it usually is not elementary because it does not represent the individual steps by which the reaction occurs. 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

In particular, reactions in heterogeneous catalysis are always a series of steps, including adsorption on the surface, reaction, and desorption back into the gas phase. In the course of this chapter we will see how the rate equations of overall reactions can be constructed from those of the elementary steps. 

Elementary reactions have integral orders. However, for overall reactions the rate often cannot be written as a simple power law. In this case orders will generally assume non-integral values that are only valid within a narrow range of conditions. This is often satisfactory for the description of an industrial process in terms of a power-rate law. The chemical engineer in industry uses it to predict how the reactor behaves within a limited range of temperatures and pressures. 

At low temperatures the orders in CO and O2 are about -1 and while at high temperatures they become +1 and + (2, respectively. Hence, the orders of overall reactions should certainly not be treated as universal constants but rather as a convenient parameterization that is valid for a specific set of reaction conditions. We shall later see how these numbers become meaningful when we construct a detailed model for the overall process in terms of a number of elementary steps. The model should, naturally, be capable of describing what has been measured. 

As explained before, a chemical reaction can seldom be described by a single elementary step, and hence we need to adapt our definition of activation for an overall reaction. Since we are not particularly interested in the effects of thermodynamics we define the apparent activation energy as... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

Define an elementary step and point out how it differs from an overall reaction. 

Section 3 deals with reactions in which at least one of the reactants is an inorganic compound. Many of the processes considered also involve organic compounds, but autocatalytic oxidations and flames, polymerisation and reactions of metals themselves and of certain unstable ionic species, e.g. the solvated electron, are discussed in later sections. Where appropriate, the effects of low and high energy radiation are considered, as are gas and condensed phase systems but not fully heterogeneous processes or solid reactions. Rate parameters of individual elementary steps, as well as of overall reactions, are given if available. 

In multistep reactions, the number of particles of any intermediate produced in unit time in one of the steps is equal to the number of particles reacting in the next step (in the steady state the concentrations of the intermediates remain nnchanged). Hence, the rates of all intermediate steps are interrelated. Writing the rate v. of an individual step as the number of elementary acts of this step that occur in nnit time, and the rate v of the overall reaction as the number of elementary acts of the overall reaction that occur within the same time, we evidently have... 

Hydrogen evolution at metal electrodes is one of the most important electrochemical processes. The mechanisms of the overall reaction depend on the nature of the electrode and solution. However, all of them involve the transfer of proton from a donor molecule in the solution to the adsorbed state on the electrode surface as the first step. The mechanism of the elementary act of proton transfer from the hydroxonium ion to the adsorbed state on the metal surface is discussed in this section. 

It is apparent from the last example cited in previous section that there is not necessarily a connection between the kinetic order and the overall stoichiometry of the reaction. This may be understood more clearly if it is appreciated that any chemical reaction must go through a series of reaction steps. The addition of these elementary steps must give rise to the overall reaction. The reaction kinetics, however, reflects the slowest step or steps in the sequence. An overall reaction is taken as for an example ... 

The chemical reactions are assumed to be elementary and the overall reaction scheme is given in Figure 1. 

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