Stoichiometry elementary reaction

We have noted previously that the order of a reaction cannot necessarily be determined from an examination of the stoichiometry of the reaction. Indeed we can define a particular type of reaction—the elementary reaction—which has the special property that its reaction order can be determined from its stoichiometry. Elementary reactions may be mon-omolecular, where a single species reacts and its concentration alone determines the rate of the reaction. Generally stated, if the reaction A -> products is elementary and monomolecular, the rate law will be... 

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. 

In the schemes considered to this point, even the complex ones, the products form by a limited succession of steps. In these ordinary reaction sequences the overall process is completed when the products appear from the given quantity of reactants in accord with the stoichiometry of the net reaction. The only exception encountered to this point has been the ozone decomposition reaction presented in Chapter 5, which is a chain reaction. In this chapter we shall consider the special characteristics of elementary reactions that occur in a chain sequence. 

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 functional form of the reaction rate in Equation (1.14) is dictated by the reaction stoichiometry. Equation (1.12). Only the constants kf and k can be adjusted to fit the specific reaction. This is the hallmark of an elementary reaction its rate is consistent with the reaction stoichiometry. However, reactions can have the form of Equation (1.14) without being elementary. 

This reaction is complex even though it has a stoichiometric equation and rate expression that could correspond to an elementary reaction. Recall the convention used in this text when a rate constant is written above the reaction arrow, the reaction is assumed to be elementary with a rate that is consistent with the stoichiometry according to Equation (1.14). The reactions in Equations (2.5) are examples. When the rate constant is missing, the reaction rate must be explicitly specihed. The reaction in Equation (2.6) is an example. This reaction is complex since the mechanism involves a short-lived intermediate, B. 

Mechanism I illustrates an important requirement for reaction mechanisms. Because a mechanism is a summary of events at the molecular level, a mechanism must lead to the correct stoichiometry to be an accurate description of the chemical reaction. The sum of the steps of a mechanism must give the balanced stoichiometric equation for the overall chemical reaction. If it does not, the proposed mechanism must be discarded. In Mechanism I, the net result of two sequential elementary reactions is the observed reaction stoichiometry. 

Mechanism I is a three-step process in which the first step is rate-determining. When the first step of a mechanism is rate-determining, the predicted rate law is the same as the rate expression for that first step. Here, the rate-determining step is a bimolecular collision. The rate expression for a bimolecular collision is first order in each collision partner Rate = j i[03 ][N0 j Mechanism I is consistent with the experimental rate law. If we add the elementary reactions, we find that it also gives the correct overall stoichiometry, so this mechanism meets all the requirements for a satisfactory one. 

Reactions for which the rate equations follow the stoichiometry as given in Equations 5.23 to 5.26 are known as elementary reactions. If there is no direct correspondence between the reaction stoichiometry and the reaction rate, these are known as nonelementary reactions and are often of the form ... 

The number of chemical species involved in a single elementary reaction is referred to as the molecularity of that reaction. Molecularity is a theoretical concept, whereas stoichiometry and order are empirical concepts. A simple reaction is referred to as uni-, bi-, or termolecular if one, two, or three species, respectively, participate as reactants. The majority of known elementary steps are bimolecular, with the balance being unimolecular and termolecular. 

For mechanisms that are more complex than the above, the task of showing that the net effect of the elementary reactions is the stoichiometric equation may be a difficult problem in algebra whose solution will not contribute to an understanding of the reaction mechanism. Even though it may be a fruitless task to find the exact linear combination of elementary reactions that gives quantitative agreement with the observed product distribution, it is nonetheless imperative that the mechanism qualitatively imply the reaction stoichiometry. Let us now consider a number of examples that illustrate the techniques used in deriving an overall rate expression from a set of mechanistic equations. 

Although reaction rate expressions and reaction stoichiometry are the experimental data most often used as a basis for the postulation of reaction mechanisms, there are many other experimental techniques that can contribute to the elucidation of these molecular processes. The conscientious investigator of reaction mechanisms will draw on a wide variety of experimental and theoretical methods in his or her research program in an attempt to obtain information about the elementary reactions taking... 

The following mechanism for a reaction of identical stoichiometry introduces a second complex into the sequence of elementary reactions. 

Reaction mechanism a postulated sequence of elementary reactions that is consistent with the observed stoichiometry and rate law these are necessary but not sufficient conditions for the correctness of a mechanism, and are illustrated in Chapter 7. 

Molecularity must be integral, but order need not be there is no necessary connection between molecularity and order, except for an elementary reaction the numbers describing molecularity, order, and stoichiometry of an elementary reaction are all the... 

Both theories yield laws for elementary reactions in which order, molecularity, and stoichiometry are the same (Section 6.1.2). 

In this chapter we will discuss some aspects of the carbonylation catalysis with the use of palladium catalysts. We will focus on the formation of polyketones consisting of alternating molecules of alkenes and carbon monoxide on the one hand, and esters that may form under the same conditions with the use of similar catalysts from alkenes, CO, and alcohols, on the other hand. As the potential production of polyketone and methyl propanoate obtained from ethene/CO have received a lot of industrial attention we will concentrate on these two products (for a recent monograph on this chemistry see reference [1]). The elementary reactions involved are the same formation of an initiating species, insertion reactions of CO and ethene, and a termination reaction. Multiple alternating (1 1) insertions will lead to polymers or oligomers whereas a stoichiometry of 1 1 1 for CO, ethene, and alcohol leads to an ester. 

A chemical reaction is in most cases the result of an overall balance of a number of steps, called elementary reactions, whose rate law can be deduced from the stoichiometry. The rate law of an elementary reaction has the form... 

Another term used to describe rate processes is molecu-larity, which can be defined as an integer indicating the molecular stoichiometry of an elementary reaction, which is a one-step reaction. Collision theory treats mo-lecularity in terms of the number of molecules (or atoms, if one or more of the reacting entities are single atoms) involved in a simple collisional process that ultimately leads to product formation. Transition-state theory considers molecularity as the number of molecules (or entities) that are used to form the activated complex. For reactions in solution, solvent molecules are counted in the molecularity, only if they enter into the overall process and not when they merely exert an environmental or solvent effect. 

A representation of all of the elementary reactions that lead to the overall chemical change being investigated. This representation would include a detailed analysis of the kinetics, thermodynamics, stereochemistry, solvent and electrostatic effects, and, when possible, the quantum mechanical considerations of the system under study. Among many items, this representation should be consistent with the reaction rate s dependence on concentration, the overall stoichiometry, the stereochemical course, presence and structure of intermediate, the structure of the transition state, effect of temperature and other variables, etc. See Chemical Kinetics... 

ELECTROSTATIO BOND ELECTROSTATIO SUREAOE POTENTIAL ELECTROSTRIOTION ELECTROTAXIS ELECTROVALENT BOND ELEMENTARY OHARGE ELEMENTARY REACTION Elementary reaction stoichiometry, MOLECULARITY CHEMICAL KINETICS UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION Element effect,... 

STOICHIOMETRIC NUMBER Stoichiometry of elementary reactions, CHEMICAL KINETICS MOLECULARITY UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION STOKE S SHIFT... 

Thus, we must be careful to distinguish between the one particular equation that represents the elementary reaction and the many possible representations of the stoichiometry. 

Stoichiometry can suggest whether a single reaction is elementary or not because no elementary reactions with molecularity greater than three have been observed to date. As an example, the reaction... 

This set of relations between reaction orders and stoichiometric coefficients defines what we call an elementary reaction, one whose kinetics are consistent with stoichiometry. We later wiU consider another restriction on an elementary reaction that is frequently used by chemists, namely, that the reaction as written also describes the mechanism by which the process occurs. We will describe complex reactions as a sequence of elementary steps by which we will mean that the molecular collisions among reactant molecules cause chemical transformations to occur in a single step at the molecular level. 

On a molecular level, reactions occur by coUisions between molecules, and the rate is usually proportional to the density of each reacting molecule. We will return to the subject of reaction mechanisms and elementary reactions in Chapter 4. Here we define elementary reactions more simply and loosely as reactions whose kinetics agree with their stoichiometry. This relationship between stoichiometry and kinetics is sometimes called the Law of Mass Action, although it is by no means a fundamental law of nature, and it is frequently invalid. 

One might expect that this is an elementary reaction because the reaction agrees with the stoichiometry (after multiplying aU coefficients in the preceding expression by two). However, one peculiarity of this reaction is that the rate actually decreases with increasing temperature or has a negative activation energy, an unreasonable situation for an elementary process. 

Smith (47) and Bjornbom (48) have discussed the introduction of restrictions into equilibrium calculations in addition to the elemental abundance constraints. Often only a restricted set of terminal species is chosen, but it would seem logical in choosing such additional restrictions to revert to Gibbs original idea of specifying possible reactions as well as possible species. The choice of elementary reactions, rather than of overall reactions with complicated stoichiometry, would be simplified by modern developments in theoretical chemistry and surface science. 

This type of reaction for which the rate equation can be written according to the stoichiometry is called an elementary reaction. Rate equations for such cases can easily be derived. Many reactions, however, are non-elementary, and consist of a series of elementary reactions. In such cases, we must assume all possible combinations of elementary reactions in order to determine one mechanism that is consistent with the experimental kinetic data. Usually, we can measure only the concentrations ofthe initial reactants and final products, since measurements of the concentrations of intermediate reactions in series are difficult. Thus, rate equations can be derived under assumptions that rates of change in the concentrations of those intermediates are approximately zero (steady-state approximation). An example of such treatment applied to an enzymatic reaction is shown in Section 3.2.2. 

Since the order refers to the empirically found rate expression, it need not be an integer. If it is a fraction, the reaction is nonelementary, giving no clue to the stoichiometry of the reaction. If the reaction order is an integer, it may or may not be an elementary reaction.Often it is not necessary to know the stoichiometry of a reaction exactly, or even the reaction order for all compounds. For example if a reactor system is desired where compound A is to be removed by reaction with B and C, the reaction partners should be in surplus in the system to ensure complete removal of A, as may be the case in the oxidation of a micropollutant in the 03/H202-process. The concentrations of B and C can be regarded as... 

The chemical equation for an elementary reaction is a description of an individual molecular event that involves breaking and/or making chemical bonds. By contrast, the balanced equation for an overall reaction describes only the stoichiometry of the overall process, but provides no information about how the reaction occurs. The equation for the reaction of N02 with CO, for example, does not tell us that the reaction occurs by direct transfer of an oxygen atom from an N02 molecule to a CO molecule. 

The above basic scheme is readily adapted to situations where the elementary reactions are of higher molecularity, with the first-order rate constants then being replaced where appropriate by products of second-order rate constants and concentrations of species involved. This leads to rate laws of higher complexity and kinetic behaviour which now may signal the existence of a transient intermediate. It is not practicable to treat all possibilities here [16], but consideration of the simplest of such situations reveals useful patterns. Scheme 9.4 presents a reaction of known stoichiometry, and four possible alternative kinetic schemes involving a reversibly formed intermediate (I) consistent with that stoichiometry. 

Another question is important for the safety assessment At which instant is the accumulation at maximum In semi-batch operations the degree of accumulation of reactants is determined by the reactant with the lowest concentration. For single irreversible second-order reactions, it is easy to determine directly the degree of accumulation by a simple material balance of the added reactant. For bimolecular elementary reactions, the maximum of accumulation is reached at the instant when the stoichiometric amount of the reactant has been added. The amount of reactant fed into the reactor (Xp) normalized to stoichiometry minus the converted fraction (A), obtained from the experimental conversion curve delivered by a reaction calorimeter (X = Xth) or by chemical analysis, gives the degree of accumulation as a function of time (Equation 7.18). Afterwards, it is easy to determine the maximum of accumulation XaCfmax and the MTSR can be obtained by Equation 7.21 calculated for the instant where the maximum accumulation occurs [7] ... 

Reactions that take place in a single step, that is, with a single transition state and no intermediates, are known as elementary reactions. They may represent an entire, kinetically simple reaction or a step in a more complex mechanism. In either case, the rate law for an elementary reaction is derived from its stoichiometry. This stands in contrast with more complex reactions, where the relationship between the overall stoichiometry and the rate law cannot be predicted, and both must be established experimentally. 

The simple relationship between the rate law and stoichiometry in elementary reactions allows one to derive a rate law for any multistep mechanistic scheme. The agreement between the derived rate law and that determined experimentally provides support for the proposed mechanism, although it does not prove it. The lack of agreement, on the other hand, definitely rules out the proposed scheme. 

Elementary reaction Reaction that has a rate equation that can be written directly from a knowledge of the stoichiometry. 

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