Unimolecular reaction rates steps

The rate coefficient for the overall decomposition is expressible as kj = 10 exp (-85,000/lir) sec. Holbrook and Forst and St. Lauren have applied unimolecular reaction rate theory to the first step in the decomposition. A recent analytical study of the decomposition products at 720° has been reported by Le Moan . ... 

There are certain general rules that are very helpful in constructing a mechanism, Laidler [10]. The initiation step can be considered from the viewpoint of classical unimolecular reaction rate theory and is first order if ... 

In Volume 1 of this series P. J. Robinson gave a brilliant and exhaustive review of experimental studies of unimolecular reactions whidi were published to the end of 1973. The present article covers the literature to early 1976. Rather than continuing to present a similarly complete compilation of experimraital data, we shall concentrate on a complementary description of recent progress in unimolecular reaction rate theory, including selected experiments wMdi deal with the more fundamental aspects of unimolecular processes. In the first part of this review the role of intermolecular energy transfer in unimolecular reactions is discussed. Ihe second part considers the truly intramolecular reaction step. Theory and experiments will be reviewed in a way which clearly shows the connection between them. 

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

Rate constants that are near the diffusion-controlled limit may need to have a correction applied, if they are to be compared with others that are slower. To see this, consider a two-step scheme. In the first, diffusion together and apart occur the second step is the unimolecular reaction within the solvent cage. We represent this as... 

The rate law of a reaction is an experimentally determined fact. From this fact we attempt to learn the molecularity, which may be defined as the number of molecules that come together to form the activated complex. It is obvious that if we know how many (and which) molecules take part in the activated complex, we know a good deal about the mechanism. The experimentally determined rate order is not necessarily the same as the molecularity. Any reaction, no matter how many steps are involved, has only one rate law, but each step of the mechanism has its own molecularity. For reactions that take place in one step (reactions without an intermediate) the order is the same as the molecularity. A first-order, one-step reaction is always unimolecular a one-step reaction that is second order in A always involves two molecules of A if it is first order in A and in B, then a molecule of A reacts with one of B, and so on. For reactions that take place in more than one step, the order/or each step is the same as the molecularity for that step. This fact enables us to predict the rate law for any proposed mechanism, though the calculations may get lengthy at times." If any one step of a mechanism is considerably slower than all the others (this is usually the case), the rate of the overall reaction is essentially the same as that of the slow step, which is consequently called the rate-determining step. ... 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

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. 

The predicted rate law is first order for a reaction whose first step is unimolecular and rate-determining. The predicted rate law is second order overall for a reaction whose first step is bimolecular and rate-determining. For example, the first step of the mechanism for the C5 Hi 1 Br reaction is unimolecular and slow, so the rate law... 

A reaction rate expression that is proportional to the square root of the reactant concentration results when the dominant termination step is reaction (4c), that is, the termination reaction occurs between two of the radicals that are involved in the unimolecular propagation step. The generalized Rice-Herzfeld mechanism contained in equations 4.2.41 to 4.2.46 may be employed to derive an overall rate expression for this case. 

Studies of the influence of total pressure on the initial reaction rate for pure reactants present in stoichiometric proportions provide a means of discriminating between various classes of Hoqgen-Watson models. Isolation of a class of probable models by means of plots of initial reaction rate versus total pressure, feed composition, and temperature constitutes the first step n developing a Hougen-Watson rate model. Hougen (14) has considered the influence of total pressure for unimolecular and bimolecular surface reactions the analysis that follows is adopted from his monograph. 

The coefficients of the balanced overall equation bear no necessary relationship to the exponents to which the concentrations are raised in the rate law expression. The exponents are determined experimentally and describe how the concentrations of each reactant affect the reaction rate. The exponents are related to the ratedetermining (slow) step in a sequence of mainly unimolecular and bimolecular reactions called the mechanism of the reaction. It is the mechanism which lays out exactly the order in which bonds are broken and made as the reactants are transformed into the products of the reaction. 

So the tertiary halide reacts by a different mechanism, which we call SnI- It s still a nucleophilic substitution reaction (hence the S and the N ) but this time it is a unimolecular reaction, hence the 1 . The rate-determining step during reaction is the slow unimolecular dissociation of the alkyl halide to form a bromide ion and a carbocation that is planar around the reacting carbon. 

The homogeneous rate coefficient khomo is found to vary linearly with total pressure indicating that it is proportional to the rate coefficient of a unimolecular reaction in its second-order range. It is generally accepted that the initiating decomposition step is... 

An Arrhenius expression, k = 1012 exp(—24,300/Hr) sec-1, was quoted for the coefficient of the rate-determining step. It is doubtful whether this step is a true unimolecular reaction. The effect of pressures has not been studied. The range of temperatures used appears to be too narrow to discuss the temperature dependence... 

The formation of a complex between the propagating end and one or more molecules of monomer can have two extreme consequences. If the incorporation of a monomer molecule from the solvation shell of the cation is the growth-rate determining step, the propagation becomes a unimolecular reaction and the rate of polymerisation becomes of zero order with respect to monomer concentration. Such a model was developed by... 

Despite occasional apparent anomalies such as this, the rate expression gives us valuable information about the likely reaction mechanism. If the reaction is unimolecular, the rate-determining step involves just one species, whereas the rate-determining step involves two species if it is bimolecular. As indicated in Table 5.1, we can then deduce the probable reaction, and our proposed mechanism must reflect this information. The kinetic rate expressions will be considered further as we meet specific types of reaction. 

Consider a surface-catalyzed unimolecular reaction A, — Bg with A and B gases with partial pressures Pas and Pbs above the catalytic surface and coverages 6a and 6b on the surface. The elementary steps and their rates for a simple unimolecular reaction might be... 

Consequently, while I jump into continuous reactors in Chapter 3, I have tried to cover essentially aU of conventional chemical kinetics in this book. I have tried to include aU the kinetics material in any of the chemical kinetics texts designed for undergraduates, but these are placed within and at the end of chapters throughout the book. The descriptions of reactions and kinetics in Chapter 2 do not assume any previous exposure to chemical kinetics. The simplification of complex reactions (pseudosteady-state and equilibrium step approximations) are covered in Chapter 4, as are theories of unimolecular and bimolecular reactions. I mention the need for statistical mechanics and quantum mechanics in interpreting reaction rates but do not go into state-to-state dynamics of reactions. The kinetics with catalysts (Chapter 7), solids (Chapter 9), combustion (Chapter 10), polymerization (Chapter 11), and reactions between phases (Chapter 12) are all given sufficient treatment that their rate expressions can be justified and used in the appropriate reactor mass balances. 

The yield of the nucleophilic substitution product from the stepwise preassociation mechanism k[ = k. Scheme 2.4) is small, because of the low concentration of the preassociation complex (Xas 0.7 M for the reaction of X-2-Y). Formally, the stepwise preassociation reaction is kinetically bimolecular, because both the nucleophile and the substrate are present in the rate-determining step ( j). In fact, these reactions are borderline between S l and Sn2 because the kinetic order with respect to the nucleophile cannot be rigorously determined. A small rate increase may be due to either formation of nucleophile adduct by bimolecular nucleophilic substitution or a positive specific salt effect, whUe a formally bhnole-cular reaction may appear unimolecular due to an offsetting negative specific salt effect on the reaction rate. 

Many of the esters which are hydrolyzed by the AalI mechanism in acid are also hydrolyzed with alkyl-oxygen fission under neutral condi-tions60,67 74 75 84 85 88 89. These reactions have the high enthalpies and entropies of activation characteristic of unimolecular reactions, and involve the ionization of (usually) tertiary alkyl esters, to the carbonium ion and a carboxylate anion in the rate-determining step, viz. 

In the first step, all the coal bulk which is readily available in the mixture of coal and solvent goes to Ri which is solid, Li which is liquid, and Gi which is gas. The rate constant for this unimolecular reaction is ki. When Reaction 1 is well advanced, Reaction 2 becomes the main route with the extraction of Ri (rate constant fa) and so on. According to Dryden (2), extraction occurs by the removal of units of colloidal size directly from the coal, and he proposes a model for extraction as follows ... 

Due to the time-resolution limitation of the method, FPTRMS can be used to determine the kinetics of only those unimolecular reactions that occur on millisecond time scales or longer. However, even if a unimolecular reaction occurs too rapidly for time resolution of the kinetics, the occurrence of a reaction can be shown by mass spectrometric detection of the products. If the unimolecular reaction is rate limited by a preceding slow step so that the product formation rates are time resolved, then a lower limit to the unimolecular rate coefficient can be estimated. In the case of atmospheric reactions this will frequently be enough information to permit reaction mechanisms to be sorted out. 

The simplest reactions have the one-step unimolecular or bimolecular mechanisms illustrated in Table 4.1 along with their differential rate equations, i.e. the relationships between instantaneous reaction rates and concentrations of reactants. That simple unimolecular reactions are first order, and bimolecular ones second order, we take as self-evident. The integrated rate equations, which describe the concentration-time profiles for reactants, are also given in Table 4.1. In such simple reactions, the order of the reaction coincides with the molecularity and the stoichiometric coefficient. 

Transition state theory thus allows the writing of a rate equation for any elementary reaction, and a transformation in which an intermediate is postulated can be treated as a sequence of elementary steps. For any particular sequence, a set of differential equations may be written. For the simplest of these, the sequence of two irreversible unimolecular reactions shown in Fig. 9.2, the exact integrated forms are available permitting calculation and plotting of the time course of anticipated concentration changes for a comparison with experimental data see Chapters 3 and 4. 

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