Second-order reaction mechanisms

The double exposure complications introduced by the first and second order reaction mechanisms in acrylate resists led to the conclusion that the flood and patterning exposure process was not a practical solution to the problem of high crosslink density in PM-15 resist. 

The decomposition of acetaldehyde into methane and carbon monoxide is a second-order reaction (mechanism 2A 2B + 2C) characterized by a specific rate constant of0.19M sec" at 791°K. 

The kinetics of hydrolysis reactions maybe first-order or second-order, depending on the reaction mechanism. However, second-order reactions may appear to be first-order, ie, pseudo-first-order, if one of the reactants is not consumed in the reaction, eg, OH , or if the concentration of active catalyst, eg, reduced transition metal, is a small fraction of the total catalyst concentration. 

However, in most cases, relation (48) does not account for results obtained under experimental conditions used in industry, i.e. high reactant concentrations. Othmer carried out a detailed study in this field and suggested second-order reactions for the esterifications of n-butanol with acetic acid245 and monobutyl terephthalate246 catalyzed by sulfuric acid. Since such relations cannot be established in all cases, no reaction order could be found for the esterification of 2,3-butanediol with acetic arid247 in the presence of sulfuric add. Moreover, Othmer s reaction orders were obtained for very concentrated media and in our opinion cannot be connected to a mechanism. In fact, this was not Othmer s objective who established these relations for practical use in industrial esterifications. 

Schmid s work marks the start of a change in the way in which the mechanism of diazotization was regarded, although it seems surprising that Schmid did not discuss further the contrast between his result indicating a reaction of third order and Hantzsch s claiming a second-order reaction. The diazotization mechanism in dilute HC1 and HBr will be discussed in Section 3.3. 

The activation entropies were considerably different from the large negative values expected for a second-order reaction and this was attributed to the effect of the internal return mechanism. 

According to the definition given, this is a second-order reaction. Clearly, however, it is not bimolecular, illustrating that there is distinction between the order of a reaction and its molecularity. The former refers to exponents in the rate equation the latter, to the number of solute species in an elementary reaction. The order of a reaction is determined by kinetic experiments, which will be detailed in the chapters that follow. The term molecularity refers to a chemical reaction step, and it does not follow simply and unambiguously from the reaction order. In fact, the methods by which the mechanism (one feature of which is the molecularity of the participating reaction steps) is determined will be presented in Chapter 6 these steps are not always either simple or unambiguous. It is not very useful to try to define a molecularity for reaction (1-13), although the molecularity of the several individual steps of which it is comprised can be defined. 

Stewart and Van der Linden also examined the incorporation of into the cyanate from labelled permanganate. The percentage of transfer varied with alkalinity and the authors believe that significant oxygen-transfer occurs in the second-order reaction, but not in the complex reaction. Accordingly the mechanism for the second-order reaction is proposed to be... 

B. l,3>2>Dioxaphospholens.—The kinetics of the addition of trialkyl phosphites to benzil have been investigated spectrophotometrically. The second-order reaction of trimethyl phosphite in dioxan has activation parameters of A// = 8.4 kcal mol and AS = — 47.5 e.u. In benzene the rate constant increases linearly with low concentrations of added organic acid and decreases linearly with low concentrations of added base. The Diels-Alder mechanism is considered unlikely on the basis of these data, and the slow step is considered to be nucleophilic addition of the phosphite to the carbon of the carbonyl group (see Scheme). 

It is obvious that to quantify the rate expression, the magnitude of the rate constant k needs to be determined. Proper assignment of the reaction order and accurate determination of the rate constant is important when reaction mechanisms are to be deduced from the kinetic data. The integrated form of the reaction equation is easier to use in handling kinetic data. The integrated kinetic relationships commonly used for zero-, first-, and second-order reactions are summarized in Table 4. [The reader is advised that basic kinetic... 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

If the surface is nearly covered (0A 1) the reaction will be first-order in the gas phase reactant and zero-order in the adsorbed reactant. On the other hand, if the surface is sparsely covered (0A KAPA) the reaction will be first-order in each species or second-order overall. Since adsorption is virtually always exothermic, the first condition will correspond to low temperature and the second condition to high temperatures. This mechanism thus offers a ready explanation of a transition from first-to second-order reaction with increasing temperature. 

As a 3-step mechanism, the electron-transfer paradigm provides a pair of discrete intermediates [D, A] and D+, A for the prior organization and the activation, respectively, of the donor and the acceptor. The quantitative evaluation of these intermediates would allow the overall second-order reaction (k2) to be determined. Although the presence of [D, A] does not necessarily imply its transformation to D+, A-, a large number and variety of donor/ acceptor couples showing transient charge-transfer absorptions associated with [D, A] have now been identified. In each case, the product can be predicted from the expected behavior of the individual ion radicals D+ and A-. Consider for example, the labile 1 1 benzene complex with bromine that has been isolated at low temperatures and characterized crystallographically (Chart 9).256... 

The reaction of E with S is of a different type, called second order. Second-order reactions are usually found in reactions of the type A + B —> C. The velocity of a second-order reaction depends on how easy it is for E and S to find each other in the abyss of aqueous solution. Obviously, lower E or lower S concentration make this harder. For second-order reactions, the velocity depends on the product of both of the reacting species (v = k[S [E]). Here k must have units of reciprocal molar minutes (M-1 min-1) so that the units on the left and right sides balance. The second-order rate constant in the mechanism of Fig. 8-3 is kx. 

Peroxynitrite easily oxidizes nonprotein and protein thiyl groups. In 1991, Radi et al. [102] have shown that peroxynitrite efficiently oxidizes cysteine to its disulfide form and bovine serum albumin (BSA) to some derivative of sulfenic acid supposedly via the decomposition to nitric dioxide and hydroxyl radicals. Pryor et al. [124] suggested that the oxidation of methionine and its analog 2-keto-4-thiomethylbutanic acid occurred by two competing mechanisms, namely, the second-order reaction of sulfide formation and the one-electron... 

Micellar rate enhancements of bimolecular, non-solvolytic reactions are due largely to increased reactant concentrations at the micellar surface, and micelles should favor third- over second-order reactions. The benzidine rearrangement typically proceeds through a two-proton transition state (Shine, 1967 Banthorpe, 1979). The first step is a reversible pre-equilibrium and in the second step proton transfer may be concerted with N—N bond breaking (17) (Bunton and Rubin, 1976 Shine et al., 1982). Electron-donating substituents permit incursion of a one-proton mechanism, probably involving a pre-equilibrium step. 

What is the significance of the parameter fi = (k2C BLDAf5 / kL in the choice and the mechanism of operation of a reactor for carrying out a second-order reaction, rate constant k2, between a gas A and a second reactant B of concentration CBL in a liquid In this expression, DA is the diffusivity of A in the liquid and kL is the liquid-film mass transfer coefficient. What is the reaction factor and how is it related to /l ... 

The reactivity of NO with O2 is dramatically affected upon coordination of one of the diatomic components to a metal center. For example, the second-order reactions of NO with oxyhemoglobin, Hb(02) and oxymyoglobin, Mb(02) (e.g. Eq. (47)) are quite fast and have been used as colorimetric tests for NO (105). The nitrogen product is NO3 rather than N02 that is the product of aqueous autoxidation (106). While the reaction of 02 with nitrosyl myoglobin Mb(NO) (Eq. (48)) might superficially appear similar it is much slower and follows a different rate law (107). Possible mechanisms will be discussed below. 

The model of a reactor consists of two equal sized CSTRs joined by a PFR whose residence time equals that of the combined CSTRs. A second order reaction with kC0t = 2 is to be studied by the maximum mixedness mechanism. More details of this problem are in problem P5.04.09 where the RTD is developed as... 

The evidence for the mechanism is that it is a second order reaction. Further, since the reaction proceeds readily in nonpolar solvents, hence the formation of ions from perbenzoic acid, as postulated earlier, is inhibited. The final evidence is that the reaction is stereospecific and proceeds with the retention of cis or trans configurations present in the initial olefine. 

The preceding approach applies to all linear systems that is, those involving mechanisms in which only first-order or pseudo-first-order homogeneous reactions are coupled with the heterogeneous electron transfer steps. As seen, for example, in Section 2.2.5, it also applies to higher-order systems, involving second-order reactions, when they obey pure kinetic conditions (i.e., when the kinetic dimensionless parameters are large). If this is not the case, nonlinear partial derivative equations of the type... 

More complicated reactions that combine competition between first- and second-order reactions with ECE-DISP processes are treated in detail in Section 6.2.8. The results of these theoretical treatments are used to analyze the mechanism of carbon dioxide reduction (Section 2.5.4) and the question of Fl-atom transfer vs. electron + proton transfer (Section 2.5.5). A treatment very similar to the latter case has also been used to treat the preparative-scale results in electrochemically triggered SrnI substitution reactions (Section 2.5.6). From this large range of treated reaction schemes and experimental illustrations, one may address with little adaptation any type of reaction scheme that associates electrode electron transfers and homogeneous reactions. 

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. 

The investigation of the kinetics of a chemical reaction serves two purposes. A first goal is the determination of the mechanism of a reaction. Is it a first order reaction, A—or a second order reaction, 2A— Is there an intermediate A—>/— and so on. The other goal of a kinetic investigation is the determination of the rate constant(s) of a reaction. 

This set includes all reaction mechanisms that contain only first order reactions, as well as very few mechanisms with second order reactions. Any textbook on chemical kinetics or physical chemistry supplies a list. A few examples for such mechanisms are given below ... 

It should be noted that the unfolding kinetics can sometimes involve quite complex unfolding schemes of different substates in equilibrium with the native state. Staphylococcal nuclease is an example of such behavior, known to unfold with three different substates that exhibit an equilibrium that does not appear to shift with temperature.49 Irreversible aggregation processes of proteins have been known to involve first- or second-order reactions.132141 The mechanism of recombinant human interferon-y aggregation is an example where thermodynamic and kinetic aspects of the reaction provided a powerful tool for understanding the pathway of instability and permitted a rationale for screening excipients that inhibited the process.141... 

An associative mechanism is supported, consistent with a low-spin d configuration. Other ligands such as arsenite reduce Ag(OH>4 in a rapid second-order reaction. It is uncertain whether it occurs via complex formation. Silver(III) macrocycles including porphyrin complexes have been characterized. 

The second-order reaction with adsorption of the ligand (2.210) signifies the most complex cathodic stripping mechanism, which combines the voltammetric features of the reactions (2.205) and (2.208) [137]. For the electrochemically reversible case, the effect of the ligand concentration and its adsorption strength is identical as for reaction (2.205) and (2.208), respectively. A representative theoretical voltammo-gram of a quasireversible electrode reaction is shown in Fig. 2.86d. The dimensionless response is controlled by the electrode kinetic parameter m, the adsorption... 

Symbols for substrates and products, respectively, in multisubstrate enzyme-catalyzed reactions. In all ordered reaction mechanisms, A represents the first substrate to bind, B is the second, eta, whereas P denotes the first product to be released, Q represents the second, eta See Cleland Nomenclature... 

The rate constant for the second order reaction was found to be at least two orders of magnitude greater than that for the corresponding Rh system. As with the corresponding Rh reaction, a modest kinetic isotope effect was observed when H-Mel was used, again consistent with an 5 2 mechanism for this step [33]. 

Figure 3.2 Test for the bimolecular mechanism A + B - R with C o or for the second-order reaction, Eq. 13.

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