Dissociative mechanism rate equation

Various Langmiiir-Hinshelwood mechanisms were assumed. GO and GO2 were assumed to adsorb on one kind of active site, si, and H2 and H2O on another kind, s2. The H2 adsorbed with dissociation and all participants were assumed to be in adsorptive equilibrium. Some 48 possible controlling mechanisms were examined, each with 7 empirical constants. Variance analysis of the experimental data reduced the number to three possibilities. The rate equations of the three reactions are stated for the mechanisms finally adopted, with the constants correlated by the Arrhenius equation. 

The catalysts used in hydroformylation are typically organometallic complexes. Cobalt-based catalysts dominated hydroformylation until 1970s thereafter rhodium-based catalysts were commerciahzed. Synthesized aldehydes are typical intermediates for chemical industry [5]. A typical hydroformylation catalyst is modified with a ligand, e.g., tiiphenylphoshine. In recent years, a lot of effort has been put on the ligand chemistry in order to find new ligands for tailored processes [7-9]. In the present study, phosphine-based rhodium catalysts were used for hydroformylation of 1-butene. Despite intensive research on hydroformylation in the last 50 years, both the reaction mechanisms and kinetics are not in the most cases clear. Both associative and dissociative mechanisms have been proposed [5-6]. The discrepancies in mechanistic speculations have also led to a variety of rate equations for hydroformylation processes. 

Thiophene is the typical model compound, which has been extensively studied for typifying gasoline HDS. Although, some results are not completely understood, a reaction network has been proposed by Van Parijs and Froment, to explain their own results, which were obtained in a comprehensive set of conditions. In this network, thiophene is hydrodesulfurized to give a mixture of -butenes, followed by further hydrogenation to butane. On the considered reaction conditions, tetrahydrothiophene and butadiene were not observed [43], The consistency between the functional forms of the rate equations for the HDS of benzothiophene and thiophene, based on the dissociative adsorption of hydrogen, were identical [43,44], suggesting equivalent mechanisms. 

Similar to irreversible reactions, biochemical interconversions with only one substrate and product are mathematically simple to evaluate however, the majority of enzymes correspond to bi- or multisubstrate reactions. In this case, the overall rate equations can be derived using similar techniques as described above. However, there is a large variety of ways to bind and dissociate multiple substrates and products from an enzyme, resulting in a combinatorial number of possible rate equations, additionally complicated by a rather diverse notation employed within the literature. We also note that the derivation of explicit overall rate equation for multisubstrate reactions by means of the steady-state approximation is a tedious procedure, involving lengthy (and sometimes unintelligible) expressions in terms of elementary rate constants. See Ref. [139] for a more detailed discussion. Nonetheless, as the functional form of typical rate equations will be of importance for the parameterization of metabolic networks in Section VIII, we briefly touch upon the most common mechanisms. 

Another way of looking at the question of creation of a vacant site and coordination of the substrate is the classical way by which substitution reactions are described (Figure 2.1). Two extreme mechanisms are distinguished, an associative and a dissociative one. In the dissociative mechanism the ratecontrolling step is the breaking of the bond between the metal and the leaving ligand. A solvent molecule occupies the open site, which is a phenomenon that does not appear in the rate equation. Subsequently the solvent is replaced by the... 

Once the dissociative mechanism is established, it is possible to apply Gutmann s theoretical treatment (40) to the elucidation of the rate-determining step of the exchange reaction. For deuterium-tritium double labeling procedures, i.e., D O 100%, TgO 1%, it may be shown that the following normalized equations apply under initial exchange conditions ... 

Symbol for the dissociation constant of an inhibitor with respect to a particular form of the enzyme. This dissociation constant is associated with the intercept term in the double-reciprocal form of the initial-rate equation. For example, consider an inhibitor that can bind to either the free enzyme, E, or the binary central complex, EX, of a Uni Uni mechanism. Ka would be the dissociation constant for the EX -t 1 EXl step and is equal to [EX][1]/[EX1]. The binding of 1 to the free enzyme (i.e., E -t 1 El) is governed by Kis (equal to [E][1]/[E1]). 

Rapid Equilibrium Mechanism. If the rate-determining step is the catalytic step and all binding steps can be described by dissociation constants (e.g., K = [E][A]/ [EA]), then, in the absense of products i.e., [P] and [Q] 0), the initial rate equation for the rapid equihbrium Uni Bi mechanism is identical to that of the Uni Uni... 

In principle it is possible to write down the rate equation for any rate determining chemical step assuming any particular mechanism. To take a specific example, the overall rate may be controlled by the adsorption of A and the reaction may involve the dissociative adsorption of A, only half of which then reacts with adsorbed B by a Langmuir-Hinshelwood mechanism. The basic rate equation which represents such a process can be transposed into an equivalent expression in terms of partial... 

The kinetic data obtained were interpreted on the basis of a redox mechanism, with two main steps (1) dissociative adsorption of 02 (surface oxidation) and (2) interaction of NH3 with oxygen adsorbed in atomic form (surface reduction). Both steps are complex, comprising several elementary reactions. This mechanism is again consistent with the rate equation (16.1). 

Solvation of thiolates is similarly low in both protic and dipolar aprotic solvents because of the size and polarisability of the large weakly basic sulfur atom, so is unlikely to contribute appreciably to the observed solvent effect. The intermediate nitro radical anion is stabilised by H-bonding in a manner which retards its dissociation in the SrnI mechanism (upper equation in Scheme 10.35). In contrast, the electron flow in the direct substitution at X (lower equation in Scheme 10.35) is such that solvation by methanol promotes the departure of the nucleofuge. In summary, protic solvation lowers the rate of the radical/radical anion reactions, but increases the rate of the polar abstraction yielding disulfide. 

Operating within the framework of the Chauvin mechanism, the main consideration for the reaction mechanism is the order of events in terms of addition, loss and substitution of ligands around the ruthenium alkylidene centre. Additionally, there is a need for two pathways (see above), both being first order in diene, one with a first-order dependence on [Ru] and the other (which is inhibited by added Cy3P) with a half-order dependence on [Ru]. From the analysis of the reaction kinetics and the empirical rate equation thus derived, the sequence of elementary steps via two pathways was proposed, one non-dissociative (I) and the other dissociative (II), as shown in Scheme 12.20. The mechanism-derived rate equation is also shown in the scheme and it can thus be seen how the constants A and B relate to elementary forward rate constants and equilibria in the proposed mechanism. 

There is an alternative pathway to II, in which the phosphine dissociates before the alkene group coordinates pathway III. On the basis of electron accountancy alone, this should be viewed as unfavourable as it involves two 14-electron intermediates (26 and 27). However, it should be noted that the mechanism-derived rate equation for reaction via pathways I/III rather than I/II would be equally consistent with the empirical rate equation. 

The mechanism for the peroxide transfer reaction of Equation 45 is not established. We know from kinetic studies that 4a-FlEtOO undergoes conversion to a peroxidizing species before reaction with the phenolate ion. The species enumerated in Scheme 7 would have no propensity to deliver both oxygen atoms of the 4a-FlEtOO to a substrate. Dissociation of 4a-FlEtOO to FlEt- and 02 and reaction of the phenolate ion with 02 can be ruled out because the bimolecular rate constant for reaction of 02 with phenolate is one hundredfold too small to account for the reaction of Equation 45. The mechanism of Equation 47 has been proposed (51). In favor of this mechanism is... 

Key Mechanism 4-1 Free-Radical Halogenation 136 4-4 Equilibrium Constants and Free Energy 138 4-5 Enthalpy and Entropy 140 4-6 Bond-Dissociation Enthalpies 142 4-7 Enthalpy Changes in Chlorination 143 4-8 Kinetics and the Rate Equation 145... 

Robb and co-workers have studied the kinetics of the anation of [Rh(H20)Cl5]2 by a variety of monoanions (equation 286 X = Cl, Br, I, N02, N3 or NCS).1213 The rates of anation are relatively independent of the nature of the anating ligand (k 2.9 ( 1) x 10-2s-1 at 35 °C), consistent with a dissociative mechanism. The rates of equilibration of the hexachloro, pentachloro and m-tetra-chloro anions were studied as a function of chloride concentration and the data were fitted to the kinetic expression kobs = + fcanutCl ]- The effect of pressure (1-1500 bar) was also mon-... 

There is a simple dissociative mechanism for [Fe(phen)3] + dissociation in acid, which is independent of acid concentration. However, when the ligand is the more flexible bipy, a monodentate protonated intermediate is kinetically significant. Here, the observed rate of dissociation increases with increasing acid concentration up to about 2moll, as shown in Scheme 3, and the reaction rate is given by equation (5). 

Characteristic of the rate equations 5.76 and 5.79 is their one-half order with respect to the dissociating reactant, in the case of eqn 5.79 with respect to the coreactants B and C as well. This is an exception to the rule that a reasonably simple mechanism does not give a rate equation with fractional exponents. Conversely, an observed, conversion-independent order of one half is an indication that the reaction might involve fast pre-dissociation. 

There is one important exception Certain types of chain reactions and reactions involving dissociation produce exponents of one half or integer multiples of one half in power-law or one-plus rate equations (see Sections 5.6, 9.2, and 10.3.1). Such exponents should be accepted if found not to vary with conversion and if there is good reason to believe that a mechanism of this kind may be operative. 

The conventional procedure of fitting a rate equation to experimental data is to use a power law reflecting the observed reaction orders. However, while fractional reaction orders may provide an acceptable fit, they cannot be produced by reasonable mechanisms. A better way is to fit the data to "one-plus" rate equations, that is, equations containing concentrations with integer exponents only, but with denominators composed of two or more additive terms of which the first is a "one." Such equations behave much like power laws with fractional exponents but, in contrast to these, can arise from reasonable mechanisms and therefore are more likely to hold over wide ranges of conditions. As an exception, rate equations with constant exponents of one half or integer (positive or negative) multiples of one half can result from chain reactions and reactions initiated by dissociation, and are acceptable if such a mechanism is probable or conceivable. 

The rates of product formation (and reactant consumption) are seen to be of order one half in the initiator or, if the reaction is initiated by a reactant converted in the propagation cycle, the rate equation involves exponents of one half or integer multiples of one half. For an example, see the hydrogen-bromide reaction below. This is one of the exceptions to the rule that reasonably simple mechanisms do not yield rate equations with fractional exponents. [The other exceptions are reactions with fast pre-dissociation (see Section 5.6) and of heterogeneous catalysis with a reactant that dissociates upon adsorption.]... 

It has been said that only termination, but not dissociation, involves a collision partner M and that the ratio klm, ikcB, in the rate equation does not equal the dissociation equilibrium constant because the two coefficients are "not linked by detailed balancing" [16], However, this argument is without merit. In the absence of H2 (or any other species with which Br- can react), thermodynamic consistency and microscopic reversibility clearly require M to participate in dissociation if it does so in recombination. The addition of any species such as H2 that takes no part in the dissociation step may cause the system to deviate from thermodynamic dissociation equilibrium, but can obviously not alter the mechanism of dissociation. 

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