Unimolecular steps

Thus mechanism B, which consists solely of bimolecular and unimolecular steps, is also consistent with the information that we have been given. This mechanism is somewhat simpler than the first in that it does not requite a ter-molecular step. This illustration points out that the fact that a mechanism gives rise to the experimentally observed rate expression is by no means an indication that the mechanism is a unique solution to the problem being studied. We may disqualify a mechanism from further consideration on the grounds that it is inconsistent with the observed kinetics, but consistency merely implies that we continue our search for other mechanisms that are consistent and attempt to use some of the techniques discussed in Section 4.1.5 to discriminate between the consistent mechanisms. It is also entirely possible that more than one mechanism may be applicable to a single overall reaction and that parallel paths for the reaction exist. Indeed, many catalysts are believed to function by opening up alternative routes for a reaction. In the case of parallel reaction paths each mechanism proceeds independently, but the vast majority of the reaction will occur via the fastest path. 

Rate Expressions for Enzyme Catalyzed Single-Substrate Reactions. The vast majority of the reactions catalyzed by enzymes are believed to involve a series of bimolecular or unimolecular steps. The simplest type of enzymatic reaction involves only a single reactant or substrate. The substrate forms an unstable complex with the enzyme, which subsequently undergoes decomposition to release the product species or to regenerate the substrate. 

A comparison of equations 7.3.43 and 7.3.38 shows that they are of the same mathematical form. Both can be written in terms of four measurable kinetic constants in the manner of equation 7.3.40. Only the relationship between the kinetic constants and the individual rate constants differs. Thus, no distinction can be made between the two mechanisms using steady-state rate studies. In general, the introduction of unimolecular steps involving only isomerization between unstable intermediate complexes does not change the form of the rate expression. 

Central to catalysis is the notion of the catalytic site. It is defined as the catalytic center involved in the reaction steps, and, in Figure 8.1, is the molybdenum atom where the reactions take place. Since all catalytic centers are the same for molecular catalysts, the elementary steps are bimolecular or unimolecular steps with the same rate laws which characterize the homogeneous reactions in Chapter 7. However, if the reaction takes place in solution, the individual rate constants may depend on the nonreactive ligands and the solution composition in addition to temperature. 

In a region of temperature where the consecutive reactions are much faster than the unimolecular step, an equilibrium between the species H20, OH, H2, H and 02 will soon be established and the disappearance of water is then governed by the complicated mechanism including (2) and the reactions... 

The studies of Michel and Wagner, however, give no information about the mechanism of the reaction, so that the measured rate coefficient, k, cannot be correlated safely with that of an initiating unimolecular step such as... 

It should be noted that application of the Marcus theory to these reactions is much more straightforward than application to reactions in solution. Since we are dealing with a single unimolecular step, namely, rearrangement of the reactant complex to the product complex, we need not be concerned with the work terms (2) which must be included in treatments of solution-phase reactions. These terms represent the work required to bring reactants or products to their mean separations in the activated complex, and include Coulombic and desolvation effects. 

A common simplification arises when the bimolecular step in (1.153) equilibrates rapidly compared with the unimolecular step (it may, for example, be a proton-base reaction). This means that the change in concentrations of A, B, and C due to the first process in (1.153) will have occurred before D even starts to change. The relaxation time t, associated with it will therefore be the same as if it were a separated equilibrium ... 

The reaction sequence shown in Scheme 8.4 is in accord with all the experimental observations and involves at least two consecutive unimolecular steps [15,18]. Silyl radical 11 adds to molecular oxygen to form the peroxyl radical 12. 

ROS and other radical intermediates dictate the oxidative decomposition of fuels. We have noted that peroxy radical intermediates provide an enormous amount of flexibility in the combustion of a given compound, specifically in the unimolecular steps available to that compound. In an instructive display of the interaction of experimental and theoretical techniques, rearrangement pathways of the peroxy radicals have been modeled computationally and provide justification for several unexpected products. 

The thermal reactions of indole have been studied. The authors65 suggested that the indole to benzyl cyanide isomerization involves a series of unimolecular steps which... 

We shall use the representative mechanism in Equation 4.7 comprising three unimolecular steps to illustrate their application each elementary step is assigned a mechanistic rate constant ... 

The mechanism of Equation 4.7 is not especially complicated, yet the rigorous derivation of the rate equations is mathematically challenging, and the concentration-time expressions in Equations 4.8 are complex. It will be clear that when more unimolecular steps are involved in a mechanism, or if bimolecular elementary steps intervene, derivation of analytical solutions may become a formidable task. If the magnitudes of the elementary rate constants are similar, mathematical simplifications are not feasible, so the difficult rigorous methods have to be used. However, approximations become possible when the elementary rate constants are appreciably unequal in magnitude. This allows considerable mathematical simplification of the concentration-time relationships. Fortunately, the approximations are valid for many reactions of interest to organic chemists as we shall demonstrate. 

The unimolecular step in the reaction of cyclohexanol with hydrogen bromide to give cyclohexyl bromide is the dissociation of the oxonium ion to a carbocation. 

This problem was resolved in 1922 when Lindemann and Christiansen proposed their hypothesis of time lags, and this mechanistic framework has been used in all the more sophisticated unimolecular theories. It is also common to the theoretical framework of bimolecular and termolecular reactions. The crucial argument is that molecules which are activated and have acquired the necessary critical minimum energy do not have to react immediately they receive this energy by collision. There is sufficient time after the final activating collision for the molecule to lose its critical energy by being deactivated in another collision, or to react in a unimolecular step. 

This mechanism has a reversible unimolecular decomposition as a first step. As will be shown later, when unimolecular steps are involved in chain reactions, this can cause a change in order or a change in the value of the rate constant if the pressure is lowered. 

Identify the unimolecular steps in this mechanism and indicate what conditions would lead to a requirement for a third body for these steps. 

A more complex analysis would be needed if third bodies were included. Because unimolecular steps can show a pressure dependence, and because termination between atoms and small radicals needs a third body, often leading to a change in overall order with pressure, it is essential to establish first whether surface effects are significant. This is easily determined by altering the size, shape and nature of the vessel. 

There is however a discrepancy in that Chaires et al. [6] proposed a final, third step. The final unimolecular step in the mechanism was postulated by... 

All reactions are fast. At least, the individual steps of a reaction when molecules rearrange in a unimolecular step, or transfer atoms in a bimolecular encounter, occur on an atomic time scale and are complete in less than about 10-9 s. The slowness of the net reaction is due to the slowness with which molecules get activated or come together. But even the net rate may become very fast when the activation energy can be provided very rapidly. 

As the efficiency of step 47 depends on the concentration of acceptor [eq. (17)], the quantum yield is also a function of [A], although the energy transfer yield is not. However, according to eq. (17), the efficiency of step 47 reaches a limiting value, independent of the concentration of A when the concentration is high enough that unimolecular steps such as 41 can be neglected. 

Very recently, Nakajima and Okawa 164) investigated the hydrolysis of PNPA by Cyclo-(His-Glu-Cys-D-Phe-Gly)2. The second-order rate constant for the hydrolysis at pH 7.73 and 25 C was 19.61 M min for the cyclic decapeptide diacetate, which wt(s larger than 6.05 min for the corresponding linear pentapeptide triacetate and 1.33 M min for histidine hydrochloride, but smaller than 32.20 M min for cystein hydrochloride. The pH-rate profile for the reaction catalyzed by the cyclic decapeptide was bell-shaped with the maximum around pH 7.6, which indicates that the cyclic decapeptide is an acid—bs catalyst. On the other hand, the reaction by the cyclic decapeptide obeyed the Michaelis-Menten kinetics (i57), wdiich was found to involve a weak binding of the substrate = 2.7xlO M) prior to the unimolecular step. It is possible for imidazole, carboxyl, and thiol functions to cooperate in the cat ysis by the cyclic decapeptide, but the determination of the solution conformation would not be an easy task because of the thirty mem-bered ring. 

Unimolecular step a reaction step involving only one molecule. (15.6)... 

The molecularity of a step indicates how many reactant molecules participate in the step. For example, a step A— P is unimolecular, steps 2A— P and A + B — P are bimolecular. Trimolecular steps are rare, and quadrimolecular steps are unheard-of. 

Thermal cracking of organic substances is an important reaction in the petroleum industry and has been extensively studied for over seventy years. At least for simple alkanes, the decay is first order in good approximation and therefore was long believed to occur in a single, unimolecular step [21]. However, in the 1930s, Rice and coworkers [22-24] established the presence of free radicals under the conditions of the reaction by means of the Paneth mirror technique [25,26], This observation led Rice and Herzfeld to propose a chain mechanism [22,27,28], Extensive later studies proved the essential features of their mechanism to be correct not only for hydrocarbons, but also for many other types of organic substances. 

Previous studies on the hydrides with odd number of hydrogen atoms were mostly done for cation species." Indeed, dehydrogenation of M2H6 through an elementary, unimolecular step would result in losing hydrogen atoms by pair. 

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