Bimolecular mechanism/step

Neither bromine nor ethylene is a polar molecule but both are polarizable and an induced dipole/mduced dipole force causes them to be mutually attracted to each other This induced dipole/mduced dipole attraction sets the stage for Br2 to act as an electrophile Electrons flow from the tt system of ethylene to Br2 causing the weak bromine-bromine bond to break By analogy to the customary mechanisms for electrophilic addition we might represent this as the formation of a carbocation m a bimolecular elementary step... 

The mechanism of alkene epoxidation is believed to be a concerted process mvolv mg a single bimolecular elementary step as shown m Figure 6 14... 

Much of the language used for empirical rate laws can also be appHed to the differential equations associated with each step of a mechanism. Equation 23b is first order in each of I and C and second order overall. Equation 23a implies that one must consider both the forward reaction and the reverse reaction. The forward reaction is second order overall the reverse reaction is first order in [I. Additional language is used for mechanisms that should never be apphed to empirical rate laws. The second equation is said to describe a bimolecular mechanism. A bimolecular mechanism implies a second-order differential equation however, a second-order empirical rate law does not guarantee a bimolecular mechanism. A mechanism may be bimolecular in one component, for example 2A I. 

The synchronous bimolecular mechanism for aromatic nucleophilic substitution involves unfavorable geometry (bonds made and broken are both in the plane of the ring and backside attack is not possible) and unfavorable energetics (one high-energy step is required... 

The results are consistent with either an ANDN-like mechanism, i.e., a concerted attack of the nucleophile with the release of N2, or a two-step AN + DN mechanism. On the other hand, substituent effects, as found by Crossley and coworkers (1940) and later verified by Schulte-Frohlinde and Blume (1968 b), cannot be understood on the basis of such bimolecular mechanisms. Instead of an accelera-... 

Note that both of the steps in the mechanism are bimolecular reactions, reactions that involve the collision of two chemical species. Unimolecular reactions are reactions in which a single chemical species decomposes or rearranges. Both bimolecular and unimolecular reactions are common, but the collision of three or more chemical species (termolecular) is quite rare. Thus, in developing or assessing a mechanism, it is best to consider only unimolecular or bimolecular elementary steps. 

The two steps add up to give the overall reaction. The second step is bimolecular, so it is chemically reasonable. The first step is termolecular, which is possible but rare. In the proposed mechanism, step 1 is the rate-determining reaction. The rate law equation for the first step is written as follows ... 

As mentioned earlier, the Srn2 mechanism sketched in Scheme 11 has been suggested to explain the effect of a change of leaving group on product distribution in the reaction of 2-substituted 2-nitropropanes with enolate ions (Russell et al., 1981, 1982a,b). It has been proposed that the bimolecular substitution step (133) would involve, rather than S, 2 substitution at the... 

Bimolecular processes are very common in biological systems. The binding of a hormone to a receptor is a bimolecular reaction, as is substrate and inhibitor binding to an enzyme. The term bimolecular mechanism applies to those reactions having a rate-limiting step that is bimolecular. See Chemical Kinetics Molecularity Reaction Order Elementary Reaction Transition-State Theory... 

Fig. 24. Kinetic mechanism for the interaction of substrates and products with RNase. The various bimolecular association steps and isomerization processes are shown. Proton binding and pH dependence are not indicated. [Adapted from Hararaes (466), Fig. 2 note that second isomerization originally inserted between EP2 and ESi was probably the result of a second binding site at high 3 -CMP concentration see Hammes and Walz (468).]...

The usually considered monomolecular mechanism of substitution implies that one-electron reduction activates a substrate sufficiently so that it could dissociate with no further assistance from a nucleophile. The next steps of the reaction consist of transformations of the resultant radical. However, in substrates having sp3 carbon as a reaction center, the influence of the leaving group has been fixed (Russell Mudryk 1982a, 1982b). This led to the formulation of the SRN2 bimolecular mechanism of radical-nucleophilic substitution. In this mechanism, the initial products of single-electron transfer are combined to form the... 

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. 

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 mechanism of the fourth category of bimolecular surface steps is peculiar to redox reactions catalysed by metals and semiconductors. Here both reactants sit on the surface, not necessarily on adjacent sites, and the electrons are transferred from the reducing to the oxidising species through the solid catalyst. The rate therefore depends not only on the concentrations at the surface but also on the potential taken up by the catalyst, and this potential in turn is a function of the concentrations of the electroactive species present. Equations (28) and (29) fail to represent the kinetics in these cases because khel is no longer independent of concentration. These kinetics must accordingly be treated by an electrochemical method of analysis and this is done in Sect. 4.1. 

Ring expansion of aromatic compounds by carbene, carbethoxycarbene, chlorocarbene, and carbenoid is well known 256, 336, 351-356). Muller and co-workers reported the reaction of aromatic compounds with carbene generated from a catalytic decomposition of diazomethane with copper salts, and proposed a bimolecular two-step mechanism involving an inverse ylid for the reaction. Miller (336) proposed another bimolecular two-step mechanism for the reaction of benzene with alkylcarbenoids of aluminum. Baldwin and Smith (25) proposed a concerted mechanism for the reaction of aromatic compounds with carbethoxycarbene. Reaction of alkylbenzene with diethylzinc and ethylidene iodide gives 7-methylcyclohepta-l,3,5-triene derivatives in yield 369). The... 

The formation of norcaradiene derivatives with naphthalene [reaction (22)] lends some support to this scheme. This mechanism resembles a bimolecular two-step process suggested for the reaction of chloromethyl-aluminum compounds with olefins (199-201). On the other hand, a bimolecular one-step methylene transfer mechanism is generally accepted for the formation of cyclopropane derivatives by the reaction of halo-methylzinc compounds with olefins. This difference between the mechanism proposed for the cyclopropane formation from olefin and that for the ring expansion of aromatic compound may be ascribable to the difference in the stability of intermediates the benzenium ion (XXII) may be more stable than an alkylcarbonium ion (369). 

Molecularities. An equally elementary criterion is the fact that a great majority of reaction steps are uni- or bimolecular trimolecular steps are rare and slow, and steps of still higher molecularities are unheard of (see Section 2.1). A trimolecular forward or reverse step in a postulated mechanism calls for an explanation why its reactants are not consumed by bimolecular steps before they have a chance to undergo the trimolecular one (e.g., see the Example 7.8 farther below). No mechanism involving a forward or reverse step of even higher molecularity should ever be considered. 

If the rate-determining step involves a reaction of SH+ with a water molecule (A2 mechanism) a Van der Waals bond of a length of ca. 3.6 A goes over to a reacting bond of a length of ca. 1.65 A. This corresponds to a volume decrease of ca. 2 x 10-2 3 cm3 per particle or 12 cm3 per mole. Another bond length may be somewhat increased at the same time, therefore we expect for a bimolecular reaction step that [31] An V % -11 cm3. 

The kinetics of the polymerization of tri- and tetraphosphonitrilic chlorides in solution and in bulk have been studied by Patat and Kol-linsky (58) and Patat and Frombling (57). Hydrocarbons are unsuitable solvents, since they react to give hydrogen chloride successful results w ere obtained in carbon tetrachloride. The proposed mechanism involves unimolecular initiation, either by oxygen (in solution) or another phosphonitrilic molecule (in bulk). A bimolecular propagation step is followed by unimolecular termination. Traces of water were foimd by Renaud to have a significant effect on the polymerization process (62, 63). 

Coombes and Katchalski [29] have considered a slightly more complex version of this mechanism in which a second propagation coefficient operates above a critical degree of polymerization. Katchalski et al. [30] calculated the molecular weight distribution obtained in a system following scheme (12) but also including a bimolecular termination step. Various authors have analysed more complex systems in which the initiator is a polymeric species. Thus Gold [31] has shown that initiation by a poly a-amino acid with a Poisson distribution leads to a polymeric product with an over-all Poisson distribution, and Katchalski et al. [32] demonstrated that in multichain polymers synthesized from polyfunctional initiators Poisson distributions also arise. 

The detection of a reaction intermediate is usually not possible in coordination chemistry because lifetimes of intermediates are commonly extremely short. The simple mechanisms of reaction are commonly designated as an associative mechanism (A, with an intermediate of expanded coordination number formed) or a dissociative mechanism (D, with an intermediate of reduced coordination number formed). Intermediates of expanded coordination number are important in ligand substitution in square-planar complexes and in a few cases can actually be detected. For example, NifCNls " is known from exchange reaction of Ni(CN)4 with CN (288). Even in octahedral complexes, some evidence for associative processes exists indirectly. The [RulNHsle] " ion reacts with NO in acid to form [RuINHslsNO] and NH4 much more rapidly than can be explained by aquation of the hexaamine as the initial step, and a bimolecular mechanism with a 7-coordinate intermediate has been proposed (11, 226). 

Basic Catalysis. The catalytic properties of alkali zeolites free of acidic sites have been investigated for the cracking of hexanes (25, 26). At 500 C K-Y zeolite cracks easily n-hexane and its isomers resulting in product distributions markedly different from those obtained over acidic zeolites or even by thermal cracking (pyrolysis). Free radical-type mechanism predominates on the zeolite surface. The relative rates of H atom abstraction (bimolecular) and B-scission (unimolecular) are greatly affected by the zeolite matrix. Zeolites also concentrate hydrocarbon reactants within the crystal, which enhances the rate of bimolecular reaction step. Comparison with silicalite (Al-free ZSM-5 zeolite) and quartz chips has been done in order to characterize the zeolitic effect. Silicalite behaves as inert quartz chips with no effect on the rate of H-abstraction step,... 

The hahde nucleophile helps to push off a water molecule from the alkyloxonium ion. According to this mechanism, both the halide ion and the alkyloxonium ion are involved in the same bimolecular elementary step. In Ingold s terminology, introduced in Section 4.11 and to be described in detail in Chapter 8, nucleophilic substimtions characterized by a bimolecular rate-determining step are given the mechanistic symbol Sn2. 

In an SN2 mechanism, substitution (alkylation) takes place in a bimolecular one-step process as follows ... 

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