Nucleophilic substitution reactions second-order rate equation

A.i. The Sn2 Reaction. In reactions where the substrate (see 61) has a leaving group (X) connected to a sp3 carbon, displacement by a nucleophile leads to a product in which X has been replaced by the nucleophile to give 63. This process can be described as a bimolecular (it follows second order rate equation) substitution that involves a nucleophile. The mechanistic descriptor is, therefore, Sn2. Reactions labeled as Sn2 may be observed in several different functional group exchange reactions and the substrate and the reagent can be either simple or complex. All Sn2 reactions can be represented by the simple reaction sequence 61 63,... 

This one-step nucleophilic substitution is an example of the SN2 mechanism. The abbreviation SN2 stands for Substitution, Nucleophilic, bimolecular. The term bimolecular means that the transition state of the rate-limiting step (the only step in this reaction) involves the collision of two molecules. Bimolecular reactions usually have rate equations that are second order overall. 

Quantities in square brackets represent concentrations and the proportionality constant k is called the rate constant. If this mechanism is right, then the rate of the reaction will be simply and linearly proportional to both [n-BuBr] and to [HO ]. And it is. Ingold measured the rates of reactions like these and found that they were second-order (proportional to two concentrations) and he called this mechanism Substitution, Nucleophilic, 2nd Order or 8 2 for short. The rate equation is usually given like this, with 2 representing the second-order rate constant. 

At a given temperature and concentration of reactants, the reaction occurs at a certain rate. If we double the concentration of OH", the frequency of encounter between the reaction partners is also doubled, and we might therefore predict that the reaction rate will double. Similarly, if we double the concentration of bromomethane, we might expect that the reaction rate will again double. This behavior is exactly what is found. We call such a reaction, in which the rate is linearly dependent on the concentrations of two species, a second-order reaction. Mathematically, we can express this second-order dependence of the nucleophilic substitution reaction by setting up a rate equation ... 

An example of a quantitative SMR study correlating electronic properties and catalytic parameters is provided by the glutathione conjugation of para-substituted l-chloro-2-nitro-benzene derivatives (183). The values of log/j2 (second order rate constant of the nonenzy-matic reaction) and log (enzymatic reaction catalyzed by various glutathione transferase preparations) were correlated with the Hammett resonance cr value of the substrates, a measure of their electrophilicity. Regression equations with positive slopes and values in the range 0.88-0.98 were obtained. These results quantitate the influence of substrate electrophilicity on nucleophilic substitutions mediated by glutathione, be they enzymatic or nonenzymatic. 

The simplest SN2 reaction involves methyl transfer between heteroatoms thus, the possibility of bell-shaped behavior of the carbon KIE for such a substitution reaction was explored. No systematic measurements of KIEs for a series of multilabeled compounds were previously reported for methyl transfer. Carbon-14 and a-deuterium KIEs for reactions of methyl-i4C brosy-late and methyl-d3 brosylate with substituted N,N-dimethylanilines (equation 2 Y = p-CH30, p-CH3, H, p-Br, and m-Br) were measured. Reactions were carried out in acetonitrile at 55 °C with 0.05 mol L-i of methyl brosylate and 0.10 mol L-1 of nucleophiles. Reactions showed good second-order rate plots (r > 0.999) through at least 70% reaction. Carbon-14 KIEs... 

For neutral nucleophiles, we have utilized a series of ring-substituted N,N-dimethylanilines. The second-order rate coefficients should now be independent of nucleophile concentration, and this was confirmed by showing that log (k/k0 obtained from the product ratios, was independent of the amine concentration for 0.008 to 0.08 M N,N-dimethyl-p-toluidine. The log (k/k0) values could also be conveniently determined for m-CH3-, H-, p-Br-, and m-Cl-substituted derivatives (equation 13). For the m-N02 derivative, even at 0.32 M, the dominant reaction is solvolysis and only an approximate value for log (k/k0) could be obtained. A Hammett plot against the tabulated a values (43) (omitting the approximate m-N02 data) led to a linear plot and a slope (p value) of —2.77 0.15 (r = —0.996). This value is similar to values for reaction with other ethyl derivatives, derived from kinetically determined k values —3.60 for reaction with ethyl iodide in nitrobenzene at... 

The reactions of P-donor nucleophiles with the metal carbonyl cluster Rh4COi2 have been studied over a considerable time period.It is widely accepted that the reaction is associative. This latest investigation is aimed at quantifying the effects of the electronic and steric properties of the nucleophiles upon the kinetic parameters. A rapid substitution reaction step using an excess of the nucleophile was monitored by SF spectrophotometry. Second-order rate constants were obtained from the variation of the pseudo-first-order rate constants with nucleophile concentration. Contributions to these constants from the properties steric effect, TT-activity, and, in addition, an aryl effect of the nucleophiles were assessed in a multi-parameter equation. The outcome is a successful understanding of the relative reactivities of many P-donors toward the rhodium cluster. The data were also represented by a three-dimensional potential energy surface. 

The systematic measurements of reaction rates of nucleophilic substitutions have shown that, depending on the structure of reactants, the reaction kinetics can follow either the first or the second order rate law. The chemical reaction rate can be expressed by kinetics equations in which the main parameter is the reaction coefficient (rate constant) k ... 

When substitution occurs by an Sn2 mechanism, the nucleophile directly attacks the substrate, with the angle of approach being 180" to the C-L bond. This is called "backside attack," and the reaction proceeds with inversion of stereochemistry, the so-called "Walden inversion." The C-L bond is being broken concurrently with the formation of the C-Nu bond, so both the substrate, R-L, and the nucleophile are involved in the transition state of the rate-determining step. Reactions in which two reactants are involved in the transition state of the rate-determining step are termed bimolecular, and the rate of such processes depends on the concentration of the substrate and the nucleophile, as shown in Equation 14.5, where k2 is the second-order rate constant. 

The second-order rate constants for the reaction of several substituted hydrazines, hydrazides, hydroxylamines, methylamines, and ammonia with benzhydrylium ions and quinone methides in water and MeCN have been measured and the N and % values [in the log k = %(At + E) equation] of the various nucleophiles determined. The effect of adding methyl or larger group(s) to the a- or -position of the nucleophiles is discussed. Although the amine and hydrazine nucleophiles react much slower in water... 

Rate data for the Menshutkin reaction between strongly activated Z-substituted benzyl / -toluenesulfonates and Y-substituted lV,lV-dimethylanilines in MeCN at 35 °C fit the equation kohs = h +k2 [DMA], which is consistent with concurrent first- and second-order processes.The 5 nI constant ki is unaffected by changing the nucleophile and conforms to Yukawa-Tsuno treatment with p — -5.2 and r — 1.3. The 5 n2 constant k2 was increased by electron-donating substituents in the nucleophile and showed upward curvature when subjected to the Brown a + treatment. 

We can use the overall reaction order to distinguish between the two possible mechanisms, A and B. Experimentally, the rate of formation of methanol is found to be proportional to the concentrations both of chloromethane and of hydroxide ion. Therefore the reaction rate is second order overall and is expressed correctly by Equation 8-2. This means that the mechanism of the reaction is the single-step process B. Such reactions generally are classified as bimolecular nucleophilic substitutions, often designated SN2, S for substitution, N for nucleophilic, and 2 for bimolecular, because there are two reactant molecules in the transition state. To summarize For an SN2 reaction,... 

Kinetics of reactions of cyclic secondary amines with benzohydrazonyl halides (31) have been measured in benzene51 at 30 °C. The products result from nucleophilic substitution at the halo-carbon via an associative addition-elimination mechanism. For X = Cl or Br, the rate equation has significant terms that are both first and second order in amine, whereas two amine molecules are essential for the fluoro compounds to react. 

The HMPA adducts of trimethylchlorosilane (32, R = Me) and trimethylbromosilane were isolated and found to be ionic as shown. If the first step shown in equation 14 is a pre-equilibrium, the observed order for substitution is first order as expected. For racemization, the rate-limiting step is invertive attack of the second HMPA molecule on 32, such that the reaction is second-order overall with respect to nucleophile. 

Reaction of bromomethane (CH3Br) with the nucleophile acetate (CH3COO") affords the substitution product methyl acetate with loss of Br as the leaving group (Equation [1]). Kinetic data show that the reaction rate depends on the concentration of both reactants that is, the rate equation is second order. This suggests a bimolecular reaction with a one-step mechanism in which the C-X bond is broken as the C—Nu bond is formed. 

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