Rate laws for SN reactions

Equipped with this principle, let us now continue the derivation of the rate law for SN reactions. The approximation [carbenium ion] = 0 must be replaced by Equation 2.6. Let us now set the left-hand side of Equation 2.6, the change of the carbenium ion concentration with time, equal to the difference between the rate of formation of the carbenium ion and its consumption. Because the formation and consumption of the carbenium ion are elementary reactions, Equation 2.7 can be set up straightforwardly. Now we set the right-hand sides of Equations 2.6 and 2.7 equal and solve for the concentration of the carbenium ion to get Equation 2.8. With this equation, it is possible to rewrite the previously unusable Equation 2.5 as Equation 2.9. The only concentration term that appears in Equation 2.9 is the concentration of the alkylating agent. In contrast to the carbenium ion concentration, it can be readily measured. 

The rate law for SN reactions at the carboxyl carbon according to the mechanism shown in Figure 6.5 can be derived as follows ... 

Let us summarize The rate laws for SN reactions at the carboxyl carbon exhibit an important common feature regardless of whether the substitution mechanism is that of Figure 6.2 (rate laws Equation 6.7 or 6.10), Figure 6.4 (rate law Equation 6.12), or Figure 6.5 (rate law Equation 6.16) ... 

While carrying out this reaction in an aqueous medium, it is impossible to change the concentration of water (nucleophile). The concentration of water in aqueous solutions is always constant and is 55.5M. The inability to change the nucleophile concentration does not permit us to distinguish the rate laws for SN and SN mechanisms. Thus, rate laws cannot provide any information regarding the mechanism of acid hydrolysis carried out in an aqueous medium. 

Group VII. The rate law for reaction of PhaM—Mn(C0)6, where M = Si, Ge, or Sn, with a variety of nitrogen and phosphorus bases, both unidentate (e.g. phosphines) and bidentate (e.g. diphos, bipy), indicates parallel dissociative and associative mechanisms in all cases. This assignment of mechanisms on the basis of the rate law is supported by activation entropies determined for the respective terms. Exceptionally, the reaction of PhaSi—Mn(CO)s with trialkyl phosphites does not result in simple substitution of carbon monoxide by the phosphite, but produces trans-Mn(COR)(CO)s[P(OR)3]2 by way of a Michaelis-Arbuzov reaction. ... 

The methods developed in the preceding section, but not the explicit equations, are applicable for reactions that are not second-order. We start with an example of the reaction between Fe(IIl) and Sn(II), as studied in solutions of HCIO4, HC1, and LiC104. With these components both [H+] and [Cr ] could be varied at constant p. We consider conditions in which the major species are Fe3 and Sn2q+. The rate law is... 

The rate law of Equation 2.9 identifies the SN reactions of Figure 2.11 as unimolecular reactions. That is why they are referred to as SN1 reactions. The rate of product formation thus depends only on the concentration of the alkylating agent and not on the concentration of the nucleophile. This is the key experimental criterion for distinguishing the SN1 from the Sn2 mechanism. 

The analogue of free radicals for inorganic ions would be intermediate valence states, and many of the kinetic results on redox reactions have required the postulation of unstable valence states for inorganic ions. One of the classic studies of this type is the slow reaction 2Fe + Sn++ 2Fe " + Sn +. The reaction is very slow in HCIO4 solution but is strongly catalyzed by C1-. At high Fe +/Sn++ ratios, the rate law has the form... 

However, it is consistent with addition of Cl to give an anionic intermediate or preliminary protonation to give [IrHCl(PEtPh2)(cod)]+. The rate law deprived from the latter process predicts that in order for the [H+] dependence to reach a limit the equilibrium for protonation will lie far to the right-hand side in favour of the protonated species. Since HCIO4 does not react with [IrCl(PEtPh2)(cod)]+ it must therefore be assumed that attack by Cl is the first step in the reaction. The kinetics of reaction (17) (M=Si, Ge, or Sn) follow a simple rate law indicative of a previously... 

The notion of concurrent SnI and Sn2 reactions has been invoked to account for kinetic observations in the presence of an added nucleophile and for heat capacities of activation,but the hypothesis is not strongly supported. Interpretations of borderline reactions in terms of one mechanism rather than two have been more widely accepted. Winstein et al. have proposed a classification of mechanisms according to the covalent participation by the solvent in the transition state of the rate-determining step. If such covalent interaction occurs, the reaction is assigned to the nucleophilic (N) class if covalent interaction is absent, the reaction is in the limiting (Lim) class. At their extremes these categories become equivalent to Sn and Sn , respectively, but the dividing line between Sn and Sn does not coincide with that between N and Lim. For example, a mass-law effect, which is evidence of an intermediate and therefore of the SnI mechanism, can be observed for some isopropyl compounds, but these appear to be in the N class in aqueous media. 

The isomerizations of n-butenes and n-pentenes over a purified Na-Y-zeolite are first-order reactions in conversion as well as time. Arrhenius plots for the absolute values of the rate constants are linear (Figure 2). Similar plots for the ratio of rate constants (Figure 1), however, are linear at low temperatures but in all cases except one became curved at higher temperatures. This problem has been investigated before (4), and it was concluded that there were no diffusion limitations involved. The curvature could be the result of redistribution of the Ca2+ ions between the Si and Sn positions, or it could be caused by an increase in the number of de-cationated sites by hydrolysis (6). In any case the process appears to be reversible, and it is affected by the nature of the olefin involved. In view of this, the following discussion concerning the mechanism is limited to the low temperature region where the behavior is completely consistent with the Arrhenius law. 

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