Elcb elimination rate equation

The rate-determining elimination step in an ElcB reaction is unimolecular, so you might imagine it would have a first-order rate equation. But, in fact, the rate is also dependent on the concentration of base. This is because the unimolecular elimination involves a species—the anion—whose concentration is itself determined by the concentration of base by the equilibrium we have just been discussing. Using the following general ElcB reaction, the concentration of the anion can be expressed as shown. 

The anti-coplanar relationship is not possible with the (E) isomer, however, so an Elcb mechanism involving formation of a vinyl carbanion and subsequent elimination of the bromide ion was proposed (equation 10.29). The ratio of the rate constant for reaction of (Z)-p-nitro-j8-bromostyrene to that of the (E) isomer was an order of magnitude smaller than the ratio of rate constants for (Z)- and (E)-)8-bromostilbenes. This difference was attributed to the stabilization of the carbanion intermediate by the p-nitro group. With a less acidic H proton, the carbanion mechanism in equation 10.29 is slower, but the concerted mechanism in equation 10.28 is not as significantly affected. Therefore, the ratio of rate constants is much greater for elimination of HCl from isomeric chloroalkenes. 

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