E1 Reaction: Kinetics and Mechanism

Elimination reactions of alkyl halides through an E1 mechanism occur in two steps analogous to its S_N1 counterpart.

The first step in both reactions is a slow rate-limiting step which proceeds with the loss of the halide leaving group forming a carbocation intermediate.

The second step in E1 reactions involves the abstraction of a beta hydrogen by a weak base forming an alkene. In contrast, an S_N1 reaction yields a substitution product.

Evidence supporting the E1 mechanism comes from kinetic studies, which show that E1 reactions are unimolecular and follow first-order kinetics. Meaning, the reaction rate depends only on the concentration of the substrate.

Deuterium isotope studies provide further evidence. For the dehydrohalogenation of tert-butyl chloride, the ratio of the rate constants of the non-deuterated and deuterated analogs, k_H/k_D is 1.1.

Since the rate constants are almost identical, this suggests that a carbon-hydrogen bond is not broken in the rate-limiting step but in the second step, consistent with the proposed mechanism.

Factors that influence E1 elimination reactions include the stability of the carbocation, the nature of the leaving group, and the type of solvent.

In an E1 reaction, the rate-limiting step involves the formation of a carbocation intermediate. Electron donating alkyl groups can stabilize the positive charge by delocalizing the carbon-hydrogen sigma electrons into the empty p-orbital of the positively charged carbon.

This stabilizing interaction, called hyperconjugation, increases with the number of alkyl groups. Therefore, E1 reactions are fastest with tertiary alkyl halides.

However, a primary carbocation can also undergo a 1,2-hydride shift to form a secondary carbocation, or a 1,2-alkyl shift, to give a more stable tertiary carbocation.

Since the carbon-halogen bond breaks in the rate-limiting step, E1 reactions further depend on the quality of the leaving group. Compared to bromides and chlorides, iodides are weak conjugate bases, and therefore, better leaving groups.

Finally, polar protic solvents, like ethanol, stabilize the carbocation and the halide ions formed in the rate-limiting step, thereby favoring E1 reactions.