Problem 13 - Advanced Organic Chemistry. Part A. Structure and Mechanisms

Question

The addition of \(\mathrm{HCl}\) to alkenes such as 2-methyl-1-butene and 2-methyl-2-butene in nitromethane follow a third-order rate expression: $$ \text { Rate }=k[\mathrm{HCl}]^{2}[\text { alkene }] $$ It has also been established that there is no incorporation of deuterium into the reactant at \(50 \%\) completion when \(\mathrm{DCl}\) is used. Added tetraalkylammonium chloride retards the reaction, but the corresponding perchlorate salt does not. Propose a reaction mechanism that is consistent with these observations.

Step-by-Step Solution

Answer

A mechanism involves an initial complex formation between HCl and the alkene, leading to a transition state retarded by chloride ions.

Step 1: Understand the Reaction Order

The rate expression given is: \(\text{Rate} = k[\mathrm{HCl}]^2[\text{alkene}]\). This indicates a third-order reaction: second order in \(\mathrm{HCl}\) and first order in the alkene.

Step 2: Analyze Deuterium Incorporation

The use of \(\mathrm{DCl}\) does not lead to deuterium incorporation at 50% reaction completion, suggesting that if a carbocation intermediate were formed, it would not sufficiently exchange with \(\mathrm{DCl}\) to incorporate deuterium before proceeding to products.

Step 3: Consider Effect of Tetraalkylammonium Chloride

Adding tetraalkylammonium chloride slows the reaction. This implies the rate-determining step might involve a chloride ion, which competes with or stabilizes any possible intermediate.

Step 4: Evaluate Effect of Perchlorate Salt

The corresponding perchlorate salt does not retard the reaction, indicating that the inhibiting effect of tetraalkylammonium salts is specific to the chloride ion, suggesting chloride plays a role in a possible transition state or intermediate.

Step 5: Propose Reaction Mechanism

Given the observations, it is likely the first step involves the reversible formation of a complex between \(\mathrm{HCl}\) and the alkene, possibly forming a \([\text{alkene}\cdot\mathrm{HCl}_2^+]\) complex. Chloride ion inhibition suggests that external chloride stabilizes this complex or participates in its formation, which matches with no deuterium incorporation and the effect of tetraalkylammonium chloride.

Key Concepts

Third-Order Reaction

In chemistry, a third-order reaction is one in which the reaction rate is proportional to the concentration of three reactant molecules. In this specific reaction involving the addition of \(\mathrm{HCl}\) to alkenes, the rate law expression takes the form \(\text{Rate} = k[\mathrm{HCl}]^2[\text{alkene}]\). This indicates that the reaction is second order with respect to \(\mathrm{HCl}\) and first order with respect to the alkene. The concentration of \(\mathrm{HCl}\) has a significant impact on the rate of reaction due to the squared term.
It implies that doubling the concentration of \(\mathrm{HCl}\) increases the rate by a factor of four. This relationship arises from the fact that two \(\mathrm{HCl}\) molecules are involved in the rate-determining step, functionally leading to a third-order reaction. Understanding the nature of this order helps in deducing the mechanistic pathway where chloride ions might stabilize the reaction's transition state.

Deuterium Incorporation

Deuterium incorporation is a concept where deuterium, a heavier isotope of hydrogen, replaces hydrogen in a chemical compound. In this reaction context, using \(\mathrm{DCl}\) instead of \(\mathrm{HCl}\) results in no observable incorporation of deuterium into the product at 50% completion. This implies that a suggested intermediate, such as a carbocation, might not be forming or is short-lived and stable enough to avoid isotopic exchange.
If deuterium were to incorporate, it would suggest a mechanism involving longer-lived intermediates. The absence of deuterium incorporation points toward the reaction proceeding directly from reactants to products without substantial interaction between the reactants and \(\mathrm{DCl}\), supporting a mechanism that avoids exchange with the deuterium.

Chloride Ion Effect

The chloride ion effect is significant because the addition of tetraalkylammonium chloride inhibits the reaction. This suggests that chloride ions influence the reaction mechanism, possibly stabilizing a charged transition state or intermediate involved in the rate-determining step. The presence of chloride ions could form a stable complex with the reactants, making it less likely for the reaction to proceed rapidly.
Moreover, the lack of effect by perchlorate ions on the reaction rate supports the specificity of the chloride's role in stabilizing intermediates. This means that the chloride ions are integral to the formation or stability of possible complexes, which aligns with the proposed mechanism's step involving reversible complex formation. Understanding the chloride ion effect underscores the mechanism where chloride acts as a stabilizer rather than as a simple spectator.

Alkene Reactions

Alkene reactions, particularly with hydrogen halides like \(\mathrm{HCl}\), typically proceed through a mechanism where the alkene's double bond acts as a nucleophile. In the presence of \(\mathrm{HCl}\), the proton from \(\mathrm{HCl}\) adds to the alkene, potentially creating a carbocation intermediate, although in this mechanism, the formation of such an intermediate may not occur or is very transient.
Typically, this process can lead to Markovnikov or anti-Markovnikov addition depending on the conditions, but in the context of this reaction, no deuterium incorporation suggests the bypass of a carbocation intermediary mechanism.
The reaction instead may proceed via a transition state involving concerted steps, potentially stabilized by chloride ions, as noted by the chloride ion effect. Thus, studying alkene reactions in this framework illuminates the complex interplay of mechanisms and external ion influences.