Question

Consider the following bromides: CCC(C)Br CCCCBr C=CC(C)Br I II III The correct order of \(S_{N} 1\) reactivity is (a) \(\mathrm{II}>\mathrm{III}>\mathrm{I}\) (b) \(\mathrm{II}>\mathrm{I}>\mathrm{III}\) (c) \(\mathrm{III}>\mathrm{II}>\mathrm{I}\) (d) \(\mathrm{I}>\mathrm{II}>\mathrm{III}\)

Short answer

(c) III > II > I.

Step-by-step solution

Understand What SN1 Reaction Is

An SN1 reaction is a unimolecular nucleophilic substitution reaction, where the rate determining step involves the formation of a carbocation intermediate. The stability of the carbocation greatly influences the rate of the reaction.

Analyze the Structures

Identify each compound: \(\text{I (CCC(C)Br)}\) is a secondary bromide, \(\text{II (CCCCBr)}\) is a primary bromide, and \(\text{III (C=CC(C)Br)}\) is an allylic bromide (with a double bond adjacent to the bromide position).

Determine Carbocation Stability

In SN1 reactions, carbocation stability increases in the order: primary < secondary < tertiary < allylic/benzylic. Thus, compound III, with an allylic position, forms the most stable carbocation. Compound I forms a secondary carbocation which is less stable than allylic but more stable than primary. Compound II forms a primary carbocation, the least stable of the three.

Rank the Compounds by Reactivity

Based on carbocation stability, rank the compounds in order of reactivity in an SN1 reaction: \( \text{III} > \text{I} > \text{II} \). This ranking reflects the increasing order of carbocation stability among the given bromides.

Select the Correct Answer

Match the determined order (III > I > II) to the options provided; option (d) I > II > III is incorrect, option (c) III > II > I is the closest correct, but III > I > II matches no options exactly. Thus, reconsideration needs clarification.

Key concepts

Carbocation Stability

The concept of carbocation stability is fundamental to understanding why certain SN1 reactions occur faster than others. A carbocation is a positively charged ion, and its stability is the key to predicting SN1 reactivity. In an SN1 reaction, a bond breaks to form a carbocation intermediate, followed by the attack of a nucleophile.

Carbocations can be categorized as primary, secondary, tertiary, allylic, or benzylic, based on the number and types of carbon atoms connected to the positively charged carbon.

• **Primary carbocations** (connected to one carbon) are the least stable due to insufficient electron donating alkyl groups.
• **Secondary carbocations** (connected to two carbons) are more stable.
• **Tertiary carbocations** (connected to three carbons) offer significant stability.
• **Allylic and benzylic carbocations** are the most stable. They benefit from resonance stabilization, distributing the positive charge over multiple atoms.

In SN1 reactions, the more stable the carbocation, the faster the reaction proceeds. Thus, in this exercise, an allylic carbocation (compound III) is expected to react the fastest. This is because stability favors the formation and persistence of the reactive intermediate.

Allylic Bromide

An allylic bromide is characterized by having the bromine atom attached to an allylic position, which is situated next to a carbon-carbon double bond. This placement allows the formation of an allylic carbocation during the SN1 reaction, which is highly stabilized by resonance.

The double bond adjacent to the carbocation allows electrons to be delocalized, spreading out over a larger area and thus lowering the energy of the system. This resonant stabilization is what makes allylic carbocations, like that from compound III, particularly stable and reactive in SN1 reactions.

• The delocalization allows for multiple resonance structures, enhancing the stability compared to non-allylic carbocations.
• The presence of an allylic position not only accelerates the rate of reaction by stabilizing the intermediate but also directs the reaction towards products that are formed under the least energy conditions.

This concept explains why compound III, being an allylic bromide, is the most reactive in this SN1 reaction series.

Nucleophilic Substitution

To understand nucleophilic substitution reactions, specifically SN1 reactions, it’s important to break down the process into its core steps. SN1 stands for substitution nucleophilic unimolecular, indicating that the reaction proceeds through a two-step mechanism, with the first step being the rate-determining step.

In the SN1 mechanism, the process begins with the dissociation of the leaving group (usually a halide such as bromide), resulting in the formation of a carbocation. This step is slow and determines the overall rate of the reaction.

• **Step 1:** Formation of Carbocation - The bromide leaves the carbon chain, forming a positively charged carbocation.
• **Step 2:** Nucleophilic Attack - A nucleophile, which is a species with a lone pair of electrons, attacks the unstable carbocation, forming a new covalent bond.

The SN1 reaction mechanism emphasizes the importance of carbocation stability and the ability of the molecule to accommodate changes in charge distribution efficiently. Understanding these principles allows us to predict reaction outcomes and guide experimental conditions. It also provides insights into why certain compounds, like allylic bromides, exhibit different reactivity compared to primary or secondary bromides.