Question

Which isomer of \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br}\) shows slowest rate of unimolecular substitution reaction? (A) 2 -bromo-2-methyl propane (B) 2-bromo butane (C) 1 -bromo-2-methyl propane (D) 1 -bromo butane

Short answer

The slowest rate of unimolecular substitution reaction (SN1) among the given isomers of C4H9Br will be for the isomer with the least stable carbocation. In this case, the correct answer is (D) 1-bromo butane, which forms a less stable 1° carbocation intermediate during the reaction.

Step-by-step solution

Identify the intermediate carbocations

In an SN1 reaction, the stability of the carbocation intermediate determines the rate of the reaction. The more stable the carbocation, the faster the reaction will be. Therefore, we need to figure out the carbocation formed during the reaction for each isomer.

Analyze the stability of carbocations

Carbocation stability follows the order: 3° > 2° > 1°. A 3° carbocation is more stable because it has more alkyl groups to supply electrons and stabilize the positive charge.

Apply the stability rule to the given isomers

Let's identify the carbocations formed for each isomer and analyze their stability: (A) 2-bromo-2-methyl propane: The intermediate carbocation formed will be a 3° carbocation. (B) 2-bromo butane: The intermediate carbocation formed will be a 2° carbocation. (C) 1-bromo-2-methyl propane: The intermediate carbocation formed will be a 2° carbocation. (D) 1-bromo butane: The intermediate carbocation formed will be a 1° carbocation.

Compare the stability and determine the slowest reaction rate

We can see that the carbocation formed in option (D) is the least stable (1°) among the given isomers. As the reaction rate is inversely related to stability, the slowest rate of unimolecular substitution reaction will be for the isomer with the least stable carbocation. Therefore, the correct answer is: (D) 1-bromo butane

Key concepts

SN1 Reaction Mechanism

The SN1 (Substitution Nucleophilic Unimolecular) reaction is a two-step process that involves the formation of a carbocation intermediate. The reaction begins with the leaving group breaking away from the substrate, which results in the formation of a positively charged carbocation. This first step is the slow, rate-determining step of the reaction. Following the formation of the carbocation, a nucleophile attacks this intermediate to form the final product.
The reaction rate depends heavily on the formation and stability of the carbocation. Since the leaving group must dissociate to allow the carbocation to form, the structure and stability of the substrate before and after the leaving group departs are of utmost importance.

Carbocation Stability

Carbocation stability is critical in determining the rate of SN1 reactions. A carbocation is a positively charged carbon atom with three substituents and a vacant p orbital. The stability of a carbocation increases with the degree of carbon due to the hyperconjugation and inductive effect provided by neighboring alkyl groups. This stability order follows:

• 3° (tertiary) carbocation is the most stable.
• 2° (secondary) carbocation offers moderate stability.
• 1° (primary) carbocation is the least stable and often unfavorable unless present in highly polarizable systems or special conditions.

In SN1 reactions, a more stable carbocation leads to a faster reaction because the energy required to form the intermediate is lower.

Isomers of C4H9Br

The compound C4H9Br, or butyl bromide, can exist as several isomers, differing in the structure of their carbon skeleton. The key isomers include:

• 2-bromo-2-methylpropane, which forms a tertiary carbocation.
• 2-bromobutane, resulting in a secondary carbocation.
• 1-bromo-2-methylpropane, leading to a secondary carbocation.
• 1-bromobutane, which results in a primary carbocation.

These isomers play a crucial role in SN1 reactions as the type of carbocation they produce greatly influences the rate and feasibility of the reaction.

Reaction Rate

The reaction rate in an SN1 mechanism is primarily dependent on the stability of the carbocation formed. A stable carbocation results in a faster reaction because the energy barrier for the rate-determining step is lower. In contrast, an unstable carbocation leads to a slower reaction rate as it is energetically more demanding to form the intermediate.
This relationship between carbocation stability and reaction rate is an essential concept: the more alkyl groups that stabilize the positive charge, the faster the reaction will proceed.
1-bromo butane, therefore, exhibits the slowest SN1 reaction rate among its isomers because it forms a primary carbocation, which offers the least stability.

Tertiary Carbocation

A tertiary carbocation refers to a carbon atom which carries a positive charge and is bonded to three other carbon atoms. It is structurally more stable than primary and secondary carbocations, due to the electron-donating nature of multiple surrounding alkyl groups. This stabilization occurs through hyperconjugation, where multiple adjacent C-H bonds rotate to overlap partially with the vacant p orbital of the positively charged carbon, dispersing the positive charge over a broader area.
The significant stability of tertiary carbocations means they form quickly and easily, thus accelerating the rate of SN1 reactions. In contrast, formations that lead to less stable carbocations, such as primary carbocations, which have fewer alkyl groups to stabilize the charge, detract from the reaction rate.