Question

When 3,3-dimethyl-2-butanol is treated with dilute acid, the most stable carbocation formed is (a) 3,3-dimethyl-2-butyl cation (b) 3,3 -dimethyl-1-butyl cation (c) 2,3-dimethyl-2-butyl cation (d) 2-methyl-2-pentyl cation

Short answer

Answer: The most stable carbocation formed when 3,3-dimethyl-2-butanol is treated with dilute acid is the 3,3-dimethyl-1-butyl cation.

Step-by-step solution

Write the structure of 3,3-dimethyl-2-butanol

First, draw the structure of 3,3-dimethyl-2-butanol. It is an alcohol with the following structure: H3C-C(CH3)2-CH(OH)-CH3

Determine the possible carbocations

When 3,3-dimethyl-2-butanol is treated with dilute acid, it forms a carbocation by losing a water molecule. We can eliminate the hydrogen from the alcohol group and draw the possible cations for each option: (a) 3,3-dimethyl-2-butyl cation: H3C-C(CH3)2-CH(+)-CH3 (b) 3,3-dimethyl-1-butyl cation: H3C-C(CH3)2-C(+)-CH2-CH3 (formed through a 1,2-hydride shift) (c) 2,3-dimethyl-2-butyl cation: H3C-CH(C+H2)-C(CH3)2 (d) 2-methyl-2-pentyl cation: H3C-CH(C+H2)-CH2-C(CH3)2

Analyze the stability of each carbocation

Evaluate each carbocation based on the number of alkyl groups attached to the positive carbon. The stability order is tert-butyl cation > secondary cation > primary cation because more electron-donating alkyl groups will distribute the positive charge and make the carbocation more stable. (a) 3,3-dimethyl-2-butyl cation: secondary cation, three hyperconjugative structures (b) 3,3 -dimethyl-1-butyl cation: secondary cation, four hyperconjugative structures (c) 2,3-dimethyl-2-butyl cation: primary cation, two hyperconjugative structures (d) 2-methyl-2-pentyl cation: secondary cation, four hyperconjugative structures

Choose the most stable carbocation

Based on the number of hyperconjugative structures, the carbocation with the maximum number of hyperconjugative structures will be the most stable. Both options (b) and (d) have four hyperconjugative structures, but option (b) is already formed within the given structure due to the 1,2-hydride shift. Therefore, the most stable carbocation formed when 3,3-dimethyl-2-butanol is treated with dilute acid is: (b) 3,3 -dimethyl-1-butyl cation

Key concepts

Hyperconjugation

Hyperconjugation is an important concept in understanding carbocation stability. It involves the interaction between the empty p-orbital of a carbocation and the adjacent C-H bonds. This interaction allows electrons from the sigma bonds to help stabilize the positive charge, creating a more stable carbocation.
Hyperconjugation can be thought of as a way electron density from neighboring bonds "spills over" to the electron-deficient area. This happens because the electrons in the sigma bonds can partially overlap with the empty p-orbital.

• The more C-H bonds adjacent to the carbocation, the more hyperconjugative structures can form.
• Each C-H bond involved adds stability by delocalizing the positive charge.
• More hyperconjugative structures generally correlate with increased stability of the carbocation.

In our problem, evaluating carbocations based on their hyperconjugation helps us determine which is the most stable.

Hydride Shift

A hydride shift is a key rearrangement reaction in organic chemistry where a hydrogen atom moves from one carbon to a neighboring carbon atom. This shift involves the migration of a hydride, which is a hydrogen ion (proton) paired with two electrons.
Hydride shifts usually occur to form a more stable carbocation. The transition involves breaking a C-H bond and forming a new one as the hydride shifts to the electron-deficient carbon.

• It is an intramolecular process, occurring within the same molecule.
• Hydride shifts result in reorganization to a more stable carbocation by relocating the positive charge to a more substituted carbon.
• In our exercise, the 3,3-dimethyl-1-butyl cation is formed via a hydride shift, moving from a less stable to a more stable state.

This rearrangement helps in achieving a more favorable electronic configuration.

Alkyl Groups

Alkyl groups play a crucial role in carbocation stability. Alkyl groups are essentially hydrocarbon branches (e.g., methyl, ethyl) that can donate electron density through sigma bonds. This electron donation stabilizes carbocations by distributing the positive charge.
Generally, the more alkyl groups attached to the carbocation, the better the stability due to increased hyperconjugation potential.

• Alkyl groups are considered electron-donating due to their ability to stabilize positive charges.
• A tertiary carbocation (three alkyl groups) is more stable than a secondary (two alkyl groups), and more stable than a primary (one alkyl group).
• Understanding this concept helps predict which carbocations in organic reactions will be more stable.

In our problem context, analyzing the number of alkyl groups helps predict the stability and reactivity of the intermediate structures.

Organic Chemistry Problem Solving

When approaching organic chemistry problems, such as determining the most stable carbocation, a strategic problem-solving approach is necessary. It involves analyzing structural components, rearrangements, and stability factors.
Begin by drawing the molecular structures involved to visually assess possible outcomes and rearrangements. Then, consider factors such as hyperconjugation, rearrangements like the hydride shift, and the effects of alkyl groups.

• Identify key functional groups and interactions, understanding how they influence stability.
• Use known principles such as those governing hyperconjugation and carbocation rearrangements to inform decisions.
• Practice assessing each possible intermediate for the greatest stability through known stability orders.

Addressing problems systematically with these tools can greatly aid in solving complex organic chemistry questions.