Problem 67 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following is a sec-allylic carbocation? (a) \(\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}\) (b) \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}\) (c) \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}=\mathrm{CH}\) (d) \(\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}\)

Step-by-Step Solution

Answer

Option (d) is the sec-allylic carbocation.

Step 1: Understanding Allylic and Sec-Allylic Carbons

An allylic carbon is a carbon atom that is directly attached to a sp2-hybridized carbon of an alkene. If this allylic carbon is secondary (sec-allylic), it is bonded to two other carbons. We need to identify such a carbon with a positive charge.

Step 2: Analyzing Each Structure

Examine each option for the presence of a sec-allylic carbocation: (a) \(\mathrm{CH}_2-\mathrm{CH}=\mathrm{CH}_2\) contains no carbocation. (b) \(\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2\) features no carbocation as written. (c) \(\mathrm{C}_6\mathrm{H}_5-\mathrm{CH}=\mathrm{CH}\) features no carbocation as written. (d) \(\mathrm{CH}_3-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_2\) could potentially contain a sec-allylic carbocation if the positive charge is on the second carbon.

Step 3: Select the Correct Structure

Option (d) can be seen as \(\mathrm{CH}_3-\overset{+}{\mathrm{CH}}-\mathrm{CH}=\mathrm{CH}_2\), where the second carbon is secondary (bonded to two other carbons) and next to a double bond, satisfying the criteria for a sec-allylic carbocation.

Key Concepts

Allylic Carbon

An allylic carbon atom holds special significance in organic chemistry because it is directly bonded to an sp2-hybridized carbon of a double bond (alkene). This makes it quite reactive, as the adjacent double bond can provide stability via resonance.

• An allylic system is characterized by the presence of a double bond next to a carbon that is involved in bonding with other groups.
• One of the primary features of allylic carbons is the ability to participate in rearrangements and resonance, which can greatly influence the outcome of chemical reactions.

In the context of the sec-allylic carbocation, the allylic carbon is further characterized as being secondary, meaning it also bonds with two other carbons in addition to the adjacent double-bonded carbon.

Carbocation Stability

Carbocations are positively charged ions where carbon holds the positive charge. Their stability is a critical concept:

• Stability of a carbocation depends on the degree of substituents—tertiary carbocations are more stable than secondary, which are more stable than primary.
• Resonance also plays a major role. If a carbocation is adjacent to a double bond, the positive charge can be delocalized over the structure, increasing stability.

In the case of the sec-allylic carbocation, stability is enhanced through resonance with the double bond system, making it more stable than a simple secondary carbocation due to this electron delocalization.

Organic Chemistry

In the realm of organic chemistry, understanding the nature and behavior of carbon-based molecules is fundamental. Organic compounds primarily consist of carbon, hydrogen, oxygen, and nitrogen, among others.

• An important area of focus is the study of reaction mechanisms, which elucidate how and why reactions proceed in certain directions.
• Carbocations are pivotal intermediates in many organic reactions, playing significant roles in processes like SN1 reactions, electrophilic additions, and rearrangements.

The identification and stability of carbocations such as the sec-allylic carbocation highlight the intricate balance of structure and reactivity that defines organic chemistry.

sp2 Hybridization

The concept of sp2 hybridization is crucial in understanding the geometry and bonding characteristics of molecules containing double bonds. In an sp2 hybridized carbon:

• The carbon atom forms three sp2 hybrid orbitals by mixing one s orbital with two p orbitals, leaving one p orbital unhybridized.
• This hybridization results in a trigonal planar geometry around the atom with bond angles around 120°.

In structures like alkenes, sp2 hybridization allows for the formation of a double bond. The pi bond, formed by the side-to-side overlap of p orbitals, restricts the rotation around the double bond, giving rise to unique chemical properties. In sec-allylic carbocations, the adjacent sp2 hybridized carbon partly shares the positive charge through pi bond resonance, influencing its stability significantly.