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) \(\mathrm{C}_{6} \mathrm{H}_{3}-\mathrm{CH}=\mathrm{CH}\) (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: Understand the Term 'Sec-Allylic Carbocation'

A 'sec-allylic carbocation' refers to a carbocation where the positively charged carbon atom is secondary and is adjacent to a carbon-carbon double bond (allylic position). In this structure, the carbocation carbon is bonded to two other carbon atoms and is adjacent to a C=C double bond.

Step 2: Analyze Option (a)

The structure given is \( \mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2} \). This structure does not have a carbocation; there is no positively charged carbon atom. Hence, it is not a sec-allylic carbocation.

Step 3: Analyze Option (b)

The structure given is \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2} \). Similar to (a), this structure also does not contain any positively charged carbon and thus isn't a carbocation, much less a sec-allylic one.

Step 4: Analyze Option (c)

The structure given is \( \mathrm{C}_{6} \mathrm{H}_{3}-\mathrm{CH}=\mathrm{CH} \), which lacks a positively charged carbon atom. This is not a sec-allylic carbocation either.

Step 5: Analyze Option (d)

The structure given is \( \mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} \). Consider if the middle carbon (second from left) is positively charged, this carbon is both secondary (as it is bonded to two other carbons) and adjacent to a C=C double bond, indicating it can form a sec-allylic carbocation.

Key Concepts

Carbocation

A carbocation is a type of ion with a positively charged carbon atom. This charge occurs because the carbon atom in the center has lost one of its electrons, making it lack a full complement of valence electrons. This creates a positive charge that is quite reactive.

Carbocations are typically unstable and seek out electrons from nearby atoms or molecules to regain their stability. The presence of other atoms around the positively charged carbon can stabilize the carbocation by distributing the positive charge across the molecule.

• Primary carbocations have the positively charged carbon bonded to only one other carbon.
• Secondary carbocations, like in our sec-allylic case, have the charged carbon bonded to two other carbon atoms.
• Tertiary carbocations have the positively charged carbon bonded to three other carbons, making them generally more stable than primary and secondary.

Secondary Carbon

A secondary carbon is one that is bonded to two other carbon atoms. In the context of a carbocation, where the carbon has a positive charge, a secondary carbon forms a key part of a sec-allylic carbocation.

The properties of a secondary carbon can influence the stability of the carbocation due to hyperconjugation and inductive effects from neighboring atoms. Because of these effects, secondary carbocations have moderate stability compared to primary and tertiary carbocations.

• They are more stable than primary carbocations because there are more neighboring carbon atoms to help share the positive charge.
• They are less stable than tertiary carbocations, which have even more carbon neighbors to aid in charge distribution.

Carbon-Carbon Double Bond

The carbon-carbon double bond is a defining characteristic of alkenes and is essentially two covalent bonds between two carbon atoms. This type of bonding includes one strong sigma bond and one weaker pi bond.

The pi bond in the double bond can be easily disrupted; it is weaker than the sigma bond, which makes it quite reactive. Double bonds are sites of high electron density and are thus attractive to electrophiles like carbocations.

• Alkenes can participate in addition reactions where these bonds might break or shift.
• The presence of a double bond allows for the resonance stabilization of a carbocation, beneficial for the sec-allylic configuration.

Allylic Position

The allylic position refers to the carbon atom that is next to a carbon-carbon double bond. Being in an allylic position allows a carbon atom to participate in resonance structures, which can stabilize positive charges.

In the case of a carbocation, being at the allylic position allows for delocalization of electrons, which distributes the positive charge over a larger area and provides enhanced stability.

• Resonance can disperse the carbocation's positive charge across multiple atoms.
• This makes allylic carbocations more stable than non-allylic carbocations, as the spread of charge reduces the energy state.
• In a sec-allylic carbocation, the secondary carbon's position adjacent to a C=C double bond offers even more stability through further electron delocalization.