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Chapter 24: Problem 206

The order of stability of the following carbocations: (I) \(\mathrm{CH}_{2}=\mathrm{CH}-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{2}\) \(\mathbf{[ 2 0 1 3}]\) (II) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{2}\) (III) is: [C+]c1ccccc1 (a) \(\mathrm{I}>\mathrm{II}>\mathrm{III}\) (b) \(\mathrm{III}>\mathrm{I}>\mathrm{II}\) (c) \(\mathrm{III}>\mathrm{II}>\mathrm{I}\) (d) \(\mathrm{II}>\mathrm{III}>\mathrm{I}\)

Short Answer

Expert verified
The order is (b) III > I > II.

Step by step solution

01

Understand Carbocation Stability

Carbocation stability is influenced by factors like hyperconjugation, resonance, and inductive effects. Generally, the more stable a carbocation, the more substituted it is due to hyperconjugation and resonance.
02

Analyze Structure I

Structure I is an allylic carbocation (\( \mathrm{CH}_{2}=\mathrm{CH}-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{2} \)). It is stabilized through resonance with the adjacent double bond, spreading the positive charge across multiple atoms.
03

Analyze Structure II

Structure II is a primary carbocation (\( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{2} \)). It lacks resonance stabilization and has no adjacent double bonds, making it relatively less stable.
04

Analyze Structure III

Structure III (\( \mathrm{C}_{6} ext{H}_{5}-\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3} \), benzyl carbocation) is very stable due to resonance with the benzene ring, which allows the positive charge to be delocalized over the aromatic ring. This is known as aromatic stabilization.
05

Compare Stabilization Effects

Resonance stabilization (as seen in III with the benzene ring) is generally stronger than the stabilization from a single adjacent double bond (as seen in I). The stability order based on resonance and hyperconjugative effects is III > I > II.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Resonance Stabilization in Carbocations
Resonance stabilization is a key concept for understanding why some carbocations are more stable than others. When a carbocation has resonance, the positive charge can be distributed across a larger number of atoms. This delocalization reduces the energy of the system, as the charge is not concentrated at a single point. For example, if a carbocation is adjacent to a double bond or an aromatic ring, the electrons in these pie bonds can move towards the carbocation, helping to spread the positive charge over multiple atoms.
  • This effect reduces the positive charge per atom, leading to greater stability.
  • Structure III, for instance, benefits from resonance with the benzene ring, which allows the charge to spread across the aromatic system.
Resonance plays a significant role in the exceptional stability often observed in these scenarios.
Characteristics of Allylic Carbocations
Allylic carbocations are a fascinating type of carbocation where the positively charged carbon is adjacent to a carbon-carbon double bond. This proximity allows for resonance stabilization, one of the main features of allylic carbocations. In allylic systems, the double bond can "share" its electrons, effectively moving the positive charge between the carbocation and the double-bonded carbons.
  • As a result, the charge is not fixed but rather shifts, balancing out the system and providing extra stability.
  • Structure I is an example of an allylic carbocation, where the positive charge enjoys resonance with the adjacent double bond.
This results in a more stable structure compared to non-resonant counterparts.
The Stability of Benzyl Carbocations
Benzyl carbocations are often more stable than many other types because of their unique ability to engage in resonance stabilization with an aromatic ring. This resonance enables a highly efficient delocalization of the positive charge among the carbone and the aromatic ring structures. The presence of a tubby benzene ring allows for significant stability. This stability comes from the overlapping p orbitals in the benzene ring, which allow the charge to spread out and minimize its effect on any single atom.
  • In Structure III, this type of stabilization is harnessed, resulting in greater overall stability.
  • Because the benzene ring can support multiple resonance forms, benzyl carbocations can effectively dissipate the positive charge over a larger area.
Thus, benzyl carbocations often have one of the highest stabilities among carbocation types.
Understanding Hyperconjugation
Hyperconjugation is another form of stabilization in carbocations that plays an important role in understanding their stability. It occurs when the sigma bonds attached to the neighboring carbons align with the empty p orbital of the carbocation, allowing for partial overlap. This overlap enables a delocalization of the charge, similar to resonance, although generally to a lesser degree.
  • In primary, secondary, or tertiary carbocations, hyperconjugation helps "spread" the charge by involving electrons from adjacent single bonds (often C-H bonds).
  • The more neighboring carbon-hydrogen (or carbon-carbon) bonds there are, the more possibilities for overlap, thereby increasing stability.
While not as strong as resonance stabilization, hyperconjugation still provides an important contribution to the stability of more substituted carbocations.
Inductive Effects in Carbocation Stability
Inductive effects are the electronic effects impacting the carbocation stability due to the polarizing ability of the surrounding atoms or groups. This concept is rooted in how the electronegativity of atoms or groups near the carbocation can pull electron density towards themselves. This ability to "pull away" electron density provides a form of electronic stabilization.
  • The inductive effect is particularly relevant for understanding differences in stability between otherwise similar carbocations.
  • For example, alkyl groups tend to donate electron density (a positive inductive effect) towards the positively charged carbon, stabilizing the carbocation.
While not as overpowering as resonance, the inductive effects contribute to carbocation stability as part of a combination of electronic factors.

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Most popular questions from this chapter

Match the following $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { (a) } \mathrm{Hg}_{2}^{2+} & \text { (p) Nucleophile } \\ \text { (b) } \mathrm{AlCl}_{3} & \text { (q) Catalyst } \\ \text { (c) } \mathrm{Br} & \text { (r) Lewis acid } \\ \text { (d) } \mathrm{H}^{+} & \text {(s) Soft acid } \\ & \text { (t) Electrophile } \\ \hline \end{array} $$

Amongst the following, the compound that can most readily get sulphonated is (a) benzene (b) toluene (c) nitrobenzene (d) chlorobenzene

Which of the following represent the correct order of nucleophillic addition for (I) \(\mathrm{HCHO}\), (II) \(\mathrm{CH}_{3} \mathrm{COCH}_{3}\), (III) \(\mathrm{CH}_{3} \mathrm{CHO}\), (IV) \(\mathrm{CH}_{3} \mathrm{COC}_{2} \mathrm{H}_{5}\) (a) \(\mathrm{I}>\mathrm{II}>\mathrm{III}>\mathrm{IV}\) (b) \(\mathrm{I}>\mathrm{III}>\mathrm{II}>\mathrm{IV}\) (c) \(\mathrm{IV}>\mathrm{II}>\mathrm{III}>\mathrm{I}\) (d) \(\mathrm{I}>\mathrm{IV}>\mathrm{III}>\mathrm{II}\)

Resonance energy per benzene ring decreases in the order (a) Naphthalene \(>\) Benzene \(>\) Anthracene \(>\) Phenanthrene (b) Benzene \(>\) Naphthalene \(>\) Anthracene \(\geq\) Phenanthrene (c) Benzene \(>\) Naphthalene \(>\) Phenanthrene \(>\) Anthracene (d) All have equal resonance energy

Which of the following intermediate has the complete octet around the carbon atom? (a) free radical (b) carbene (c) carbanion (d) carbonium ion
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