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Q9.12(ii):

Explain why the following systems are not aromatic?

(ii) 

Solution :

Analysis of Aromaticity Requirements

To determine if a cyclic system is aromatic, it must satisfy Hückel's Rule and associated criteria [Per Hückel's Rule for aromaticity]:

  • Cyclic Structure: The molecule must be cyclic.
  • Planarity: The atoms in the ring must be $sp^2$ or $sp$ hybridized to allow for a continuous $p$-orbital overlap.
  • Conjugation: The system must possess a continuous cyclic cloud of delocalized $\pi$ electrons.
  • Hückel's Rule ($4n + 2$): The system must contain $(4n + 2) \pi$ electrons, where $n = 0, 1, 2, \dots$

Step 1: Structural Identification of the Molecule

The provided image depicts Cyclooctatetraene ($C_8H_8$). This is an eight-membered ring consisting of four alternating double bonds and four single bonds.

CCCCCC

Step 2: Evaluation of Electron Count

The molecule has four double bonds, meaning there are $4 \times 2 = 8$ electrons involved in $\pi$ bonding. We test this against the $4n + 2$ condition:

$4n + 2 = 8$

$4n = 6 \implies n = 1.5$

Since $n$ must be an integer, the molecule fails the Hückel rule requirement [By mathematical constraint of Hückel's Rule].

Step 3: Evaluation of Geometry and Planarity

Even if the system were to attempt conjugation, it would be an $8\pi$ electron system, which is categorized as anti-aromatic if planar. However, cyclooctatetraene adopts a "tub-shaped" (non-planar) conformation to minimize angle strain and electronic repulsion [Per VSEPR Theory and geometric strain analysis]. Because the molecule is non-planar, the $p$-orbitals cannot achieve parallel alignment, thereby breaking the cyclic conjugation.

Summary Table of Aromaticity Criteria

Criterion Status for Cyclooctatetraene
Cyclic Yes
Planar No (Tub-shaped)
Conjugated No (Non-planar, no continuous overlap)
$\pi$ Electron Count 8 ($4n$ system, not $4n+2$)

Final Solution: The system is not aromatic because it possesses $8\pi$ electrons (violating the $4n+2$ rule) and adopts a non-planar "tub" shape, which prevents the continuous cyclic conjugation of $p$-orbitals required for aromatic stabilization.


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