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Q9.12(ii):

Explain why the following systems are not aromatic?

(ii) 

Solution :

Step 1: Structural Analysis of the System

The provided chemical structure represents 1,3,5,7-cyclooctatetraene ($C_8H_8$). To determine aromaticity, we apply Hückel's Rule and the criteria for aromatic systems:

  • The molecule must be cyclic and planar.
  • The system must be fully conjugated (a continuous ring of overlapping $p$-orbitals).
  • The system must follow the Hückel rule of $(4n + 2) \pi$ electrons, where $n$ is an integer ($0, 1, 2, ...$).

Step 2: Electron Count and Hückel Calculation

In 1,3,5,7-cyclooctatetraene, there are four double bonds within the eight-membered ring.

  • Total $\pi$ electrons = $4 \times 2 = 8$ electrons.
  • Applying the $(4n + 2)$ formula: $4n + 2 = 8 \Rightarrow 4n = 6 \Rightarrow n = 1.5$.
[Per Hückel's Rule, $n$ must be an integer. Since $n=1.5$, the molecule does not satisfy the $(4n+2)\pi$ electronic requirement.]

Step 3: Geometric Configuration and Planarity

While the molecule is cyclic and possesses a conjugated system of double bonds, it does not adopt a planar conformation. A planar cyclooctatetraene would experience significant angle strain and transannular steric repulsion between internal hydrogens.
To minimize potential energy, the molecule adopts a "tub-shaped" (non-planar) conformation.

Cyclooctatetraene (Tub Shape) Non-planar Non-planar

Step 4: Synthesis of Ineligibility

Criterion Status for Cyclooctatetraene
Cyclic Yes
Planarity No (Tub-shaped)
$(4n+2)\pi$ Electrons No ($8 \pi$ electrons, satisfies $4n$ system, not $4n+2$)

Because the molecule fails to remain planar and possesses $8\pi$ electrons (which characterizes anti-aromaticity if planar, but instability leads to the non-planar deviation), it is classified as a non-aromatic, tub-shaped hydrocarbon.

Final Solution: The system is not aromatic because it does not contain $(4n+2)\pi$ electrons ($8 \pi$ electrons present) and, primarily, because it adopts a non-planar "tub-shaped" geometry to minimize strain, thereby breaking the required orbital overlap for aromaticity.


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