Aromatic Hydrocarbons

The skeleton. Benzene is a planar, hexagonal ring of six carbon atoms, each $sp^2$-hybridised. Each carbon forms three $\sigma$ bonds in the ring plane — two to its ring neighbours and one to a hydrogen atom — with bond angles of $120^\circ$, and carries one unhybridised $2p$ orbital standing perpendicular to the ring plane. It is this leftover $p$ orbital on every carbon, all lined up in parallel, that makes the ring's chemistry unusual.

The delocalised $\pi$ cloud. The six parallel $2p$ orbitals overlap sideways with both neighbours at once, forming a continuous ring of electron density above and below the plane of the carbons. The six $\pi$ electrons therefore belong to the whole ring, not to three fixed C=C double bonds. This is captured on paper by resonance: benzene is drawn as a hybrid of two equivalent Kekulé structures, each showing alternating single and double bonds, but positioned on opposite bonds in the two structures. The real molecule is neither structure — it is one single, time-averaged arrangement in which every C–C bond is identical, at about $139\ \text{pm}$, intermediate between a pure single bond ($\approx 154\ \text{pm}$) and a pure double bond ($\approx 134\ \text{pm}$). The energy benzene gains from this delocalisation, compared with a hypothetical single Kekulé structure, is its resonance (delocalisation) energy, and it is the reason benzene is far less reactive toward addition than an ordinary alkene (the syllabus asks you to know that this stabilisation exists and explains benzene's behaviour, not to calculate its numerical value).

Hückel's rule (stated, not derived). A cyclic system is aromatic only if it satisfies all four conditions at once: it is cyclic, it is planar, every ring atom carries a $p$ orbital available for continuous conjugation around the ring, and the number of delocalised $\pi$ electrons fits

where: $n$ is any non-negative whole number, and the count on the left is only the electrons in the delocalised $\pi$ system, not every electron in the molecule. Benzene has 6 delocalised $\pi$ electrons, and $6 = 4(1) + 2$ with $n = 1$, so it passes. A ring with $4n$ delocalised $\pi$ electrons instead (no integer $n$ satisfies $4n+2$) is called anti-aromatic and is destabilised rather than stabilised by its ring current.

Why substitution beats addition. Because the delocalised ring is a source of real, extra stability, any reaction that would consume a ring double bond and force two carbons back to $sp^3$ — an addition reaction — destroys that stabilisation. Benzene instead reacts by electrophilic substitution: an electrophile replaces one ring hydrogen while the aromatic ring itself, and its delocalisation, survive intact. The detailed mechanisms of nitration, sulphonation, halogenation and Friedel–Crafts reactions belong to the companion article on electrophilic substitution of benzene; here the point is only that aromaticity is why substitution is preferred.

Question. Explain why all six C–C bond lengths in benzene are equal at about $139\ \text{pm}$, even though drawing a single Kekulé structure would suggest three bonds at single-bond length and three at double-bond length.

Step 1. Write one Kekulé structure. It shows alternating bonds: three at $154\ \text{pm}$ (single) and three at $134\ \text{pm}$ (double), so a naive reading of that one drawing predicts two different bond lengths in the ring.

Step 2. Recognise that a single Kekulé structure is only one resonance contributor — a convenient drawing convention on paper, not a real, isolable molecule. Benzene does not flip back and forth between two such structures; it exists as one single electronic arrangement at all times.

Step 3. The true structure is the resonance hybrid of the two equivalent Kekulé forms: the six $\pi$ electrons are delocalised evenly over all six carbons through continuous sideways $p$-orbital overlap, so no individual bond is "purely" single or "purely" double.

Step 4. Since every C–C bond in the ring experiences the same, averaged $\pi$ electron density, every bond has the same intermediate bond order and therefore the same length — measured experimentally at about $139\ \text{pm}$, between the single-bond and double-bond values used in Step 1. Answer: the equal 139 pm bond lengths are direct experimental evidence that benzene is a delocalised resonance hybrid, not a molecule alternating between two Kekulé structures.

Competitive stretch

Apply the same $4n+2$ logic to cyclooctatetraene, $\text{C}_8\text{H}_8$, an eight-membered ring with four formal double bonds and therefore $4 \times 2 = 8$ potential $\pi$ electrons. Solving $4n + 2 = 8$ gives $n = 1.5$, not an integer, so a planar version would fail Hückel's rule and land on the destabilising $4n$ pattern instead. Real cyclooctatetraene avoids this penalty by puckering into a non-planar "tub" shape, which breaks the continuous $p$-orbital overlap the rule requires in the first place — so it behaves as an ordinary, non-aromatic polyene rather than as an aromatic or even anti-aromatic ring, a neat illustration that the planarity condition in Step 1 is not a formality.

• Drawing benzene as if it rapidly flickers between two Kekulé structures — the real molecule is one resonance hybrid with permanently delocalised electrons, not an equilibrium mixture of two distinct molecules.
• Expecting benzene to undergo addition readily because it "has three double bonds" — the resonance stabilisation specifically disfavours addition, which would destroy the delocalised ring, and favours substitution instead.
• Applying Hückel's rule by counting every electron in the ring rather than only the delocalised $\pi$ electrons available for conjugation.
• Forgetting the planarity and full-conjugation conditions — a system can have exactly $4n+2$ $\pi$ electrons and still fail to be aromatic if it is not planar or the ring is not fully conjugated, as with puckered cyclooctatetraene.

Ask the tutor: want to try Hückel's rule on a ring system of your own choosing, or see how this delocalisation picture connects to the electrophilic substitution mechanisms benzene actually undergoes?