18A.1-18A.3 - Benzene Models And Evidence

Kekule And Delocalised Benzene Models

Benzene has molecular formula $\ce{C6H6}$. A tempting first drawing is a six-carbon ring with alternating $\ce{C-C}$ and $\ce{C=C}$ bonds: the Kekule representation. It is useful as a drawing convention, but if it were a literal bonding model it would make two predictions:

• there would be three ordinary $\ce{C=C}$ bonds and three ordinary $\ce{C-C}$ bonds
• the carbon-carbon bond lengths would alternate around the ring

Those predictions are testable. Chemists do not choose the delocalised model because it looks neater; they choose it because thermochemical and structural data do not behave like a ring containing three separate alkene double bonds.

[DIAGRAM: asset_name: Kekule And Delocalised Benzene Models; asset_slug: edexcel_a_level_chemistry_l085_benzene_models; recommended_method: deterministic_chart; description: Compares the alternating Kekule representation with a delocalised ring and p-orbital overlap model]

The delocalised model keeps the six carbon atoms in a planar hexagonal ring. Each carbon forms sigma bonds to two neighbouring carbon atoms and one hydrogen atom. The remaining p orbital on each carbon overlaps with p orbitals on both neighbouring carbons, so the six pi electrons are spread over the whole ring rather than locked into three separate $\ce{C=C}$ bonds.

This means the circle-in-a-hexagon drawing is a shorthand for delocalised pi electron density. It is not meant to show an extra bond or a seventh atom. In equations and mechanisms, either benzene representation may be used, but the chemical model underneath should be the delocalised one.

A literal fixed alternating-bond model also predicts two different adjacent (1,2-) disubstituted arrangements: the substituted carbons could share a single or a double bond. Only one 1,2-dibromobenzene is found. The delocalised model makes every adjacent C–C position equivalent, fitting this observation.

How The Delocalised Pi System Forms

Each carbon atom in benzene is bonded to three atoms: two carbons and one hydrogen. The sigma-bond framework is planar and gives approximately $120^\circ$ angles around each carbon. The p orbital on each carbon is perpendicular to this plane.

For a localised alkene $\ce{C=C}$ bond, two neighbouring p orbitals overlap sideways to make one pi bond between two carbon atoms. In benzene, each p orbital can overlap sideways with p orbitals on both sides. The result is a continuous pi system above and below the ring.

"Delocalised electrons" alone is not a full description:

That model explains why all carbon-carbon bonds in benzene are equivalent. It also explains why benzene is energetically more stable than a hypothetical cyclohexatriene with three isolated $\ce{C=C}$ bonds.

The C–C sigma bonds form by head-on overlap of orbitals along the line joining adjacent nuclei. The π system forms by sideways overlap of the perpendicular p orbitals. These are different overlaps: the delocalised π system sits above and below an already bonded planar sigma framework.

Evidence From Hydrogenation Enthalpy

Hydrogenation adds hydrogen across a carbon-carbon double bond. For an ordinary cycloalkene, one $\ce{C=C}$ bond is hydrogenated to a $\ce{C-C}$ bond:

cyclohexene + $\ce{H2}$ → cyclohexane

Using a typical gas-phase data set, the enthalpy change for this reaction is about $-119\,\mathrm{kJ\,mol^{-1}}$. If benzene really behaved like a ring with three isolated $\ce{C=C}$ bonds, a simple prediction would be about three times this value:

The measured hydrogenation enthalpy for benzene to cyclohexane is much less exothermic, about $-206\,\mathrm{kJ\,mol^{-1}}$:

benzene + $\ce{3H2}$ → cyclohexane

[DIAGRAM: asset_name: Hydrogenation Enthalpy Evidence For Benzene Stability; asset_slug: edexcel_a_level_chemistry_l085_hydrogenation_enthalpy_evidence; recommended_method: deterministic_chart; description: Shows predicted hydrogenation enthalpy for three isolated C=C bonds versus actual benzene hydrogenation]

Worked example: calculate the extra stability

Use these values: hydrogenation of cyclohexene $= -119\,\mathrm{kJ\,mol^{-1}}$; hydrogenation of benzene $= -206\,\mathrm{kJ\,mol^{-1}}$.

If benzene contained three ordinary isolated $\ce{C=C}$ bonds, the predicted value would be $3 \times (-119) = -357\,\mathrm{kJ\,mol^{-1}}$. The actual value is $-206\,\mathrm{kJ\,mol^{-1}}$.