Benzene, with the molecular formula \( \text{C}_6\text{H}_6 \), is the simplest member of the class of hydrocarbons known as arenes (or aromatic hydrocarbons). The structure of benzene is a key topic in organic chemistry, serving as a classic example of how experimental evidence can disprove a historical model and lead to a more accurate understanding of chemical bonding.
🔑 Key Principle
Rather than possessing alternating double and single bonds, benzene contains a planar ring of carbon atoms with a delocalised ring of \( \pi \)-electrons above and below the plane of the carbon ring, giving it thermodynamic and chemical stability.
Historical Kekulé Model vs The Delocalised Model
In 1865, Friedrich August Kekulé proposed that benzene consisted of a flat ring of six carbon atoms with alternating single and double carbon-to-carbon bonds (cyclohexa-1,3,5-triene). In contrast, the modern delocalised model states that:
- Each carbon atom is \( sp^2 \) hybridised, forming three \( \sigma \)-bonds: two to adjacent carbon atoms and one to a hydrogen atom.
- This leaves a single unhybridised p-orbital on each carbon atom, containing one electron, oriented perpendicular to the planar ring.
- Instead of pairing into individual \( \pi \)-bonds, all six p-orbitals overlap sideways. This forms a continuous, ring-shaped cloud of delocalised \( \pi \)-electron density above and below the plane of the carbon ring.
A historical model of benzene consisting of a six-membered carbon ring with alternating carbon-carbon single and double covalent bonds.
A aromatic hydrocarbon containing a planar ring of carbon atoms with a delocalised ring of \( \pi \)-electrons.
Evidence for the Delocalised Model
Three main lines of experimental evidence proved Kekulé's model incorrect, supporting the modern delocalised model:
1. Carbon-to-Carbon Bond Lengths
In Kekulé's structure, the ring contains three single carbon-carbon bonds (\( \text{C-C} \)) and three double bonds (\( \text{C}=\text{C} \)). Single bonds are longer (\( 0.154\text{ nm} \)) than double bonds (\( 0.134\text{ nm} \)), which would make benzene an irregular hexagon.
However, X-ray diffraction measurements show that all six carbon-carbon bonds in benzene are identical in length (\( 0.140\text{ nm} \)). This length is intermediate between a single and a double bond, proving the bonds are equal and symmetry is perfectly hexagonal.
2. Chemical Reactivity (Addition Resistance)
If benzene had three double bonds, it should easily undergo electrophilic addition reactions, similar to alkenes (such as decolourising bromine water at room temperature). Instead, benzene is resistant to addition and undergoes electrophilic substitution reactions, which require a catalyst. Substitution is preferred because addition would require breaking the stable delocalised \( \pi \)-system, which is energetically unfavourable.
3. Enthalpy of Hydrogenation Evidence
The enthalpy change of hydrogenation is the energy released when hydrogen is added to an unsaturated ring. By comparing these values, we can determine the thermodynamic stability of benzene:
- Hydrogenation of cyclohexene (one \( \text{C}=\text{C} \) bond) has an enthalpy change of \( -120\text{ kJ mol}^{-1} \): \[ \text{C}_6\text{H}_{10} + \text{H}_2 \rightarrow \text{C}_6\text{H}_{12} \quad \Delta H = -120\text{ kJ mol}^{-1} \]
- If benzene had Kekulé's structure (cyclohexa-1,3,5-triene, with three \( \text{C}=\text{C} \) bonds), we would expect the hydrogenation enthalpy to be three times that of cyclohexene: \[ 3 \times (-120\text{ kJ mol}^{-1}) = -360\text{ kJ mol}^{-1} \]
- The actual experimental value for the enthalpy of hydrogenation of benzene is \( -208\text{ kJ mol}^{-1} \): \[ \text{C}_6\text{H}_6 + 3\text{H}_2 \rightarrow \text{C}_6\text{H}_{12} \quad \Delta H = -208\text{ kJ mol}^{-1} \]
The extra stability gained by a molecule due to the delocalisation of its \( \pi \)-electrons. For benzene, this is \( 152\text{ kJ mol}^{-1} \).
The experimental value is \( 152\text{ kJ mol}^{-1} \) less exothermic than expected. This means benzene is \( 152\text{ kJ mol}^{-1} \) more stable than the hypothetical cyclohexa-1,3,5-triene. This difference is known as the delocalisation energy (or resonance energy) of benzene.
When discussing the formation of the delocalised system in benzene, you must state that the unhybridised p-orbitals overlap sideways, above and below the plane of the carbon atoms. In addition, make sure you can list the three types of evidence disproving Kekulé's model, as this is a common exam question.
Solution:
1. State the expected value: Cyclohexene has one double bond and an enthalpy of hydrogenation of \( -120\text{ kJ mol}^{-1} \). For a triene like cyclohexa-1,3,5-triene, we expect three times this value, which is \( -360\text{ kJ mol}^{-1} \).
2. State the actual value: The experimental enthalpy of hydrogenation of benzene is \( -208\text{ kJ mol}^{-1} \).
3. Calculate the stability difference: The difference in energy is \( -360 - (-208) = -152\text{ kJ mol}^{-1} \).
4. Conclude: Because the actual hydrogenation is less exothermic by \( 152\text{ kJ mol}^{-1} \), benzene contains less energy than the triene, meaning it is more stable. This extra stability is its delocalisation energy, caused by the ring of delocalised \( \pi \)-electrons.