Resonance and Resonance Energy: MDCAT Chemistry notes

What resonance means

Some molecules cannot be shown correctly by one Lewis structure. Resonance describes such a molecule as a hybrid of two or more structures (contributing or canonical structures) that differ only in the positions of electrons, not atoms. The real molecule is a single structure with delocalised electrons; it does not flip between the forms.

• Only $\pi$ electrons and lone pairs move; atoms stay in place.
• The hybrid is more stable (lower in energy) than any single contributing structure.
• Resonance is shown with a double-headed arrow $\leftrightarrow$.

Conjugation in benzene

Benzene, $\mathrm{C_6H_6}$, is drawn by Kekulé as a six-membered ring of alternate single and double bonds. Alternating single and double bonds form a conjugated system. Each carbon is $sp^2$ hybridised and has one unhybridised p-orbital; the six p-orbitals overlap sideways all round the ring to make a continuous $\pi$ cloud above and below the ring. The six $\pi$ electrons are delocalised over all six carbons.

Evidence for delocalisation:

• All six C–C bonds are the same length, about 139–140 pm, between a single bond (154 pm) and a double bond (134 pm).
• Benzene prefers substitution over addition, and it resists oxidation by $\mathrm{KMnO_4}$, unlike a true alkene.
• Only one ortho-disubstituted benzene exists, not two.

Resonance energy

Resonance energy is the difference between the energy of the real molecule and that of its most stable contributing structure. For benzene it is measured from heats of hydrogenation.

Species	Heat of hydrogenation
Cyclohexene (one C=C)	$-119.5\ \mathrm{kJ\,mol^{-1}}$
Hypothetical cyclohexa-1,3,5-triene (three C=C, expected)	$3 \times -119.5 = -358.5\ \mathrm{kJ\,mol^{-1}}$
Benzene (observed)	$-208\ \mathrm{kJ\,mol^{-1}}$

$$\text{Resonance energy} = 358.5 - 208 = 150.5\ \mathrm{kJ\,mol^{-1}}$$

So benzene is about 150.5 kJ per mole more stable than the imaginary triene. This extra stability explains its aromatic behaviour.

Key formulas

• Resonance energy = expected heat of hydrogenation $-$ observed heat of hydrogenation (magnitudes).
• Benzene: $3(119.5) - 208 = 150.5\ \mathrm{kJ\,mol^{-1}}$.

Common MDCAT traps

• The unit is kJ per mole, not J per mole or kJ per molecule.
• Alternate single and double bonds are conjugated, not coordinate, fixed or ionic bonds.
• Contributing structures are not real; benzene does not oscillate between Kekulé forms.
• Benzene's C–C bonds are all equal, not three short and three long.

Quick revision

• Resonance: same atoms, different electron positions.
• Hybrid is more stable than any contributor.
• Benzene carbons are $sp^2$; six $\pi$ electrons are delocalised.
• C–C bond length in benzene is about 139 pm.
• Resonance energy of benzene = 150.5 kJ/mol.