Why All Six Carbon Bonds in Benzene Are the Same Length

Lewis structures and hybridisation explain many molecules, but they cannot explain why liquid oxygen clings to a magnet, why all the carbon-carbon bonds in benzene are equal, or why water boils so much higher than hydrogen sulphide. Molecular orbital theory, resonance and hydrogen bonding fill those gaps.

This lesson covers molecular orbital diagrams and bond order, resonance, and hydrogen bonding.

In molecular orbital theory, atomic orbitals combine into bonding orbitals of lower energy and antibonding orbitals of higher energy that belong to the whole molecule, and bond order is half the difference between the numbers of bonding and antibonding electrons.

Bond order:

$$\text{Bond order}=\frac{1}{2}(N_b-N_a)$$

where $N_b$ and $N_a$ are the numbers of electrons in bonding and antibonding orbitals. A positive bond order means a stable molecule, and a higher bond order means a shorter, stronger bond.

Energy order:

- For oxygen and fluorine: $\sigma 1s<{\sigma }^{\ast }1s<\sigma 2s<{\sigma }^{\ast }2s<\sigma 2p_z<(\pi 2p_x=\pi 2p_y)<({\pi }^{\ast }2p_x={\pi }^{\ast }2p_y)<{\sigma }^{\ast }2p_z$
- For nitrogen and lighter molecules: the $\pi 2p$ orbitals lie below $\sigma 2p_z$

Worked example 1 — nitrogen, 14 electrons. $N_b=10$ and $N_a=4$:

$$\text{Bond order}=\frac{1}{2}(10-4)=3$$

All electrons are paired, so nitrogen is diamagnetic.

Worked example 2 — oxygen, 16 electrons. $N_b=10$ and $N_a=6$, so the bond order is 2. The last two electrons occupy the two ${\pi }^{\ast }$ orbitals singly, so oxygen is paramagnetic.

Worked example 3 — ions and helium.

- ${\mathrm{O}}_2^{+}$: $\frac{1}{2}(10-5)=2.5$; ${\mathrm{O}}_2^{-}$: $\frac{1}{2}(10-7)=1.5$
- $\mathrm{H}{\mathrm{e}}_2$: $\frac{1}{2}(2-2)=0$, so it does not exist

An everyday example. Oxygen analysers used with hospital oxygen supplies can work by detecting the paramagnetism that molecular orbital theory predicts for oxygen.

The substance. A Lewis structure of oxygen shows every electron paired — only the molecular orbital picture explains its two unpaired electrons.

Resonance describes a molecule that no single Lewis structure can represent; its real structure is a resonance hybrid of several canonical structures, with delocalised electrons that make it more stable than any one of them.

Key ideas:

- Canonical structures differ only in the positions of electrons, not of atoms
- The resonance hybrid is one real structure — it does not switch between the canonical forms
- Delocalisation lowers the energy, and the difference is the resonance energy

Benzene:

- Two Kekule structures show alternating single and double bonds around the ring
- In reality, all six carbon-carbon bonds are equal, 139 pm long — between a C-C single bond (154 pm) and a C=C double bond (134 pm)
- Its six pi electrons are delocalised over the ring, making benzene unusually stable and slow to undergo addition reactions

**Carbonate ion, $\mathrm{C}{\mathrm{O}}_3^{2-}$:

- Three canonical structures each show one C=O double bond and two C-O single bonds
- In reality, all three carbon-oxygen bonds are identical
- The two negative charges are spread over all three oxygen atoms

Worked example.** In the carbonate ion, four shared pairs are spread over three carbon-oxygen bonds:

$$\text{Bond order}=\frac{4}{3}=1.33$$

An everyday example. Marble and limestone used in Indian buildings are calcium carbonate, whose carbonate ions owe part of their stability to resonance.

The substance. Canonical structures are not real molecules — no benzene molecule ever has alternating short and long bonds.

A hydrogen bond is the attraction between a hydrogen atom bonded to fluorine, oxygen or nitrogen and a lone pair on another such atom, and it raises boiling points, increases solubility in water and gives ice its open structure.

Conditions. Hydrogen must be bonded to F, O or N, and a lone pair on a nearby F, O or N must be available.

Types:

- Intermolecular — between different molecules, as in water, hydrogen fluoride and ethanol
- Intramolecular — within one molecule, as in o-nitrophenol, where the OH and nitro groups sit side by side

Effects on physical properties:

- Boiling point — water boils at 100 °C, while hydrogen sulphide, with no hydrogen bonding, boils at about -60 °C
- Isomers — ethanol boils far higher than its isomer dimethyl ether, which cannot hydrogen bond with itself
- Nitrophenols — p-nitrophenol forms intermolecular hydrogen bonds and boils higher than o-nitrophenol, whose hydrogen bonding stays within the molecule
- Solubility — ethanol, sugar and ammonia dissolve readily in water by hydrogen bonding with it
- Density — ice has an open network of hydrogen bonds, so it is less dense than liquid water

Worked comparison. Hydrogen fluoride boils at about 20 °C, but hydrogen chloride, without hydrogen bonding, boils at about -85 °C.

An everyday example. Sugar dissolving easily in a glass of nimbu pani happens because its many OH groups form hydrogen bonds with water.

The substance. Hydrogen bonds are much weaker than covalent bonds — but there are so many of them that they control boiling points and hold together the structures of proteins and DNA.