Benzene

Lessons

Senior 6 · Chemistry

Benzene

4 lessons

Lesson 1 of 4

The Structure of Benzene: Kekulé and the Delocalised Model

25 min

A formula that did not make sense

In 1825 Michael Faraday isolated a colourless liquid from the oily residue of the gas used for street lighting in London. Its formula turned out to be $\mathrm{C_6H_6}$ . An alkane with six carbon atoms, hexane, is $\mathrm{C_6H_{14}}$ , so benzene is eight hydrogen atoms short: by the rules you learned in S5 it should be highly unsaturated, with several double or triple bonds, and should react like an alkene. It does not. It does not decolourise bromine water, and it resists oxidation. Working out why took chemists more than a hundred years.

Worked example

Problem. 0.390 g of a hydrocarbon burns completely to give 1.320 g of carbon dioxide and 0.270 g of water. Its relative molecular mass is 78. Find its molecular formula. (C = 12.01, H = 1.008, O = 16.00)

Solution.

$m(\mathrm{C}) = 1.320 \times \frac{12.01}{44.01} = 0.3602\,\mathrm{g} \qquad m(\mathrm{H}) = 0.270 \times \frac{2.016}{18.02} = 0.0302\,\mathrm{g}$

Check: $0.3602 + 0.0302 = 0.3904$ g, the mass burned, so there is no oxygen.

$n(\mathrm{C}) = \frac{0.3602}{12.01} = 0.02999 \qquad n(\mathrm{H}) = \frac{0.0302}{1.008} = 0.02997$

The ratio is 1 : 1, so the empirical formula is CH, with $M_{r} = 13.02$ . Then $\frac{78}{13.02} = 6$ .

Answer: $\mathrm{C_6H_6}$ , benzene.

Kekulé's model

In 1865 the German chemist August Kekulé proposed that the six carbon atoms form a ring, joined by alternating single and double bonds, with one hydrogen on each carbon. In 1872 he added that the double bonds must be constantly swapping positions (Figure 1.1 A). His model explained the formula and the fact that all six hydrogen atoms behave the same. But three kinds of evidence show it cannot be right.

Figure 1.1: Two models of benzene. Each corner is a carbon atom joined to one hydrogen atom, which is not drawn.

Evidence 1: all the bonds are the same length

X-ray diffraction measures the distances between atoms in a crystal. In 1929 Kathleen Lonsdale used it to show that the ring of hexamethylbenzene is flat and a regular hexagon. Later measurements on benzene itself gave the values in Table 1.1.

Table 1.1: Carbon–carbon bond lengths

Bond	Example	Length / nm
C–C single	ethane, cyclohexane	0.154
C=C double	ethene, cyclohexene	0.134
carbon–carbon bond in benzene	all six bonds	0.139

A Kekulé molecule would have three short and three long bonds, making an irregular hexagon. In benzene all six bonds are equal and in between the two, as if each were "one and a half" bonds.

Evidence 2: benzene is more stable than expected

Adding hydrogen to cyclohexene, which has one C=C bond, releases 120 kJ mol⁻¹:

$\mathrm{C_6H_{10}(l) + H_2(g) \rightarrow C_6H_{12}(l)} \qquad \Delta H = -120\,\mathrm{kJ\,mol^{-1}}$

A molecule with three separate C=C bonds, cyclohexa-1,3,5-triene, should release about three times as much, −360 kJ mol⁻¹. Benzene releases only 208 kJ mol⁻¹:

$\mathrm{C_6H_6(l) + 3H_2(g) \rightarrow C_6H_{12}(l)} \qquad \Delta H = -208\,\mathrm{kJ\,mol^{-1}}$

Real benzene is therefore $360 - 208 = 152\,\mathrm{kJ\,mol^{-1}}$ lower in energy than Kekulé's structure (Figure 1.3).

Figure 1.3: Enthalpy of hydrogenation shows that benzene is 152 kJ mol⁻¹ more stable than Kekulé's structure.

Worked example

Problem. Use average bond enthalpies to estimate $\Delta H$ for hydrogenating one mole of Kekulé's cyclohexa-1,3,5-triene to cyclohexane, and compare your answer with the measured value for benzene, −208 kJ mol⁻¹. (Average bond enthalpies / kJ mol⁻¹: C=C 612, C–C 348, H–H 436, C–H 412)

Solution. $\mathrm{C_6H_6 + 3H_2 \rightarrow C_6H_{12}}$ . Three C=C bonds become C–C bonds, and six new C–H bonds form; the other bonds are unchanged.

$\text{bonds broken} = 3(612) + 3(436) = 3144\,\mathrm{kJ} \qquad \text{bonds made} = 3(348) + 6(412) = 3516\,\mathrm{kJ}$

$\Delta H = 3144 - 3516 = -372\,\mathrm{kJ\,mol^{-1}}$

Answer: about −372 kJ mol⁻¹ for a Kekulé molecule, against −208 kJ mol⁻¹ measured for benzene. Real benzene is roughly 160 kJ mol⁻¹ more stable than Kekulé's structure; the estimate differs a little from the 152 kJ mol⁻¹ found from cyclohexene because average bond enthalpies are only approximate.

Evidence 3: benzene does not behave like an alkene

Alkenes decolourise bromine water at once by electrophilic addition. Benzene does not react with bromine water at all, and reacts with pure bromine only with a catalyst, by substitution, keeping its ring intact (Lesson 3). There is also only one 1,2-dibromobenzene. A Kekulé ring would give two: one with the bromine atoms on either side of a single bond, and one on either side of a double bond.

Definition

Delocalised electrons: bonding electrons that are shared by more than two atoms, instead of being held between one pair. In benzene, six π electrons are spread evenly over all six carbon atoms.

Delocalisation energy (resonance energy): the extra stability of a molecule with delocalised electrons compared with a model structure in which they are localised. For benzene it is about 152 kJ mol⁻¹.

Arene (aromatic compound): a compound that contains a benzene ring. Example: methylbenzene, $\mathrm{C_6H_5CH_3}$ .

The delocalised model

Each carbon atom in benzene is $s p^{2}$ hybridised (S4): it uses three hybrid orbitals to form σ bonds to two carbons and one hydrogen, all in one plane at 120°. So the molecule is flat. Each carbon has one electron left in a $p$ orbital at right angles to the ring. Instead of pairing up to make three separate π bonds, the six $p$ orbitals overlap sideways all the way round, forming two rings of π electron density, one above and one below the plane (Figure 1.2). This explains all the evidence: the bonds are equal because the electrons are shared evenly; the molecule is extra stable because delocalisation lowers its energy; and it resists addition because addition would destroy the delocalised system.

Figure 1.2: Bonding in benzene. The six p orbitals overlap all round the ring, so the six π electrons are delocalised.

Important

Draw benzene as a hexagon with a circle inside for the delocalised model. The Kekulé drawing is still accepted in many exam answers and is handy for counting electrons in mechanisms, but it does not describe the real molecule.

Warning

Not a fast flip. Benzene is not switching between two Kekulé structures. It is always one single structure, a blend of the two, with six identical bonds. Modern books sometimes join the two Kekulé drawings with a double-headed arrow (↔). That arrow means "the real molecule lies between these drawings", not "these are changing into each other".

Tip

Remember the evidence as "length, energy, reactivity": equal bond lengths (0.139 nm), a hydrogenation enthalpy 152 kJ mol⁻¹ less than expected, and substitution instead of addition.

Launchpad Learning: Kekulé Structure of Benzene (9 min). Watch for the three pieces of evidence against Kekulé's model and how the delocalised model explains each one.

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Practice

State the molecular formula of benzene and explain why it suggests that benzene is highly unsaturated.
Give three pieces of experimental evidence that Kekulé's structure is not correct.
The enthalpy of hydrogenation of cyclohexene is −119 kJ mol⁻¹ and that of benzene is −207 kJ mol⁻¹. Calculate the delocalisation energy of benzene from these data.
Describe, in terms of orbitals, how the six π electrons in benzene are arranged. State the H–C–C bond angle.
0.260 g of a hydrocarbon gives 0.880 g of $\mathrm{CO_2}$ and 0.180 g of $\mathrm{H_2O}$ on complete combustion. Its $M_{r}$ is 78. Find its molecular formula.
How many isomers of 1,2-dichlorobenzene would Kekulé's model predict? How many exist? Explain.
Cyclohexa-1,3-diene, with two C=C bonds, has an enthalpy of hydrogenation of −232 kJ mol⁻¹. Compare this with the value expected from cyclohexene, and suggest why the difference is so much smaller than for benzene.
A student says: "Benzene is just a cyclic alkene with three double bonds." Evaluate this statement.

Show answersHide answers

$\mathrm{C_6H_6}$ . A saturated hydrocarbon with six carbons (hexane) is $\mathrm{C_6H_{14}}$ ; benzene has eight fewer hydrogen atoms, which suggests four "degrees of unsaturation" (rings or π bonds).
All C–C bonds are the same length (0.139 nm); the enthalpy of hydrogenation (−208 kJ mol⁻¹) is much less exothermic than predicted (−360 kJ mol⁻¹); benzene does not decolourise bromine water and reacts by substitution, not addition; only one 1,2-disubstituted isomer exists.
Predicted: $3 \times (-119) = -357$ kJ mol⁻¹. Delocalisation energy = $357 - 207 = 150$ kJ mol⁻¹.
Each carbon is $s p^{2}$ hybridised, with one $p$ orbital at right angles to the plane of the ring. The six $p$ orbitals overlap sideways to form a delocalised π system, with rings of electron density above and below the plane. Bond angles are 120°.
C: $0.880 \times \frac{12.01}{44.01} = 0.2401$ g, 0.02000 mol; H: $0.180 \times \frac{2.016}{18.02} = 0.0201$ g, 0.0200 mol. Ratio 1 : 1, empirical formula CH (13.02); $\frac{78}{13.02} = 6$ , so $\mathrm{C_6H_6}$ .
Kekulé predicts two: the chlorines could be joined by a single bond or a double bond between their carbons. Only one exists, because all six ring bonds are identical.
Expected: $2 \times (-120) = -240$ kJ mol⁻¹. The measured value, −232, is only 8 kJ mol⁻¹ less exothermic. The two double bonds in the diene are conjugated, which gives a little delocalisation, but they do not form a complete ring of six π electrons, so the extra stability is small.
The statement is wrong. An alkene with three C=C bonds would have unequal bond lengths, a hydrogenation enthalpy near −360 kJ mol⁻¹, and would decolourise bromine water by addition. Benzene has equal bonds, is 152 kJ mol⁻¹ more stable, and reacts by substitution, because its six π electrons are delocalised round the ring. It is an arene, not an alkene.

Sources and credits

Written by Ganzaa. Bond lengths and enthalpies of hydrogenation are standard textbook values.
Image: Friedrich August Kekulé von Stradonitz (1890er).jpg, unknown photographer, via Wikimedia Commons, public domain.
Video: Kekule Structure of Benzene, Launchpad Learning, embedded from YouTube.
The diagrams, table, worked example and Practice items were written and drawn by Ganzaa.

1A formula that did not make sense

2Kekulé's model

3Evidence 1: all the bonds are the same length

4Evidence 2: benzene is more stable than expected

5Evidence 3: benzene does not behave like an alkene

6The delocalised model