Topic 18 · page 2 of 10
Bond lengths and infrared evidence
X-ray diffraction shows six equal carbon–carbon bonds, all 0.139 nm, and infrared shows no alkene C=C absorption. Together with the energy data, that rules out the Kekulé ring.
Read first: Benzene and the energy evidence
Evidence 2: bond lengths from X-ray diffraction 18.1
X-rays are scattered by electrons. When a beam passes through a crystal, the scattered rays form a pattern. From the pattern, a computer builds a map of electron density, which locates the atoms and gives the bond lengths between them.
Typical carbon–carbon bond lengths:
| Bond | Length / nm |
|---|---|
| C–C single bond (as in cyclohexane) | 0.154 |
| C=C double bond (as in cyclohexene) | 0.134 |
| every C–C bond in benzene | 0.139 |
Benzene's six carbon–carbon bonds are all the same length, and that length lies between the single and double values. The molecule is a planar, regular hexagon with all bond angles 120°.
A Kekulé ring would have three long bonds (0.154 nm) alternating with three short ones (0.134 nm). That is an uneven hexagon. The data show nothing of the kind.
Evidence 3: infrared spectra 18.1
Bonds absorb infrared radiation at wavenumbers that depend on the type of bond. A peak in a particular region of a spectrum shows that a bond of that type is present.
The two regions that matter here, as quoted in the Data Booklet, are:
| Absorption | Wavenumber / cm⁻¹ | Cyclohexene | Benzene |
|---|---|---|---|
| alkene C=C stretch | 1669–1645 | present | absent |
| arene ring C=C stretch | about 1600 and 1500–1450 | absent | present |
| C–H stretch | 3100–3000 | present | present |
Cyclohexene, with a localised C=C bond, absorbs in the alkene C=C region. Benzene does not. If benzene contained three ordinary C=C bonds, it would show that peak. Its absorptions are in different places, so its carbon–carbon bonds are not ordinary C=C bonds.
Putting the three kinds of evidence together 18.1
Each piece of evidence compares Kekulé's prediction with what is measured.
| Evidence | Kekulé structure predicts | What is observed | Conclusion |
|---|---|---|---|
| enthalpy of hydrogenation | −360 kJ mol⁻¹ | −208 kJ mol⁻¹ | benzene is 152 kJ mol⁻¹ more stable |
| X-ray diffraction | alternating 0.154 and 0.134 nm bonds | six equal bonds, 0.139 nm | no separate single and double bonds |
| infrared spectrum | an alkene C=C absorption | none in 1669–1645 cm⁻¹ | no localised C=C bonds |
Check yourself
- What does X-ray diffraction show about the carbon–carbon bonds in benzene, and why does this disagree with the Kekulé structure?
- A student states that the C–C bonds in benzene are 0.144 nm, the average of 0.154 nm and 0.134 nm. What should the student have said?
- The infrared spectrum of cyclohexene has an absorption at about 1655 cm⁻¹. Benzene's does not. What does this show?
- Give one piece of evidence of each type (thermochemical, X-ray, infrared) that benzene is not cyclohexa-1,3,5-triene.
- Which type of evidence gives (a) a bond length, (b) a number in kJ mol⁻¹, (c) the presence or absence of a type of bond?
Answers cover these until you have tried the questions
- All six C–C bonds are the same length, 0.139 nm, between the single bond (0.154 nm) and the double bond (0.134 nm). The ring is a regular hexagon. A Kekulé ring would have alternating long (0.154 nm) and short (0.134 nm) bonds, so would be an uneven hexagon.
- The bonds are all 0.139 nm, which is intermediate in length between a C–C single bond and a C=C double bond. The average of the two values is 0.144 nm, but the measured value is 0.139 nm, so "average" is not correct.
- 1655 cm⁻¹ lies in the alkene C=C range (1669–1645 cm⁻¹). The absence of any peak there for benzene shows it has no ordinary localised C=C bonds, so the Kekulé structure is wrong.
- Thermochemical: enthalpy of hydrogenation is −208 kJ mol⁻¹, not the −360 kJ mol⁻¹ predicted, so benzene is 152 kJ mol⁻¹ more stable. X-ray: all six C–C bonds are 0.139 nm, not alternating 0.154 and 0.134 nm. Infrared: no absorption in 1669–1645 cm⁻¹, so no C=C as in an alkene.
- (a) X-ray diffraction. (b) Enthalpy (thermochemical) data. (c) Infrared spectroscopy.