3.9: Conformations of Cycloalkanes

Adolf von Baeyer attempted to explain the instabilities of small and large cycloalkane rings using the concept of angle strain — the strain caused by the deviation of bond angles from the ideal 109.5° tetrahedral value for sp³ hybridized carbons. However, while cyclopropane and cyclobutane are strained, as expected from their highly compressed bond angles, cyclopentane is more strained than predicted, and cyclohexane is virtually strain-free. Hence, Baeyer’s theory that was based on the assumption that all cycloalkanes are flat was wrong, and, in reality, most cycloalkanes adopt a non-planar structure.

Cyclopropane, the three-carbon cyclic alkane, has the highest angle strain since its planar structure is highly compressed, deviating by 49.5° from the ideal value. Additionally, cyclopropane has a torsional strain due to the eclipsing interaction between six C-H bonds. Hence, cyclopropane has an overall ring strain of 116 kJ/mol. Unlike cyclopropane, which is planar, cyclobutane takes up a more stable, folded non-planar conformation. Folding causes the angle strain to be slightly elevated compared to the hypothetical planar cyclobutane, but the torsional strain from the ten eclipsing hydrogens is greatly relieved. Cyclobutane has an overall strain of 110 kJ/mol. Cyclopentane also adopts a non-planar conformation known as envelope conformation. Compared to the hypothetical planar form of cyclopentane, the envelope form has its bond angles slightly reduced, which marginally increases the angle strain. However, it significantly alleviates the torsional strain from ten eclipsing C-H bonds. Hence, the overall strain in cyclopentane is 27 kJ/mol.

The relative stabilities of cycloalkanes vary with their ring sizes. The variations arise from the combined effects of angle strain and torsional strain, together known as the ring strain of cyclic compounds.

Angle strain is introduced in a cycloalkane when the C-C-C bond angle deviates from the regular tetrahedral bond angle of 109.5°, as predicted for all sp³  hybridized carbons of alkanes.

On the other hand, the torsional strain exists between the eclipsing bonds and is a result of repulsive dispersion forces.

In cyclopropane, the internal angle of 60°, which is significantly smaller than the ideal angle, introduces a severe angle strain in the molecule, forcing the sp³ orbitals to overlap at an angle to give weaker “bent” carbon-carbon bonds.

Cyclopropane, owing to its planar nature, also experiences considerable torsional strain from the six pairs of fully eclipsed C-H bonds.

In essence, cyclopropane is a highly strained molecule with strain energy as high as 116 kJ/mol. For this reason, cyclopropanes are highly reactive.

Unlike cyclopropane, cyclobutane is non-planar and takes up a folded conformation. Folded cyclobutane is more stable than its hypothetical planar form.

Although folding of the ring increases the angle strain slightly, by lowering the bond angle from 90° to 88°, it substantially reduces the torsional strain associated with eight eclipsing C-H bonds, resulting in the net strain energy of 110 kJ/mol.

Like cyclobutane, cyclopentane is also non-planar and assumes an envelope conformation, with one or two atoms bending out of the plane. 

Although a hypothetical planar cyclopentane would have a 108° bond angle — very close to the ideal value, the envelope conformation greatly relieves the torsional strain from ten eclipsing bonds with only a slight rise in the angle strain.

Therefore, the overall ring strain in cyclopentane is as low as 27 kJ/mol.