4.2 Cycloalkanes and Their Relative Stabilities

While the open chain alkanes have conformational isomers because of bond rotation, will this apply to cycloalkanes as well? In this section, we will take a look at the properties of cycloalkanes first, then investigate how the different conformers of cycloalkanes contribute to the different stabilities.

The short line structural formulas of cycloalkenes simply look like shapes such as a triangle, square, etc. The internal angles of the shapes can be calculated with geometry, as shown below.

An interesting fact about the cycloalkanes is that they have different relative stabilities, and the stability depends on the size of the ring. It has been observed that cyclic compounds found in nature are usually in 5- or 6-membered rings and 3- or 4-membered rings are rare.

To explain this stability difference, German chemist Adolf von Baeyer proposed the “Bayer Strain Theory”. By assuming all the rings are in a flat (or planar) shape, Bayer Theory suggests that the difference between the ideal bond angle (which is 109.5° for sp³ carbon) and the angle in the planer cycloalkane causes the strain, which is called angle strain. According to the Bayer Theory, cyclopentane would be the most stable because its bond angle, 108°, is closest to the ideal angle of 109.5°. Cyclopropane would be the least stable one since it has the largest angle deviation of 49.5° (60° vs 109.5°). It was also predicted that cyclohexane would be less stable than cyclopentane because of the larger angle deviation (10.5° deviation for cyclohexane vs 1.5° for cyclopentane), and as the number of sides in the cycloalkanes increases beyond six, the stability decreases.

However, experimental results show a different trend. It turns out that cyclohexane is the most stable ring that is strain-free and is as stable as a chain alkane. Furthermore, cyclic compounds do not become less and less stable as the number of rings increases.

To measure the relative stability of cycloalkanes, the heat of combustion (ΔH_comb) for each cycloalkane was measured. The heat of combustion is the amount of heat released when the compounds burn completely with oxygen. The cycloalkanes will be in higher energy levels than corresponding chain alkanes because of strain energy. Therefore, when cycloalkane burns, more heat will be released, so the difference of ΔH_comb between cycloalkane vs the “strainless” chain alkane is just the amount of strain energy, as shown below. The larger the difference, the higher the strain energy of the cycloalkane. The strain energy for different cycloalkanes measured by this method is listed in Table 4.1.

Table 4.1 Strain Energies of Cycloalkanes

The major drawback of the Baeyer Theory is that we must assume that all the rings are flat. The highest stability of cyclohexane from experimental results indicates that the rings may not be in a planar shape. We will have a closer look at the actual shape and conformation of 3-, 4-, 5- and 6-membered cycloalkanes.

Cyclopropane

With three carbons for the ring, cyclopropane must be planar.

The bond angle in cyclopropane is 60°, derived significantly from the optimal angle of 109.5°, so it has very high angle strains. The sp³-sp³ orbitals can only overlap partially because of the angle deviation, so the overlapping is not as effective as it should be, and as a result, the C-C bond in cyclopropane is relatively weak.

This bent shape of cyclopentane is also called the “envelope” conformation. The envelope conformation can undergo a process called “ring flipping” as a result of C-C bond rotation. Further discussion about ring flipping will be included in the section on cyclohexane.