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12.4: Strain in Cycloalkane Rings

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    The Baeyer Theory

    Many of the properties of cyclopropane and its derivatives are similar to the properties of alkenes. In 1890, the famous German organic chemist, A. Baeyer, suggested that cyclopropane and cyclobutane derivatives are different from cyclopentane and cyclohexane, because their \(\ce{C-C-C}\) angles cannot have the tetrahedral value of \(109.5^\text{o}\). At the same time, Baeyer hypothesized that the difficulties encountered in synthesizing cycloalkane rings from \(\ce{C_7}\) upward was the result of the angle strain that would be expected if the large rings were regular planar polygons (see Table 12-3). Baeyer also believed that cyclohexane had a planar structure like that shown in Figure 12-2, which would mean that the bond angles would have to deviate \(10.5^\text{o}\) from the tetrahedral value. However, in 1895, the then unknown chemist H. Sachse suggested that cyclohexane exists in the strain-free chair and boat forms discussed in Section 12-3. This suggestion was not accepted at the time because it led to the prediction of several possible isomers for compounds such as chlorocyclohexane. The idea that such isomers might act as a single substance, as the result of rapid equilibration, seemed like a needless complication, and it was not until 1918 that E. Mohr proposed a definitive way to distinguish between the Baeyer and Sachse cyclohexanes. As will be discussed in Section 12-9, the result, now known as the Sachse-Mohr theory, was complete confirmation of the idea of nonplanar large rings.

    Table 12-3: Strain and Heats of Combustion of Cycloalkanes

    Roberts and Caserio Screenshot 12-4-1.png

    Because cyclopentane and cyclobutane (Sections 12-3E and 12-3F) also have nonplanar carbon rings, it is clear that the Baeyer postulate of planar rings is not correct. Nonetheless, the idea of angle strain in small rings is important. There is much evidence to show that such strain produces thermodynamic instability and usually, but not always, enhanced chemical reactivity.

    Heats of Combustion of Cycloalkanes and Strain Energies

    The strain in ring compounds can be evaluated quantitatively by comparing the heats of combustion per \(\ce{CH_2}\) group, as in Table 12-3. The data indicate that cyclohexane is virtually strain-free, because the heat of combustion per \(\ce{CH_2}\) is the same as for alkanes \(\left( 157.4 \: \text{kcal mol}^{-1} \right)\). The increase for the smaller rings clearly reflects increasing angle strain and, to some extent, unfavorable interactions between nonbonded atoms. For rings from \(\ce{C_7}\) to \(\ce{C_{12}}\) there appears to be a residual strain for each additional \(\ce{CH_2}\) of \(1\) to \(1.5 \: \text{kcal mol}^{-1}\). These rings can be puckered into flexible conformations with normal \(\ce{C-C-C}\) angles, but as will be shown in Section 12-6, from \(\ce{C_7}\) to \(\ce{C_{13}}\) such arrangements all have pairs of partially eclipsed or interfering hydrogens. The larger cycloalkanes such as cyclopentadecane appear to be essentially strain-free.

    We expect that the total strain in cycloalkanes of the type \(\ce{(CH_2)}_n\) should decrease rapidly in the order \(n = 2 > n = 3 > n = 4\). However, the data of Table 12-3 show that the order actually is \(3 \cong 4 > 2\). This difference in order often is disguised by dividing the heats of combustion by the numbers of \(\ce{CH_2}\) groups and showing that the heats of combustion per \(\ce{CH_2}\) are at least in the order expected from bond-angle strain. This stratagem does not really solve the problem.

    It is important to recognize that when we evaluate strain from the heats of combustion per \(\ce{CH_2}\) group, we are assuming that the \(\ce{C-H}\) bonds have the same strength, independent of \(n\). However, the bond-dissociation energies of each of the \(\ce{C-H}\) bonds of ethene and cyclopropane are greater than of the \(\ce{C_2-H}\) bonds of propane (Table 4-6). Any amount that these bonds are stronger than normal will make the strain energies judged from heats of combustion appear to be less. If we take the \(\ce{C-H}\) bonds to be on average \(2 \: \text{kcal mol}^{-1}\) stronger in cyclobutane, \(6 \: \text{kcal mol}^{-1}\) stronger in cyclopropane, and \(13 \: \text{kcal mol}^{-1}\) in ethene, we can correct the carbon-carbon strain energies accordingly. For cyclobutane the corrected strain then is \(8 \times 2\) (for the eight \(\ce{C-H}\) bonds) \(+ \: 26.3\) (total strain from Table 12-3) \(= 42.3 \: \text{kcal mol}^{-1}\). The corresponding figures for cyclopropane are \(6 \times 6 + 27.6 = 63.6 \: \text{kcal mol}^{-1}\), and for ethene, \(4 \times 13 + 22.4 = 74.4 \: \text{kcal mol}^{-1}\). The results support the intuitive expectations by giving larger differences in the right direction for the strain energies of cyclobutane, cyclopropane, and ethene. Whether this analysis is quantitatively correct or not, it does give some indication of why strain energy is not a very precise concept - unless we can reliably estimate the net effects of a strain.

    Contributors and Attributions

    John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."

    This page titled 12.4: Strain in Cycloalkane Rings is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by John D. Roberts and Marjorie C. Caserio.