Relative Stabilities of Cycloalkanes

let us consider the structures of cycloalkanes and ask if there are any differences in their stabilities. To do this, we can compare the standard enthalpy changes that occur when the compounds are formed from their elements, a quantity called the standard heat of formation, AH° Table 4.5 lists the heats of formation of cycloalkanes. 

Column three of Table 4.5 also lists the heat of formation per CH unit in cycloalkanes, which is obtained by dividing the heat of formation by the number of carbon atoms— the same as the number of —CHj— groups in the compound. If the stabihties of the cycloalkanes were all more or less the same, then the values in column three of Table 4.5 should also be about the same. But, they aren t. If we examine the heats of formation of alkanes that differ from one another by one CHj unit, we find that they differ by 20.6 kj mole . The heat of formation per CH group for cyclohexane is 20.5 kj mole not much different from the value observed for the alkanes. The heats of formation per CHj group for most cycloalkanes are similar, ranging from 15 to 20 kJ mole . There are two conspicuous exceptions cyclopropane and cyclobutane. The standard heats of formation of the latter two compounds are positive, which indicates that they are unstable. Why is that  

Cycloalkanes that do not have internuclear angles of 109.5° cannot have efficient overlap of hybrid orbitals. The internuclear bond angle of cyclopropane is 60°, far less than 109.5°. However, the interorbital angle is larger. As a result, the electron density lies outside the bond axis and is called a bent bond, or sometimes, more whimsically, a banana bond. 

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The relative stabilities of cycloalkanes can be determined by comparing their AH s of combustion (Problem 4.39) on a per-CH2-unit basis. Rings have different AH s of combustion per CH, unit because they have different amounts of ring strain. 

The molar heat of combustion of cyclohexane is nearly twice that of cyclopropane, simply because cyclohexane contains twice as many methylene (CH2) groups per mole. To compare the relative stabilities of cycloalkanes, we divide the heat of combustion by the number of methylene (CH2) groups. The result is the energy per CH2 group. These normalized energies allow us to compare the relative amounts of ring strain (per methylene group) in the cycloalkanes. 

Problem 3.14. Using Table 3.3, compare the heats of combustion of alkenes with cycloalkanes. What can you conclude (if anything) about the relative stabilities of cycloalkanes compared to alkenes ... 

The single most important factor that determines whether a cyclic monomer can be converted to linear polymer is the thermodynamic factor, that is, the relative stabilities of the cyclic monomer and linear polymer structure [Allcock, 1970 Sawada, 1976]. Table 7-1 shows the semiempirical enthalpy, entropy, and free-energy changes for the conversion of cycloalkanes to the corresponding linear polymer (polymethylene in all cases) [Dainton and Ivin, 1958 Finke et al. 1956]. The Ic (denoting liquid-crystalline) subscripts of AH, AS, and AG indicate that the values are those for the polymerization of liquid monomer to crystalline polymer. 

We recall (Sec. 2.6) that the heat of combustion is the quantity of heat evolved when one mole of a compound is burned to carbon dioxide and water. Lik heats of hydrogenation (Secs. 6.4 and 8.16), heats of combustion can often fur nish valuable information about the relative stabilities of organic compounds. Let us see if the heats of combustion of the various cycloalkanes support Baeyer s proposal that rings smaller or larger than cyclopentane and cyclohexane are unstable. 

Although it s sometimes possible to find relative stabilities of alkene isomers by establishing a cis-trans equilibrium through treatment with strong acid, there are easier ways to gain the same information. One way is simply to measure the heats of combustion for the two isomers, as we did in determining cycloalkane strain energies (Section 4.5). cis-2-Butene is found to be more strained than [Pg.202]

B. Heats of Combustion and Relative Stability of Alkanes and Cycloalkanes... 

Does this observation tell us anything about the relative stability of the cycloalkanes—for example, as measured by their heats of combustion, AH° h How does strain affect structure and function This section and Section 4-3 address these questions. 

While the conformation of cycloalkanes has been discussed in detail later, it will be worth while to see how the ring strain in such compounds is calculated as this will give us a broad picture about their relative stability. 

The kinetic data for the radical chain chlorination of several cycloalkanes (see the table below) illustrate that the C-H bonds of cyclopropane and, to a lesser extent, cyclobutane are somewhat abnormal, (a) What do these data tell you about the strength of the cyclopropane C-H bond and the stability of the cyclopropyl radical (b) Suggest a reason for the stability characteristics of the cyclopropyl radical. (Hint Consider bond-angle strain in the radical relative to cyclopropane itself.)... 

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