An important and interesting group of hydrocarbons, known as cycloalkanes, contain rings of carbon atoms linked together by single bonds. The simple unsubstituted cycloalkanes of the formula (CH2,)n make up a particularly important homologous series in which the chemical properties change in a much more striking way than do the properties of the open-chain hydrocarbons, CH3(CH2),-,CH3. The reasons for this will be developed with the aid of two concepts, steric hindrance and angle strain, each of which is simple and easy to understand, being essentially mechanical in nature.
The conformations of the cycloalkanes, particularly cyclohexane, will be discussed in some detail, because of their importance to the chemistry of many kinds of naturally occurring organic compounds.
Cyclohexane is a typical cycloalkane and has six methylene (CH,) groups joined together to form a six-membered ring. Cycloalkanes with one ring have the general formula C,H,, and are named by adding the prefix cyclo to
the name of the corresponding n-alkane having the same number of carbon atoms as in the ring. Substituents are assigned numbers consistent with their positions in such a way as to keep the sum of the numbers to a minimum.
The substituent groups derived from cycloalkanes by removing one hydrogen are named by replacing the ending -ane of the hydrocarbon with -yl to give cycloalkyl. Thus cyclohexane becomes cyclohexyl; cyclopentane, cyclopentyl; and so on.
Frequently it is convenient to write the structure of a cyclic compound in an abbreviated form as in the following examples. Each line junction represents a carbon atom and the normal number of hydrogens on each carbon atom is understood.
A. PHYSICAL PROPERTIES OF CYCLOALKANES
The melting and boiling points of cycloalkanes (Table 3.6) are somewhat higher than for the corresponding alkanes. The general "floppiness" of open-chain hydrocarbons makes them harder to fit into a crystal lattice (hence lower melting points) and less hospitable to neighboring molecules of the same type (hence lower boiling points) than the more rigid cyclic compounds.
B. CONFORMATIONS OF CYCLOHEXANE
If cyclohexane existed as a regular planar hexagon with carbon atoms at the corners, the C-C-C bond angles would be 120" instead of the normal
valence angle of carbon, 109.5". Thus, a cyclohexane molecule with a planar structure could be said to have an angle strain of 10.5" at each of the carbon atoms. Puckering of the ring, however, allows the molecule to adopt conformations that are free of angle strain.
Inspection of molecular models reveals that there are actually two extreme conformations of the cyclohexane molecule that may be constructed if the
carbon valence angles are held at 109.5". These are known as the "chair" and "boat" conformations (Figure 3.4). These two forms are so rapidly interconverted at ordinary temperatures that they cannot be separated. It is known, however, that the chair conformation is considerably more stable and comprises more than 99 % of the equilibrium mixture at room temperature.
The higher energy of the boat form is not due to angle strain because all the carbon atoms in both forms have their bond angles near the tetrahedral angle of 109.5". It is caused, instead, by relatively unfavorable interactions between the hydrogen atoms around the ring. If we make all the bond angles normal and orient the carbons in the ring to give the extreme boat conformation shown in Figure 3.5, we see that a pair of 1,4 hydrogens (the so-called flagpole hydrogens) have to be so close together (1.83 A) that they repel one another. This is an example of steric hindrance.
There is still another factor which makes the extreme boat formunfavorable; namely, that the eight hydrogens around the "sides" of the boat are eclipsed, which brings them substantially closer together than they would be in a staggered arrangement (about 2.27 A compared with 2.50 A). This is in striking contrast with the chair form (Figure 3.6) for which adjacent hydrogens are seen to be in staggered positions with respect to one another all the way around the ring. The chair form is therefore expected to be the more stable of the two. Even so, its equilibrium with the boat form produces inversion about lo6 times per second at room temperature. If you make a molecular model of
cyclohexane you will find that the chair form has a considerable rigidityand the carbon-carbon bonds have to be slightly bent in going to the boat form. You will find that the boat form is extremely flexible and even if the bond angles are held exactly at 109.5", simultaneous rotation around all the carboncarbon bonds at once permits the ring to twist one way or the other to reduce the iepulsions between the flagpole hydrogens and between the eight hydrogens around the sides of the ring. These arrangements are called twist-boat (sometimes skew-boat) conformations (Figure 3.7) and are believed to be only about 5 kcal less stable than the chair form.
It will be seen that there are two distinct kinds of hydrogens in the chair form of cyclohexane. Six are almost contained by the "average" plane of the ring (called equatorial hydrogens) and three are above and three below this average plane (dlled axial hydrogens). This raises an interesting question in connection with substituted cyclohexanes: For example, is the methyl group in methylcyclohexane equatorial or axial?
There is considerable evidence which shows that the equatorial form of methylcyclohexane predominates in the equilibrium mixture (K- 15), and the same is generally true of all monosubstituted cyclohexane derivatives. The reason can be seen from scale models which show that a substituent group has more room in an equatorial conformation than in an axial conformation (see Figure 3.8). The bigger the substituent, the greater the tendency for it to occupy an equatorial position.
The forms with axial and equatorial methyl are interconverted about lo6
times/second at room temperature. The rate decreases as the temperature is lowered. If one cools the normal mixture of chlorocyclohexane conformations dissolved in a suitable solvent to very low temperatures (- 150°), the pure equatorial conformation crystallizes out. This conformation can then be dissolved in solvents at - 150" and, when warmed to - 60°, is converted to the equilibrium mixture in a few tenths of a second. However, the calculated half-time of the conversion of the equatorial to the axial form is 22 years at - 160".
C. OTHER CYCLOALKANE RINGS
The three cycloalk6nes with smaller rings than cyclohexane are cyclopentane, cyclobutane, and cyclopropane, each with bond angles less than the tetrahedral value of 109.5". If you consider a carbon-carbon double bond as a twomembered ring, then ethene, C,H,, is the simplest cycloalkane ("cycloethane") and, as such, has carbon bond angles of 0" and, therefore, a very large degree of angle strain.
Table 3.7 shows how strain decreases stability and causes the heat of combustion per methylene group (or per gram) to rise.
The idea that cyclopropane and cyclobutane should be strained because their C-C-C bond angles cannot have the normal tetrahedral value of 109.5" was advanced by Baeyer in 1885. It was also suggested that the diffi-
culties encountered up to that time in synthesizing cycloalkane rings from C7, upward was the direct result of the angle strain which would be expected if the large rings were regular planar polygons (see again Table 3.7).
We now know that the Baeyer strain theory cannot be applied to large rings because cyclohexane and the higher cycloalkanes have puckered rings with normal or nearly normal bond angles. Much of the difficulty in synthesizing large rings from open-chain compounds is due to the low probability of having reactive groups on the two fairly remote ends of a long hydrocarbon chain come together to effect cyclization. Usually, coupling of reactive groups on the ends of dzfferent molecules occurs in preference to cyclization, unless the reactions are carried out in very dilute solutions.
For cyclopentane, a planar structure would give bond angles of 108", very close to the natural bond angle of 109.5". Actually, the angle strain is believed to be somewhat greater than 1.5" in this molecule; the eclipsing of all of the hydrogens causes the molecule to distort substantially even though this increases the angle strain. Cyclobutane is also not completely flat for the same reason. (It should be remembered that molecules such as these are in vibrational motion at all times and the shapes that have been described refer to the mean atomic positions averaged over a period of time corresponding to several vibrations.)
D. CHEMICAL PROPERTIES OF CYCLOALKANES
We have already observed how strain in the small-ring cycloalkanes affects their heats of combustion. We can reasonably expect other chemical properties also to be affected by ring strain, and indeed cyclopropane and cyclobutane are considerably more reactive than saturated, open-chain hydrocarbons. In fact, they undergo some of the reactions which are typical of compounds with carbon-carbon double bonds, their reactivity depending on the degree of angle strain and the vigor of the reagent.
The result of these reactions is always opening of the ring by cleavage of a C-C bond to give an open-chain compound having normal bond angles. Relief of angle strain may therefore be considered to be an important part of the driving force of these reactions. A summary of a number of ringopening reactions is given in Table 3.8. Ethene is highly reactive, while cyclopropane and cyclobutane are less so (in that order). The C-C bonds of the larger, relatively strain-free cycloalkanes are inert, so that these substances resemble the n-alkanes in their chemical behavior. Substitution reactions of these cycloalkanes are generally less complex than those of the corresponding alkanes because there are fewer possible isomeric substitution products. Thus, cyclohexane can give only one monochlorination product while n-hexane can give three.
E. Cis-Trans ISOMERISM OF SUBSTITUTED CYCLOALKANES
The form of stereoisomerism (isomerism caused by different spatial arrangements) called geometrical isomerism or cis-trans isomerism was discussed in the preceding chapter. This type of isomerism arises when rotation is prevented by, for example, the presence of a double bond. A ring prevents rotation equally well and we find that cis and truns isomers can also exist with appropriately substituted cycloalkanes. Thus, when a cycloalkane is disub
stituted at different ring positions, as in 1,2-dimethylcyclopropane, two isomeric structures are possible according to whether the substituents are both situated above (or both below) the plane of the ring (cis isomer), or one above and one below (trans isomer), as shown in Figure 3.9.
The cis and trans isomers of 1,2-dimethylcyclopropane cannot be interconverted without breaking one or more bonds. One way of doing this is to break open the ring and then close it again with a substituent on the opposite side from where it started. Alternatively, the bond to the substituent (or the hydrogen) can be broken and reformed on the opposite side of the ring. Examples of both processes will be discussed in later chapters.
Cis and trans isomers of cyclohexane derivatives have the additional possibility of different conformational forms. For example, 4-t-butylcyclohexyl chloride can theoretically exist in four stereoisomeric chair forms,
Structures  and  have the substituents trans to one another, but in  they are both equatorial while in  they are both axial. Structures  and [lo] have the cis relationship between the groups, but the t-butyl and chlorine are equatorial-axial in  and axial-equatorial in [lo]. t-Butyl groups are very large and bulky and much more steric hindrance results when a t-butyl group is in an axial position than when chlorine is in an axial position (Figure 3.10). Hence the equilibrium between the two conformational forms of the trans isomer strongly favors structure  over structure  because both t-butyl and chlorine are equatorial. For the cis isomer, structure  is favored over [lo] to accommodate the t-butyl group in the equatorial position.
When there are two substituents in the cis-1,4 arrangement on a cyclohexane ring, neither of which will go easily into an axial position, then it
appears that the twist-boat conformation (Section 3.4B) is most favorable (Figure 3.1 1).
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