Jones M., Fleming S.A. Organic Chemistry

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5.5 Monosubstituted Cyclohexanes 199

WORKED PROBLEM 5.8 Draw a Newman projection looking down

the “side” bond of the full-boat cyclohexane.

ANSWER This task is relatively easy. Once again, set your eye slightly

to one side so as to see the carbon–hydrogen bonds on the rear carbon.

One chair cyclohexane will equilibrate with another as long as the environment

supplies the requisite 10.8 kcal/mol to traverse the energy barrier. Under normal con-

ditions this process is easy, but at very low temperature, we can freeze out one chair

form by lowering the temperature to the point at which there isn’t enough energy

available to cross the energy barrier to the other chair.

How much of the relatively high-energy twist form is there at 25 °C? We will see

many such calculations in Chapter 8, but the chair–twist equilibrium can be treated like

any equilibrium process. A calculation shows that a relatively small energy differ-

ence of ΔG  5.5 kcal/mol results in an enormous preference for the more stable

isomer of the pair, about 10

:1.The “take-home lesson”here is that small energy dif-

ferences between two molecules in equilibrium result in a very large excess of the

more stable isomer.

5.5 Monosubstituted Cyclohexanes

The danger of relying too strongly on two-dimensional representations of molecules

is shown nicely by methylcyclohexane.Two-dimensional structures give no hint of the

richness of the complicated, three-dimensional structure of this molecule; they even

hide the presence of two conformational isomers of methylcyclohexane (Fig. 5.26).

Axial methyl

Equatorial methyl

ring flip

WEB 3D WEB 3D

FIGURE 5.26 The uninformative

two-dimensional structure hides the

existence of two conformational

isomers of methylcyclohexane. In one

isomer, the methyl group is

equatorial, and in the other it is axial.

flip

FIGURE 5.27 In cyclohexane, a ring

flip interconverts axial and equatorial

hydrogens.

Recall (Problems 5.2–5.4, p. 192) that flipping the cyclohexane chair forms intercon-

verts the set of six axial hydrogens and the set of six equatorial hydrogens (Fig. 5.27).

Therefore, a methyl group, or any substituent, can be in either an axial or equatorial

position. These two molecules are diastereomers. (Remember: Diastereomers are

stereoisomers that are not mirror images—see Chapter 4, p. 165.)

Given that two isomers of methylcyclohexane exist, our next job is to determine

which is more stable. As it turns out, we can even make a reasonable guess at the

magnitude of the difference in energy between the two diastereomers. First of all,

notice that axial and equatorial methylcyclohexane are interconverted by a chair flip

(Fig. 5.26). What turns out to be the crucial factor in creating the energy difference

200 CHAPTER 5 Rings

between the two forms is shown by the Newman projections made by sighting down

the bond attaching a ring methylene group to the carbon bearing the methyl group.

In the axial form, there are two gauche interactions between the methyl group and

the nearby ring CH

group (Fig. 5.28). Note the destabilizing 1,3-diaxial interac-

tion between the axial hydrogen shown in the figure and the axial methyl group.

Although it is easy to see one of the gauche interactions, the perspective of the

drawing hides the other unless you are careful. No amount of words can help you

here as much as working out this stereochemical problem yourself. It is very impor-

tant to try Problem 5.9. The answer follows immediately.

One of two gauche

methyl-ring interactions

A gauche

methyl–methyl

interaction

Methylcyclohexane (methyl group axial)

gauche-Butane

Ring CH

Look down

this bond

FIGURE 5.28 Methylcyclohexane with the methyl group axial.The Newman projection shows the gauche

interaction with one of the two equivalent ring methylene groups. Each of the two gauche interactions in this

compound resembles a gauche interaction in gauche-butane.

WORKED PROBLEM 5.9 Draw the Newman projection of methylcyclohexane

looking from the other adjacent methylene group toward the methyl-bearing car-

bon. Be sure that you see the second gauche methyl–ring interaction. Next, com-

pare this gauche interaction to that in gauche-butane. Are the two exactly the same?

ANSWER It is difficult to place your “eye”correctly for this view, but if you look along

the red carbon–carbon bond, you can construct the appropriate Newman projection.

One of two

gauche methyl-ring

interactions; this

involves bumping

between CH

and the

ring CH

Ring CH

Methylcyclohexane (methyl group axial)

Ring CH

Bump

gauche-Butane

Here, the gauche

interaction is a methyl–

methyl bumping

The two interactions are very similar, but not exactly the same. In butane two

methyl groups bump, whereas in axial methylcyclohexane a methyl group bumps

with a .CH

5.5 Monosubstituted Cyclohexanes 201

A Newman projection of the conformation of methylcyclohexane with the equa-

torial methyl group made from the same perspective reveals none of these gauche

interactions—this arrangement resembles the anti form of butane (Fig. 5.29).

The two methyl groups

are as far apart as possible

Meth

clohexane

(

meth

rou

uatorial

)

anti-Butane

This ring carbon and the

methyl group are as far

apart as possible

FIGURE 5.29 Methylcyclohexane with an equatorial methyl group.There are no gauche methyl–ring

interactions.This isomer is 1.74 kcal/mol more stable than the molecule with the methyl group axial.

Note the resemblance to the anti form of butane.

Recall our conformational analysis of butane in Chapter 2 (p. 73).The gauche

form of butane was about 0.6 kcal/mol less stable than the anti form, in which

the terminal methyl groups of butane were as far apart as possible. Accordingly,

we might guess that the isomer with the methyl group equatorial would be

more stable than the axial isomer, and that the energy difference between the

two would be approximately twice the difference between gauche- and anti-butane,

2  0.6  1.2 kcal/mol. We’d be close. The real difference is 1.74 kcal/mol.

PROBLEM 5.10 Why isn’t the difference exactly 1.2 kcal/mol? Point out some of

the differences between the gauche interaction in butane and the gauche interac-

tion in axial methylcyclohexane.

Calculations of the percentage of isomers in the equatorial and axial forms of

methylcyclohexane will become clearer in Chapter 8. For now it’s fair to say that

about 95% of the molecules will have the methyl group equatorial at any given

instant. Once more, a small energy difference (1.74 kcal/mol) has resulted in a

large excess of the more stable isomer. Don’t make the mistake of thinking that

methylcyclohexane consists of a mixture of 95% molecules locked forever in the

conformation with the methyl group equatorial, and 5% of similarly frozen

molecules with their methyl groups axial. These molecules are in rapid equilib-

rium. At any given moment 95% will have their methyl groups equatorial, but

all molecules are continuously equilibrating between equatorial and axial

methyl isomers.

PROBLEM 5.11 The formula for doing equilibrium calculations is ΔG RT lnK,

where R is about 2 cal/deg mol, T is the absolute temperature, and K the equi-

librium constant sought. Calculate the amounts at equilibrium at 25 °C of two

compounds differing in energy by ΔG  2.8 kcal/mol.

202 CHAPTER 5 Rings

A group larger than methyl would result in an even greater dominance of the

equatorial conformation over the less stable axial conformation. The 1,3-diaxial

bumpings responsible for the destabilizing gauche interactions will be magnified,

and reflected in the equilibrium constant (Fig. 5.30; Table 5.3).

If R is large, this gauche

interaction will be more

destabilizing than the

interaction with a

methyl group

In this form, in which the

R is equatorial, there are

no gauche interactions

between R and the ring

FIGURE 5.30 The larger R, the more

favored will be the partner in the

equilibrium with the R group

equatorial.

TABLE 5.3 Axial–Equatorial Energy Differences for Some

Alkylcyclohexanes at 25 °C

Compound ≤G (ax/eq) (kcal/mol) K

Methylcyclohexane 1.74 19.5

Ethylcyclohexane 1.79 21.2

Propylcyclohexane 2.21 43.4

Isopropylcyclohexane 2.61 86.0

tert-Butylcyclohexane 5.5 11,916

Note the large axial–equatorial (ax/eq) energy difference for the tert-butyl group.

This approximately 5–5.5 kcal/mol translates into an equilibrium constant of almost

12,000 at 25 °C. The situation is complicated for the tert-butyl group, because the

conformation with an axial tert-butyl group is so greatly destabilized that a twist con-

formation, with an energy about 5 kcal/mol higher than the conformation with an

equatorial tert-butyl group,may be lower in energy than the pure chair with an axial

tert-butyl group (Fig. 5.31). Regardless, the conformation of tert-butylcyclohexane

with the tert-butyl group equatorial is favored enormously.

C(CH

)

C(CH

)

(CH

)

ring flip

Chair

Twist

WEB 3D

FIGURE 5.31 The large tert-butyl

group distorts the equilibrium far

toward the much more stable

equatorial form. The geometrical

relationships in the molecule can be

estimated with confidence because

this form dominates the equilibrum

mixture so strongly.

5.5 Monosubstituted Cyclohexanes 203

WORKED PROBLEM 5.12 It is often said that the tert-butyl group locks tert-

butylcyclohexane into the form with the tert-butyl group equatorial.Is this a good

way to put it? Why not?

ANSWER No! The molecule is not locked at all. The forms with the large tert-

butyl group axial and equatorial are in rapid equilibrium, with the equatorial form

greatly predominating. Very few molecules are in the axial form at any one time,

but the equilibrium is mobile. This molecule is not locked into one form and

immobilized forever.

(CH

)

(CH

)

ring flip

PROBLEM 5.13 How many carbons will the

C NMR spectrum of tert-

butylcyclohexane reveal at 25 °C?

PROBLEM 5.14 How many carbons will the

C NMR spectra of trans-

1,4-di-tert-butylcyclohexane and all-cis-1,3,5-tri-tert-butylcyclohexane reveal?

PROBLEM SOLVING

In many problems there are clues to the answer that are exceptionally important

to recognize. Here is a perfect example. Whenever you see a tert-butyl group

attached to a cyclohexane, you can be certain that it is there in order to fix the

cyclohexane in one of the possible chairs. tert-Butyl groups are always equatorial!

That observation allows you to fix the positions of any other groups of the ring

with certainty. If the problem involves a tert-butyl-substituted cyclohexane, you

can be sure that the solution will require you to draw the ring in three

dimensions, and that you must put the tert-butyl group in an equatorial position.

In studies of reaction mechanisms it is often very helpful to know with some pre-

cision the spatial relationships among groups. Ring compounds are quite helpful in

this regard. For example, the rigid frame of cyclopropane allows quite accurate

estimations of angles and distances to be made. But cyclopropanes are so strained

as to be sometimes too reactive for mechanistic work. In fact, the ring is often

opened in chemical reactions. One wouldn’t want one’s rigid framework disappear-

ing as the reaction occurred, but this is all too likely for cyclopropanes. Other rings

are flexible and don’t allow us the firm predictions of angles and distances we want.

204 CHAPTER 5 Rings

However, a large group such as tert-butyl enables us to prejudice the mobile equi-

librium between cyclohexane rings so strongly in favor of the form with the tert-

butyl group equatorial that we can determine with confidence the positions of

other atoms in the molecule (Fig. 5.31). We will see later that this technique is

used frequently.

Summary

All cycloalkanes except cyclopropane distort from planarity so as to minimize

strain.The amount of strain can be measured in a variety of ways,including meas-

urements of heats of combustion or heats of formation. Cyclohexane adopts an

energy-minimum chair form in which there are six hydrogens in the axial posi-

tion and six in the equatorial position. Cyclohexane is a mobile system, as chair

forms interconvert. This interconversion exchanges substituents in the axial and

equatorial positions.

5.6 Disubstituted Ring Compounds

We have already mentioned that cis and trans diastereomers exist for dichlorocy-

clopropanes (Chapter 4, pp. 173–176) and that the trans form is chiral (Fig. 5.32).

Mirror

trans-1,2-Dichlorocyclopropane

(chiral—there is a pair of enantiomers)

cis-1,2-Dichlorocyclopropane

(an achiral molecule, a meso compound)

FIGURE 5.32 cis- and trans-

1,2-Dichlorocyclopropane.

Mirror

trans-1-Bromo-2-chlorocyclopropane

is also chiral, and, of course, there is

a pair of enantiomers

FIGURE 5.33 cis- and trans-1-Bromo-

2-chlorocyclopropane.

When the two substituents on the ring are different, as in 1-bromo-2-chloro-

cyclopropane, two pairs of enantiomers are possible,and both the cis and trans forms

of this molecule are chiral (Fig. 5.33).

Stereochemical relationships become harder to see in cyclohexanes, where

the molecules are not planar, but they don’t really change. We will first take a

look at 1,1-dialkylcyclohexanes and then at the somewhat more complicated

1,2-dialkylcyclohexanes.

Mirror

cis-1-Bromo-2-chlorocyclopropane

is a chiral molecule—there is

a pair of enantiomers

5.6 Disubstituted Ring Compounds 205

1-Isopropyl-1-methylcyclohexane is only slightly more complicated. There are

two isomers, nearly equal in energy, neither of which is chiral (Fig. 5.35).

flip

K = 1

Axial methyl

Equatorial methyl

WEB 3D

FIGURE 5.34 1,1-Dimethylcyclohexane.

WEB 3D

Mirror

CH(CH

)

CH(CH

)

(CH

)

CH(CH

)

180 rotation

flip flip

180

CH(CH

)

CH(CH

)

FIGURE 5.35 Both isomers of 1-isopropyl-1-methylcyclohexane

are achiral—the mirror images are superimposable.

PROBLEM 5.15 Use the data in Table 5.3 to calculate the energy difference

between the possible isomers of 1-isopropyl-1-methylcyclohexane.

5.6b 1,2-Disubstituted Cyclohexanes Just like 1,2-dimethylcyclopropane,

1,2-dimethylcyclohexane can exist in cis and trans forms (as can any 1,2-disubstituted

ring compound), but the chair form of cyclohexane makes the compounds look

somewhat different from the more familiar rigid isomers of cis and trans disubsti-

tuted cyclopropanes (Fig. 5.36).

WEB 3D WEB 3D

Methyl groups cis

hydrogens cis

Methyl groups trans

hydrogens trans

FIGURE 5.36 Three-dimensional

representations of cis- and trans-1,2-

dimethylcyclohexane and cis- and

trans-1,2-dimethylcyclopropane.

5.6a 1,1-Disubstituted Cyclohexanes 1,1-Dimethylcyclohexane is a simple,

achiral molecule in which the axial–equatorial equilibration induced by flipping one

chair to the other interconverts equivalent molecules, each of which has one methyl

group axial and one equatorial. The ring flip converts the axial methyl group into

an equatorial methyl group and the equatorial methyl group into an axial methyl

group. There is no net change and, as for cyclohexane itself, the equilibrium con-

stant for the equilibration must be 1 (Fig. 5.34).

206 CHAPTER 5 Rings

PROBLEM 5.16 Figure 5.37b shows only the equatorial–equatorial form of trans-

1,2-dimethylcyclohexane. What is the dihedral angle between the methyl groups

in the much less stable axial–axial trans-1,2-dimethylcyclopropane isomer?

The words cis and trans refer to the “sidedness”of a molecule and do not depend

strictly on the angles between the groups. In a cis disubstituted cyclopropane, the

dihedral angle between the cis groups is 0°, whereas it is 60° in the disubstituted

cyclohexane (Fig. 5.37a). The methyl groups are referred to as cis in either case. In

trans-1,2-dimethylcyclopropane, the dihedral angle between the methyl groups is

120°, whereas in the six-membered ring it is 60° (Fig. 5.37b).

(a) (b)

Two views of cis-1,2-dimethylcyclopropane;

the dihedral angle between the methyl groups is 0

0

Dihedral

angle

Two views of trans-1,2-dimethylcyclopropane;

the dihedral angle between the methyl groups is 120

120

Dihedral

angle

Two views of cis-1,2-dimethylcyclohexane;

the dihedral angle between the methyl groups is 60

60

Two views of trans-1,2-dimethylcyclohexane;

the dihedral angle between the

methyl groups is also 60

60

FIGURE 5.37 Isomerism in the planar, inflexible cyclopropanes and the nonplanar, flexible cyclohexanes: (a) cis, (b) trans.

In cis-1,2-dimethylcyclohexane,one methyl group is axial and the other is equa-

torial (Fig. 5.38).The conformational ring flip does not alter the structure—the axial

methyl becomes equatorial, and the equatorial methyl becomes axial. The equilib-

rium constant between these two equivalent compounds must be 1.

ring flip

K = 1

This axial methyl becomes equatorial

This equatorial methyl becomes axial

FIGURE 5.38 cis-1,2-Dimethylcyclohexane.

Note that the two conformational isomers of cis-1,2-dimethylcyclohexane are

enantiomers.The equilibration between the two conformations produces a racemic

mixture of the two enantiomers.Have we seen a similar situation before? Indeed we

5.6 Disubstituted Ring Compounds 207

have; just recall our discussion of the gauche forms of butane (Chapter 4, p. 163).

The equilibration of the two cis-1,2-dimethylcyclohexanes is very similar to the equi-

libration of the two gauche forms of butane (Fig. 5.39).

ring flip

120° Rotation

120°

rotation

FIGURE 5.39 The ring flip in cis-

1,2-dimethylcyclohexane converts

one enantiomer into the other. A very

similar process interconverts the two

enantiomers of gauche-butane.

flip

This axial methyl becomes equatorial

This axial methyl also becomes equatorial

FIGURE 5.40 The ring flip in trans-

1,2-dimethylcyclohexane converts a

molecule with two axial methyl

groups into one with two equatorial

methyl groups.

The trans form of 1,2-dimethylcyclopropane presents a different picture. trans-1,2-

Dimethylcyclohexane can either have both methyl groups axial or both equatorial

(Fig. 5.40).The ring flip converts the diaxial form into the diequatorial form.Let’s apply

conformational analysis to predict which of these two diastereomers is more stable.

As usual, Newman projections are vital, and in Figure 5.41 we sight along the

carbon–carbon bond attaching the two methyl-substituted carbons. In the diequa-

torial isomer, there is one gauche methyl–methyl interaction costing 0.6 kcal/mol.

gauche

Interaction

Methyl–methyl gauche

interaction, but no

methyl–ring gauche

interactions

gauche Interactions give

 1.74 = 3.48 kcal/mol

of destabilization

One methyl–methyl gauche

interaction gives 0.6 kcal/mol

of destabilization

gauche

Interaction

Diaxial Diequatorial

flip

Less stable More stable

flip

FIGURE 5.41 Diequatorial trans-

1,2-dimethylcyclohexane is more

stable than the diaxial isomer.

208 CHAPTER 5 Rings

In the diaxial isomer, the two methyl groups occupy anti positions, and therefore

their interaction with one another is not destabilizing.However, for each axial methyl

group we still have the two gauche interactions with the ring methylene groups (see

p. 199), and this will cost the molecule 2  1.74 kcal/mol  3.48 kcal/mol. We can

predict that the diequatorial isomer should be (3.48  0.6) kcal/mol  2.88 kcal/mol

more stable than the diaxial isomer. In turn, this calculation predicts that at 25 °C

there will be more than 99% of the diequatorial form present.

PROBLEM 5.17 Show that the ring flip of the diequatorial form to the diaxial

form will not racemize optically active trans-1,2-dimethylcyclohexane. What is

the relation between the equatorial–equatorial and axial–axial forms of trans-

1,2-dimethylcyclohexane?

In principle, both the diaxial and diequatorial forms should be separable into a

pair of enantiomers, resolvable (p. 169)—they are both chiral molecules. In practice,

we cannot isolate trans-diaxial-1,2-dimethylcyclohexane; it simply flips to the much

more stable diequatorial form. The diequatorial form can be isolated and resolved.

Summary

Neither cis-1,2-dimethylcyclopropane nor cis-1,2-dimethylcyclohexane can be

resolved, because the cyclopropane is a meso compound (Chapter 4, p. 168), and

the cyclohexane flips into its mirror image. However, both trans-1,2-dimethyl-

cyclopropane and trans-1,2-dimethylcyclohexane can be resolved; they are not

superimposable on their mirror images.The point is that in a practical sense the

planar cyclopropanes and nonplanar cyclohexanes behave in the same way. This

finding has important consequences. In deciding questions of stereochemistry, we

can treat the decidedly nonplanar 1,2-dimethylcyclohexanes as if they were pla-

nar. Indeed, all cyclohexanes can be treated as planar for the purposes of stereo-

chemical analysis,because the planar forms represent the average positions of ring

atoms in the rapid chair–chair interconversions.

Now let’s look at some slightly more complicated molecules in which the two

substituents on the ring are different. In 1-isopropyl-2-methylcyclohexanes cis and

trans isomers exist, and once more we will have to worry about the effects of flip-

ping from one chair form to the other. In the cis compound, there are two differ-

ent conformational isomers (Fig. 5.42). In one isomer, the isopropyl group is axial

and the methyl group is equatorial. When the ring flips, the axial isopropyl group

becomes equatorial and the equatorial methyl group becomes axial.

Equatorial

CH(CH

)

CH(CH

)

Axial

flip

WEB 3D

FIGURE 5.42 cis-1-Isopropyl-

2-methycyclohexane flips from the

conformer with an axial isopropyl

group and an equatorial methyl, to

the conformer with an equatorial

isopropyl group and an axial methyl.

Unlike the dimethyl case, these two compounds are not enantiomeric.They are

conformational diastereomers—conformational isomers that have different physical