Solution -

PROBLEM Prostaglandin $\mathrm{F}_{2 \alpha}$, a hormone that causes uterine contraction during childbirth, has the following
4-6 structure. Are the two hydroxyl groups $(-\mathrm{OH})$ on the cyclopentane ring cis or trans to each other? What about the two carbon chains attached to the ring?
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Solution -

Prostaglandin $\mathrm{F}_{2 \alpha}$


Solution -

PROBLEM Name the following substances, including the cis- or trans- prefix (red-brown $=\mathrm{Br}$ ):
4-7 (a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0104.jpg?height=362&width=432&top_left_y=1353&top_left_x=489)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0104.jpg?height=310&width=491&top_left_y=1363&top_left_x=996)


Solution - 4.3 Stability of Cycloalkanes: Ring Strain

Chemists in the late 1800s knew that cyclic molecules existed, but the limitations on ring size were unclear. Although numerous compounds containing five-membered and six-membered rings were known, smaller and larger ring sizes had not been prepared, despite many attempts.


A theoretical interpretation of this observation was proposed in 1885 by Adolf von Baeyer, who suggested that small and large rings might be unstable due to angle strain-the strain induced in a molecule when bond angles are forced to deviate from the ideal $109^{\circ}$ tetrahedral value. Baeyer based his suggestion on the simple geometric notion that a three-membered ring (cyclopropane) should be an equilateral triangle with bond angles of $60^{\circ}$ rather than $109^{\circ}$, a four-membered ring (cyclobutane) should be a square with bond angles of $90^{\circ}$, a fivemembered ring should be a regular pentagon with bond angles of $108^{\circ}$, and so on. Continuing this argument, large rings should be strained by having bond angles that are much greater than $109^{\circ}$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0105.jpg?height=305&width=1649&top_left_y=189&top_left_x=238)


What are the facts? To measure the amount of strain in a compound, we have to measure the total energy of the compound and then subtract the energy of a strain-free reference compound. The difference between the two values should represent the amount of extra energy in the molecule due to strain. The simplest experimental way to do this for a cycloalkane is to measure its heat of combustion, the amount of heat released when the compound burns completely with oxygen. The more energy (strain) the compound contains, the more energy (heat) is released by combustion.


$$
\left(\mathrm{CH}_{2}\right)_{n}+3 n / 2 \mathrm{O}_{2} \longrightarrow n \mathrm{CO}_{2}+n \mathrm{H}_{2} \mathrm{O}+\text { Heat (add) }
$$


Because the heat of combustion of a cycloalkane depends on size, we need to look at heats of combustion per $\mathrm{CH}_{2}$ unit. Subtracting a reference value derived from a strain-free acyclic alkane and then multiplying by the number of $\mathrm{CH}_{2}$ units in the ring gives the overall strain energy. FIGURE 4.4 shows the results.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0105.jpg?height=494&width=914&top_left_y=978&top_left_x=603)

FIGURE 4.4 Cycloalkane strain energies, as calculated by taking the difference between cycloalkane heat of combustion per $\mathbf{C H}_{2}$ and acyclic alkane heat of combustion per $\mathbf{C H}_{2}$, and multiplying by the number of $\mathbf{C H}_{2}$ units in a ring. Small and medium rings are strained, but cyclohexane rings and very large rings are strain-free.

The data in FIGURE 4.4 show that Baeyer's theory is only partially correct. Cyclopropane and cyclobutane are indeed strained, just as predicted, but cyclopentane is more strained than predicted, and cyclohexane is strainfree. Cycloalkanes of intermediate size have only modest strain, and rings of 14 carbons or more are strain-free. Why is Baeyer's theory wrong?

Baeyer's theory is wrong for the simple reason that he assumed all cycloalkanes to be flat. In fact, as we'll see in the next section, most cycloalkanes are not flat; instead, they adopt puckered three-dimensional conformations that allow bond angles to be nearly tetrahedral. As a result, angle strain occurs only in three- and fourmembered rings, which have little flexibility. For most ring sizes, particularly the medium-ring ( $\mathrm{C}_{7}-\mathrm{C}_{11}$ ) cycloalkanes, torsional strain caused by $\mathrm{H} \leftrightarrows \mathrm{H}$ eclipsing interactions at adjacent carbons (Section 3.6) and steric strain caused by the repulsion between nonbonded atoms that approach too closely (Section 3.7) are the most important factors. Thus, three kinds of strain contribute to the overall energy of a cycloalkane.


- Angle strain-the strain due to expansion or compression of bond angles
- Torsional strain-the strain due to eclipsing of bonds between neighboring atoms
- Steric strain-the strain due to repulsive interactions when atoms approach each other too closely


PROBLEM Each $\mathrm{H} \longleftrightarrow \mathrm{H}$ eclipsing interaction in ethane costs about $4.0 \mathrm{~kJ} / \mathrm{mol}$. How many such interactions $\mathbf{4 - 8}$ are present in cyclopropane? What fraction of the overall $115 \mathrm{~kJ} / \mathrm{mol}(27.5 \mathrm{kcal} / \mathrm{mol})$ strain energy of cyclopropane is due to torsional strain?


PROBLEM cis-1,2-Dimethylcyclopropane has more strain than trans-1,2-dimethylcyclopropane. How can you 4-9 account for this difference? Which of the two compounds is more stable?


Solution - 4.4 Conformations of Cycloalkanes


Cyclopropane -

Cyclopropane is the most strained of all rings, primarily due to the angle strain caused by its $60^{\circ} \mathrm{C}-\mathrm{C}-\mathrm{C}$ bond angles. In addition, cyclopropane has considerable torsional strain because the $\mathrm{C}-\mathrm{H}$ bonds on neighboring carbon atoms are eclipsed (FIGURE 4.5).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=329&width=1147&top_left_y=475&top_left_x=489)

FIGURE 4.5 The structure of cyclopropane, showing the eclipsing of neighboring C-H bonds that gives rise to torsional strain. Part (b) is a Newman projection along a $\mathrm{C}-\mathrm{C}$ bond.


Cyclopropane -

How can the hybrid-orbital model of bonding account for the large distortion of bond angles from the normal $109^{\circ}$ tetrahedral value to $60^{\circ}$ in cyclopropane? The answer is that cyclopropane has bent bonds. In an unstrained alkane, maximum bonding is achieved when two atoms have their overlapping orbitals pointing directly toward each other. In cyclopropane, though, the orbitals can't point directly toward each other; instead, they overlap at a slight angle. The result is that cyclopropane bonds are weaker and more reactive than typical alkane bonds- $255 \mathrm{~kJ} / \mathrm{mol}$ ( $61 \mathrm{kcal} / \mathrm{mol}$ ) for a C-C bond in cyclopropane versus $370 \mathrm{~kJ} / \mathrm{mol}(88 \mathrm{kcal} / \mathrm{mol}$ ) for a $\mathrm{C}-\mathrm{C}$ bond in open-chain propane.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=285&width=573&top_left_y=1321&top_left_x=462)


Cyclopropane -

Typical alkane $\mathrm{C}-\mathrm{C}$ bonds
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=388&width=389&top_left_y=1237&top_left_x=1215)


Cyclopropane -

Typical bent cyclopropane $\mathrm{C}-\mathrm{C}$ bonds


Cyclobutane -

Cyclobutane has less angle strain than cyclopropane but has more torsional strain because of its larger number of ring hydrogens. As a result, the total strain for the two compounds is nearly the same $-110 \mathrm{~kJ} / \mathrm{mol}(26.4 \mathrm{kcal} /$ $\mathrm{mol})$ for cyclobutane versus $115 \mathrm{~kJ} / \mathrm{mol}(27.5 \mathrm{kcal} / \mathrm{mol})$ for cyclopropane. Cyclobutane is not quite flat but is slightly bent so that one carbon atom lies about $25^{\circ}$ above the plane of the other three (FIGURE 4.6). The effect of this slight bend is to increase angle strain but to decrease torsional strain, until a minimum-energy balance between the two opposing effects is achieved.
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=245&width=329&top_left_y=2078&top_left_x=340)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=259&width=475&top_left_y=2077&top_left_x=803)
(c) Not quite
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0106.jpg?height=389&width=443&top_left_y=2104&top_left_x=1399)


Cyclobutane -

FIGURE 4.6 The conformation of cyclobutane. Part (c) is a Newman projection along a $\mathrm{C}-\mathrm{C}$ bond, showing that neighboring $\mathrm{C}-\mathrm{H}$ bonds are
not quite eclipsed.


Cyclopentane -

Cyclopentane was predicted by Baeyer to be nearly strain-free, but it actually has a total strain energy of 26 $\mathrm{kJ} / \mathrm{mol}(6.2 \mathrm{kcal} / \mathrm{mol})$. Although planar cyclopentane has practically no angle strain, it has a large torsional strain. Cyclopentane therefore twists to adopt a puckered, nonplanar conformation that strikes a balance between increased angle strain and decreased torsional strain. Four of the cyclopentane carbon atoms are in approximately the same plane, with the fifth carbon atom bent out of the plane. Most of the hydrogens are nearly staggered with respect to their neighbors (FIGURE 4.7).
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=256&width=359&top_left_y=609&top_left_x=338)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=383&width=486&top_left_y=605&top_left_x=809)
Observer
(c)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=330&width=456&top_left_y=613&top_left_x=1379)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=310&width=445&top_left_y=631&top_left_x=1385)


Cyclopentane -

FIGURE 4.7 The conformation of cyclopentane. Carbons $1,2,3$, and 4 are nearly coplanar, but carbon 5 is out of the plane. Part (c) is a Newman projection along the C1-C2 bond, showing that neighboring C-H bonds are nearly staggered.


Cyclopentane -

PROBLEM How many $\mathrm{H} \longleftrightarrow \mathrm{H}$ eclipsing interactions would be present if cyclopentane were planar? Assuming
4-10 an energy cost of $4.0 \mathrm{~kJ} / \mathrm{mol}$ for each eclipsing interaction, how much torsional strain would planar cyclopentane have? Since the measured total strain of cyclopentane is $26 \mathrm{~kJ} / \mathrm{mol}$, how much of the torsional strain is relieved by puckering?


Cyclopentane -

PROBLEM Two conformations of cis-1,3-dimethylcyclobutane are shown. What is the difference between
4-11 them, and which do you think is likely to be more stable?
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=220&width=378&top_left_y=1446&top_left_x=467)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=267&width=332&top_left_y=1444&top_left_x=902)


Cyclopentane - 4.5 Conformations of Cyclohexane

Substituted cyclohexanes are the most common cycloalkanes and occur widely in nature. A large number of compounds, including steroids and many pharmaceutical agents, have cyclohexane rings. The flavoring agent menthol, for instance, has three substituents on a six-membered ring.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0107.jpg?height=505&width=600&top_left_y=1970&top_left_x=757)


Menthol


Cyclohexane adopts a strain-free, three-dimensional shape that is called a chair conformation because of its similarity to a lounge chair, with a back, seat, and footrest (FIGURE 4.8). Chair cyclohexane has neither angle strain nor torsional strain-all C-C-C bond angles are near the $109^{\circ}$ tetrahedral value, and all neighboring $\mathrm{C}-\mathrm{H}$ bonds are staggered.
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0108.jpg?height=318&width=440&top_left_y=391&top_left_x=341)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0108.jpg?height=239&width=498&top_left_y=390&top_left_x=884)
Observer
(c)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0108.jpg?height=196&width=345&top_left_y=390&top_left_x=1481)

FIGURE 4.8 The strain-free chair conformation of cyclohexane. All C-C-C bond angles are $111.5^{\circ}$, close to the ideal $109^{\circ}$ tetrahedral angle, and all neighboring $\mathrm{C}-\mathrm{H}$ bonds are staggered.


The easiest way to visualize chair cyclohexane is to build a molecular model if you have access to a model kit, or alternatively to explore with one of the many computer-based modeling programs you may have access to.


The chair conformation of cyclohexane can be drawn in three steps.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0108.jpg?height=721&width=327&top_left_y=968&top_left_x=891)


STEP 1 -

Draw two parallel lines, slanted downward and slightly offset from each other. This means that four of the cyclohexane carbons lie in a plane.


STEP 2 -

Place the topmost carbon atom above and to the right of the plane of the other four, and connect the bonds.


STEP 3 -

Place the bottommost carbon atom below and to the left of the plane of the middle four, and connect the bonds. Note that the bonds to the bottommost carbon atom are parallel to the bonds to the topmost carbon.


STEP 3 -

When viewing cyclohexane, it's helpful to remember that the lower bond is in front and the upper bond is in back. If this convention isn't defined, it can appear that the reverse is true. For clarity, all cyclohexane rings drawn in this book will have the front (lower) bond heavily shaded to indicate nearness to the viewer.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0108.jpg?height=147&width=529&top_left_y=2252&top_left_x=798)


STEP 3 -

In addition to the chair conformation of cyclohexane, there is an alternative conformation of cyclohexane that bears a slight resemblance to a twisted boat. Called the twist-boat conformation, it is nearly free of angle strain. It does, however, have both steric strain and torsional strain and is about $23 \mathrm{~kJ} / \mathrm{mol}(5.5 \mathrm{kcal} / \mathrm{mol})$ higher in
energy than the chair conformation. As a result, molecules adopt the twist-boat geometry only rarely.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0109.jpg?height=440&width=434&top_left_y=252&top_left_x=561)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0109.jpg?height=261&width=399&top_left_y=325&top_left_x=1134)


STEP 3 -

Twist-boat cyclohexane ( $23 \mathrm{~kJ} / \mathrm{mol}$ strain)


STEP 3 - 4.6 Axial and Equatorial Bonds in Cyclohexane

The chair conformation of cyclohexane has many consequences. We'll see in Section 11.9, for instance, that the chemical behavior of many substituted cyclohexanes is influenced by their conformation. In addition, we'll see in Section 25.5 that simple carbohydrates, such as glucose, adopt a conformation based on the cyclohexane chair and that their chemistry is directly affected as a result.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0109.jpg?height=237&width=657&top_left_y=1020&top_left_x=304)


Cyclohexane (chair conformation)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0109.jpg?height=296&width=744&top_left_y=958&top_left_x=1078)


Glucose
(chair conformation)


Another trait of the chair conformation is that there are two kinds of positions for substituents on the cyclohexane ring: axial positions and equatorial positions (as shown in FIGURE 4.9). The six axial positions are parallel to the ring axis, while the six equatorial positions are in the rough plane of the ring, around the ring equator.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0109.jpg?height=434&width=960&top_left_y=1553&top_left_x=580)

FIGURE 4.9 Axial and equatorial positions in chair cyclohexane. The six axial hydrogens are parallel to the ring axis, and the six equatorial hydrogens are in a band around the ring equator.

As shown in FIGURE 4.9, each carbon atom in chair cyclohexane has one axial and one equatorial hydrogen. Furthermore, each side of the ring has three axial and three equatorial hydrogens in an alternating arrangement. For example, if the top side of the ring has axial hydrogens on carbons 1, 3, and 5, then it has equatorial hydrogens on carbons 2,4 , and 6 . The reverse is true for the bottom side: carbons 1,3 , and 5 have equatorial hydrogens, but carbons 2, 4, and 6 have axial hydrogens (FIGURE 4.10).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0110.jpg?height=424&width=731&top_left_y=189&top_left_x=697)

FIGURE 4.10 Alternating axial and equatorial positions in chair cyclohexane, looking directly down the ring axis. Each carbon atom has one axial and one equatorial position, and each face has alternating axial and equatorial positions.


Note that we haven't used the words cis and trans in this discussion of cyclohexane conformation. Two hydrogens on the same side of the ring are always cis, regardless of whether they're axial or equatorial and regardless of whether they're adjacent. Similarly, two hydrogens on opposite sides of the ring are always trans.


Axial and equatorial bonds can be drawn following the procedure shown in FIGURE 4.11. If possible, look at a molecular model as you practice.


Axial bonds: The six axial bonds, one on each carbon, are parallel and alternate up-down.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0110.jpg?height=201&width=207&top_left_y=970&top_left_x=948)


Equatorial bonds: The six equatorial bonds, one on each carbon, come in three sets of two parallel lines. Each set is also parallel to two ring bonds. Equatorial bonds
<img class="imgSvg" id = "m6sn3mm9ej5efx3yn6" 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alternate between sides around the ring.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0110.jpg?height=196&width=316&top_left_y=1515&top_left_x=945)


FIGURE 4.11 A procedure for drawing axial and equatorial bonds in chair cyclohexane.
Because chair cyclohexane has two kinds of positions-axial and equatorial-we might expect to find two isomeric forms of a monosubstituted cyclohexane. In fact, we don't. There is only one methylcyclohexane, one bromocyclohexane, one cyclohexanol (hydroxycyclohexane), and so on, because cyclohexane rings are conformationally mobile at room temperature. Different chair conformations readily interconvert, exchanging axial and equatorial positions. This interconversion, called a ring-flip, is shown in FIGURE 4.12.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0111.jpg?height=529&width=1086&top_left_y=180&top_left_x=514)

FIGURE 4.12 A ring-flip in chair cyclohexane interconverts axial and equatorial positions. What is axial in the starting structure becomes equatorial in the ring-flipped structure, and what is equatorial in the starting structure is axial after ring-flip.


As shown in FIGURE 4.12, a chair cyclohexane can be ring-flipped by keeping the middle four carbon atoms in place while folding the two end carbons in opposite directions. In so doing, an axial substituent in one chair form becomes an equatorial substituent in the ring-flipped chair form and vice versa. For example, axial bromocyclohexane becomes equatorial bromocyclohexane after a ring-flip. Since the energy barrier to chair-chair interconversion is only about $45 \mathrm{~kJ} / \mathrm{mol}(10.8 \mathrm{kcal} / \mathrm{mol})$, the process is rapid at room temperature and we see what appears to be a single structure rather than distinct axial and equatorial isomers.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0111.jpg?height=350&width=947&top_left_y=1088&top_left_x=589)
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Axial bromocyclohexane
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0111.jpg?height=240&width=402&top_left_y=1124&top_left_x=1130)


Equatorial bromocyclohexane


WORKED EXAMPLE 4.2 -


Drawing the Chair Conformation of a Substituted Cyclohexane -

Draw 1,1-dimethylcyclohexane in a chair conformation, indicating which methyl group in your drawing is axial and which is equatorial.


Strategy -

Draw a chair cyclohexane ring using the procedure in FIGURE 4.11, and then put two methyl groups on the same carbon. The methyl group in the rough plane of the ring is equatorial, and the one directly above or below the ring is axial.


Solution -


Solution -

PROBLEM Draw two different chair conformations of cyclohexanol (hydroxycyclohexane), showing all 4-12 hydrogen atoms. Identify each position as axial or equatorial.

PROBLEM Draw two different chair conformations of trans-1,4-dimethylcyclohexane, and label all positions 4-13 as axial or equatorial.


Solution -

PROBLEM Identify each of the colored positions-red, blue, and green-as axial or equatorial. Then carry out a 4-14 ring-flip, and show the new positions occupied by each color.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0112.jpg?height=282&width=971&top_left_y=542&top_left_x=436)


Solution - 4.7 Conformations of Monosubstituted Cyclohexanes

Even though cyclohexane rings flip rapidly between chair conformations at room temperature, the two conformations of a monosubstituted cyclohexane aren't equally stable. In methylcyclohexane, for instance, the equatorial conformation is more stable than the axial conformation by $7.6 \mathrm{~kJ} / \mathrm{mol}(1.8 \mathrm{kcal} / \mathrm{mol})$. The same is true of other monosubstituted cyclohexanes: a substituent is almost always more stable in an equatorial position than in an axial position.


You might recall from your general chemistry course that it's possible to calculate the percentages of two isomers at equilibrium using the equation $\Delta E=-R T \ln K$, where $\Delta E$ is the energy difference between isomers, $R$ is the gas constant [8.315 J/(K•mol)], $T$ is the Kelvin temperature, and $K$ is the equilibrium constant between isomers. For example, an energy difference of $7.6 \mathrm{~kJ} / \mathrm{mol}$ means that about $95 \%$ of methylcyclohexane molecules have an equatorial methyl group at any given instant while only $5 \%$ have an axial methyl group. FIGURE 4.13 plots the relationship between energy and isomer percentages.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0112.jpg?height=728&width=934&top_left_y=1441&top_left_x=590)

FIGURE 4.13 A plot of the percentages of two isomers at equilibrium versus the energy difference between them. The curves are calculated using the equation $\Delta E=-R T \ln K$.


The energy difference between axial and equatorial conformations is due to steric strain caused by $\mathbf{1 , 3} \mathbf{3}$ diaxial interactions. The axial methyl group on C1 is too close to the axial hydrogens three carbons away on C3 and C5, resulting in $7.6 \mathrm{~kJ} / \mathrm{mol}$ of steric strain (FIGURE 4.14).
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0113.jpg?height=789&width=1494&top_left_y=191&top_left_x=310)


FIGURE 4.14 Interconversion of axial and equatorial methylcyclohexane, represented in several formats. The equatorial conformation is more stable than the axial conformation by $7.6 \mathrm{~kJ} / \mathrm{mol}$.

The 1,3-diaxial steric strain in substituted methylcyclohexane is already familiar-we saw it previously as the steric strain between methyl groups in gauche in Section 3.7. Gauche butane is less stable than anti butane by $3.8 \mathrm{~kJ} / \mathrm{mol}(0.9 \mathrm{kcal} / \mathrm{mol})$ because of steric interference between hydrogen atoms on the two methyl groups. Comparing a four-carbon fragment of axial methylcyclohexane with gauche butane shows that the steric interaction is the same in both (FIGURE 4.15). Because axial methylcyclohexane has two such interactions, it has $2 \times 3.8=7.6 \mathrm{~kJ} / \mathrm{mol}$ of steric strain. Equatorial methylcyclohexane has no such interactions and is therefore more stable.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0113.jpg?height=408&width=1294&top_left_y=1433&top_left_x=410)

FIGURE 4.15 The origin of 1,3-diaxial interactions in methylcyclohexane. The steric strain between an axial methyl group and an axial hydrogen atom three carbons away is identical to the steric strain in gauche butane. (To display clearly the diaxial interactions in methylcyclohexane, two of the equatorial hydrogens are not shown.)


The exact amount of 1,3-diaxial steric strain in a given substituted cyclohexane depends on the nature and size of the substituent, as indicated in TABLE 4.1. Not surprisingly, the amount of steric strain increases through the series $\mathrm{H}_{3} \mathrm{C}-<\mathrm{CH}_{3} \mathrm{CH}_{2}-<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\ll\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-$, paralleling the increasing size of the alkyl groups. Note that the values given in TABLE 4.1 refer to 1,3-diaxial interactions of the substituent with a single hydrogen atom. These values must be doubled to arrive at the amount of strain in a monosubstituted cyclohexane.

TABLE 4.1 Steric Strain in Monosubstituted Cyclohexanes


| 1,3-Diaxial strain
 (kJ/mol)
 (kcal/mol) |  |  |  |
| :--- | :--- | :--- | :--- |
| Y |  |  |  |
| F | 0.5 | 0.12 |  |


TABLE 4.1 Steric Strain in Monosubstituted Cyclohexanes


| 1,3-Diaxial strain |  |  |  |
| :---: | :---: | :---: | :---: |
| Y | ( $\mathrm{kJ} / \mathrm{mol}$ ) | ( $\mathrm{kcal} / \mathrm{mol}$ ) | $\sim$ |
| $\mathrm{Cl}, \mathrm{Br}$ | 1.0 | 0.25 |  |
| OH | 2.1 | 0.5 |  |
| $\mathrm{CH}_{3}$ | 3.8 | 0.9 |  |
| $\mathrm{CH}_{2} \mathrm{CH}_{3}$ | 4.0 | 0.95 |  |
| $\mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}$ | 4.6 | 1.1 |  |
| $\mathrm{C}\left(\mathrm{CH}_{3}\right)_{3}$ | 11.4 | 2.7 |  |
| $\mathrm{C}_{6} \mathrm{H}_{5}$ | 6.3 | 1.5 |  |
| $\mathrm{CO}_{2} \mathrm{H}$ | 2.9 | 0.7 |  |
| CN | 0.4 | 0.1 |  |


PROBLEM What is the energy difference between the axial and equatorial conformations of cyclohexanol 4-15 (hydroxycyclohexane)?


PROBLEM Why do you suppose an axial cyano (-CN) substituent causes practically no 1,3-diaxial steric strain 4-16 ( $0.4 \mathrm{~kJ} / \mathrm{mol}$ )?


PROBLEM Look back at Figure 4.13 and estimate the percentages of axial and equatorial conformations 4-17 present at equilibrium in bromocyclohexane.


Solution - 4.8 Conformations of Disubstituted Cyclohexanes

Monosubstituted cyclohexanes are always more stable with their substituent in an equatorial position, but the situation with disubstituted cyclohexanes is more complex because the steric effects of both substituents must be taken into account. All steric interactions for both possible chair conformations must be analyzed before deciding which conformation is favored.


Let's look at 1,2-dimethylcyclohexane as an example. There are two isomers, cis-1,2-dimethylcyclohexane and trans-1,2-dimethylcyclohexane, which must be considered separately. In the cis isomer, both methyl groups are on the same face of the ring and the compound can exist in either of the two chair conformations shown in FIGURE 4.16. (It may be easier for you to see whether a compound is cis- or trans-disubstituted by first drawing the ring as a flat representation and then converting it to a chair conformation.)
cis-1,2-Dimethylcyclohexane
One gauche
interaction ( $3.8 \mathrm{~kJ} / \mathrm{mol}$ ) Two $\mathrm{CH}_{3} \leftrightarrow \mathrm{H}$ diaxial interactions ( $7.6 \mathrm{~kJ} / \mathrm{mol}$ )
Total strain: $\mathbf{3 . 8}+\mathbf{7 . 6}=\mathbf{1 1 . 4} \mathbf{~ k J} / \mathbf{m o l}$
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0115.jpg?height=367&width=883&top_left_y=196&top_left_x=875)


One gauche interaction ( $3.8 \mathrm{~kJ} / \mathrm{mol}$ ) Two $\mathrm{CH}_{3} \leftrightarrow \mathrm{H}$ diaxial interactions ( $7.6 \mathrm{~kJ} / \mathrm{mol}$ )
Total strain: $3.8+7.6=11.4 \mathrm{~kJ} / \mathbf{m o l}$
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0115.jpg?height=302&width=905&top_left_y=559&top_left_x=871)