Cis,Trans Isomerism in Cycloalkanes

Cycloalkanes with substituents on two or more carbons of the ring show a type of stereoisomerism called cis,trans isomerism, which we can illustrate by considering 1,2-dimethylcyclopentane. In the following structural formulas, the cyclopentane ring is drawn as a regular pentagon viewed through the plane of the ring. Carbon- carbon bonds of the ring projecting toward you are shown as heavy lines.

trans-1,2-Dimethyl- cyclopentane H

H H H3C

H H

CH3 H H

cis-1,2-Dimethyl- cyclopentane H

H H H H

CH3 CH3 H H

In one isomer of 1,2-dimethylcyclopentane, the methyl groups are on the same side of the ring; in the other, they are on opposite sides of the ring. The prefi x cis (Latin: on the same side) indicates that the substituents are on the same side of the ring; the prefi x trans (Latin: across) indicates that they are on opposite sides of the ring. The cis isomer cannot be converted to the trans isomer, and vice versa, without breaking and reforming one or more bonds, a process that does not occur at or near room temperature. The cis isomer is approximately 7.1 kJ (1.7 kcal)/mol higher in energy (less stable) than the trans isomer because of the steric strain of the methyl groups on adjacent carbons in the cis isomer.

Alternatively, the cyclopentane ring can be viewed as a regular pentagon seen from above, with the ring in the plane of the page. Substituents on the ring then either project toward you (they project up, above the plane of the page) and are shown by solid wedges, or they project away from you (they project down, below the plane of the page) and are shown by broken wedges. In the following structural formulas, only the two methyl groups are shown; hydrogen atoms of the ring are not shown.

trans-1,2-Dimethyl- cyclopentane

CH3 H3C

cis-1,2-Dimethyl- cyclopentane

CH3 H3C

We say that 1,2-dimethylcyclopentane has two stereocenters. A stereocenter is an atom, most commonly carbon, about which exchange of two groups produces

Cis,trans isomers Stereoisomers that have the same connectivity but a different arrangement of their atoms in space as a result of the presence of either a ring or a carbon-carbon double bond.

Cis

A prefi x meaning on the same side.

Trans

A prefi x meaning across from.

Stereocenter

An atom, most commonly carbon, about which exchange of two groups produces a different stereoisomer.

Isomers

Different compounds with the same molecular formula

Different compounds with the same molecular formula but a different connectivity

Constitutional isomers Stereoisomers Different compounds with the same molecular formula, the same connectivity, but a different orientation of their atoms in space

Figure 2.22

Relationship between

stereoisomers and constitutional isomers.

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90 Chapter 2 Alkanes and Cycloalkanes

a different stereoisomer. Both carbons 1 and 2 of 1,2-dimethylcyclopentane, for example, are stereocenters; in this molecule, exchange of H and CH3 groups at either stereocenter converts a trans isomer to a cis isomer, or vice versa. Alternatively, we refer to the stereoisomers of 1,2-dimethylcyclobutane as having either a cis or a trans confi guration. Confi guration refers to the arrangement of atoms about a stereocenter. We say, for example, that exchange of groups at either stereocenter in the cis confi guration gives a stereoisomer with the trans confi guration.

Example 2.12

Which cycloalkanes show cis,trans isomerism? For each that does, draw the cis and trans isomers.

(a) Methylcyclopentane (b) 1,1-Dimethylcyclopentane (c) 1,3-Dimethylcyclobutane

Confi guration

Refers to the arrangement of atoms about a stereocenter.

Following are three different stereorepresentations of cis-1,2-dimethylcyclohexane, each with the ring drawn as a planar hexagon.

cis-1,2-Dimethylcyclohexane (planar hexagon representations)

CH3 CH3 H

CH3 CH3

‘‘Down’’

(Below)

‘‘Up’’

(Above)

H CH3 H3C

3 6

2 1

Students often fi nd it diffi cult to convert substituted cyclohexanes from a planar hexagon representation such as these to a chair conformation. A good rule of thumb is that “up is up and down is down.” If a substituent is up in a planar hexagon representation, place it up on the same carbon of the chair conformation. If a substituent is down on a planar hexagon representation, place it down on the same carbon of the chair conformation. Note that up or down on a chair conformation may be axial or equatorial, depending on which ring carbon you are considering.

For cis-1,2-dimethylcyclohexane on which both methyl groups are up in the planar hexagon representation, the two methyl groups are also up in a chair conformation.

Each of the alternative chair conformations has one methyl group axial and one equatorial. It is generally helpful to draw the hydrogen atoms bonded to the ring carbons bearing substituents, to make it absolutely clear which positions are equatorial and which are axial.

‘‘down’’

(below)

‘‘Up’’ (above) ‘‘Up’’ (above)

‘‘down’’

(below) cis-1,2-Dimethylcyclohexane

(alternative chair conformations) (e)

CH(a)3 (a)

CH3(e)

1 4

3 2 2 3

5 6 6

4 1

H H H

CH3 H CH3

Convert Planar Cyclohexanes to Chair Cyclohexanes

How To

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2.6 Cis,Trans Isomerism in Cycloalkanes and Bicycloalkanes 91 Solution

(a) Methylcyclopentane does not show cis,trans isomerism. It has only one substituent on the ring.

(b) 1,1-Dimethylcyclobutane does not show cis,trans isomerism. Because both methyl groups are bonded to the same carbon, only one arrangement is possible for them.

(c) 1,3-Dimethylcyclobutane shows cis,trans isomerism. In the following structural formulas, cyclobutane is drawn as a planar ring viewed fi rst from the side, and then from above.

cis-1,3-Dimethylcyclobutane CH3

trans-1,3-Dimethylcyclobutane H3C

CH3

H3C

CH3 H

H H3C

CH3

H3C

Problem 2.12

Which cycloalkanes show cis,trans isomerism? For each that does, draw both isomers.

(a) (b) (c)

Two cis,trans isomers are possible for 1,4-dimethylcyclohexane. For the pur- poses of determining the number of cis,trans isomers in substituted cycloalkanes, it is adequate to draw the cycloalkane ring as a planar polygon as is done here.

trans-1,4-Dimethylcyclohexane CH3

H H

H3C

cis-1,4-Dimethylcyclohexane CH3

H H

H3C

CH3 H3C

We can also draw the cis and trans isomers of 1,4-dimethylcyclohexane as non- planar chair conformations. In working with alternative chair conformations, it is helpful to remember that all groups axial in one chair become equatorial in the alternative chair, and vice versa. In one chair conformation of trans-1,4- dimethylcyclohexane, the two methyl groups are axial; in the alternative chair conformation, they are equatorial. Of these chair conformations, the one with both methyl groups equatorial is more stable by approximately 14.6 kJ (3.5 kcal)/mol and makes up the large majority of a sample of trans -1,4-dimethylcyclohexane.

axial

equatorial

More stable chair Less stable chair

trans-1,4-Dimethylcyclohexane H

CH3

CH3 H H3C

H H

The alternative chair conformations of cis-1,4-dimethylcyclohexane are of equal energy. In one chair, one methyl group is equatorial and the other is axial.

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92 Chapter 2 Alkanes and Cycloalkanes

In the alternative chair, the orientations in space of the methyl groups are reversed.

The result is that a collection of cis-1,4-dimethylcyclohexane molecules is composed of rapidly equilibrating alternative chairs in equal proportions.

axial axial

equatorial

cis-1,4-Dimethylcyclohexane (these conformations are of equal stability)

H CH3

CH3 CH3

H H3C

H H

Example 2.13

Following is a chair conformation of 1,3-dimethylcyclohexane.

H3C H H

CH3

(a) Is this a chair conformation of cis-1,3-dimethylcyclohexane or of trans-1,3- dimethylcyclohexane?

(b) Draw the alternative chair conformation of this compound. Of the two chair conformations, which is the more stable?

(c) Draw a planar hexagon representation of the isomer shown in this example.

Solution

(a) The isomer shown is cis-1,3-dimethylcyclohexane; the two methyl groups are on the same side of the ring.

Diequatorial conformation (more stable)

Diaxial conformation (less stable)

(b) H

H H

CH3

H CH3

CH3

H H

H3C

H3C or (c)

CH3 H3C

Problem 2.13

Following is a planar hexagon representation for one isomer of 1,2,4-trimethylcy- clohexane. Draw the alternative chair conformations of this compound, and state which of the two is the more stable.

H H

H3C

H CH3

CH3

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2.6 Cis,Trans Isomerism in Cycloalkanes and Bicycloalkanes 93

Example 2.14

Here is one cis,trans isomer of 2,4-dimethylcyclohexanol. Complete the alternative chair conformations on the right.

CH3 OH H3C

4 2

1 (a)

4 OH

2 1

(b) OH

Solution

For (a), the CH3 group on carbon 2 must be below the plane of the ring, which on this carbon is axial. The CH3 group on carbon 4 must be above the plane of the ring, which on this carbon is equatorial. (b) The methyl group on carbon 2 is equatorial; the methyl group on carbon 4 is axial.

(a) OH

4 2

1 4

2 1

(b) CH3

CH3 OH

H3C

CH3

Problem 2.14

Here is one cis,trans isomer of 3,5-dimethylcyclohexanol. Complete the alternative chair conformations.

OH OH

3 3

5 5

CH3 OH H3C

5 3

Electron Confi guration of Atoms

Bond Angles and Shapes of Molecules