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5.3: Cyclohexane: A Strain-Free Cycloalkane

  • Page ID
    201126
  • Objectives

    After completing this section, you should be able to

    1. explain why cyclohexane rings are free of angular strain.
    2. draw the structure of a cyclohexane ring in the chair conformation.

    Key Terms

    Make certain that you can define, and use in context, the key terms below.

    • chair conformation
    • twist-boat conformation

    We will find that cyclohexanes tend to have the least angle strain and consequently are the most common cycloalkanes found in nature.  A wide variety of compounds including, hormones, pharmaceuticals, and flavoring agents have substituted cyclohexane rings.

    4.5 testosterone.svg

    Example hormone, testosterone, which contains three cyclohexane rings and one cyclopentane ring

     

    Rings larger than cyclopentane would have angle strain if they were planar. However, this strain, together with the eclipsing strain inherent in a planar structure, can be relieved by puckering the ring. Cyclohexane is a good example of a carbocyclic system that virtually eliminates eclipsing and angle strain by adopting non-planar conformations. Cycloheptane and cyclooctane have greater strain than cyclohexane, in large part due to transannular crowding (steric hindrance by groups on opposite sides of the ring). Cyclohexane has the possibility of forming multiple conformations each of which have structural differences which lead to different amounts of ring strain.

     

    Conformations of Cyclohexane

    A planar structure for cyclohexane is clearly improbable. The bond angles would necessarily be 120º, 10.5º larger than the ideal tetrahedral angle. Also, every carbon-hydrogen bond in such a structure would be eclipsed. The resulting angle and eclipsing strains would severely destabilize this structure. The ring strain of planar cyclohexane is in excess of 84 kJ/mol so it rarely discussed other than in theory.

     

    Cyclohexane in the strained planar configuration showing how the hydrogens become eclipsed.

    Chair Conformation of Cyclohexane

    The flexibility of cyclohexane allows for a conformation which is almost free of ring strain. If two carbon atoms on opposite sides of the six-membered ring are bent out of the plane of the ring, a shape is formed that resembles a reclining beach chair.  This chair conformation is the lowest energy conformation for cyclohexane with an overall ring strain of 0 kJ/mol.  In this conformation, the carbon-carbon ring bonds are able to assume bonding angles of ~111o which is very near the optimal tetrahedral 109.5o so angle strain has been eliminated.

    Also, the C-H ring bonds are staggered so torsional strain has also been eliminated.  This is clearly seen when looking at a Newman projection of chair cyclohexane sighted down the two central C-C bonds.

     

    Newman projection of cyclohexane

    Interactive Element

    The 3D Structure of Chair Cyclohexane

     
    How to Draw the Chair Conformation

     

    drawing chairs.png

    Boat Conformation of Cyclohexane

    The Boat Conformation of cyclohexane is created when two carbon atoms on opposite sides of the six-membered ring are both lifted up out of the plane of the ring creating a shape which slightly resembles a boat.  The boat conformation is less stable than the chair form for two major reasons.  The boat conformation has unfavorable steric interactions between a pair of 1,4 hydrogens (the so-called "flagpole" hydrogens) that are forced to be very close together . This steric hindrance creates a repulsion energy of about 12 kJ/mol.  An additional cause of the higher energy of the boat conformation is that adjacent hydrogen atoms on the 'bottom of the boat' are forced into eclipsed positions. For these reasons, the boat conformation about 30 kJ/mol less stable than the chair conformation.

    4.5 boat cyclohexane.svg

    A boat structure of cyclohexane (the interfering "flagpole" hydrogens are shown in red)

     

    Twist-Boat Conformation of Cyclohexane

    The boat form is quite flexible and by twisting it at the bottom created the twist-boat conformer. This conformation reduces the strain which characterized the boat conformer. The flagpole hydrogens move farther apart (the carbons they are attached to are shifted in opposite directions, one forward and one back) and the eight hydrogens along the sides become largely but not completely staggered. Though more stable than the boat conformation, the twist-boat (sometimes skew-boat) conformation is roughly 23 kJ/mol less stable than the chair conformation.

    4.5 twistboat cyclohexane.svg

    A twist-boat structure of cyclohexane

     

    Half Chair Conformation of Cyclohexane

    Cyclohexane can obtain a partially plane conformation called "half chair" but with only with excessive amounts of ring strain. The half chair conformation is formed by taking planar cyclohexane and lifting one carbon out of the plane of the ring.  The half chair conformation has much of the same strain effects predicted by the fully planar cyclohexane.  In the planar portion of half chair cyclohexane the C-C bond angles are forced to 120o which creates significant amounts of angle strain. Also, the corresponding C-H bonds are fully eclipsed which create torsional strain.  The out-of-plane carbon allows for some of the ring's bond angles to reach 109.5o and for some of C-H bonds to not be fully eclipsed. Overall, the half chair conformation is roughly 45 kJ/mol less stable than the chair conformation.

    Conformation Changes in Cyclohexane - "Ring Flips"

    Cyclohexane is rapidly rotating between the two most stable conformations known as the chair conformations in what is called the "ring flip" shown below. The importance of the ring flip will be discussed in the next section. 

    4.5 ring flip.svg

    "Ring flip" describes the rapid equilibrium of cyclohexane rings between the two chair conformations

    image043.png

    It is important to note that one chair does not immediately become the other chair, rather the ring must travel through the higher energy conformations as transitions. At room temperature the energy barrier created by the half chair conformation is easily overcome allowing for equilibration between the two chair conformation on the order of 80,000 times per second. Although cyclohexane is continually converting between these different conformations, the stability of the chair conformation causes it to comprises more than 99.9% of the equilibrium mixture at room temperature.

    cyclohexane conformation energy diag complete.png

     

    Exercises

    1) Consider the conformations of cyclohexane: half chair, chair, boat, twist boat. Order them in increasing ring strain in the molecule.

    Solutions

    1) Chair < Twist Boat < Boat < half chair (most ring strain)

    Questions

    Q4.5.1

    Consider the conformations of cyclohexane, chair, boat, twist boat. Order them in increasing strain in the molecule.

    Solutions

    S4.5.1

    Chair < Twist Boat < Boat (most strain)

    Contributors and Attributions

    >Robert Bruner (http://bbruner.org)

    William Reusch, Professor Emeritus (Michigan State U.), Virtual Textbook of Organic Chemistry

    Prof. Steven Farmer (Sonoma State University)

    Layne Morsch (University of Illinois Springfield)

    Objectives

    After completing this section, you should be able to

    1. Draw the chair conformation of cyclohexane, with axial and equatorial hydrogen atoms clearly shown and identified.
    2. identify the axial and equatorial hydrogens in a given sketch of the cyclohexane molecule.
    3. explain how chair conformations of cyclohexane and its derivatives can interconvert through the process of ring flip.

    Key Terms

    Make certain that you can define, and use in context, the key terms below.

    • axial position
    • equatorial position
    • ring flip

    Axial and Equatorial Positions in Cyclohexane

    Careful examination of the chair conformation of cyclohexane, shows that the twelve hydrogens are not structurally equivalent. Six of them are located about the periphery of the carbon ring, and are termed equatorial. The other six are oriented above and below the approximate plane of the ring (three in each location), and are termed axial because they are aligned parallel to the symmetry axis of the ring.

    image042.png

    In the figure above, the equatorial hydrogens are colored blue, and the axial hydrogens are black. Since there are two equivalent chair conformations of cyclohexane in rapid equilibrium, all twelve hydrogens have 50% equatorial and 50% axial character. 

     

    How To Draw Axial and Equatorial Bonds

    clipboard_e7543668cbeb664e52474afdcc16517f9.png

    How not to draw the chair:

    clipboard_ece7a9c7f57cfb53636e866497b71e535.png

    Aside from drawing the basic chair, the key points are:

    • Axial bonds alternate up and down, and are shown "vertical".
    • Equatorial groups are approximately horizontal, but actually somewhat distorted from that (slightly up or slightly down), so that the angle from the axial group is a bit more than a right angle -- reflecting the common 109.5o bond angle.
    • Each carbon has an axial and an equatorial bond.
    • Each face of the cyclohexane ring has three axial and three equatorial bonds.
    • Each face alternates between axial and equatorial bonds. Then looking at the "up" bond on each carbon in the cyclohexane ring they will alternate axial-equatorial-axial ect.
    • When looking down at a cyclohexane ring:
      • the equatorial bonds will form an "equator" around the ring. 
      • The axial bonds will either face towards you or away. These will alternate with each axial bond. The first axial bond will be coming towards with the next going away.  There will be three of each type.
    • Note! The terms cis and trans in regards to the stereochemistry of a ring are not directly linked to the terms axial and equatorial. It is very common to confuse the two.  It typically best not to try and directly inter convert the two naming systems.

    Axial vs. Equatorial Substituents

    When a substituent is added to cyclohexane, the ring flip allows for two distinctly different conformations.  One will have the substituent in the axial position while the other will have the substituent in the equatorial position.  In the next section will discuss the energy differences between these two possible conformations.  Below are the two possible chair conformations of methylcyclohexane created by a ring-flip.  Although the conformation which places the methyl group in the equatorial position is more stable by 7 kJ/mol, the energy provided by ambient temperature allows the two conformations to rapidly interconvert. 

    The figure below illustrates how to convert a molecular model of cyclohexane between two different chair conformations - this is something that you should practice with models. Notice that a 'ring flip' causes equatorial groups to become axial, and vice-versa.

    image043.png

    Example \(\PageIndex{1}\)

    For the following please indicate if the substituents are in the axial or equatorial positions.

    Solution

    Due to the large number of bonds in cyclohexane it is common to only draw in the relevant ones (leaving off the hydrogens unless they are involved in a reaction or are important for analysis). It is still possible to determine axial and equatorial positioning with some thought.  With problems such as this it is important to remember that each carbon in a cyclohexane ring has one axial and one equatorial bond.  Also, remember that axial bonds are perpendicular with the ring and appear to be going either straight up or straight down. Equatorial bonds will be roughly in the plane of the cyclohexane ring (only slightly up or down). Sometimes it is valuable to draw in the additional bonds on the carbons of interest.

    With this it can be concluded that the bromine and chlorine substituents are attached in equatorial positions and the CH3 substituent is attached in an axial position.

     

    Exercises

    1) Draw two conformations of cyclohexyl amine (C6H11NH2). Indicate axial and equatorial positions.

    2) Draw the two isomers of 1,4-dihydroxylcyclohexane, identify which are equatorial and axial.

    3) In the following molecule, label which are equatorial and which are axial, then draw the chair flip (showing labels 1,2,3).

    Solutions

     

    1)

    2)

    3) Original conformation: 1 = axial, 2 = equatorial, 3 = axial

    Flipped chair now looks like this.

    clipboard_ed20a8930e07bacc5ab37a679d99f2c9d.png

    Questions

    Q4.6.1

    Draw two conformations of cyclohexyl amine (C6H11NH2). Indicate axial and equatorial positions.

    Q4.6.2

    Draw the two isomers of 1,4-dihydroxylcyclohexane, identify which are equatorial and axial.

    Q4.6.3

    In the following molecule, label which are equatorial and which are axial, then draw the chair flip (showing labels 1,2,3).

    Solutions

    S4.6.1

    S4.6.2

    S4.6.3

    Original conformation: 1 = axial, 2 = equatorial, 3 = axial

    Flipped chair now looks like this.

    Contributors and Attributions