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Unit 5

Cycloalkanes

Stereochemistry & Conformations  

 

                         

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Nomenclature / Molecular Formula

An alkane is a hydrocarbon that contains only single bonds. Cycloalkanes are alkanes that contain a closed ring (alicyclic or aromatic) of three or more carbon atoms. They have a molecular formula given by:

                                                                   CnH2n 

For example, cyclohexane C6H12 is composed of a 6-membered non-aromatic carbon ring, with 2 hydrogen atoms bonded to each of the 6 carbon atoms in the ring. Cyclohexane is named by adding the prefix cyclo- to the name of the unbranched alkane with the same number of carbons as the ring. Substituent positions are specified by numbering the carbon atoms of the ring in the direction that gives the lowest number to the substituents at the first point of difference. 

If there are two or more substituents on the ring, the ring carbons are numbered to give the lowest possible numbers of the substituted carbon atoms. With just one substituent, no numbering is needed. With multiple substituents, the substituents are listed in alphabetical order in the name. Numbering on the ring should begin with the substituent that is alphabetically first. When the acyclic portion of the molecule contains more carbon atoms than the cyclic portion (or when it contains an important functional group), the cyclic portion is often named as a cycloalkyl substituent.

cis-trans Isomerism

Open-chain alkanes undergo rotations about the carbon-carbon single bonds, so they are free to assume any of an infinite number of conformations. Alkenes have rigid double bonds that prevent rotation, giving ride to cis and trans isomers with different orientations of the groups on the double bond. Cycloalkanes are similar to alkenes in this respect. A cycloalkane has two distinct 'faces'. The faces are defined by the plane of the carbon ring, which bisects the molecular space. If two substituents point towards the same face, then they are cis. If they point towards opposite faces, they are trans. These geometric isomers cannot interconvert without the rupture and rejoining of chemical bonds.  

Conformations of Cycloalkanes

Cyclopropane (C3H6), cyclobutane (C4H8) and cyclopentane (C5H10) all approximate standard structures which can be predicted based on considerations of symmetry and VSEPR theory. The 3-membered carbon ring forms a triangle, the 4-membered ring forms a square, the 5-membered ring forms a pentagon, and the 6-memebered ring forms a hexagon. 

However, there is a noticeable amount of ring strain that results form the formation of these carbon rings. If a cycloalkane requires bond angles other than 109.5 degrees, the orbitals of its C-C bonds cannot achieve maximum overlap, resulting in a significant amount of angle strain. In addition, the bonds are all eclipsed (see figure e.g. cyclobutane C4H8), resembling the totally eclipsed conformation of butane. This eclipsing of bonds gives rise to torsional strain.

The total amount of ring strain depends primarily on the size of the ring. With its 60 degree bond angles, cyclopropane (C3H6) bears more ring strain per methylene group than any other cycloalkane. Cyclopropane is also generally more reactive than other alkanes. Reactions that open the 3-membered ring release 115 kJ/mol of ring strain energy, which provides an additional driving force for these reactions.

The total ring strain in cyclobutane (C4H8) is almost as great as that in cyclopropane. but is distributed over four carbon atoms instead of three. If cyclobutane were perfectly square and planar, it would have 90 degree bond angles, which would require eclipsing of all bonds. To reduce this element of torsional strain, the molecule assumes a slightly folded form, with bond angles of 88 degrees. These smaller bond angles require slightly more angle strain that 90 degree angles. But the relief of some of the torsional strain appears to compensate.

 

If cyclopentane (C5H10) had the shape of a planar, regular pentagon, its bond angles would be 108 degrees -- close to the tetrahedral angle of 109.5 degrees. A planar structure would require all the bonds to be eclipsed, however. The molecule actually assumes a slightly puckered 'envelope' conformation which reduces the eclipsing and lowers the torsional strain. The flap of the envelope is not associated with any particular carbon atom -- but rather it rotates around the ring as the molecule undulates as a result of thermal agitation.  

 

Cyclohexane: Conformations   

We will cover the conformations of cyclohexane (C6H12) in more detail than other cycloalkanes, chiefly because 6-membered alicyclics are particularly common. Carbohydrates, steroids, plant products, pesticides, and many other important compounds contain 6-membered rings whose conformations and stereochemistry are critically important to their stability and reactivity. The abundance of these rings in nature is likely due to their relative stability, as well as their selectivity or specificity regarding reaction sites and structural consistency.

We begin by pointing out that cyclohexane has no ring strain. Thus, the molecule must adopt a conformation having bond angles that are near the tetrahedral angle (no angle strain) and also have no eclipsing of bonds (no torsional strain). A planar, regular hexagon would have bond angles of 120 degrees (rather than 109.5) implying some angle strain. A planar ring would also have torsional strain because the bonds on the adjacent CH2 groups would be eclipsed. Therefore, the ring cannot be planar.  

Cyclohexane achieves tetrahedral bond angles and staggered conformations by assuming a puckered conformation. The most stable conformation is the 'chair' conformation.   

The chair conformation of cyclohexane takes its name from the similarities to an actual chair. The plane which corresponds to the seat of the chair is composed of four corners where C atoms reside. The two sets of parallel lines which constitute this plane are horizontal lines of single (hybridized) C - C Bonds.

                                             

Instead of numbering the carbon atoms, we utilize the 2 lines of planar intersection. There are 3 planes in the chair. Thus there are 2 lines where planes meet or intersect. 1) The line in which the seat plane intersects with the upward  plane or “back of the chair”. We call this the “upline”.  2) The line in which the seat plane intersects with the downward plane or “foot of the chair”- the “downline”.  

Try to fixate these 2 lines in your mind for the remainder of the discussion. They have the potential to be quite helpful in the visualization of a complex cycloalkane. Before continuing with this image, bear in mind that the chair depiction is an oversimplification, and is thus a bit misleading for several reasons.

 1) The back of the chair would not sit vertically w/r/to the seat, or base, of the chair (as implied by the drawing above). Rather, it would angle backward from the normal by nearly 10 degrees (109.5 – 90).  

2)  If the legs of the chair were symbolic of C-H bonds, then only the rear legs would be valid – dropping vertically downward from the upline.  However, from the downline, the front legs of the chair would rise vertically upward as depicted below. 

There are the two types of H atoms in the most stable conformation of the cyclohexane molecule. Axial hydrogens point either straight up or straight down. Alternatively, equatorial (skewed) hydrogens will be staggered (vs. eclipsed) for conformational stability.  Depicted below are the axial hydrogens which point either straight up or straight down.

If we now view the chair directly from the front, then pointing directly at us will be an ethyl group which sits at the occupant’s feet. Picture the downline as a dotted line as splitting the image into a top and bottom half. The downline is the line of planar intersection connecting the center points of the two circles. The center points of the two circles are actually eclipsed lines along C – C bonds which both extend from the front of the chair (the downline) to the rear of the chair (the upline).

The forward axial H atoms rise vertically from the two centers at the ends of the downline, while the rear axial H atoms drop vertically from the two (eclipsed) centers at the ends of the (eclipsed) upline.  The head of the occupant would rest near the upward rear of the chair, where we find another ethyl group in the projection.               

We next consider the added effects of the equatorial (skewed) H atoms, which will be staggered (vs. eclipsed) for conformational stability. The skewed H atoms extend outward from the ends of the (invisible) upline and the (invisible) downline of planar intersection as depicted below.

                             

Note that from the upline, axial bonds (the “legs” of the chair) extend vertically downward while equatorial bonds are skewed upwards. Alternatively, from the downline, axial bonds extend vertically upwards, while equatorial bonds are skewed downwards. The projection of the equatorial H atoms is depicted below.

                                   

We are now prepared to construct the complete cyclohexane molecule and its Newman projection. The arrows and dashed lines represent the line of sight that we have been using to look at the molecule --from the front of the chair. The imaginary line extends horizontally along the plane of the seat of the chair (or the 2 horizontal lines of C - C bonds).  The only 2 carbon atoms which are not in this plane are the ones located at the head of the chair and the foot of the chair. They are both depicted here in ethyl groups.     

                                     

Consider the primary factors determining the mechanical stability of a molecular conformation. Angle Strain: All atoms tend to have bond angles equal to that of its bonding orbitals. Tetrahedral (109.5 °) for sp3  hybridized carbon. Any deviations from the normal bond angle are accompanied by angle strain. Torsional Strain: Any tetrahedral carbons attached to each other tend to place H atoms in staggered positions (vs. “eclipsed” conformations).

The chair conformation of cyclohexane has neither angle strain nor eclipsed configurations. In fact, it has zero strain energy -- resulting from a high degree of structural symmetry and balance, and few eclipsed elements.  

In general, substituents are most stable when in equatorial positions. The Newman projection emphasizes that all H atoms in cyclohexane, including the axial ones, are staggered. This results in structural balance, and an elimination of any net forces which might contribute to molecular strain energy. Thus, the chair conformation is the most stable form of cyclohexane, and, indeed, of nearly every derivative of cyclohexane.

Secondary factors affecting the mechanical stability of alternative molecular conformations include:  1) Non-bonded atoms (or groups) that just touch each other exert an attraction. But if crowded, the steric repulsion will result in van der Waals (steric) strain. 2) Non-bonded atoms (or groups) tend to take positions that result in the most favorable dipole-dipole interactions. I.E. They will minimize dipole-dipole repulsions and maximize dipole-dipole attractions. (The strongest attraction of this nature is that due to hydrogen bonding in H-O, H-F, or H-N compounds).     

The most stable conformation inevitably results in a compromise between the ideal bond angles, angles of rotation, and even bond lengths. In actuality, few molecules have the idealized conformations that we assign them, and, for convenience, often work with. For example, it is highly unlikely that any tetravalent carbon compound – except one with four identical substituents – has exactly tetrahedral bond angles. Molecules accept a finite degree of angle strain in order to relieve these factors.

Let us now take the “chair” conformation and flip up the right-hand side (or “foot of the chair”).

Note that this transformation strictly involves rotations about single bonds. This new “boat” conformation of cyclohexane also has bond angles of 109.5 ° and thus avoids any elements of angle strain. The boat conformation resembles the chair conformation, except that the “footrest” methylene group is folded upward.

The boat conformation suffers from torsional strain, however, due to the eclipsing of bonds. This eclipsing also forces two of the hydrogens on the ends of the “boat” to interfere with each other. (These hydrogens are called “flagpole” hydrogens because they point upwards from the ends of the boat like two flagpoles).  

There is considerable van der Walls strain due to crowding between “flagpole” hydrogens, which lie only 1.83 Angstroms apart (where the sum of their van der Waals radii would be closer to 2.5 Angstroms).Thus, sighting along either of two carbon-carbon bonds (along the sides of the “boat”), we see sets of totally eclipsed bonds. The projection below (along the dotted lines in the depiction above) shows this total eclipsing of bonds.

                                                                                                                

The symmetrical boat conformation is therefore rarely observed in nature due to significant torsional strain resulting from the eclipsed bonds. A cyclohexane molecule in the “boat” conformation therefore actually exists in a skewed “twist boat” conformation, as depicted below.  

           

If we take the “boat” conformation and twist it slightly, then the flagpole hydrogens move away from each other (one moves upwards and the other moves downwards), and the eclipsing of the C–C bonds is also reduced as they become skewed w/r/to each other. Even though the “twist boat” is lower in energy than the symmetrical “boat”, it is still ~ 23 kJ / mole higher in energy than the “chair” conformation.

The energy barrier between the “boat” and “chair” is sufficiently low that the frequency of interconversion is relatively high. (The interconversion takes place by flipping the “footrest of the chair” upwards). The highest energy point in this process (which will ultimately determine the activation energy for the calculation of the rate of reaction) is where the “footrest” lies in the same plane as the “seat of the chair” (or the sides of the molecule). This highly unstable co-planar arrangement called the half-chair conformation.        

Thus, in addition to the “chair” (1), other conformations can also exist in the following forms: “half-chair” (2), “twist” or “twist-boat” (3 or 5), or symmetrical “boat” (4). We can list these forms in terms of stability by placing them all on a diagram or illustration where the vertical axis is scaled in units of energy.                           

The 'twist boat' form can be isolated as (like the 'chair')  it represents an energy minimum. The symmetrical 'boat' conformation does not suffer from angle strain. But it has a higher energy than the chair form due to steric strain resulting from the two axial 'flagpole' hydrogens. The torsional strain in the symmetrical boat conformation has a maximum value because all the carbon bonds are eclipsed.

Compare this to the chair conformation with all bonds staggered and complete absence of torsional strain. Compare this to the twist-boat conformation with 2 out 6 bonds partially eclipsed. In the half chair conformation, 4 carbon atoms are located on a plane in which two bonds are fully eclipsed.

The symmetrical boat and half-chair forms are impossible to isolate, as they are transition states between the twist boat and chair forms respectively. The twist boat conformation is 5.5 kcal/mol (23 kJ/mol) less stable than the chair conformation. The energies of the two transition states are 28 kJ / mol (for the boat) and 45 kJ / mol (for the half chair) higher than that of the chair. The process of transformation can now be described with more precision as taking place through a twist boat conformation and through two half chair transition states.

The difference in energy between the chair and the twist-boat conformations of cyclohexane can be measured indirectly by taking the difference in activation energy for the conversion of the chair to the twist-boat conformation and that of the reverse isomerization. The concentration of twist-boat conformation at room temperature is very low (< 0.1%). But @ 800 ?C this concentration can reach 30%.

The reverse reaction is measured by IR spectroscopy after rapidly cooling cyclohexane and freezing in the large concentration of twist-boat conformation.