The energy cost of having one tert-butyl group axial versus equatorial can be calculated from the values in table 4. That means that the conformer with the tert -butyl group axial is approximately 3. This means that 1- tert -butylmethylcyclohexane will spend the majority of its time in the more stable conformation.
The situation is more complex when the effect of conformations on the relative stability of cis and trans disubstituted cyclohexanes is analyzed. Remember, configurational stereoisomers do not interconvert without breaking bonds, whereas conformational isomers normally interconvert rapidly by the ring flip process.
Let's apply a similar analysis to the cis and trans stereoisomers of 1,2-dimethylcyclohexane. In cis -1,2-dimethylcyclohexane, one methyl group is axial and one methyl group is equatorial in both ring flip conformers, so neither conformer is more stable than the other. It is important to note, that this molecule cannot get both methyl groups axial without breaking bonds to make a new molecule. In trans -1,2-dimethylcyclohexane, one conformer has both methyl groups axial and the other has both methyl groups equatorial.
The conformer with both methyl groups axial is 3. Obviously, the equilibrium will favor the conformer with both methyl groups in the equatorial position. To decide whether the cis or trans isomer of 1,2-dimethylcyclohexane is more stable, compare the relative energy of the most stable conformer of cis -1,2-dimethylcyclohexane to the most stable conformer of trans -1,2-dimethylcyclohexane.
The trans -1,2-dimethylcyclohexane has the most stable conformer, so it is the more stable isomer. Does this mean that the trans isomer of a disubstituted cyclohexane is always more stable than the cis isomer? Let's examine both the cis and trans isomers of 1,3-dimethylcyclohexane and find out.
As can be seen in the structures above, cis -1,3-dimethylcyclohexane's most stable conformer has both methyl groups equatorial, while trans -1,3-dimethylcyclohexane always has one methyl group is equatorial and one methyl group axial. Determining the more stable chair conformation becomes more complex when there are two or more substituents attached to the cyclohexane ring.
To determine the stable chair conformation, the steric effects of each substituent, along with any additional steric interactions, must be taken into account for both chair conformations. In this section, the effect of conformations on the relative stability of disubstituted cyclohexanes is examined using the two principles:.
The more stable chair conformation can often be determined empirically or by using the energy values of steric interactions previously discussed in this chapter. Note, in some cases there is no discernable energy difference between the two chair conformations which means they are equally stable. Both chair conformers have one methyl group in an axial position and one methyl group in an equatorial position giving both the same relative stability.
The steric strain created by the 1,3-diaxial interactions of a methyl group in an axial position versus equatorial is 7. Thus, the equilibrium between the two conformers does not favor one or the other. Note, that both methyl groups cannot be equatorial at the same time without breaking bonds and creating a different molecule. However, if the two groups are different, as in 1- tert -butylmethylcyclohexane, then the equilibrium favors the conformer in which the larger group tert -butyl in this case is in the more stable equatorial position.
The energy cost of having one tert-butyl group axial versus equatorial can be calculated from the values in table 4. The conformer with the tert -butyl group axial is approximately Solving for the equilibrium constant K shows that the equatorial is preferred about over axial. This means that 1- tert -butylmethylcyclohexane will spend the majority of its time in the more stable conformation, with the tert -butyl group in the equatorial position.
In cis -1,2-dimethylcyclohexane, both chair conformations have one methyl group equatorial and one methyl group axial. As previously discussed, the axial methyl group creates 7. It is important to note, that both chair conformations also have an additional 3. Overall, both chair conformations have In trans -1,2-dimethylcyclohexane, one chair conformer has both methyl groups axial and the other conformer has both methyl groups equatorial.
The conformer with both methyl groups equatorial has no 1,3-diaxial interactions however there is till 3. The conformer with both methyl groups axial has four 1,3-Diaxial interactions which creates 2 x 7.
This conformer is The equilibrium will therefore favor the conformer with both methyl groups in the equatorial position. A similar conformational analysis can be made for the cis and trans stereoisomers of 1,3-dimethylcyclohexane. For cis -1,3-dimethylcyclohexane one chair conformation has both methyl groups in axial positions creating 1,3-diaxial interactions.
The other conformer has both methyl groups in equatorial positions thus creating no 1,3-diaxial interaction. Because the methyl groups are not on adjacent carbons in the cyclohexane rings gauche interactions are not possible.
Even without energy calculations it is simple to determine that the conformer with both methyl groups in the equatorial position will be the more stable conformer. For trans -1,3-dimethylcyclohexane both conformations have one methyl axial and one methyl group equatorial. Each conformer has one methyl group creating a 1,3-diaxial interaction so both are of equal stability. When considering the conformational analyses discussed above a pattern begins to form.
There are only two possible relationships which can occur between ring-flip chair conformations:. The other conformer places both substituents in equatorial positions creating no 1,3-diaxial interactions. This diequatorial conformer is the more stable regardless of the substituents. This transition state proceeds to a twist boat energy minimum, but this is not highly popupulated and generally plays little or no role in cyclohexane's structure or chemistry.
However, the twist boat can interconvert with another equivalent twist boat via the true boat conformation as a transition state to give another chair structure, in which the sense of the ring puckering is reversed. This is significant in cyclohexane itself, because in this process the axial and equatorial hydrogens are interconverted.
However, at any given instant, there are always two types of hydrogen. Since axial and equatorial bonds are non-equivalent, there are two non-equivalent positions in which to place any substituent. We use the simple methyl group as an example, but the same concept applies to any substituent.
Equatorial methyl cyclohexane is the more stable conformation. When the ring flip occurs, however, it converts to axial methylcyclohexane. These two conformations are in rapid equilibrium at room temperature, but can be frozen out as distinct compounds at degrees. The equatorial conofrmation is favored in the equilibrium by a modest amount because the axial isomer has about 1.
This strain arises from the interaction of one of the hydrogens of the axial methyl group with each of the two other axial hydrogens on the same side of the ring, as illustrated above. Each of these steric interacgions is approximately equivalent to one gauche butane interaction of 0.
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