Question

Draw the planar representations of the three isomers of tetramethylcyclohexane that have all four of the methyl groups cis on the ring. Now draw each of the molecules in a chair conformation. Draw the ring-flipped chair for each of your molecules. Circle the more stable chair conformation for each of the three molecules.

Short answer

Draw planar diagrams of three isomers with cis methyl groups, convert them to chair conformations and their flips, then circle the stable conformations where methyl groups are equatorial.

Step-by-step solution

- Understanding the Problem

The problem requires drawing the three isomers of tetramethylcyclohexane with all cis methyl groups and representing them as planar diagrams. Additionally, each isomer needs to be shown in both chair conformations, and the more stable chair conformation must be circled.

- Draw Planar Representations

Draw the planar representations of three isomers of tetramethylcyclohexane ensuring that each has all four methyl groups in cis positions. Label these isomers for clarity.

- Convert Planar to Chair Conformations

For each planar structure, draw the corresponding chair conformation. Make sure to position the methyl groups correctly so they remain cis relative to each other.

- Draw Ring-flipped Chair Conformations

For each chair conformation draw the ring-flipped version. This involves flipping the axial and equatorial positions of all substituents. Ensure that all methyl groups remain cis.

- Determine Stability

Compare both chair conformations of each isomer. The conformation with the maximum number of equatorial methyl groups is more stable. Circle the more stable chair conformation for each isomer.

Key concepts

cis configuration

In organic chemistry, cis configuration refers to a type of geometric isomerism where similar or identical substituents are positioned on the same side of a molecule. In our case with tetramethylcyclohexane, all four methyl groups (-CH₃) must be on the same side of the six-membered cyclohexane ring.
Essentially, each methyl group needs to be oriented in the same direction which could be either all 'up' or all 'down'. This uniformity creates the cis isomer. When represented in a planar diagram, the ring's substituents will all project parallel relative to the ring, emphasizing this same-side arrangement.
Understanding the cis configuration is crucial for predicting the physical and chemical properties of isomers including their stability and interactions during reactions.

chair conformation

Cyclohexane exhibits several conformations due to its flexible ring strcuture, the most stable being the chair conformation. This chair form minimizes steric strain and torsional strain; it resembles a chair, hence the name.
For tetramethylcyclohexane, it's important to draw this conformation correctly: imagine the cyclohexane ring as a 3D structure. This chair form has alternating axial (vertical) and equatorial (horizontal) positions for substituents.
In this form, two parallel planes can be visualized. Here, positioning the four methyl groups correctly ensures that they stay cis. Depending on their axial or equatorial position, the stability of the conformation changes.
Drawing the chair conformation accurately will help in predicting the next concept, ring-flipping, and determining the most stable form.

ring-flipping

Ring-flipping refers to the process where cyclohexane interconverts between two chair conformations, changing the axial and equatorial positions of its substituents.
During the ring-flip, axial positions become equatorial and vice versa. For tetramethylcyclohexane, each methyl group in an axial position will move to an equatorial position and all those in equatorial positions will move to axial ones.
This rearrangement is crucial because it affects the stability of the molecule: steric hindrance is reduced when bulky groups like methyl substituents occupy equatorial positions.
After performing the ring flip, comparing the two chair conformations shows which is more stable by evaluating the position of the bulky methyl groups.

conformational stability

The stability of different conformations of cyclohexane and its derivatives, like tetramethylcyclohexane, depends largely on the spatial arrangement of substituents. In the case of ring conformations, this means comparing the chair forms.
Conformations where bulky substituents are in equatorial positions tend to be more stable. This is because equatorial positions mitigate steric hindrance caused by large groups being too close to each other, seen especially with multiple substituents.
In our example, after drawing the ring-flipped versions of the three tetramethylcyclohexane isomers, you should compare the two chair conformations of each to determine which has more methyl groups in equatorial positions. This will be the more stable conformation.
Circling these more stable chair conformations will visually reinforce the effect of substituent positioning on molecular stability.