Question

(a) trans-1, 2-Dimethylcyclohexane exists about \(99 \%\) in the diequatorial conformation; trans-1, 2-Dibromocyclohexane on the other hand, exists about equally in diequatorial and diaxial conformations. Furthermore, the fraction of the diaxial conformation decreases with increasing polarity of the solvent. How do you account for the contrast between the dimethyl and dibromo compounds? (b) If trans-3-cis-4-dibromo-tert-butylcyclohexane is subjected to prolonged heating, it is converted into an equilibrium mixture (about \(50: 50\) ) of itself and a diastereomer. What is the diastereomer likely to be? How do you account for the approximately equal stability of these two diastereomers? [Here, and in (c), consider the more stable conformation of each diastereomer to be the one with an equatorial tert-buty1 group]. (c) There, are two more diastereomeric 3,4 -dibromo tert-butylcyclohexanes. What are they? How do you account for the fact that neither is present to an appreciable extent in the equilibrium mixture?

Short answer

In trans-1,2-dimethylcyclohexane, the diequatorial conformation is more stable due to minimal steric repulsion while in trans-1,2-dibromocyclohexane, the stability of diequatorial and diaxial conformations is roughly equal. The fraction of diaxial conformation decreases with increasing solvent polarity due to better solvation of polar bromine atoms. The diastereomer formed during prolonged heating of trans-3-cis-4-dibromo-tert-butylcyclohexane is cis-3-trans-4-dibromo-tert-butylcyclohexane, with a 50:50 ratio in the equilibrium mixture due to similar steric hindrance in both diastereomers. The other two diastereomers, cis-3-cis-4-dibromo-tert-butylcyclohexane and trans-3-trans-4-dibromo-tert-butylcyclohexane, are less stable due to increased steric repulsion and are not present in the equilibrium mixture to an appreciable extent.

Step-by-step solution

Analyze the conformations of trans-1,2-dimethylcyclohexane and trans-1,2-dibromocyclohexane.

Figure out the most stable conformations for both molecules. For trans-1,2-dimethylcyclohexane, the diequatorial conformation is favorable because the two methyl groups are in equatorial positions, which leads to minimal steric repulsion. For trans-1,2-dibromocyclohexane, we have to consider two factors: steric repulsion between bromine atoms and the preference of bromine atoms to be in the axial position due to hyperconjugation effect with the cyclohexane ring.

Compare the stabilities of these conformations.

In trans-1,2-dimethylcyclohexane, the diequatorial conformation is much more stable (99%) because the steric repulsion is minimized. In trans-1,2-dibromocyclohexane, the stability of diequatorial and diaxial conformations is approximately the same.

Explain the effect of solvent polarity on conformations.

The fraction of diaxial conformation of trans-1,2-dibromocyclohexane decreases with increasing solvent polarity because polar solvents can better solvate the polar bromine atoms, which leads to a decrease in the hyperconjugation effect. This effect makes the diequatorial conformation more favorable. (b)

Identify the possible diastereomer of trans-3-cis-4-dibromo-tert-butylcyclohexane.

For obtaining the change in conformation, it needs one of the bromine atoms to change its position. The equilibrium mixture will be formed by the trans to cis flip of the C3-C4 bond.

Write down the expected diastereomer.

The diastereomer is cis-3-trans-4-dibromo-tert-butylcyclohexane.

Explain the approximately equal stability of the two diastereomers.

Both diastereomers have similar steric hindrance since the tert-butyl group is equatorial in both of the conformations, and both have bromine atoms with one being axial and one being equatorial. Therefore, their energies are very close to each other, and the mixture has a 50:50 ratio. (c)

Identify two more diastereomeric 3,4-dibromo-tert-butylcyclohexanes.

The other two diastereomers are cis-3-cis-4-dibromo-tert-butylcyclohexane and trans-3-trans-4-dibromo-tert-butylcyclohexane.

Explain why these diastereomers are not present in the equilibrium mixture.

For cis-3-cis-4-dibromo-tert-butylcyclohexane, both bromine atoms will be in equatorial positions which will increase the steric repulsion. In the case of trans-3-trans-4-dibromo-tert-butylcyclohexane, both bromine atoms will be in axial positions which will increase the steric repulsion with a 1,3-diaxial interaction. That's why both these diastereomers are less stable and not present to an appreciable extent in the equilibrium mixture.

Key concepts

Cyclohexane Conformation

Cyclohexane molecules can adopt different shapes, or conformations, based on the orientation of its hydrogen atoms and substituents like methyl or bromine groups. The two primary conformations are the "chair" and "boat" forms, with the chair being the most stable due to minimal steric strain and torsional strain. Within the chair conformation, groups can occupy axial (perpendicular) or equatorial (parallel to the ring plane) positions. Conformations are analyzed by evaluating their steric interactions, and typically, the molecule favors the lowest energy state where repulsive forces are minimized.

• In a diequatorial conformation, larger substituent groups at the carbon positions are found equatorially, leading to less steric strain.
• Conversely, in the diaxial conformation, substituents are axial, causing higher 1,3-diaxial interactions and greater steric hindrance.

Understanding these conformation differences is crucial when predicting the behavior and stability of cyclic compounds, especially when analyzing reactions or molecular interactions.

Steric Hindrance

Steric hindrance arises when atoms or groups of atoms in a molecule occupy space close to one another, causing a reduction in the molecule's reactivity. It is an important concept in organic chemistry as it affects how molecules interact and react. Large groups, like tert-butyl or bromine, can cause significant steric hindrance, disrupting favorable molecular conformations. In cyclohexane derivatives, placing these bulky groups equatorially tends to minimize steric hindrance and increases conformational stability. Consider trans-1,2-dimethylcyclohexane and trans-1,2-dibromocyclohexane:

• The dimethyl variant favors a diequatorial conformation to minimize methyl collisions.
• The dibromo variant faces a balance, as bromine's bulkiness and axial preference due to hyperconjugation modify its conformation.

Hyperconjugation

Hyperconjugation occurs when electrons in a sigma bond (typically C-H or C-C) interact with an adjacent empty or partially filled p-orbital or a pi orbital to give an extended orbital system which results in increased stability. It plays a role in determining molecular conformation and stability. In cyclohexane halides like trans-1,2-dibromocyclohexane:

• Bromine atoms exhibit hyperconjugation more when positioned axially due to the improved overlap with adjacent antibonding orbitals on the cyclohexane.
• This axial hyperconjugation can be more stable despite steric hindrance, accounting for the comparable stability of diaxial conformations in brominated cyclohexanes.

Hyperconjugation can subtly dictate which conformation is more energetically favored and help explain differences in stability between similar molecules.

Diastereomers

Diastereomers are stereoisomers with two or more chiral centers that are not mirror images of each other. Unlike enantiomers, which are completely identical in chemical properties except in a chiral environment, diastereomers have different physical and chemical properties. In the context of the cyclohexane exercise:

• Diastereomers such as trans-3-cis-4-dibromo-tert-butylcyclohexane and its counterpart result from the distinct spatial arrangement of bromine atoms and tert-butyl groups.
• The equilibrium between diastereomers occurs even at similar stabilities. This is because one conformation isn't significantly sterically or energetically favored over the other.

Recognizing diastereomers and analyzing their stability is essential in predicting reaction products and understanding thermodynamic preferences.

Solvent Polarity

Solvent polarity refers to a solvent’s ability to dissolve various compounds due to its dielectric constant. Polar solvents can stabilize charged or polar molecules through dipole interactions. The polarity profoundly affects molecular conformations in solvation scenarios:

• In solutions of trans-1,2-dibromocyclohexane, polar solvents enhance stability of the diequatorial conformation by better solvating bromine atoms, reducing the hyperconjugation pull from axial positions.
• This effect decreases the diaxial concentration—polarity essentially changes the energetic profile of dissolved conformers.

Understanding solvent effects is instrumental in reaction chemistry and phase behaviors of organic molecules.