(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?

Step by step solution

01

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.

02

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.

03

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)

04

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.

05

Write down the expected diastereomer.

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

06

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)

07

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.

08

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!