Q: Given the following Gibbs free energy difference for a methyl group on cyclohexane: $$\Delta G^\circ = -1.8$$ kcal/mol, what is the equilibrium constant $$K_{eq} at$$ $$298 K$$? (Use $$R = 1.987 \times 10$$^{-3}$$ kcal/(mol·K))

$$K_{eq} = e$$^{\frac{-1.8}$${(1.987 \times 10$$^{-3}$$) \times 298}}$$

Question 1

Which type of strain is primarily responsible for the high energy of the boat conformation of cyclohexane?

Accepted Answer

Torsional strain and steric strain

Question 2

What is the main reason cyclohexane prefers the chair conformation over the boat conformation?

Accepted Answer

The chair conformation minimizes both torsional and steric strain

Question 3

Given the following Gibbs free energy difference for a methyl group on cyclohexane: $$\Delta G^\circ = -1.8$$ kcal/mol, what is the equilibrium constant $$K_{eq} at$$ $$298 K$$? (Use $$R = 1.987 	imes 10$$^{-3}$$ kcal/(mol·K))

Accepted Answer

$$K_{eq} = e$$^{\frac{-1.8}$${(1.987 	imes 10$$^{-3}$$) 	imes 298}}$$

Question 4

Which of the following best describes a 1,3-diaxial interaction in cyclohexane?

Accepted Answer

A steric interaction between axial substituents on carbons 1 and 3

Question 5

Why does tert-butyl substitution on cyclohexane show a much greater preference for the equatorial position compared to methyl substitution?

Accepted Answer

Tert-butyl is much larger, causing greater steric strain in the axial position

Question 6

Which of the following is NOT a factor that contributes to the stability of a conformation?

Accepted Answer

Hydrogen bonding

Question 7

In the context of cyclohexane conformations, what is the energy barrier (in kcal/mol) for interconversion between two chair forms?

Accepted Answer

$$\approx 10-12$$ kcal/mol

Question 8

Which molecular representation is most useful for visualizing 1,3-diaxial interactions in cyclohexane?

Accepted Answer

Chair conformation

Question 9

Which of the following best explains why cyclopropane has weak $$\sigma$$ bonds compared to a typical alkane?

Accepted Answer

Poor overlap of $$sp^3$$ orbitals due to bond angle strain

Question 10

How many 1,3-diaxial interactions are present when a methyl group is in the axial position on cyclohexane?

Accepted Answer

2

Question 11

Which of the following substituents on cyclohexane would have the SMALLEST preference for the equatorial position based on $$\Delta G^\circ$$ values?

Accepted Answer

F

Question 12

Which of the following is a correct statement about the relationship between gauche interactions in butane and 1,3-diaxial interactions in cyclohexane?

Accepted Answer

A single 1,3-diaxial interaction is energetically equivalent to a gauche interaction

Question 13

Which of the following best describes the difference between cis and trans isomers of 1,4-dimethylcyclohexane?

Accepted Answer

Cis isomers have both methyl groups on the same side of the ring; trans isomers have them on opposite sides

Question 14

Which of the following is the most stable conformation of cyclohexane?

Accepted Answer

Chair

Question 15

If a cyclohexane ring has a tert-butyl group and a methyl group, which conformation is most stable?

Accepted Answer

Both groups equatorial

Question 16

Which of the following statements about the energy diagram for cyclohexane conformers is correct?

Accepted Answer

The chair conformation is the lowest in energy

Question 17

Which of the following is a configurational isomer?

Accepted Answer

Cis- and trans-1,2-dimethylcyclohexane

Question 18

Which of the following best explains why the energy difference between isopropyl and tert-butyl substitution is much greater than between methyl and isopropyl substitution on cyclohexane?

Accepted Answer

Tert-butyl is significantly bulkier, causing more severe 1,3-diaxial interactions

Question 19

Which of the following is the correct order of stability for the conformers of cyclohexane from least stable to most stable?

Accepted Answer

Half-chair, boat, twist-boat, chair

Conformations and Stability of Cyclohexane and Substituted Cyclohexanes

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