Chapter: Conformational Analysis

1. Introduction to Conformations and Strain

• Conformational Analysis: This branch of stereochemistry investigates the different spatial arrangements (conformations) that a molecule can adopt due to rotation around single bonds. It also examines the relative stabilities of these conformations and the energy barriers to their interconversion. Understanding conformations is crucial because a molecule’s shape can significantly influence its physical properties, reactivity, and biological activity.
• Conformers (Rotamers): These are different conformations of the same molecule that can be interconverted by rotation around single bonds without breaking any covalent bonds. Due to relatively low energy barriers for rotation around single bonds (typically 10−60kJ/mol), conformers interconvert rapidly at room temperature and are generally not isolable. However, they exist in equilibrium, and the most stable conformer is typically the most abundant.
• Types of Strain: Molecular strain refers to the increase in potential energy of a molecule due to unfavorable spatial arrangements. Minimizing these strains leads to more stable conformations.
  • Torsional Strain (Eclipsing Strain): This arises from the repulsive interactions between electron clouds of bonds that are in an eclipsed orientation when viewed down a single bond. It’s most significant when atoms/groups are directly aligned, causing electron-electron repulsion. The magnitude of torsional strain depends on the size and electronegativity of the eclipsing groups.
  • Steric Strain (Van der Waals Strain): This type of strain occurs when atoms or groups are forced too close to each other in space, leading to an overlap of their electron clouds and a resulting repulsive interaction. It’s also known as Van der Waals repulsion or non-bonded interaction. The larger the groups, the greater the steric strain.
  • Angle Strain (Baeyer Strain): This occurs when bond angles within a molecule deviate significantly from their ideal values. For sp3-hybridized carbon atoms, the ideal bond angle is 109.5∘. Rings smaller or larger than cyclohexane often experience angle strain because their cyclic structure constrains bond angles, forcing them to be compressed or expanded.

2. Conformations of Acyclic Molecules

2.1. Ethane (CH3​−CH3​)

• Newman Projections: This is a powerful visualization tool used to represent conformations by looking directly down a specific carbon-carbon bond. The front carbon is represented by a dot, and the back carbon by a circle. Bonds from the front carbon radiate from the dot, while bonds from the back carbon extend from the circumference of the circle.
• Staggered Conformation: In this conformation, the C-H bonds on the front carbon are positioned exactly halfway between the C-H bonds on the back carbon. This arrangement maximizes the distance between the electron clouds of the bonds, resulting in the most stable conformation due to minimum torsional strain. Each H-H staggered interaction is relatively stable.
• Eclipsed Conformation: Here, the C-H bonds on the front carbon are directly aligned with (eclipsed by) the C-H bonds on the back carbon. This orientation leads to maximum electron-electron repulsion between the bonding orbitals, resulting in the least stable conformation due to maximum torsional strain. Each H-H eclipsing interaction contributes approximately 4kJ/mol to the strain.
• Energy Profile: As the front methyl group rotates 360∘ relative to the back methyl group around the C-C bond, the potential energy of the molecule changes periodically. It reaches minima at 60∘ intervals corresponding to staggered conformations and maxima at 0∘, 120∘, 240∘, and 360∘ corresponding to eclipsed conformations.
  • The energy difference between the eclipsed and staggered conformations of ethane is approximately 12kJ/mol (≈2.8kcal/mol). This value is the torsional barrier to rotation.

2.2. Butane (CH3​CH2​−CH2​CH3​)

• Viewing down the C2​−C3​ bond: Butane’s conformational analysis is more complex than ethane’s due to the presence of two larger methyl groups (CH3​) instead of hydrogen atoms at the ends of the central C-C bond. This introduces steric strain in addition to torsional strain.
• Key Conformations and their Stabilities:
  • Anti (Staggered): In this most stable conformation, the two methyl groups are 180∘ apart, positioned as far away from each other as possible. This minimizes both torsional strain (all bonds are staggered) and steric strain (no significant repulsive interactions between the methyl groups).
  • Gauche (Staggered): Here, the two methyl groups are 60∘ apart. While still a staggered conformation (minimizing torsional strain compared to eclipsed forms), it is less stable than the anti conformation. This reduced stability is due to a specific type of steric strain called the gauche-butane interaction (or gauche interaction), which is the repulsion between the two methyl groups that are relatively close to each other. This interaction contributes approximately 3.8kJ/mol (0.9kcal/mol) to the energy of the gauche conformer.
  • Partially Eclipsed: In this conformation, one methyl group eclipses a hydrogen atom on the adjacent carbon, and the other methyl group eclipses another hydrogen. This results in significant torsional strain and some steric interaction, making it higher in energy than the gauche conformation.
  • Totally Eclipsed: This is the least stable conformation of butane. The two methyl groups are directly eclipsing each other, leading to maximum torsional strain and severe steric strain. This strong repulsion between the bulky methyl groups makes this conformation the highest energy point on the rotation profile.
• Energy Profile: The energy profile for butane rotation is more intricate than ethane’s, showing two types of energy minima (anti and gauche) and two types of energy maxima (partially eclipsed and totally eclipsed). The anti conformation represents the global energy minimum.

3. Conformations of Cyclic Molecules

3.1. Cyclopropane (C3​H6​)

• Planar Structure: Due to its small ring size, cyclopropane is constrained to a planar (or nearly planar) structure.
• High Angle Strain: The internal bond angles are forced to be 60∘, which is a severe deviation from the ideal tetrahedral angle of 109.5∘. This angle strain is often described as “bent bonds” or “banana bonds,” where the electron density of the C-C bonds lies outside the internuclear axis.
• High Torsional Strain: All C-H bonds on adjacent carbon atoms are eclipsed when viewed along any C-C bond. This results in significant torsional strain, adding to the overall instability of the ring.

3.2. Cyclobutane (C4​H8​)

• Puckered Conformation: Unlike cyclopropane, cyclobutane is not planar. It adopts a slightly puckered, or “butterfly,” conformation. This puckering allows for a reduction in torsional strain by making the C-H bonds slightly staggered.
• Angle Strain vs. Torsional Strain Relief: The puckering introduces a small amount of additional angle strain (angles deviate slightly from 90∘), but the benefit of relieving torsional strain outweighs this energetic cost, making the puckered form more stable than a hypothetical planar cyclobutane.

3.3. Cyclopentane (C5​H10​)

• Non-Planar Conformations: Cyclopentane is also non-planar, primarily to relieve torsional strain. Planar cyclopentane would have significant torsional strain due to all C-H bonds being eclipsed.
• Envelope Conformation: The most common and stable conformation. In this form, four carbon atoms lie in a plane, and the fifth carbon atom is positioned out of that plane (like the flap of an envelope). This puckering minimizes torsional strain.
• Half-Chair Conformation: Another puckered conformation, less stable than the envelope, that involves a greater degree of twist.
• Low Angle Strain: The internal angles in puckered cyclopentane are close to 109.5∘, meaning angle strain is relatively low compared to smaller rings. The dominant strain relieved by puckering is torsional strain.

3.4. Cyclohexane (C6​H12​)

• The Most Stable Cycloalkane: Cyclohexane is the archetypal example in conformational analysis due to its unique ability to adopt a strain-free conformation.
• Chair Conformation: This is the most stable and prevalent conformation of cyclohexane.
  • No Angle Strain: All C-C-C bond angles are approximately 109.5∘, perfectly matching the ideal tetrahedral angle for sp3 carbons.
  • No Torsional Strain: All C-H bonds on adjacent carbons are in a staggered orientation when viewed down any C-C bond, eliminating torsional strain.
• Axial and Equatorial Hydrogens: In the chair conformation, there are two distinct types of hydrogen atoms (or substituents):
  • Axial: These six hydrogens are oriented parallel to the axis of symmetry passing through the center of the ring. Three point straight up, and three point straight down, alternating around the ring.
  • Equatorial: These six hydrogens are oriented roughly in the plane of the ring, pointing outwards. They are positioned at an angle of approximately 109.5∘ to the C-C bonds, away from the ring axis. Each carbon has one axial and one equatorial hydrogen.
• Chair Interconversion (Ring Flip): Cyclohexane undergoes a rapid interconversion between two equivalent chair conformations at room temperature. This dynamic process involves the “flipping” of the ring, where one “point” of the chair moves up and the other moves down.
  • During a ring flip, all axial positions become equatorial, and all equatorial positions become axial. Crucially, an “up” axial hydrogen becomes an “up” equatorial hydrogen, and a “down” axial hydrogen becomes a “down” equatorial hydrogen. The relative orientation (up/down) on a specific carbon remains the same.
  • The ring passes through higher-energy intermediate conformations: half-chair (highest energy transition state), twist-boat, and boat.
• Boat Conformation:
  • Significantly less stable than the chair conformation (approximately 27kJ/mol or 6.5kcal/mol higher in energy).
  • Contains significant torsional strain due to eclipsing interactions between hydrogens on carbons 2 and 3, and 5 and 6.
  • Suffers from steric strain due to “flagpole interactions” (also called prow-stern interactions), which are repulsions between the two hydrogens at carbons 1 and 4 (the “flagpoles”) that are pointed towards each other.
• Twist-Boat Conformation:
  • Slightly more stable than the pure boat conformation (approximately 23kJ/mol or 5.5kcal/mol higher than the chair).
  • It is formed by twisting the boat conformation, which partially relieves some of the torsional and flagpole strains. It is the true intermediate between the two chair forms.

3.5. Substituted Cyclohexanes

• Monosubstituted Cyclohexanes:
  • When a substituent (R) is present on a cyclohexane ring, the two chair conformations resulting from a ring flip are no longer equivalent.
  • The preferred conformation is invariably the one where the substituent is in the equatorial position.
  • 1,3-Diaxial Interactions: The primary reason for this preference is the steric repulsion between an axial substituent and the axial hydrogens located on carbons 3 and 5 relative to the substituent. These are unfavorable “gauche-like” interactions that destabilize the axial conformer. The larger the substituent, the greater these 1,3-diaxial interactions and the stronger the preference for the equatorial position.
  • The energy difference between the axial and equatorial conformations is called the A-value (or A-strain), which is a quantitative measure of the steric bulk of a substituent in the cyclohexane ring system. A larger A-value indicates a greater preference for the equatorial position. For example, −CH3​ has an A-value of 3.8kJ/mol, while a tert-butyl group (-C(CH3​)3​) has a very large A-value, almost exclusively forcing it into the equatorial position (effectively “locking” the ring).
• Disubstituted Cyclohexanes:
  • Cis/Trans Isomers: For disubstituted cyclohexanes, the terms cis and trans describe the relative orientation of the two substituents: cis means they are on the same side of the ring (both up or both down relative to a plane), and trans means they are on opposite sides (one up, one down).
  • For any given cis or trans isomer, there are two possible chair conformations that can interconvert via a ring flip. The most stable conformation will be the one that minimizes steric interactions, usually by placing the largest substituent in the equatorial position and minimizing 1,3-diaxial interactions.
  • 1,2-Disubstituted Cyclohexanes:
    • Cis-1,2: Always exists with one substituent axial and the other equatorial in both chair conformations. (e.g., cis-1,2-dimethylcyclohexane will have one methyl axial and one equatorial in both flipped forms).
    • Trans-1,2: Can exist as either both axial or both equatorial. The trans-diequatorial conformation is much more stable than the trans-diaxial conformation due to the absence of 1,3-diaxial interactions and the minimization of torsional strain.
  • 1,3-Disubstituted Cyclohexanes:
    • Cis-1,3: Can exist as either both axial or both equatorial. The cis-diequatorial conformation is more stable.
    • Trans-1,3: Always exists with one substituent axial and the other equatorial.
  • 1,4-Disubstituted Cyclohexanes:
    • Cis-1,4: Always exists with one substituent axial and the other equatorial.
    • Trans-1,4: Can exist as either both axial or both equatorial. The trans-diequatorial conformation is more stable.

4. Bicyclic and Polycyclic Systems (Brief Mention)

• Decalin (Bicyclodecane): A common example of fused cyclohexane rings. Decalin exists as two main isomers: cis-decalin and trans-decalin.
  • Trans-Decalin: More stable than cis-decalin. In trans-decalin, the two cyclohexane rings are fused in a way that their ring fusion carbons are trans to each other, and the two bridgehead hydrogens are on opposite sides of the molecule. This arrangement allows both rings to adopt stable chair-like conformations with minimal strain.
  • Cis-Decalin: Less stable. The two rings are fused in a way that their ring fusion carbons are cis to each other, and the two bridgehead hydrogens are on the same side. This introduces more steric interactions and some ring distortion, making it less stable than the trans isomer.

Multiple Choice Questions (MCQ) on Conformational Analysis

Instructions: Choose the best answer for each question.

1. What is conformational analysis primarily concerned with? a) Breaking and forming chemical bonds. b) The spatial arrangements of a molecule due to rotation around single bonds. c) The study of different constitutional isomers. d) The analysis of reaction mechanisms.

2. Which of the following defines conformers? a) Molecules with the same molecular formula but different connectivity. b) Stereoisomers that are non-superimposable mirror images. c) Different spatial arrangements of the same molecule that can be interconverted by bond rotation. d) Isomers that differ in the arrangement of atoms in space and cannot be interconverted by rotation around single bonds.

3. What type of strain arises from the repulsion between electron clouds of bonds that are aligned (e.g., C-H bonds in ethane)? a) Angle strain b) Steric strain c) Torsional strain d) Van der Waals strain

4. Which conformation of ethane is the most stable? a) Eclipsed b) Staggered c) Anti d) Gauche

5. How are the C-H bonds oriented relative to each other in the staggered conformation of ethane when viewed down the C-C bond? a) Directly aligned. b) Perpendicular. c) Bisecting the angles of the opposite bonds. d) Parallel.

6. What is the approximate energy difference between the eclipsed and staggered conformations of ethane? a) 0kJ/mol b) 4kJ/mol c) 12kJ/mol d) 25kJ/mol

7. In butane, which conformation is the most stable when viewed down the C2​−C3​ bond? a) Totally eclipsed b) Partially eclipsed c) Gauche d) Anti

8. What is the primary reason for the higher energy of the gauche conformation compared to the anti conformation in butane? a) Torsional strain b) Angle strain c) Steric strain (gauche-butane interaction) d) Hydrogen bonding

9. What is the approximate energy difference associated with a gauche-butane interaction? a) 0.5kJ/mol b) 3.8kJ/mol c) 12kJ/mol d) 27kJ/mol

10. Which conformation of butane is the least stable when viewed down the C2​−C3​ bond? a) Anti b) Gauche c) Partially eclipsed d) Totally eclipsed

11. Which type of strain is most significant in cyclopropane? a) Steric strain only. b) Torsional strain only. c) Both angle strain and torsional strain. d) Flagpole strain.

12. What is the bond angle in cyclopropane? a) 109.5∘ b) 90∘ c) 60∘ d) 120∘

13. What is the characteristic conformation of cyclobutane that helps relieve some torsional strain? a) Planar b) Chair c) Envelope d) Puckered (folded or “butterfly”)

14. What is the preferred conformation of cyclopentane? a) Planar b) Chair c) Envelope d) Boat

15. Which conformation of cyclohexane is the most stable? a) Boat b) Twist-boat c) Half-chair d) Chair

16. What is the ideal bond angle in the chair conformation of cyclohexane? a) 60∘ b) 90∘ c) 109.5∘ d) 120∘

17. In a chair conformation of cyclohexane, which type of hydrogen atoms are perpendicular to the average plane of the ring? a) Equatorial b) Axial c) Both axial and equatorial d) Planar

18. During a chair interconversion (ring flip) of cyclohexane, what happens to the axial and equatorial positions? a) Axial remains axial, equatorial remains equatorial. b) Axial becomes equatorial, equatorial becomes axial. c) All positions become axial. d) All positions become equatorial.

19. Which of the following is an intermediate conformation during the chair interconversion of cyclohexane? a) Staggered b) Gauche c) Half-chair d) Anti

20. What are “flagpole interactions” associated with in cyclohexane? a) Chair conformation b) Boat conformation c) Twist-boat conformation d) Planar conformation

21. What is the approximate energy difference between the boat and chair conformations of cyclohexane? a) 3.8kJ/mol b) 12kJ/mol c) 27kJ/mol d) 40kJ/mol

22. For a monosubstituted cyclohexane, which position is generally preferred by the substituent for maximum stability? a) Axial b) Equatorial c) Either axial or equatorial, no preference. d) Depends on the size of the ring.

23. What are 1,3-diaxial interactions? a) Repulsion between two substituents on adjacent carbons. b) Repulsion between an axial substituent and axial hydrogens on carbons 3 and 5 relative to it. c) Repulsion between two equatorial substituents. d) Repulsion between a flagpole hydrogen and a prow hydrogen.

24. The energy difference between the axial and equatorial conformations of a substituent is known as its: a) Torsional energy b) Steric hindrance c) A-value d) Bond energy

25. Which substituent would exhibit the largest A-value? a) −CH3​ b) −Cl c) −C(CH3​)3​ (tert-butyl) d) −OH

26. In cis-1,2-dimethylcyclohexane, which conformation is more stable after a ring flip? a) Both methyl groups axial. b) Both methyl groups equatorial. c) One methyl group axial, one equatorial. d) It depends on the temperature.

27. What is the preferred conformation for trans-1,4-dimethylcyclohexane? a) Both methyl groups axial. b) Both methyl groups equatorial. c) One methyl group axial, one equatorial. d) A twisted boat.

28. Why is trans-decalin generally more stable than cis-decalin? a) Trans-decalin has less torsional strain. b) Trans-decalin is planar. c) Trans-decalin has fewer steric interactions (e.g., 1,3-diaxial). d) Trans-decalin has more favorable angle strain.

29. Which of the following is NOT a type of strain contributing to molecular instability? a) Torsional strain b) Steric strain c) Angle strain d) Hydrogen bonding strain

30. Which of the following is a representation used to visualize the conformations of acyclic molecules? a) Haworth projection b) Fischer projection c) Newman projection d) Sawhorse projection (though Newman is more common for this purpose)

31. How many sp3 hybridized carbon atoms are there in a cyclohexane ring? a) 4 b) 5 c) 6 d) 7

32. The term “banana bonds” is sometimes used to describe the nature of bonds in which cycloalkane? a) Cyclobutane b) Cyclopentane c) Cyclopropane d) Cyclohexane

33. Which conformation of butane has the methyl groups 60∘ apart? a) Anti b) Gauche c) Partially eclipsed d) Totally eclipsed

34. In the boat conformation of cyclohexane, which atoms experience “flagpole interactions”? a) Hydrogens at C1​ and C2​ b) Hydrogens at C1​ and C3​ c) Hydrogens at C1​ and C4​ d) Hydrogens at C2​ and C5​

35. A conformation that is rapidly interconvertible with another conformation at room temperature is called a(n): a) Diastereomer b) Enantiomer c) Conformational isomer d) Constitutional isomer

**36. If a molecule has high torsional strain, it means: ** a) Its bond angles are severely distorted. b) Atoms are too close in space, causing repulsion. c) There is significant repulsion between aligned bonds. d) It has a very stable conformation.

37. When comparing the stability of chair and boat conformations of cyclohexane, which statement is true? a) Boat is more stable due to less angle strain. b) Chair and boat have similar stabilities. c) Chair is more stable due to absence of angle and torsional strain. d) Boat is more stable due to no 1,3-diaxial interactions.

38. Which type of strain is characteristic of small cyclic molecules where bond angles are forced to deviate from ideal values? a) Torsional strain b) Steric strain c) Angle strain d) Eclipsing strain

39. In a ring flip of methylcyclohexane, if the methyl group starts in an axial position, where does it end up after the flip? a) Still axial, but pointing in the opposite direction. b) Equatorial, pointing in the same relative “up” or “down” direction. c) Equatorial, pointing in the opposite relative “up” or “down” direction. d) It is destroyed.

40. The energy profile of rotation around the C-C bond in ethane is best described as: a) A straight line. b) A parabolic curve. c) A periodic curve with maxima and minima. d) A random distribution of energies.

Answer Key with Explanations

1. b) The spatial arrangements of a molecule due to rotation around single bonds.
   • Explanation: Conformational analysis specifically deals with the different shapes molecules can adopt by rotating around single bonds, without breaking any bonds.
2. c) Different spatial arrangements of the same molecule that can be interconverted by bond rotation.
   • Explanation: Conformers (or rotamers) are rapidly interconverting spatial arrangements achieved solely by rotation around σ bonds. They are not distinct isomers that can be isolated under normal conditions.
3. c) Torsional strain.
   • Explanation: Torsional strain, also known as eclipsing strain, is the repulsion that occurs when bonds on adjacent atoms are directly aligned (eclipsed), leading to electron-electron repulsion.
4. b) Staggered.
   • Explanation: In the staggered conformation of ethane, the C-H bonds are maximally separated, minimizing torsional strain and making it the most stable.
5. c) Bisecting the angles of the opposite bonds.
   • Explanation: In the staggered conformation, the bonds on the front carbon are positioned between the bonds on the back carbon, bisecting the angles created by the back bonds.
6. c) 12kJ/mol.
   • Explanation: The energy difference between the eclipsed and staggered conformations of ethane is approximately 12kJ/mol (or 2.8kcal/mol). This is the rotational barrier for the C-C bond.
7. d) Anti.
   • Explanation: The anti conformation of butane has the two bulky methyl groups 180∘ apart, minimizing both torsional and steric strain. This makes it the global energy minimum for butane.
8. c) Steric strain (gauche-butane interaction).
   • Explanation: In the gauche conformation, the methyl groups are 60∘ apart, leading to a mild steric repulsion between them due to their close proximity. This specific type of steric interaction is called the gauche-butane interaction.
9. b) 3.8kJ/mol.
   • Explanation: A single gauche-butane interaction destabilizes the molecule by approximately 3.8kJ/mol (or 0.9kcal/mol). This energy contribution makes the gauche conformer less stable than the anti.
10. d) Totally eclipsed.
    • Explanation: The totally eclipsed conformation has the two methyl groups directly eclipsing each other, resulting in maximum torsional strain and severe steric strain. This combination makes it the highest energy conformation.
11. c) Both angle strain and torsional strain.
    • Explanation: Cyclopropane is planar, leading to significant angle strain (bond angles 60∘ instead of 109.5∘) and all C-H bonds being eclipsed, causing high torsional strain. Both contribute significantly to its high energy.
12. c) 60∘.
    • Explanation: Cyclopropane is a three-membered ring, and thus its internal bond angles are forced to be 60∘, causing considerable angle strain.
13. d) Puckered (folded or “butterfly”).
    • Explanation: Cyclobutane puckers slightly out of planarity to reduce the torsional strain by introducing a small amount of staggering between adjacent C-H bonds. The “butterfly” refers to the way the ring folds.
14. c) Envelope.
    • Explanation: Cyclopentane adopts a non-planar “envelope” conformation, where one carbon is out of the plane defined by the other four, to relieve torsional strain, as a planar form would have significant eclipsing interactions.
15. d) Chair.
    • Explanation: The chair conformation of cyclohexane is the most stable because it is free of both angle strain (all bond angles are 109.5∘) and torsional strain (all C-H bonds are staggered).
16. c) 109.5∘.
    • Explanation: The bond angles in the chair conformation are essentially tetrahedral, allowing for ideal sp3 hybridization and thus no angle strain.
17. b) Axial.
    • Explanation: Axial hydrogens (or substituents) are oriented perpendicular (parallel to the ring’s imaginary axis) to the average plane of the cyclohexane ring.
18. b) Axial becomes equatorial, equatorial becomes axial.
    • Explanation: During a ring flip, all positions that were axial transform into equatorial positions, and all equatorial positions transform into axial positions. The “up” or “down” orientation relative to the ring is preserved.
19. c) Half-chair.
    • Explanation: The half-chair is the highest energy transition state that the cyclohexane ring passes through during its interconversion from one chair form to another.
20. b) Boat conformation.
    • Explanation: Flagpole interactions are steric repulsions between the two hydrogens pointing “up” from carbons 1 and 4 in the boat conformation, contributing to its higher energy.
21. c) 27kJ/mol.
    • Explanation: The boat conformation is approximately 27kJ/mol (or 6.5kcal/mol) higher in energy than the chair due to significant torsional and flagpole steric strain.
22. b) Equatorial.
    • Explanation: For a monosubstituted cyclohexane, the substituent prefers the equatorial position to minimize unfavorable 1,3-diaxial interactions with the axial hydrogens on carbons 3 and 5.
23. b) Repulsion between an axial substituent and axial hydrogens on carbons 3 and 5 relative to it.
    • Explanation: 1,3-diaxial interactions are steric repulsions that occur when a group is in an axial position, interacting with other axial groups (usually hydrogens) three carbons away, contributing to the strain of the axial conformer.
24. c) A-value.
    • Explanation: The A-value quantifies the energy difference between a substituent being in the axial versus equatorial position. It’s a measure of the steric bulk of a group and its preference for the equatorial position.
25. c) −C(CH3​)3​ (tert-butyl).
    • Explanation: The tert-butyl group is exceptionally bulky. When forced into an axial position, it experiences very severe 1,3-diaxial interactions, leading to a very large A-value and an overwhelming preference for the equatorial position.
26. c) One methyl group axial, one equatorial.
    • Explanation: For cis-1,2-dimethylcyclohexane, the two methyl groups are on the same side. Due to their relative positions, one must be axial and the other equatorial in both interconvertible chair conformations. There is no diequatorial option for cis-1,2.
27. b) Both methyl groups equatorial.
    • Explanation: For trans-1,4-dimethylcyclohexane, the two methyl groups are on opposite sides. The most stable conformation is the one where both methyl groups are in the less hindered equatorial positions, minimizing all steric interactions.
28. c) Trans-decalin has fewer steric interactions (e.g., 1,3-diaxial).
    • Explanation: In trans-decalin, the two cyclohexane rings are fused in a way that allows them both to adopt low-energy chair-like conformations with minimized 1,3-diaxial-like interactions. Cis-decalin, due to its fusion, introduces more steric strain.
29. d) Hydrogen bonding strain.
    • Explanation: Hydrogen bonding is an attractive intermolecular or intramolecular interaction that can stabilize certain conformations or structures, not a type of strain that causes instability. Torsional, steric, and angle strains all contribute to molecular instability.
30. c) Newman projection.
    • Explanation: Newman projections are specifically designed to visualize the conformations of acyclic molecules by looking down a carbon-carbon bond axis, showing the relative orientation of groups on adjacent carbons.
31. c) 6.
    • Explanation: All six carbon atoms in a cyclohexane ring are sp3 hybridized, forming a saturated six-membered ring.
32. c) Cyclopropane.
    • Explanation: Due to its extreme angle strain (60∘ bond angles), the covalent bonds in cyclopropane are often described as “bent” or “banana bonds” because the electron density is not directly along the internuclear axis.
33. b) Gauche.
    • Explanation: The gauche conformation in butane is defined by the two methyl groups being 60∘ apart when viewed down the C2​−C3​ bond.
34. c) Hydrogens at C1​ and C4​.
    • Explanation: In the boat conformation, the hydrogens at carbons 1 and 4 are pointed towards each other like “flagpoles,” leading to steric repulsion known as flagpole interactions.
35. c) Conformational isomer.
    • Explanation: A conformational isomer (or conformer) is a specific spatial arrangement of atoms that can be interconverted with another by rotation about single bonds, and these interconversions are generally rapid at room temperature.
36. c) There is significant repulsion between aligned bonds.
    • Explanation: High torsional strain specifically implies that there are many bonds in an eclipsed orientation, leading to electron cloud repulsion.
37. c) Chair is more stable due to absence of angle and torsional strain.
    • Explanation: The chair conformation of cyclohexane is uniquely stable because it can adopt a geometry where all bond angles are ideal (109.5∘) and all adjacent bonds are staggered, thereby eliminating both angle and torsional strain.
38. c) Angle strain.
    • Explanation: Angle strain is the most characteristic type of strain in small cyclic molecules (like cyclopropane and cyclobutane) where the ring geometry forces bond angles to significantly deviate from their ideal tetrahedral values.
39. b) Equatorial, pointing in the same relative “up” or “down” direction.
    • Explanation: A ring flip interconverts axial and equatorial positions. If a substituent is axial and pointing “up” before the flip, it will become equatorial and still be pointing “up” (relative to the ring’s face) after the flip.
40. c) A periodic curve with maxima and minima.
    • Explanation: The energy profile for rotation around the C-C bond in ethane shows a repeating pattern of energy highs (eclipsed conformations) and energy lows (staggered conformations) as the dihedral angle changes.