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Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics
Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition
Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471Not the one you use?Change textbook
All textbooksMullins 1st EditionCh. 5 - Chemical Reaction Analysis: Thermodynamics and KineticsProblem 50c
Chapter 4, Problem 50c

The A value of a substituent on a cyclohexane ring is essentially the ∆G° for a substituent going from the equatorial to the axial position in a chair–chair interconversion. Because most substituents prefer to be in the equatorial position, A values are, by definition, positive numbers. Use the table of A values to calculate ∆G° and Keq for the chair–chair interconversions shown.
(c) Structural representation of chair conformations showing substituents on a cyclohexane ring interconverting positions.

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1
Identify the substituent on the cyclohexane ring and locate its A value from the provided table. The A value represents the Gibbs free energy change (∆G°) for the substituent moving from the equatorial to the axial position.
Recall the relationship between ∆G° and the equilibrium constant (K_eq): ∆G° = -RT ln(K_eq), where R is the gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin. This equation will help you calculate K_eq once ∆G° is known.
Determine the sign of ∆G°. Since most substituents prefer the equatorial position, the A value (∆G°) is positive, indicating that the equatorial position is more stable than the axial position.
Rearrange the equation to solve for K_eq: K_eq = e^(-∆G° / RT). Substitute the known values of ∆G°, R, and T into the equation. Ensure that the units are consistent (e.g., convert ∆G° to joules if it is given in kilojoules).
Perform the calculation to find K_eq. This value will indicate the ratio of the concentrations of the equatorial and axial conformers at equilibrium. A larger K_eq suggests a strong preference for the equatorial position.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Chair Conformation of Cyclohexane

Cyclohexane can adopt a chair conformation, which minimizes steric strain and torsional strain. In this conformation, substituents can occupy either axial or equatorial positions. The equatorial position is generally more stable for larger substituents due to reduced steric hindrance with other axial hydrogens, making it crucial for understanding substituent behavior in cyclohexane derivatives.
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What is a chair conformation?

A Values and Free Energy Change (∆G°)

A values represent the free energy change associated with the transition of a substituent from the equatorial to the axial position in cyclohexane. A positive A value indicates that the equatorial position is favored, reflecting the increased steric strain when a substituent is in the axial position. This concept is essential for calculating the stability of different conformations and understanding the thermodynamics of chair interconversions.
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Introduction to free energy diagrams.

Equilibrium Constant (K_eq)

The equilibrium constant (K_eq) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. In the context of chair-chair interconversions, K_eq can be calculated using the relationship K_eq = e^(-∆G°/RT), where R is the gas constant and T is the temperature in Kelvin. This relationship allows for the determination of the favorability of the equatorial versus axial conformations based on the calculated free energy change.
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Related Practice
Textbook Question

For each set of reactive intermediates, rank them in order of reactivity (1 = most reactive).

(a)

1
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Textbook Question

For each of the following reactions, identify the bonds that are broken and formed. Be sure to indicate whether the bond that is broken is a σ bond or a π bond.

(e)

1
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Textbook Question

The A value of a substituent on a cyclohexane ring is essentially the ∆G° for a substituent going from the equatorial to the axial position in a chair–chair interconversion. Because most substituents prefer to be in the equatorial position, A values are, by definition, positive numbers. Use the table of A values to calculate ∆G° and Keq for the chair–chair interconversions shown.

(b)

Textbook Question

For each set of reactive intermediates, rank them in order of reactivity (1 = most reactive).

(b)

2
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Textbook Question

The A value of a substituent on a cyclohexane ring is essentially the ∆G° for a substituent going from the equatorial to the axial position in a chair–chair interconversion. Because most substituents prefer to be in the equatorial position, A values are, by definition, positive numbers. Use the table of A values to calculate ∆G° and Keq for the chair–chair interconversions shown.

(d)

Textbook Question

The A value of a substituent on a cyclohexane ring is essentially the ∆G° for a substituent going from the equatorial to the axial position in a chair–chair interconversion. Because most substituents prefer to be in the equatorial position, A values are, by definition, positive numbers. Use the table of A values to calculate ∆G° and Keq for the chair–chair interconversions shown.

(a)

1
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