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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 50d
Chapter 4, Problem 50d

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) Structural representation of a cyclohexane ring showing substituents in equatorial and axial positions.

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Step 1: Understand the concept of A values. A values represent the free energy difference (∆G°) between the equatorial and axial positions of a substituent on a cyclohexane ring during a chair–chair interconversion. Positive A values indicate that the equatorial position is favored.
Step 2: Recall the relationship between ∆G° and the equilibrium constant (K_eq). The equation is: ∆G° = -RT ln(K_eq), where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
Step 3: Use the given A value from the table to determine ∆G°. Since A values are equivalent to ∆G° for the equatorial-to-axial transition, you can directly use the A value provided in the table for the substituent in question.
Step 4: Rearrange the equation to solve for K_eq. The formula becomes: K_eq = e^(-∆G°/RT). Substitute the values for ∆G°, R, and T into the equation to calculate K_eq.
Step 5: Interpret the results. A large positive ∆G° corresponds to a small K_eq, indicating that the equatorial position is strongly favored. Conversely, a smaller ∆G° would result in a larger K_eq, showing less 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 preferences in cyclohexane derivatives.
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What is a chair conformation?

A Values

A values represent the free energy change (∆G°) associated with the transition of a substituent from the equatorial to the axial position in cyclohexane. Positive A values indicate that substituents favor the equatorial position due to lower steric interactions. These values are essential for calculating the equilibrium constant (K_eq) for chair-chair interconversions, as they quantify the stability difference between the two positions.
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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. Understanding K_eq helps predict the favored conformation of cyclohexane derivatives based on their substituents.
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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

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)

1
views
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

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

(c)

5
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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.

(a)

1
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