Ch. 5 - Alkenes: Structure, Nomenclature, and an Introduction to Reactivity • Thermodynamics and Kinetics

Bruice8th EditionOrganic ChemistryISBN: 9780135213711Not the one you use?Change textbook

Bruice 8th Edition

Ch. 5 - Alkenes: Structure, Nomenclature, and an Introduction to Reactivity • Thermodynamics and Kinetics

Problem 19

Chapter 6, Problem 19

The ∆G° for conversion of “axial” fluorocyclohexane to “equatorial” fluorocyclohexane at 25 °C is -0.25kcal/mol. Calculate the percentage of fluorocyclohexane molecules that have the fluoro substituent in an equatorial position at equilibrium.

Verified step by step guidance

Step 1: Understand the relationship between Gibbs free energy (∆G°) and the equilibrium constant (K). The equation to use is ∆G° = -RT ln(K), where R is the gas constant (1.987 cal/(mol·K)) and T is the temperature in Kelvin (25 °C = 298 K).

Step 2: Rearrange the equation to solve for K, the equilibrium constant. This gives K = e^(-∆G° / RT). Substitute the given values for ∆G° (-0.25 kcal/mol, converted to -250 cal/mol), R (1.987 cal/(mol·K)), and T (298 K) into the equation.

Step 3: Once K is calculated, recognize that K represents the ratio of the concentrations of the equatorial form to the axial form at equilibrium. Specifically, K = [equatorial]/[axial].

Step 4: Use the relationship between K and the percentage of molecules in the equatorial position. The percentage of equatorial molecules can be calculated as: % equatorial = (K / (1 + K)) × 100.

Step 5: Substitute the value of K obtained in Step 2 into the percentage formula to determine the percentage of fluorocyclohexane molecules with the fluoro substituent in the equatorial position.

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Key Concepts

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

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ∆G indicates that a reaction is spontaneous, while a positive ∆G suggests non-spontaneity. In this context, the negative value of -0.25 kcal/mol implies that the conversion from axial to equatorial fluorocyclohexane is favored, leading to a higher proportion of equatorial molecules at equilibrium.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. It is related to the Gibbs Free Energy change by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. By calculating K from the given ∆G°, we can determine the ratio of equatorial to axial fluorocyclohexane, which helps in finding the percentage of equatorial molecules.

Percentage Calculation at Equilibrium

To find the percentage of molecules in a specific conformation at equilibrium, we use the equilibrium constant (K) derived from the Gibbs Free Energy. The formula K = [equatorial]/[axial] allows us to express the fraction of equatorial molecules as [equatorial] / ([equatorial] + [axial]). By converting this fraction into a percentage, we can determine how many of the fluorocyclohexane molecules are in the equatorial position at equilibrium.

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Related Practice

Textbook Question

Calculate the percentage of isopropylcyclohexane molecules that have the isopropyl substituent in an equatorial position at equilibrium. (Its ∆G° value at 25 °C is -2.1 kcal/mol.)

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Textbook Question

For each of the reactions in Problem 15, indicate which reactant is the nucleophile and which is the electrophile.

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Textbook Question

Calculate ∆G° for the conversion of “axial” methylcyclohexane to “equatorial” methylcyclohexane at 25 °C.

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Textbook Question

Why is the percentage of molecules with the substituent in an equatorial position greater for isopropylcyclohexane than for fluorocyclohexane?

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Textbook Question

a. For which reaction in each set will ∆S° be more significant?

b. For which reaction will ∆S° be positive?

1. A ⇌ B or A + B ⇌ C

2. A ⇌ B + C or A + B ⇌ C + D

Textbook Question

Use curved arrows to show the movement of electrons in the following reaction steps

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