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 18b

Chapter 6, Problem 18b

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

Verified step by step guidance

Step 1: Understand the problem. The question asks to calculate the Gibbs free energy change (∆G°) for the conversion of axial methylcyclohexane to equatorial methylcyclohexane at 25 °C. This involves using the relationship between ∆G°, equilibrium constant (K), and temperature.

Step 2: Recall the formula for Gibbs free energy change:

∆G° = -RT ln(K)

, where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and K is the equilibrium constant for the reaction.

Step 3: Convert the temperature from Celsius to Kelvin. Since the temperature is given as 25 °C, use the formula

T(K) = T(°C) + 273.15

to find the temperature in Kelvin.

Step 4: Determine the equilibrium constant (K). The equilibrium constant can be derived from the energy difference between the axial and equatorial conformations. Typically, the equatorial conformation is more stable due to reduced steric hindrance, and the energy difference is often provided or can be looked up in reference materials.

Step 5: Substitute the values of R, T, and K into the formula

∆G° = -RT ln(K)

to calculate the Gibbs free energy change. Ensure the units are consistent (e.g., R in J/mol·K, T in Kelvin, and K as a dimensionless quantity).

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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. It indicates the spontaneity of a reaction; a negative ∆G° suggests that the reaction is spontaneous, while a positive value indicates non-spontaneity. In the context of conformational changes, it helps predict the stability of different molecular conformations.

Conformational Analysis

Conformational analysis is the study of the different spatial arrangements of atoms in a molecule that can be interconverted by rotation around single bonds. In cyclohexane derivatives, such as methylcyclohexane, the axial and equatorial positions significantly influence the molecule's stability due to steric interactions. Understanding these conformations is crucial for predicting the energy changes associated with their interconversion.

Temperature and Reaction Conditions

Temperature plays a vital role in determining the Gibbs Free Energy and the equilibrium between different molecular conformations. At 25 °C, the standard conditions for thermodynamic calculations, the energy difference between axial and equatorial conformations can be quantitatively assessed. This temperature is often used as a reference point for calculating thermodynamic properties, making it essential for accurate predictions in organic chemistry.

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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

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

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.

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Textbook Question

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

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Textbook Question

Identify the nucleophile and the electrophile in the following acid–base reactions:

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