Ch. 3 - An Introduction to Organic Compounds:Nomenclature, Physical Properties, and Structure

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

Bruice 8th Edition

Ch. 3 - An Introduction to Organic Compounds:Nomenclature, Physical Properties, and Structure

Problem 88

Chapter 4, Problem 88

Using the data obtained in Problem 81, calculate the percentage of molecules of trans-1,2-dimethylcyclohexane that will have both methyl groups in equatorial positions.

Verified step by step guidance

Step 1: Understand the conformational analysis of trans-1,2-dimethylcyclohexane. In this molecule, the trans configuration means that one methyl group is positioned above the plane of the cyclohexane ring and the other is below the plane. The equatorial positions are generally more stable due to reduced steric hindrance compared to axial positions.

Step 2: Recall that cyclohexane adopts a chair conformation, and each carbon atom alternates between axial and equatorial positions. For trans-1,2-dimethylcyclohexane, both methyl groups can occupy equatorial positions in one of the chair conformations.

Step 3: Use the data from Problem 81 to determine the relative stability of the chair conformations. The stability is influenced by the steric interactions of the substituents. Typically, the conformation with both methyl groups in equatorial positions is more stable.

Step 4: Apply the Boltzmann distribution formula to calculate the percentage of molecules in the more stable conformation. The formula is:

P_{equatorial} = \frac{1}{/}

, where ΔG is the free energy difference between the conformations, R is the gas constant, and T is the temperature in Kelvin.

Step 5: Substitute the values for ΔG, R, and T into the Boltzmann distribution formula to calculate the percentage of molecules with both methyl groups in equatorial positions. Ensure the units are consistent when performing the calculation.

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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 that minimizes steric strain. In this conformation, substituents can occupy either equatorial or axial positions. Equatorial positions are generally more stable for larger groups, as they reduce steric hindrance with other axial substituents.

Stability of Substituted Cyclohexanes

The stability of substituted cyclohexanes is influenced by the positioning of substituents. For 1,2-dimethylcyclohexane, the most stable configuration occurs when both methyl groups are in equatorial positions, as this arrangement minimizes steric interactions and torsional strain.

Equilibrium Between Chair Conformations

Substituted cyclohexanes can interconvert between different chair conformations. The percentage of molecules in each conformation can be calculated using the Gibbs free energy difference between the conformations, which affects the distribution of equatorial versus axial substituents in a dynamic equilibrium.

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Related Practice

Textbook Question

Name the following compounds:

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Textbook Question

Name the following compounds:

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Textbook Question

Bromine is a larger atom than chlorine, but the equilibrium constants in Table 3.9 indicate that a chloro substituent has a greater preference for the equatorial position than does a bromo substituent. Suggest an explanation for this fact.

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Textbook Question

Using the data obtained in Problem 85, calculate the amount of steric strain in each of the chair conformers of 1,1,3-trimethylcyclohexane. Which conformer predominates at equilibrium?

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Textbook Question

Draw the conformers for the following trisubstituted cyclohexane. Calculate the strain energy of each conformer. (The gauche interaction between a methyl and an ethyl group is 0.96 kcal/mol; the 1,3-diaxial interaction between a methyl and an H is 0.87 kcal/mol and between an ethyl and an H is 1.00 kcal/mol.)

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