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 81

Chapter 4, Problem 81

Calculate the energy difference between the two chair conformers of trans-1,2-dimethylcyclohexane.

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Understand the problem: The energy difference between the two chair conformers of trans-1,2-dimethylcyclohexane arises due to steric interactions and 1,3-diaxial interactions. In cyclohexane chair conformations, substituents can occupy axial or equatorial positions, and the energy depends on these positions.

Draw the two chair conformers of trans-1,2-dimethylcyclohexane: In the trans configuration, one methyl group will be axial while the other will be equatorial in one conformer, and vice versa in the other conformer.

Identify steric interactions: In the conformer where a methyl group is axial, it will experience 1,3-diaxial interactions with the axial hydrogens on the same side of the ring. These interactions contribute to the energy difference between the conformers.

Use energy values for 1,3-diaxial interactions: The energy penalty for a methyl group in the axial position is typically around 1.8 kcal/mol. Calculate the total energy for each conformer based on the positions of the methyl groups.

Compare the energies of the two conformers: The conformer with both methyl groups in equatorial positions will have lower energy due to reduced steric interactions. The energy difference between the two conformers is the result of the axial methyl group's 1,3-diaxial interactions.

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Key Concepts

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

Chair Conformation

Chair conformation is the most stable arrangement of cyclohexane rings, minimizing steric strain and torsional strain. In this conformation, the carbon atoms are arranged in a staggered manner, allowing for optimal bond angles and minimizing interactions between substituents. Understanding chair conformations is crucial for analyzing the stability of substituted cyclohexanes.

Steric Strain

Steric strain arises when atoms are forced closer together than their atomic radii allow, leading to increased energy and instability. In the context of cyclohexane derivatives, bulky substituents can create steric hindrance, affecting the stability of different conformers. Evaluating steric strain is essential for predicting the preferred conformer of a molecule.

Energy Difference Calculation

Calculating the energy difference between conformers involves comparing their relative stabilities, often expressed in kilojoules per mole. This calculation typically considers factors such as steric interactions and torsional strain. Understanding how to quantify these energy differences is key to predicting which conformer is more favorable in a given molecular structure.