Table of contents

1. A Review of General Chemistry5h 5m
2. Molecular Representations1h 14m
3. Acids and Bases2h 46m
4. Alkanes and Cycloalkanes4h 17m
5. Chirality3h 39m
6. Thermodynamics and Kinetics1h 22m
7. Substitution Reactions1h 48m
8. Elimination Reactions2h 30m
9. Alkenes and Alkynes2h 9m
10. Addition Reactions3h 19m
11. Radical Reactions1h 58m
12. Alcohols, Ethers, Epoxides and Thiols2h 42m
13. Alcohols and Carbonyl Compounds2h 17m
14. Synthetic Techniques1h 26m
15. Analytical Techniques:IR, NMR, Mass Spect7h 3m
16. Conjugated Systems6h 13m
17. Ultraviolet Spectroscopy51m
18. Aromaticity2h 34m
19. Reactions of Aromatics: EAS and Beyond5h 1m
20. Phenols55m
21. Aldehydes and Ketones: Nucleophilic Addition4h 56m
22. Carboxylic Acid Derivatives: NAS2h 51m
23. The Chemistry of Thioesters, Phophate Ester and Phosphate Anhydrides1h 10m
24. Enolate Chemistry: Reactions at the Alpha-Carbon1h 53m
25. Condensation Chemistry2h 9m
26. Amines1h 43m
27. Heterocycles2h 0m
28. Carbohydrates5h 53m
29. Amino Acids4h 20m
30. Peptides and Proteins2h 42m
31. Catalysis in Organic Reactions1h 30m
32. Lipids 2h 50m
33. The Organic Chemistry of Metabolic Pathways2h 52m
34. Nucleic Acids1h 32m
35. Transition Metals6h 14m
36. Synthetic Polymers1h 49m

4. Alkanes and Cycloalkanes

A-Values

Organic Chemistry

4. Alkanes and Cycloalkanes

A-Values

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3:19 minutes

Problem 50b

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 K_eq for the chair–chair interconversions shown.
(b)

Verified step by step guidance

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 given by:

∆G ° = - R T ln K_eq

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

Step 3: Use the provided table of A values to find the ∆G° for the substituent in question. The A value directly corresponds to the ∆G° for the equatorial-to-axial transition.

Step 4: Rearrange the equation to solve for K_eq:

K_eq = e^{- ∆G ° / R T}

. Substitute the values for ∆G°, R, and T into the equation to calculate K_eq.

Step 5: Interpret the results. If K_eq > 1, the equatorial position is strongly favored. If K_eq < 1, the axial position is favored. Use the calculated values to understand the preference of the substituent in the chair–chair interconversion.

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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

The chair conformation is the most stable arrangement of cyclohexane, minimizing steric strain and torsional strain. In this conformation, carbon atoms adopt a staggered arrangement, allowing substituents to occupy either equatorial or axial positions. Equatorial substituents are generally more stable due to reduced steric hindrance with adjacent hydrogen atoms, making understanding this conformation crucial for analyzing substituent effects.

A Values and Free Energy Change (∆G°)

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 energy and greater stability. Understanding A values is essential for calculating the equilibrium constant (K_eq) for chair-chair interconversions, as they directly influence the stability of different conformations.

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. This concept is vital for understanding the relative stability of different conformations and predicting the favored position of substituents in cyclohexane.

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Open Question

Estimate the equilibrium composition of the chair conformers of the following cyclohexanes at room temp:

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Estimate the equilibrium composition of the chair conformers of trans-1-methyl-3-phenylcyclohexane at room temperature.

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Textbook Question

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.

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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 K_eq for the chair–chair interconversions shown.

(c)

(d)

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

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

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