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a) Calculate the difference in the Gibbs free energy between the second and first conformation including the algebraic sign. kJ/mol b) Given your value in (a), calculate the percent of the chair, indicated as B, presented in an equilibrium mixture of the conformers at 25°C. %-

a) Calculate the difference in the Gibbs free energy between the second and first conformation including the algebraic sign. kJ/mol b) Given your value in (a), calculate the percent of the chair, indicated as B, presented in an equilibrium mixture of the conformers at 25°C. %-

Organic Chemistry
Organic Chemistry
8th Edition
ISBN:9781305580350
Author:William H. Brown, Brent L. Iverson, Eric Anslyn, Christopher S. Foote
Publisher:William H. Brown, Brent L. Iverson, Eric Anslyn, Christopher S. Foote
Chapter2: Alkanes And Cycloalkanes
Section: Chapter Questions
Problem 2.45P: Gibbs free energy differences between axial-substituted and equatorial-substituted chair...
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### Chair Conformations of trans-1-bromo-2-methylcyclohexane The image depicts the alternative chair conformations for trans-1-bromo-2-methylcyclohexane, labeled as Conformation A and Conformation B. #### Given Data: Using the data for the change in Gibbs free energy (ΔG°) for monosubstituted cyclohexanes at room temperature (25°C) and the representative value* for the gauche interaction of two equatorially positioned substituents in the 1,2-position: #### Table of ΔG° Values: | Group | ΔG° (kJ/mol) Axial → Equatorial | Group | ΔG° (kJ/mol) Axial → Equatorial | |-------|---------------------------------|-------|---------------------------------| | C≡N | -0.8 | NH₂ | -5.9 | | Br | -2.4 | CH₃ | -7.3 | | OH | -3.9 | 1,2-gauche | 3.8 | 1. **Calculate the difference in the Gibbs free energy (ΔG) between the second and first conformation including the algebraic sign.** \[ \boxed{ \text{kJ/mol} } \] 2. **Given your value in (1), calculate the percent of the chair conformation, indicated as B, in an equilibrium mixture of the conformers at 25°C.** \[ \boxed{ \% } \] #### Notes: * The actual value will depend on the substituents. * The values of the gas constant (R) and the temperature (T) for 25°C are 8.314 JK⁻¹mol⁻¹ and 298 K respectively. ### Explanation of the Diagram: 1. **Structural Representations:** - **Conformation A:** Displays the bromine atom in the axial position and the methyl group in the equatorial position. - **Conformation B:** Depicts the bromine atom in the equatorial position and the methyl group in the axial position. - An arrow is shown indicating the interchange between these two chair conformations. 2. **Calculations:** - The calculations of ΔG° are based on the provided data in the table for different substituents. - The equilibrium mixture percentage calculation will use
Transcribed Image Text:### Chair Conformations of trans-1-bromo-2-methylcyclohexane The image depicts the alternative chair conformations for trans-1-bromo-2-methylcyclohexane, labeled as Conformation A and Conformation B. #### Given Data: Using the data for the change in Gibbs free energy (ΔG°) for monosubstituted cyclohexanes at room temperature (25°C) and the representative value* for the gauche interaction of two equatorially positioned substituents in the 1,2-position: #### Table of ΔG° Values: | Group | ΔG° (kJ/mol) Axial → Equatorial | Group | ΔG° (kJ/mol) Axial → Equatorial | |-------|---------------------------------|-------|---------------------------------| | C≡N | -0.8 | NH₂ | -5.9 | | Br | -2.4 | CH₃ | -7.3 | | OH | -3.9 | 1,2-gauche | 3.8 | 1. **Calculate the difference in the Gibbs free energy (ΔG) between the second and first conformation including the algebraic sign.** \[ \boxed{ \text{kJ/mol} } \] 2. **Given your value in (1), calculate the percent of the chair conformation, indicated as B, in an equilibrium mixture of the conformers at 25°C.** \[ \boxed{ \% } \] #### Notes: * The actual value will depend on the substituents. * The values of the gas constant (R) and the temperature (T) for 25°C are 8.314 JK⁻¹mol⁻¹ and 298 K respectively. ### Explanation of the Diagram: 1. **Structural Representations:** - **Conformation A:** Displays the bromine atom in the axial position and the methyl group in the equatorial position. - **Conformation B:** Depicts the bromine atom in the equatorial position and the methyl group in the axial position. - An arrow is shown indicating the interchange between these two chair conformations. 2. **Calculations:** - The calculations of ΔG° are based on the provided data in the table for different substituents. - The equilibrium mixture percentage calculation will use
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