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. %-
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8fbab86-0ccb-4a47-9a90-4171489497c4%2Ff5687fca-683e-4e47-9657-002a7c52e322%2Fyz8snsk_processed.jpeg&w=3840&q=75)
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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