The two alternative chair conformations of cis-1-bromo-2-methylcyclohexane differ in their Gibbs free energy. Using the data for 4G (Axial-Equatorial) for monosubstituted cyclohexanes at room temperature (25°C): Axial Equatorial Group AGo (kJ/mol) Group 46° (kJ/mol) C=N -0.8 NH2 CH3 5.9 22.4 -73 OH -3.9 L.2-gauche 3.8 Calculate the absolute value of the difference in the Gibbs free energy between the alternative chair conformations: kJ/mol. Which group in this compound is in the axial position in the energetically preferred chair conformation? Methyl. Submlt Answer Try Another Item attempts remaining amino
The Correct Answer and Explanation is:
Here are the correct answers and a detailed explanation.
Part a: The absolute value of the difference in the Gibbs free energy between the alternative chair conformations is 4.9 kJ/mol.
Part b: The Br group in this compound is in the axial position in the energetically preferred chair conformation.
Explanation
1. Understanding the Conformations of cis-1-bromo-2-methylcyclohexane
The compound is cis-1-bromo-2-methylcyclohexane. In a cyclohexane ring, a cis-1,2 relationship means that both substituents are on the same side of the ring. For this to occur in a chair conformation, one substituent must be in an axial position and the other in an equatorial position. The molecule exists as an equilibrium between two chair conformations that interconvert via a “ring flip”.
- Conformation A: The bromo (Br) group is axial and the methyl (CH₃) group is equatorial.
- Conformation B: After a ring flip, the bromo (Br) group becomes equatorial and the methyl (CH₃) group becomes axial.
2. Analyzing Steric Strain using A-values
The stability of a substituted cyclohexane conformation depends on the steric strain, primarily the 1,3-diaxial interactions experienced by axial substituents. The provided ΔG° values, often called A-values, quantify this strain. They represent the energy cost of having a group in the axial position versus the more stable equatorial position.
From the table:
- A-value for Br: The energy cost for an axial Br is 2.4 kJ/mol. (ΔG° for Axial → Equatorial is -2.4 kJ/mol, so the axial state is 2.4 kJ/mol higher in energy).
- A-value for CH₃: The energy cost for an axial CH₃ is 7.3 kJ/mol. (ΔG° for Axial → Equatorial is -7.3 kJ/mol, so the axial state is 7.3 kJ/mol higher in energy).
The 1,2-gauche interaction (3.8 kJ/mol) exists between the two substituents in both conformations (axial-equatorial is a gauche relationship), so it cancels out when we calculate the difference in energy between them.
3. Calculating the Energy of Each Conformation
We can estimate the relative energy of each conformation by summing the A-values for the axial substituents.
- Energy of Conformation A (axial Br, equatorial CH₃): The only axial substituent is Br.
- Strain = A-value (Br) = 2.4 kJ/mol
- Energy of Conformation B (equatorial Br, axial CH₃): The only axial substituent is CH₃.
- Strain = A-value (CH₃) = 7.3 kJ/mol
4. Solving Part a: Difference in Gibbs Free Energy
The difference in Gibbs free energy (ΔΔG°) between the two conformations is the difference in their total strain energies.
- ΔΔG° = Energy(Conformation B) – Energy(Conformation A)
- ΔΔG° = 7.3 kJ/mol – 2.4 kJ/mol = 4.9 kJ/mol
The absolute value of this difference is 4.9 kJ/mol.
5. Solving Part b: The Preferred Conformation
The energetically preferred (most stable) conformation is the one with the lowest Gibbs free energy (i.e., the least steric strain).
- Energy of Conformation A = 2.4 kJ/mol
- Energy of Conformation B = 7.3 kJ/mol
Since 2.4 kJ/mol < 7.3 kJ/mol, Conformation A is the preferred conformation. This follows the general principle that the larger, bulkier group (the one with the higher A-value, in this case, methyl) will preferentially occupy the less crowded equatorial position to minimize steric strain.
In the preferred conformation (Conformation A), the methyl group is equatorial, and the bromo (Br) group is in the axial position.
