Question

Calculate the difference in Gibbs free energy in kilojoules per mole between the alternative chair conformations of: (a) trans-4-Methylcyclohexanol (b) cis-4-Methylcyclohexanol

Short answer

Answer: The differences in Gibbs free energy are: (a) trans-4-Methylcyclohexanol: 1.74 kJ/mol (b) cis-4-Methylcyclohexanol: 1.74 kJ/mol (c) trans-1,4-Dicyanocyclohexane: 5.24 kJ/mol

Step-by-step solution

Draw the structure and identify chair conformations

First, draw the structure of trans-4-Methylcyclohexanol. Next, draw the two possible chair conformations, with the trans relationship and the 4-methyl substituent in both the axial and equatorial positions.

Calculate energy difference using A value theory

According to A value theory, a substituent prefers to be in the equatorial position as it is more stable. The A value for a methyl group is 1.74 kJ/mol and the A value for a hydroxyl group is 0 kJ/mol (since it's smaller in size). In one conformer 4-methyl is in axial and in the other one it's in the equatorial position. Therefore, the energy difference between the two conformers is equal to the A value of the methyl group: 1.74 kJ/mol. (b) cis-4-Methylcyclohexanol

Draw the structure and identify chair conformations

First, draw the structure of cis-4-Methylcyclohexanol. Next, draw the two possible chair conformations, with the cis relationship and the 4-methyl substituent in both the axial and equatorial positions.

Calculate energy difference using A value theory

In this case, both the hydroxyl group and the methyl group are cis to each other. In one conformer both groups are in axial position and in other both are in the equatorial position. The energy difference between the two conformers is equal to the sum of the A values of the hydroxyl group (0 kJ/mol) and the methyl group (1.74 kJ/mol), so the total energy difference is 1.74 kJ/mol. (c) trans-1,4-Dicyanocyclohexane

Draw the structure and identify chair conformations

First, draw the structure of trans-1,4-Dicyanocyclohexane. Next, draw the two possible chair conformations, with the trans relationship and the cyanide substituents in both the axial and equatorial positions.

Calculate energy difference using A value theory

In this case of trans-1,4-dicyanocyclohexane the A value for a cyanide group is 2.62 kJ/mol. In one conformer both cyanide groups are in axial positions and in the other both are in equatorial positions. The energy difference between the two conformers is equal to the sum of the A values of the two cyanide groups (2 * 2.62 kJ/mol), so the total energy difference is 5.24 kJ/mol. So, the differences in Gibbs free energy are: (a) 1.74 kJ/mol (b) 1.74 kJ/mol (c) 5.24 kJ/mol