Calculate the difference in Gibbs free energy in kilojoules per mole between the alternative chair conformations of: (a) trans-4-Methylcyclohexanol (b) cis-Methylcyclohexanol (c) trans-1,4-Dicyanocyclohexane

Draw the chair conformations of trans-4-Methylcyclohexanol and cis-4-Methylcyclohexanol, remembering that the "cis" and "trans" designations refer to the relative positions of the methyl group and alcohol group in the cyclic structure.

Determine the most stable conformation of each molecule by evaluating the positions of the methyl group and alcohol group in the chair. Generally, larger groups (like a methyl group) prefer the equatorial position to minimize steric strain. The axial position increases 1,3-diaxial interactions which are destabilizing. For both molecules, identify which of the chair conformations has the least steric strain and destabilizing interactions.

A-values are used to quantify the energetic preference of groups to occupy an axial or equatorial position. The A-value is positive when the group prefers to occupy the equatorial position, and negative when it prefers the axial position. A general rule of thumb is that larger groups have larger A-values, so a methyl group has a larger A-value than an alcohol group. For trans-4-Methylcyclohexanol (a): Calculate the Gibbs free energy difference (ΔG) between the two chair conformations using the A-values of the methyl group (1.74 kJ/mol) and the alcohol group (0.9 kJ/mol). ΔG = A_value(methyl) + A_value(alcohol) ΔG = 1.74 kJ/mol + 0.9 kJ/mol ΔG = 2.64 kJ/mol For cis-4-Methylcyclohexanol (b): Calculate the Gibbs free energy difference (ΔG) the same way as for the trans derivative: ΔG = -A_value(methyl) + A_value(alcohol) ΔG = -1.74 kJ/mol + 0.9 kJ/mol ΔG = -0.84 kJ/mol For both molecules, the calculated Gibbs free energy differences are as follows: a) trans-4-Methylcyclohexanol: ΔG = 2.64 kJ/mol b) cis-4-Methylcyclohexanol: ΔG = -0.84 kJ/mol