Final answer:
The most stable conformation of trans-1-tert-butyl-2-methylcyclohexane is one where both the tert-butyl and methyl groups are in equatorial positions to minimize steric repulsion, thus stabilizing the molecule.
Step-by-step explanation:
The most stable conformation of trans-1-tert-butyl-2-methylcyclohexane is the one in which the bulky substituents, tert-butyl and methyl groups, are in the more spacious equatorial positions. This conformation reduces steric interactions, particularly the 1,3-diaxial interactions that would otherwise occur if the bulky groups were in the axial positions. Since the molecule is trans, the substituents are on opposite sides of the cyclohexane ring, therefore, the most stable conformation would have the tert-butyl group equatorial on one face of the ring and the methyl group equatorial on the opposite face.
These orientations minimize steric repulsion between the bulky groups and the hydrogens on the cyclohexane ring, thus following similar principles to those observed in conformations of butane and monosubstituted cyclohexanes. Cyclohexane chair conformations, as well as cis-trans isomerism in cycloalkanes, influences the stability of the molecule depending on the spatial arrangement of the substituents.