Final answer:
The most stable chair conformation for 1,4-diethylcyclohexane is the one in which both ethyl groups are in the equatorial positions, known as 'Equatorial-1,4-diethylcyclohexane'.
Step-by-step explanation:
To identify the most stable chair conformation of the most stable isomer of 1,4-diethylcyclohexane, we must consider the steric strain involved in different substituent positions on the cyclohexane ring. Due to 1,3-diaxial interactions that create steric repulsion between axial substituents and adjacent hydrogen atoms, groups that are larger than hydrogen prefer to adopt the equatorial position to minimize this strain. Therefore, for each ethyl group in 1,4-diethylcyclohexane, an equatorial position is preferred over an axial one. The boat and twist conformations are higher in energy and less stable than the chair conformation, due to increased repulsive interactions between the hydrogen atoms and/or the lack of complete staggering of bonds.
Given the options, 'Equatorial-1,4-diethylcyclohexane' is the most stable chair conformation. In this conformation, both ethyl groups are positioned equatorially, eliminating the destabilizing 1,3-diaxial interactions that would be present if the ethyl groups were in the axial positions.