
Josh G. answered 03/29/19
PhD in Chemistry, specializing in organic chemistry
Staggered will still be a better confirmation eclipsed due to the steric effects. A better question is in the staggered form, how does the gauche interaction compare to the anti? In the case of ethylene glycol the gauche interaction is more stable due to the hydrogen bonding being stronger than the steric repulsion. The eclipsed form would still be too energetically unstable even with the hydrogen bonding.
In the second case of a 1,3-diaxial interaction: a single hydroxy group would still have steric effects. 2 hydroxides in a 1,3 diaxial position would be more favorable only in a nonpolar solvent. In more polar solvents there is competition for hydrogen bonding interactions, which means sterics wins over H bonding.