Are the following structures chiral as drawn? When placed in solution at 298 K, which structures ...

The above structures are chiral as drawn if the chair conformation shown has no plane or center of symmetry.
Therefore, structures (a), (b), (d), and (f) are chiral. Structure (c) has a plane of symmetry, and structure (e)
has a center of symmetry. To show optical rotation when placed in solution, the molecule must retain chirality
even when considering both of the equilibrating chair structures. The easiest way to identify the chiral
molecules is to examine the planar representations as shown below.

Analyzing the planar structures reveals that compounds (b), (c), (e), and (f) all have planes of symmetry and
are therefore not chiral. Only compounds (a) and (d) are chiral, so only (a) and (d) will show optical rotation.