Determining if an isomer is optically active

Question

Determine if either isomer of [Fe(CO)_3 Cl_3] is optically active.

Answer 1

This is a tough one to do on a text only forum like this. The short answer is no, neither structural isomer is optically active.  To prove it, we have to remember that if any plane of symmetry can be drawn through the molecule, it is achiral and thus not optically active.

The complex is octahedral, with the Fe in the center. Picture a 3D cartesian coordinate system, with Fe at the origin. For the first isomer, place Cls on the +x, +y, and -x positions. A CO can be placed on the -y position, and on the z and -z positions. The xy plane contains one plane of symmetry, with z and -z reflections of one another (the yz plane is the other plane of symmetry).

For the other isomer, place Cls on the x,y,and z positions, and CO on the -x,-y,and -z positions. One plane of symmetry is the one that contains z, -z, and the origin, and bisects the xy plane at 45 degrees. In other words, the plane of symmetry is that plane that is perpendicular to the xy plane and contains the line y=x. There are two other planes of symmetry, all perpendicular to this first one. Thus, both isomers are achiral.