Which one of the following can show optical isomerism? (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{Cr}\left[\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) (c) \(\mathrm{FeSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\)

Coordination compounds are molecules that typically consist of a central metal atom or ion bonded to one or more ligands, which are ions or molecules that donate electrons to the metal. These ligands are held by coordinate covalent bonds, forming a coordination complex. In chemistry, such complexes play a critical role in the color, reactivity, and magnetic properties of a substance, among other character traits.

The geometry of coordination compounds is determined by the number and type of ligands that are coordinated to the central metal as well as the electronic configurations of the metal. For instance, some metals tend to form octahedral complexes with six ligands, while others prefer tetrahedral geometry with four ligands. The type of ligands determines how they bind to the metal and can lead to different isomeric forms, including the phenomena of optical isomerism, where two or more isomers of a compound differ only in the way atoms are oriented in space.

A chirality center, often referred to as a stereocenter, is a specific atom within a molecule that has four different groups attached to it, typically creating an asymmetry that is not superimposable on its mirror image. This is like comparing your left and right hands—they are mirror images but cannot be perfectly overlaid onto each other.

In the context of coordination compounds, chirality centers can arise from a metal ion when it coordinates with ligands in such a way that it forms a non-superimposable mirror image. The presence of chirality centers is a prerequisite for a compound to exhibit optical isomerism; it allows the compound to rotate plane-polarized light, which is a key characteristic of optically active substances. A compound with chirality centers can therefore exist in two isomeric forms, known as enantiomers, which have identical physical properties, except for the direction in which they rotate plane-polarized light.

Octahedral complex geometry is one of the most common shapes encountered in the field of coordination chemistry. This geometry involves a central metal ion surrounded by six ligands positioned at the corners of an octahedron. The ligands are equidistant from the metal ion, and the angles between any two bonds from the metal to its ligands are 90° or 180°.

The particular spatial arrangement of ligands in an octahedral complex can introduce the possibility of isomers, including optical isomers. For optical isomerism to occur in an octahedral compound, there must be a lack of symmetry that creates non-superimposable mirror images. If, however, the ligands are all identical and arranged symmetrically around the metal, the complex will not be chiral and therefore cannot exhibit optical isomerism. Bidentate ligands, which can attach to the metal at two points, substantially increase the likelihood of forming a chiral octahedral complex, as they can create a fixed spatial arrangement that is asymmetrical and conducive to chirality.