Figure \(21.17\) shows that the cis isomer of \(\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}^{+}\) is optically active while the trans isomer is not optically active. Is the same true for \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}^{+} ?\) Explain.

Chirality is a fundamental concept in chemistry that relates to the geometric property of a molecule being non-superposable on its mirror image. Think of your hands as an example; your left hand is a non-superposable mirror image of your right hand — this is a common analogy to explain chirality. In the context of coordination compounds, chirality occurs when the arrangement of ligands around the central metal cannot be superimposed on its mirror image, thus creating two distinct entities known as enantiomers.

Enantiomers have identical physical properties except for the way they interact with plane-polarized light, causing the rotation in opposite directions. This is the basis for optical activity in molecules. It's crucial to understand that a molecule's structure will determine its chirality and subsequently, whether it can exhibit optical activity.

Coordination chemistry is the study of compounds formed between metal ions and ligands, where ligands are molecules or ions that can donate electrons to the metal. These compounds, called coordination compounds or complexes, feature a central metal atom or ion surrounded by ligands. Coordination compounds play critical roles in various biological systems, catalysis, and material science.

The geometry of these complexes, which includes shapes like octahedral, tetrahedral, and square planar, results from the coordination number, the number of ligand bonds to the metal ion. The specific arrangement of ligands around a central metal ion can vastly influence the properties of the coordination compound, including their color, magnetic properties, and reactivity.

Geometric isomers are two or more coordination compounds that contain the same sequence of bonded atoms but differ in the three-dimensional orientations of the atoms around the central metal ion. In coordination chemistry, this phenomenon is most commonly discussed in terms of cis and trans isomers in octahedral and square planar complexes.

The cis isomer has two identical ligands adjacent to each other, while the trans isomer has them positioned opposite each other. This difference can affect the chemical and physical properties, including the dipole moment, solubility, and stability of the isomers. Understanding the differences between geometric isomers is essential to predicting and explaining the behavior of coordination compounds.