Question

Determine if each of the following complexes exhibits geometric isomerism. If geometric isomers exist, determine how many there are. (a) tetrahedral \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right],(\mathbf{b})\) square-planar \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-},(\mathbf{c})\) octahedral \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}.\)

Short answer

a) Tetrahedral complex \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right]\) does not exhibit geometric isomerism. b) Square-planar complex \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-}\) exhibits geometric isomerism with 2 isomers: cis and trans. c) Octahedral complex \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}\) exhibits geometric isomerism with 2 isomers: cis and trans.

Step-by-step solution

Analyze the geometry and ligands of each complex

For each complex, determine the geometry, the central atom and its ligands, and check if there are two or more different types of ligands in the complex. a) \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right]\) has a tetrahedral geometry with the central atom Cd and ligands \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{Cl}\). b) \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-}\) has a square-planar geometry with the central atom Ir and ligands \(\mathrm{Cl}\) and \(\mathrm{PH}_3\). c) \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}\) has an octahedral geometry with the central atom Fe and ligands \(o-\mathrm{phen}\) and \(\mathrm{Cl}\).

Determine if geometric isomerism is possible

To determine if geometric isomerism is possible, analyze if there are two or more different types of ligands in the complex. a) \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right]\) - Geometric isomerism is not possible as tetrahedral complexes do not exhibit geometric isomerism. b) \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-}\) - Geometric isomerism is possible in square-planar complexes with two different types of ligands. c) \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}\) - Geometric isomerism is possible in octahedral complexes with two different types of ligands.

Determine the number of geometric isomers in complexes showing isomerism

For each complex showing geometric isomerism, determine the number of geometric isomers. b) \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-}\) - There are two geometric isomers: cis and trans. c) \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}\) - There are two geometric isomers: cis and trans. #Final answer# a) Tetrahedral complex \(\left[\operatorname{Cd}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right]\) does not exhibit geometric isomerism. b) Square-planar complex \(\left[\operatorname{IrCl}_{2}\left(\mathrm{PH}_{3}\right)_{2}\right]^{-}\) exhibits geometric isomerism with 2 isomers: cis and trans. c) Octahedral complex \(\left[\mathrm{Fe}(o-\mathrm{phen})_{2} \mathrm{Cl}_{2}\right]^{+}\) exhibits geometric isomerism with 2 isomers: cis and trans.

Key concepts

Tetrahedral Complexes

Tetrahedral complexes consist of a central metal atom bonded to four ligands arranged at the corners of a tetrahedron. This geometry is characterized by having bond angles of approximately 109.5°, which provide a symmetric environment ideal for equal access to electron donors.
In a tetrahedral complex like \( \text{[Cd(H}_2\text{O})_2\text{Cl}_2] \), the central atom cadmium (Cd) is surrounded by two water molecules and two chloride ions. The identical spatial distance and angles among the ligands make it impossible for tetrahedral complexes to form geometric isomers. Geometric isomerism relies on the spatial arrangement of different groups around a central point. However, the symmetrical nature of a tetrahedron with only four ligands ensures no such differentiation can occur.
This is why for tetrahedral complexes, understanding their symmetry is key; if all positions look the same spatially, geometric isomerism doesn’t occur. Keep this in mind when analyzing other tetrahedral complexes.

Square-Planar Complexes

Square-planar complexes are another fascinating geometry type found primarily in certain transition metal complexes. In this shape, the central metal is bonded to four ligands, similar to the four points or corners of a square lying on a single plane.
Let's consider the square-planar complex \( \text{[IrCl}_2(\text{PH}_3)_2]^- \). The central atom here is iridium (Ir), surrounded by two chloride ions and two phosphine groups. The unique aspect of square-planar complexes is that they can exhibit geometric isomerism when two different types of ligands are present.
In this structure, because of the planar arrangement, the two chloride ions can either be adjacent to each other (cis isomer) or opposite each other (trans isomer). These different spatial arrangements result in distinct physical and chemical properties even though the chemical formula remains the same. Hence, square-planar complexes are excellent demonstrations of geometric isomerism, where arrangements in a plane create both cis and trans isomers.

Octahedral Complexes

Octahedral complexes present a geometric configuration where a central metal atom is surrounded by six ligands at the vertices of an octahedron. This is perhaps the most common geometry in coordination chemistry, accommodating a high coordination number.
Consider the octahedral complex \( \text{[Fe}(o\text{-phen})_2 \text{Cl}_2]^+ \), in which the central iron (Fe) atom is bonded to two chloride ions and two 1,10-phenanthroline (o-phen) ligands. Octahedral complexes with different types of ligands can exhibit geometric isomerism, similarly to square-planar complexes. However, the possibilities increase due to the higher number of ligands involved.
For instance, in this complex, when both chloride ions can occupy adjacent positions on the same face of the octahedron, it forms a cis isomer. Conversely, if they are placed opposite each other, a trans isomer emerges. Understanding geometric isomers in octahedral complexes is crucial because it influences their reactivity and interaction with other molecules in their environments, which has vast implications in fields such as medicinal chemistry and material sciences.