Question

Draw geometrical isomers of each of the following complex ions. a. \(\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{-}\) c. \(\left[\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) b. \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{I}_{2}\right]^{2+}\) d. \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}\right]^{+}\)

Short answer

The geometrical isomers for each complex ion are as follows: a. \(\left[\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{-}\): Only one isomer is possible with both water molecules in cis positions. b. \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{I}_{2}\right]^{2+}\): Two isomers (cis and trans) with ammonia molecules forming different arrangements with respect to the iodide ions. c. \(\left[\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{3}\mathrm{Cl}_{3}\right]\): Two isomers (cis and trans) with ammonia molecules forming different arrangements with respect to the chloride ions. d. \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{I}_{2}\right]^{+}\): Two isomers (cis and trans) with ammonia molecules forming different arrangements with respect to the ethylenediamine ligands.

Step-by-step solution

Determine the coordination geometry

For each complex ion, we should first determine the coordination geometry of the metal ion, this will be based on the coordination number, which is the number of ligands bonded to the metal ion. a. In \(\left[\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{-}\), the coordination number of Co is 6 (2 oxalate ions and 2 water molecules). This means the geometry is octahedral. b. In \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{I}_{2}\right]^{2+}\), the coordination number of Pt is also 6 (4 ammonia molecules and 2 iodide ions). The geometry is also octahedral. c. In \(\left[\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{3}\mathrm{Cl}_{3}\right]\), the coordination number of Ir is 6 (3 ammonia molecules and 3 chloride ions). The geometry is octahedral. d. In \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{I}_{2}\right]^{+}\), the coordination number of Cr is 6 (2 ethylenediamine ligands, which are bidentate, 2 ammonia molecules and 2 iodide ions). The geometry is also octahedral.

Identify the ligand positions

In octahedral complexes, we can have two types of geometrical isomers: trans and cis. Cis: The ligands are adjacent to each other. Trans: The ligands are opposite to each other.

Draw geometrical isomers for each complex ion

For each complex ion, we will draw the trans and cis geometrical isomers of the ligands. a. For \(\left[\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{-}\), only 1 isomer is possible where both water molecules are adjacent and in cis positions. b. For \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{I}_{2}\right]^{2+}\), we have 2 geometrical isomers: - Cis: 2 ammonia molecules are adjacent to one iodide ion, making it cis. Remaining two ammonia molecules form a cis pair on the opposite side of the iodide ions. - Trans: All ammonia molecules form pairs on opposite sides of the iodides, making it trans. c. For \(\left[\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{3}\mathrm{Cl}_{3}\right]\), we have 2 geometrical isomers: - Cis: two ammonia molecules adjacent to one chloride ion, making it cis. Remaining ammonia molecule forms a cis pair on an opposite side of chloride ions. - Trans: All ammonia molecules form pairs on opposite sides of the chloride ions, making it trans. d. For \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{I}_{2}\right]^{+}\), we have 2 geometrical isomers: - Cis: both ammonia molecules are adjacent to the same ethylenediamine ligand, making it cis. - Trans: ammonia molecules are opposite and adjacent to different ethylenediamine ligands, making it trans. In conclusion, we have drawn the geometrical isomers for each complex ion, identifying cis and trans isomers.

Key concepts

Coordination Geometry

Coordination geometry refers to the three-dimensional arrangement of ligands around a central metal ion in a coordination complex. It is determined by the coordination number, which is the number of ligand atoms bonded directly to the metal ion. Common geometries include:

• Octahedral: coordination number of 6
• Tetrahedral: coordination number of 4
• Square planar: coordination number of 4, but differs from tetrahedral in shape

In the given exercise, all the complex ions have a coordination number of 6, indicating that they all adopt an octahedral geometry. This means in each case, six ligand atoms arrange themselves in space, forming an octahedron around the central metal.

Octahedral Complexes

Octahedral complexes are a type of coordination complex where six ligands are symmetrically arranged around a metal ion. This structure looks like two pyramids base to base, forming an eight-sided figure called an octahedron.
Octahedral complexes are highly common in transition metal chemistry.
Characteristics of octahedral complexes include:

• High symmetry: The symmetrically placed ligands create a uniform electric field that affects the energy levels of the d-orbitals of the metal.
• Geometrical isomerism: Possible due to different spatial arrangements of the ligands around the metal center, such as cis and trans arrangements.

In the exercise provided, each complex, including those with varying ligands, exhibits the octahedral geometry, allowing for the examination of different isomeric forms.

Ligand Positions

Understanding ligand positions in octahedral complexes is crucial for analyzing their geometrical isomers, which can impact the properties and reactivity of the complex.
Ligand positions are often described as cis or trans, particularly when discussing octahedral complexes. - **Cis Arrangement:** - In a cis arrangement, similar or identical ligands occupy adjacent positions. This arrangement can create distinct physical and chemical properties due to the closer proximately of particular ligands. - **Trans Arrangement:** - In a trans arrangement, similar or identical ligands are located opposite each other across the central metal ion. This often stabilizes the complex by maximizing the distance between similar ligands. In the complexes from the exercise, drawing and understanding these arrangements help identify the possible isomers and provide insight into the potential variations in behavior or reactivity based on the arrangement of ligands.