Question

Consider an octahedral complex \(\mathrm{MA}_{3} \mathrm{~B}_{3} .\) How many geometric isomers are expected for this compound? Will any of the isomers be optically active? If so, which ones?

Short answer

There are two geometric isomers for the octahedral complex MA3B3: facial (fac) and cissoid (cis) arrangements. However, neither of these isomers is optically active as the fac isomer has a plane of symmetry and the cis isomer has a center of symmetry.

Step-by-step solution

Understand octahedral complex and geometric isomers

An octahedral complex has six ligands arranged around a central metal atom in the shape of an octahedron. Geometric isomers are complexes with the same molecular formula but different spatial arrangements of ligands.

Determine the possible arrangements of ligands

The octahedral complex has six ligands with three A and three B ligands. These ligands can be arranged in the following ways: 1. All three A ligands can be on one side (facial arrangement, abbreviated as fac). 2. All three A ligands and all three B ligands can be at the alternating positions (cissoid arrangement, abbreviated as cis). Let's explore these possibilities in detail.

Find the number of geometric isomers

1. Facial arrangement (fac): In this case, all A ligands occupy three adjacent vertices of the octahedron, and all B ligands occupy the opposite vertices. There is only one possible way of arranging the A and B ligands in this manner. Hence, there is only one fac isomer. 2. Cissoid arrangement (cis): In this case, the different A and B ligands occupy alternate vertices of the octahedron. There is only one possible way of arranging the A and B ligands in this manner. Hence, there is only one cis isomer. Therefore, there are 2 geometric isomers for the octahedral complex MA3B3.

Determine optical activity of isomers

Optical activity is the ability of a compound to rotate plane-polarized light. A compound is optically active if it lacks a plane of symmetry or a center of symmetry. 1. Facial arrangement (fac): The fac isomer has a plane of symmetry passing through the central atom and the midpoints of the opposite edges. This means that the fac isomer is not optically active. 2. Cissoid arrangement (cis): The cis isomer has a center of symmetry at the central atom. This means that the cis isomer is also not optically active. After analyzing both isomers, neither of them are optically active. In conclusion, there are two geometric isomers for the octahedral complex MA3B3: facial (fac) and cissoid (cis). Neither of these isomers is optically active.

Key concepts

Geometric Isomers

Geometric isomers are fascinating aspects of octahedral complexes like \( \mathrm{MA}_{3} \mathrm{B}_{3} \). These isomers arise from different spatial arrangements of ligands around a central metal atom, but with the same connectivities. In simpler terms, you can imagine them as having the same chemical formula, but looking different in 3D space. This variation alters their properties and functions without changing their basic makeup.
In an octahedral complex, ligands are placed around a central metal in the shape of an octahedron. The ligands can be the same or different, and their arrangement can significantly change the properties of the complex. Geometric isomers are typically labeled as "fac" (facial) and "cis" (cissoid), depending on how the ligands are positioned relative to one another.

• "Facial" arrangement involves three identical ligands forming a triangle face of the octahedron.
• "Cissoid" arrangement involves different ligands alternating positions.

This octahedral complex \( \mathrm{MA}_{3} \mathrm{B}_{3} \) can exist in two geometric isomer forms, due simply to how its ligands are arranged.

Optical Activity

Optical activity is a property of a molecule that enables it to rotate plane-polarized light. This is an important feature in chemistry, as it helps in identifying the three-dimensional arrangement of atoms within a molecule. For a molecule to be optically active, it must lack a plane of symmetry or a center of symmetry.
In our octahedral complex \( \mathrm{MA}_{3} \mathrm{B}_{3} \), optical activity is determined by analyzing each geometric isomer for asymmetries:

• The facial (fac) isomer displays a plane of symmetry that disallows optical activity.
• The cis (cis) isomer has a center of symmetry, ultimately leading it to be optically inactive as well.

Both isomers of this complex do not have the required asymmetry to exhibit optical activity. Thus, despite their interesting geometric differences, neither can rotate plane-polarized light. This indicates how a molecule's symmetry plays a crucial role in its optical properties.

Ligand Arrangement

The arrangement of ligands in an octahedral complex influences its geometry and properties. In \( \mathrm{MA}_{3} \mathrm{B}_{3} \), there are three ligands of type A and three of type B. How these ligands align around the central metal atom determines the complex's specific isomer form.
Considering our complex:

• The facial (fac) arrangement results when three identical ligands form a face of the octahedron.
• The cissoid (cis) arrangement achieves a specific alternating pattern among the different ligands.

These distinct arrangements give rise to two different geometric isomer types, each having a unique spatial distribution. The arrangement not only determines the isomer type but also heavily influences the symmetry properties and thus the optical activity of the complex.
Understanding these arrangements assists in predicting chemical behavior and interactions within such complexes.

Facial and Cis Arrangements

Facial and cis arrangements are specific terms used to describe particular geometric arrangements of ligands in an octahedral complex. These terms highlight the differing ways in which ligands can occupy positions around the central metal atom.
The facial (fac) arrangement is observed when three identical ligands are placed together on one triangular face of the octahedron. This creates an arrangement where those three ligands are adjacent to each other. As a result of this symmetry, the fac isomer often has specific symmetry elements like a plane of symmetry, making it non-optically active.
In contrast, the cis (cis) arrangement occurs when alternating ligand types are positioned throughout the octahedral complex. This results in the ligands being spread alternately rather than being clustered on one face. Although this arrangement is symmetrical, it includes a center of symmetry, causing the cis isomer to be optically inactive as well.
Understanding these terms and their implications helps provide a foundational knowledge of how ligand positioning can alter the overall properties of octahedral complexes.