Question

Consider an octahedral complex, ${\mathrm{MA}}_2{\mathrm{B}}_4$. 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 four geometric isomers for the octahedral complex ${\mathrm{MA}}_2{\mathrm{B}}_4$, with one cis and three trans configurations. Out of these, only one trans isomer (with one A ligand in an axial position and the other in an equatorial position) is optically active, as it lacks a plane of symmetry.

Step-by-step solution

Understanding the structure of an octahedral complex

An octahedral complex has a central metal atom (M) surrounded by six ligands. In this case, we have two ligands of type A and four ligands of type B. To determine the geometric isomers, we need to consider all the possible arrangements for the A and B ligands around the central metal atom.

Finding geometric isomers based on ligand positions

To find the geometric isomers, we will consider the following scenarios: 1. Both A ligands are next to each other (cis configuration). 2. Both A ligands are opposite to each other (trans configuration). Here are the possible geometric isomers: - Cis configuration: The two A ligands are adjacent, and the remaining four positions are occupied by B ligands. There is only one way to arrange the ligands in this configuration. - Trans configuration: The two A ligands are opposite each other, and the remaining four positions are occupied by B ligands. In this configuration, we have three possibilities (A ligands in axial position, A ligands in the equatorial position, A ligands in the axial and equatorial position). Hence, we have a total of $1+3=4$ geometric isomers.

Identify optically active isomers

An optically active substance has the ability to rotate plane-polarized light. A molecule is optically active if it is not superimposable on its mirror image (i.e., it lacks a plane of symmetry). For the octahedral complex ${\mathrm{MA}}_2{\mathrm{B}}_4$: - Cis configuration: In this configuration, there is a plane of symmetry passing through the central metal atom and the two A ligands, making it optically inactive. Trans configuration: 1. Both A ligands are in axial positions: This configuration also has a plane of symmetry passing through the axial ligands and perpendicular to the equatorial plane, making this isomer optically inactive. 2. Both A ligands are opposite in the equatorial plane: This configuration has a plane of symmetry passing through the M atom and between A ligands; thus, this isomer is optically inactive. 3. A ligands are in one axial position and one equatorial position such that they are opposite: There is no plane of symmetry in this case, making this isomer optically active. In conclusion, there are four geometric isomers, and only one of them (one trans isomer with A ligands in one axial and one equatorial position) is optically active.

Key concepts

Octahedral Complex

An octahedral complex is a fascinating structure in coordination chemistry. It involves a central metal atom surrounded by six ligands, which can be atoms, molecules, or ions. This six-ligand arrangement forms an octahedral shape, resembling two four-sided pyramids joined at their bases.

When considering the complex ${\mathrm{MA}}_2{\mathrm{B}}_4$, it includes two ligands of type A and four ligands of type B. This set-up leads to the formation of different isomers based on the positioning of these ligands around the metal center.

• **Cis Configuration**: Both A ligands are next to each other, with the remaining four positions filled by B ligands.
• **Trans Configuration**: Both A ligands are opposite each other, resulting in three possible arrangements.

• Axial positions for A ligands
• Equatorial positions for A ligands
• Combination of one axial and one equatorial position

Thus, this particular complex can produce four geometric isomers in total. Understanding the basic structure of octahedral complexes lays the foundation for further intriguing properties like optical activity.

Optical Activity

Optical activity is a property that occurs when a compound can rotate the plane of polarized light. This phenomenon arises due to molecular asymmetry, meaning the molecule cannot be superimposed on its mirror image, lacking a plane of symmetry.

In the world of chemistry, such molecules are chiral, which sources their unique optical properties. Not all isomers are optically active, but some can achieve this under specific arrangements. Optical activity is typically tested using polarimeters, devices designed to measure the degree of rotation of polarized light by optical isomers.

For the octahedral complex ${\mathrm{MA}}_2{\mathrm{B}}_4$, only one geometric isomer shows optical activity. This is the isomer where one A ligand occupies an axial and the other an equatorial position. This configuration lacks a reflective plane of symmetry, allowing it to rotate the plane of polarized light—evidence of its chiral nature.

Understanding which configurations are optically active helps in applications ranging from pharmaceuticals to materials science, where such properties are crucial.

Cis-Trans Isomerism

Cis-trans isomerism is a fascinating concept encountered in coordination chemistry, particularly when dealing with isomers in an octahedral complex. This type of isomerism depends on the angles and positioning of ligands around a central atom.

**Cis Isomers**: These occur when identical ligands are adjacent to each other. In the case of our complex ${\mathrm{MA}}_2{\mathrm{B}}_4$, this means the A ligands sit next to each other, sharing a bond angle.

**Trans Isomers**: These appear when identical ligands sit opposite each other. In the complex we're examining, trans configurations can yield three distinct isomers based on their position - all having unique spatial arrangements.

• Cis isomer offers one configuration.
• Trans isomer provides three configurations: axial, equatorial, and a mix of both.

These different configurations result in four possible geometric isomers. Among them, the trans isomer with one A ligand in an axial position and the other in an equatorial position does not have a plane of symmetry, rendering it optically active. Cis-trans isomerism offers fascinating insights into molecular architecture and is crucial for developing substances with specific properties.