How many optically active and optically inactive isomers are formed by [CoCl2(en)(NH3)2]+ ?

To determine the number of optically active and optically inactive isomers for the complex ion [CoCl2(en)(NH3)2]+, we first need to analyze its structure and coordination environment. This complex features cobalt (Co) as the central metal ion, coordinated by two chloride ions (Cl), one ethylenediamine (en) ligand, and two ammonia (NH3) ligands. The ethylenediamine is a bidentate ligand, meaning it can form two bonds with the metal center, while the ammonia and chloride ligands are monodentate.

Understanding the Coordination Geometry

Cobalt typically exhibits an octahedral coordination geometry in its complexes. In this case, the arrangement of the ligands around the cobalt ion will significantly influence the optical activity of the isomers.

Identifying Isomers

For octahedral complexes with the formula MA2B2C, where A is a bidentate ligand and B and C are monodentate ligands, we can expect several geometric isomers. Here, we have:

• A = en (bidentate)
• B = Cl (monodentate)
• C = NH3 (monodentate)

In this specific case, the arrangement of the ligands can lead to different isomers based on how the bidentate ligand (en) is positioned relative to the monodentate ligands (Cl and NH3).

Types of Isomers

1. **Facial (fac) Isomer**: In this arrangement, the two chloride ions and the two ammonia ligands occupy adjacent positions, while the ethylenediamine occupies the remaining positions. This configuration can lead to optical activity.

2. **Meridional (mer) Isomer**: Here, the two chloride ions and the two ammonia ligands are positioned opposite each other, which typically results in a symmetrical arrangement that is optically inactive.

Counting the Isomers

Now, let’s summarize the optical activity of these isomers:

• The **fac isomer** is optically active because it lacks a plane of symmetry.
• The **mer isomer** is optically inactive due to its symmetrical nature.

Final Tally

Thus, for the complex [CoCl2(en)(NH3)2]+, we can conclude:

• 1 optically active isomer (fac)
• 1 optically inactive isomer (mer)

In total, there are two distinct isomers: one that is optically active and one that is optically inactive. This analysis highlights the importance of ligand arrangement in determining the optical properties of coordination complexes.