How many stereoisomers of octahedral CoCl2(NH3)2(CN)2¯ are possible?

To determine the number of stereoisomers for the complex CoCl2(NH3)2(CN)2¯, we first analyze its structure and the coordination of the ligands around the cobalt center. Cobalt typically forms octahedral complexes and in this case, it has six ligands: two chloride ions, two ammonia molecules, and two cyanide ions.

In an octahedral complex, stereoisomers arise from the different spatial arrangements of the ligands. For CoCl2(NH3)2(CN)2¯, we can consider the ligand types and their positions to determine how many different arrangements are possible.

Given that there are two pairs of identical ligands (the two chlorides and the two ammines), and two distinct ligands (cyanides), we must explore the arrangements based on the geometrical placement.

1. Facial (fac) vs. Meridional (mer) Isomers: The ligands can be arranged in either a facial or a meridional fashion. In this case, for each of the meridional arrangements of the chloride and cyanide, one can have different placement of the ammine ligands, leading to distinct configurations.

2. **Ch