Complex Structure Analysis

The complex given is $[(NH_3)_2M(CN)_2]$.

• It is a square planar complex.
• It is mononuclear (contains only one metal atom, M).
• The ligands are ammonia ($NH_3$) and cyanide ($CN$).
• The formula type is $MA_2B_2$, where M is the metal, A represents $NH_3$, and B represents $CN$.

Identifying Possible Isomers

For a square planar complex of the type $MA_2B_2$, there are two possible geometric isomers based on the relative positions of the ligands:

• Cis Isomer: The two identical ligands (in this case, $NH_3$ or $CN$) are adjacent to each other (at a 90° angle).
  • Example arrangement: $NH_3$ ligands at positions 1 and 2, $CN$ ligands at positions 3 and 4.
• Trans Isomer: The two identical ligands are opposite to each other (at a 180° angle).
  • Example arrangement: $NH_3$ ligands at positions 1 and 3, $CN$ ligands at positions 2 and 4.

Determining the Number of Isomers

In the complex $[(NH_3)_2M(CN)_2]$:

• The two $NH_3$ ligands can be adjacent (cis) or opposite (trans).
• The two $CN$ ligands will correspondingly be opposite or adjacent.
• These two arrangements (cis and trans) represent the only distinct spatial arrangements (stereoisomers).
• Therefore, there are exactly 2 possible isomers for this complex.

The possible isomers are the cis-diamminedicyanido complex and the trans-diamminedicyanido complex.