Total Isomers for Square Planar Complex

To find the total number of all possible isomers for the square planar complex $\text{K}[\text{M}(\text{NCS})(\text{NO}_2)(\text{gly})]$, we analyze the nature of the ligands present in the coordination sphere $[\text{M}(\text{NCS})(\text{NO}_2)(\text{gly})]^-$:

1. Analysis of Ligands:

1. Glycinato ligand ($\text{gly}^-$):

   • An unsymmetrical bidentate ligand containing two different donor atoms: Nitrogen ($\text{N}$) from $-\text{NH}_2$ and Oxygen ($\text{O}$) from $-\text{COO}^-$.
   • Denoted as an $(\text{A-B})$ type ligand. Since it is bidentate, it must occupy two adjacent (cis) positions in a square planar complex.

2. Ambidentate Monodentate Ligands:

   • $\text{NCS}^-$: Can coordinate either through Nitrogen ($-\text{NCS}$, isothiocyanato) or through Sulfur ($-\text{SCN}$, thiocyanato). (2 linkage possibilities)
   • $\text{NO}_2^-$: Can coordinate either through Nitrogen ($-\text{NO}_2$, nitrito-N) or through Oxygen ($-\text{ONO}$, nitrito-O). (2 linkage possibilities)

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2. Linkage Isomers:

The total number of linkage combinations formed by the two ambidentate ligands is: $\text{Linkage combinations} = 2 \times 2 = 4$

These combinations are:

1. $-\text{NCS}$ and $-\text{NO}_2$
2. $-\text{NCS}$ and $-\text{ONO}$
3. $-\text{SCN}$ and $-\text{NO}_2$
4. $-\text{SCN}$ and $-\text{ONO}$

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3. Geometrical Isomers per Linkage Combination:

For a square planar complex of type $[\text{M}(\text{A-B})\text{C D}]$, where $\text{A-B}$ is the unsymmetrical bidentate glycinate ligand and $\text{C}, \text{D}$ are the two monodentate ligands:

• The bidentate ligand occupies two adjacent positions.
• The remaining two positions can be filled in two distinct spatial arrangements:
  • Isomer 1: Ligand $\text{C}$ is trans to the donor atom $\text{N}$ of $\text{gly}^-$, and ligand $\text{D}$ is trans to the donor atom $\text{O}$ of $\text{gly}^-$.
  • Isomer 2: Ligand $\text{D}$ is trans to the donor atom $\text{N}$ of $\text{gly}^-$, and ligand $\text{C}$ is trans to the donor atom $\text{O}$ of $\text{gly}^-$.

Thus, each linkage mode yields 2 geometrical isomers.

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4. Optical Isomerism:

All square planar complexes lie in a single plane, which acts as a plane of symmetry ($\sigma_h$). Consequently, square planar complexes are achiral and do not exhibit optical isomerism.

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5. Total Number of Isomers:

$\text{Total Isomers} = (\text{Number of Linkage Combinations}) \times (\text{Geometrical Isomers per Combination})$

$\text{Total Isomers} = 4 \times 2 = 8$

Thus, the total number of all possible isomers for the complex is 8.