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Q5.9(i):
How many geometrical isomers are possible in the following coordination entities? \([Cr(C_{2}O_{4})_{3}]^{3-}\)

Solution :

Step 1: Identifying the Coordination Entity

The coordination entity is given as $\left[Cr(C_{2}O_{4})_{3}\right]^{3-}$.

  • Central Metal Ion: Chromium ($Cr^{3+}$).
  • Ligand: Oxalate ion ($C_{2}O_{4}^{2-}$), denoted as $ox$.
  • Denticity: The oxalate ion is a symmetrical bidentate ligand, meaning it coordinates through two oxygen atoms per ligand molecule to the same metal center [Per Werner’s Coordination Theory].
  • Coordination Number: Since there are three bidentate ligands, the coordination number is $3 \times 2 = 6$.

Step 2: Analysis of Geometrical Isomerism in Octahedral Complexes

For a coordination entity of the type $[M(AA)_3]$, where $AA$ represents a symmetrical bidentate ligand, the spatial arrangement is constrained by the geometry of the chelate rings.

In an octahedral complex with three identical bidentate ligands, the ligands are fixed in such a way that they occupy the edges of the octahedron. Because the ligands are symmetrical and identical, every position is geometrically equivalent relative to the central metal ion.

Step 3: Evaluating Geometrical Isomerism

Geometrical isomerism (cis-trans or fac-mer) requires the existence of distinct spatial arrangements of ligands relative to each other. In the $[M(AA)_3]$ structure:

  • The chelate rings are constrained to span the cis-positions of the octahedral coordination sphere.
  • There is no possible arrangement where two identical donor atoms can occupy trans-positions (180° relative to the metal center) because the bite angle of the oxalate ligand is too small to span the distance between trans-positions [Per Geometric constraints of chelate rings].
  • Consequently, the ligands are forced to exist in a single arrangement where all donor atoms occupy cis-positions.

Step 4: Visualizing the Coordination Geometry

Cr ox ox ox

Step 5: Conclusion on Isomeric Possibility

Since the geometry of the complex is rigid and allows for only one spatial arrangement of the three bidentate ligands, it does not exhibit geometrical isomerism.

Note: While the complex $\left[Cr(C_{2}O_{4})_{3}\right]^{3-}$ does exhibit optical isomerism (existence of non-superimposable mirror images/enantiomers), the question specifically restricts the query to geometrical isomerism.

Final Solution: The number of geometrical isomers possible for $\left[Cr(C_{2}O_{4})_{3}\right]^{3-}$ is 0.


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