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

Solution :

1. Analysis of the Coordination Entity

The given complex is $[Cr(C_{2}O_{4})_{3}]^{3-}$.

  • Central Metal Atom: Chromium ($Cr$), which exhibits an oxidation state of $+3$ in this complex ($x + 3(-2) = -3 \implies x = +3$).
  • Ligand: Oxalate ion ($C_{2}O_{4}^{2-}$), denoted as $ox$.
  • Ligand Nature: $ox$ is a bidentate ligand, meaning it coordinates through two donor atoms (oxygen) to the central metal ion.
  • Coordination Number: Since there are $3$ bidentate ligands, the coordination number is $3 \times 2 = 6$.
  • Geometry: An octahedral geometry is formed.

2. Determining Geometrical Isomerism

Geometrical isomerism in coordination compounds arises due to the different spatial arrangements of ligands around the central metal atom. For an octahedral complex of the type $[M(AA)_{3}]$, where $AA$ represents a symmetrical bidentate ligand:

The ligands occupy positions such that each bidentate ligand connects two adjacent (cis) positions. Because all three ligands are identical and bidentate, any substitution of one ligand for another results in a configuration that is superimposable upon rotation. The ligands are essentially "stapled" into the octahedral framework, preventing the formation of $trans$ isomers where the donor atoms of the same ligand would be $180^\circ$ apart.

Cr ox ox ox

3. Logical Conclusion based on Stereochemistry

Per the rules of stereoisomerism in coordination chemistry [IUPAC Red Book criteria]:

  • For complex $[M(AA)_{3}]$, the spatial arrangement is rigid.
  • The structure possesses $D_{3}$ point group symmetry.
  • Because the ligands are symmetrical and bidentate, it is impossible to arrange them in a $trans$ fashion ($180^\circ$ apart).
  • Consequently, only one form exists in terms of connectivity and spatial orientation of the ligands relative to each other.

Final Solution: The number of geometrical isomers possible for $[Cr(C_{2}O_{4})_{3}]^{3-}$ is 0 (it does not exhibit geometrical isomerism).


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