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Q5.15(iii):
Discuss the nature of bonding in the following coordination entities on the basis of valence bond theory: \([Co(C_{2}O_{4})_{3}]^{3-}\)

Solution :

Step 1: Identification of Central Metal Ion and Oxidation State

The coordination entity is $[Co(C_2O_4)_3]^{3-}$. The ligand is the oxalate ion ($C_2O_4^{2-}$), which is a bidentate ligand [Per IUPAC nomenclature and ligand classification].

Let the oxidation state of Cobalt be $x$:

$x + 3(-2) = -3$

$x - 6 = -3 \implies x = +3$

The electronic configuration of neutral $Co$ ($Z=27$) is $[Ar] 3d^7 4s^2$. Therefore, the electronic configuration of $Co^{3+}$ is $[Ar] 3d^6$.

Step 2: Electronic Configuration and Ligand Field Effect

In the ground state of $Co^{3+}$ ($3d^6$):

  • $3d$ subshell: $\uparrow\downarrow \uparrow \uparrow \uparrow \uparrow$ (4 unpaired electrons)
  • $4s$ subshell: empty
  • $4p$ subshell: empty

The oxalate ion ($C_2O_4^{2-}$) acts as a strong field ligand in the presence of $Co^{3+}$. According to Valence Bond Theory, strong field ligands induce pairing of electrons in the $d$-orbitals [Per Spectrochemical Series].

After pairing, the $3d$ configuration becomes:

$3d$: $\uparrow\downarrow \uparrow\downarrow \uparrow\downarrow$ (all electrons paired)

Step 3: Hybridization and Geometry

To accommodate 6 coordinate bonds from 3 bidentate oxalate ligands (total 6 donor atoms), the metal ion requires 6 vacant hybrid orbitals. The available orbitals are two $3d$, one $4s$, and three $4p$ orbitals.

The hybridization involved is $d^2sp^3$.

3d orbital pair: [ ][ ][ ][ ][ ] (hybridized to d²sp³) Resulting complex: [Co(C₂O₄)₃]³⁻ is inner orbital, octahedral.

Step 4: Magnetic and Structural Properties

Property Analysis
Hybridization $d^2sp^3$
Geometry Octahedral
Magnetic Nature Diamagnetic (all electrons paired)
Inner/Outer Orbital Inner orbital complex (uses $3d$ orbitals)

Final Solution: The complex $[Co(C_2O_4)_3]^{3-}$ involves $d^2sp^3$ hybridization, resulting in an octahedral geometry. As all electrons are paired due to the strong field nature of the oxalate ligand, the complex is diamagnetic in nature.


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