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Q5.15 (iv):
Discuss the nature of bonding on the basis of valence bond theory: ([CoF_{6}]^{3-})

Solution :

Step 1: Determining the Oxidation State and Electronic Configuration

To analyze the complex $[CoF_{6}]^{3-}$, we first determine the oxidation state of the central metal ion, Cobalt ($Co$):

  • Let the oxidation state of $Co$ be $x$.
  • The fluoride ion ($F^-$) has a charge of $-1$.
  • The overall charge of the complex is $-3$.
  • Equation: $x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3$.

Cobalt has an atomic number of $27$. The electronic configuration of neutral $Co$ is $[Ar] 3d^7 4s^2$.
For $Co^{3+}$, the configuration is $[Ar] 3d^6$.

Step 2: Analysis of Ligand Field Strength

The ligand involved is the fluoride ion ($F^-$). According to the Spectrochemical Series [Per Crystal Field Theory], $F^-$ is a weak field ligand. Consequently, it is incapable of forcing the pairing of electrons in the $3d$ subshell [Hund’s Rule of Maximum Multiplicity].

Step 3: Orbital Hybridization and Electronic Distribution

Since the ligand is weak, the six $3d$ electrons remain in the following arrangement within the $3d$ orbitals:

Orbital$d_{xy}$$d_{yz}$$d_{zx}$$d_{x^2-y^2}$$d_{z^2}$
Electrons$\uparrow\downarrow$$\uparrow$$\uparrow$$\uparrow$$\uparrow$

To accommodate the six coordinate bonds from six $F^-$ ions, the metal ion utilizes one $4s$, three $4p$, and two $4d$ orbitals. This results in $sp^3d^2$ hybridization [Valence Bond Theory].

Step 4: Geometric Representation

Co³⁺ F⁻ F⁻ F⁻ F⁻ F⁻ F⁻

Step 5: Conclusions on Magnetic and Electronic Nature

  • Hybridization: $sp^3d^2$ (Outer orbital complex).
  • Geometry: Octahedral.
  • Magnetic Property: The complex contains four unpaired electrons ($3d^6$ configuration where two are paired and four are lone). Therefore, it is paramagnetic.
  • Magnetic Moment: Calculated via $\mu_{eff} = \sqrt{n(n+2)} \mu_B$, where $n=4$. $\mu_{eff} = \sqrt{4(6)} = \sqrt{24} \approx 4.90 \mu_B$.

Final Solution: The $[CoF_{6}]^{3-}$ complex undergoes $sp^3d^2$ hybridization, resulting in an octahedral geometry; it is an outer orbital high-spin complex that is paramagnetic due to the presence of four unpaired electrons.


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