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

Solution :

Step 1: Determining the Oxidation State of the Central Metal Ion

To analyze the bonding in $[FeF_{6}]^{3-}$, we first determine the oxidation state of the iron (Fe) atom. Let the oxidation state be $x$.

$x + 6(-1) = -3$ [Since Fluoride ($F^-$) is an anionic ligand with a charge of $-1$]

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

The central metal ion is $Fe^{3+}$.

Step 2: Electronic Configuration of the Metal Ion

The atomic number of Iron ($Fe$) is $26$.

Ground state configuration of $Fe$: $[Ar] 3d^6 4s^2$

Configuration of $Fe^{3+}$: $[Ar] 3d^5 4s^0$

In the $3d^5$ state, there are five unpaired electrons present in the $d$-orbitals, as the orbital energy is degenerate before ligand approach [Per Hund’s Rule of Maximum Multiplicity].

Step 3: Nature of the Ligand and Hybridization

The ligand $F^-$ is a weak field ligand. According to the Spectrochemical Series, weak field ligands are incapable of forcing the pairing of electrons in the $d$-orbitals [Per Valence Bond Theory (VBT) postulates regarding ligand strength].

Consequently, the hybridization must involve the outer $d$-orbitals. The coordination number is $6$, requiring a total of six vacant orbitals. The available orbitals are one $4s$, three $4p$, and two $4d$ orbitals.

Hybridization: $sp^3d^2$

Step 4: Orbital Diagram and Bonding Representation

The six $F^-$ ions donate six pairs of electrons into the hybridized $sp^3d^2$ orbitals.

3d (5 electrons) sp³d² Hybridized Orbitals (6 occupied by F⁻)

Step 5: Analysis of Magnetic and Structural Properties

Parameter Observation
Hybridization $sp^3d^2$
Geometry Octahedral
Magnetic Nature Paramagnetic (contains 5 unpaired electrons)
Complex Type Outer Orbital Complex (High spin complex)

The magnetic moment ($\mu$) is calculated as $\mu = \sqrt{n(n+2)} B.M.$, where $n=5$.

$\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ B.M.}$

Final Solution: The $[FeF_{6}]^{3-}$ complex undergoes $sp^3d^2$ hybridization, resulting in an octahedral geometry. It is a high-spin, outer-orbital paramagnetic complex with a magnetic moment of approximately $5.92 \text{ B.M.}$ due to the presence of five unpaired electrons.


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