Crystal Field Theory (CFT) – 10 Questions

 

Class 12 Chemistry – Coordination Compounds

Crystal Field Theory (CFT) – 10 Questions

1. Explain the splitting of d-orbitals in an octahedral complex according to Crystal Field Theory.

2. Draw the crystal field splitting diagram for an octahedral complex and label the $t_{2g}$ and $e_g$ orbitals.

3. What is meant by crystal field splitting energy $(\Delta_o)$? Write its relationship with the energies of $t_{2g}$ and $e_g$ orbitals.

4. Explain the splitting of d-orbitals in a tetrahedral complex according to CFT. Why is $\Delta_t$ smaller than $\Delta_o$?

5. Draw the crystal field splitting diagram for a tetrahedral complex and label the $e$ and $t_2$ orbitals.

6. Using CFT, determine the number of unpaired electrons in $[Fe(CN)_6]^{4-}$.

7. Using CFT, determine the number of unpaired electrons in $[FeF_6]^{3-}$.

8. Explain why $[Fe(CN)_6]^{4-}$ is low-spin, whereas $[FeF_6]^{3-}$ is high-spin.

9. Calculate the CFSE for a $d^4$ metal ion in an octahedral field when it forms a high-spin complex.

10. Calculate the CFSE for a $d^6$ metal ion in an octahedral field for both high-spin and low-spin configurations.

Class 12 Chemistry – CFT

Answers to 10 Questions

1. Splitting of d-orbitals in an octahedral complex

In an octahedral field, the five d-orbitals split into two sets:

• $t_{2g}$: $d_{xy}, d_{yz}, d_{xz}$ — lower energy

• $e_g$: $d_{x^2-y^2}, d_{z^2}$ — higher energy

The energy difference between these two sets is $\Delta_o$.

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2. Octahedral splitting diagram

          eg
       ────────
       ────────
          ↑
          │ Δo
          ↓
    ─────────────
        t2g
    ─────────────

$e_g$ orbitals have higher energy, while $t_{2g}$ orbitals have lower energy.

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3. Crystal Field Splitting Energy $(\Delta_o)$

The energy difference between the $t_{2g}$ and $e_g$ levels in an octahedral complex is called octahedral crystal field splitting energy $(\Delta_o)$.

Energy of each electron:

$$t_{2g}=-0.4\Delta_o$$ $$e_g=+0.6\Delta_o$$

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4. Splitting in a tetrahedral complex

In a tetrahedral field, d-orbitals split into:

• $e$: lower energy

• $t_2$: higher energy

The splitting energy is $\Delta_t$.

$$\boxed{\Delta_t \approx \frac{4}{9}\Delta_o}$$

Therefore, $\Delta_t$ is smaller than $\Delta_o$.

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5. Tetrahedral splitting diagram

          t2
       ───────
       ───────
       ───────
          ↑
          │ Δt
          ↓
       ───────
       ───────
          e

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6. Number of unpaired electrons in $[Fe(CN)_6]^{4-}$

Oxidation state of Fe:

$$x+6(-1)=-4$$ $$x=+2$$

Fe²⁺ = $3d^6$

$CN^-$ is a strong-field ligand → low spin.

Configuration:

$$t_{2g}^{6}e_g^0$$

Unpaired electrons = $\boxed{0}$

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7. Number of unpaired electrons in $[FeF_6]^{3-}$

Fe oxidation state:

$$x+6(-1)=-3$$ $$x=+3$$

Fe³⁺ = $3d^5$

$F^-$ is a weak-field ligand → high spin.

Configuration:

$$t_{2g}^{3}e_g^2$$

Unpaired electrons = $\boxed{5}$

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8. Why is $[Fe(CN)_6]^{4-}$ low-spin while $[FeF_6]^{3-}$ is high-spin?

• $CN^-$ is a strong-field ligand, so $\Delta_o > P$, causing pairing.

• $F^-$ is a weak-field ligand, so $\Delta_o < P$, so electrons remain unpaired as far as possible.

Therefore:

$$[Fe(CN)_6]^{4-} \rightarrow \text{Low spin}$$ $$[FeF_6]^{3-} \rightarrow \text{High spin}$$

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9. CFSE for $d^4$ high-spin octahedral complex

High-spin $d^4$ configuration:

$$t_{2g}^3e_g^1$$

Therefore,

$$CFSE=(3\times-0.4\Delta_o)+(1\times+0.6\Delta_o)$$ $$=-1.2\Delta_o+0.6\Delta_o$$ $$\boxed{CFSE=-0.6\Delta_o}$$

Magnitude = $0.6\Delta_o$.

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10. CFSE for $d^6$ octahedral complexes

High-spin $d^6$:

$$t_{2g}^4e_g^2$$ $$CFSE=(4\times-0.4)+(2\times0.6)$$ $$=-1.6+1.2$$ $$\boxed{-0.4\Delta_o}$$

Low-spin $d^6$:

$$t_{2g}^6e_g^0$$ $$CFSE=6(-0.4\Delta_o)$$ $$\boxed{-2.4\Delta_o}$$

So:

• High spin: $\boxed{-0.4\Delta_o}$

• Low spin: $\boxed{{\displaystyle -2.4{\mathrm{\Delta }}_o}}$