Q.$[Fe(CN)_6]^{4-}$ and $[Fe(H_2O)_6]^{2+}$ are of different colours in dilute solutions. Why?

The key idea is that the colour of a coordination compound arises from d-d transitions — the energy gap between split d-orbitals depends on the ligand field strength.

Reasoning:

1. In $[Fe(CN)_6]^{4-}$, the ligand CN⁻ is a strong field ligand. It causes a large crystal field splitting ($\Delta_o$), so the d-d transition requires high-energy (blue/violet) light. The complex appears yellow.

2. In $[Fe(H_2O)_6]^{2+}$, the ligand H₂O is a weak field ligand. It causes a small $\Delta_o$, so the d-d transition absorbs lower-energy (red/orange) light. The complex appears pale green. …

The colour of a transition metal complex in solution is a direct consequence of electronic transitions between d-orbitals. When white light falls on the complex, certain wavelengths are absorbed to promote an electron from a lower-energy d-orbital to a higher-energy one. The colour we see is the complementary colour of the absorbed light.

For octahedral complexes of $Fe^{2+}$ (d⁶ configuration), the key factor is the magnitude of the crystal field splitting energy, $\Delta_{\text{oct}}$. This $\Delta$ value depends strongly on the nature of the ligand.

1. Ligand strength determines $\Delta$.

   CN⁻ is a strong-field ligand (high up in the spectrochemical series), while H₂O is a weak-field ligand.

   $\Delta_{\text{oct}}(\text{CN}^-) \gg \Delta_{\text{oct}}(\text{H}_2\text{O})$

2. Electron configuration differs.

   For $[Fe(CN)_6]^{4-}$, the large $\Delta$ forces the six d-electrons to pair up in the three lower $t_{2g}$ orbitals — this is a low-spin complex ($t_{2g}^6 e_g^0$).

   For $[Fe(H_2O)_6]^{2+}$, the small $\Delta$ means electrons occupy all five d-orbitals singly before pairing — this is a high-spin complex ($t_{2g}^4 e_g^2$).

3. Energy of the d-d transition differs.

   In the low-spin cyano complex, the energy gap between the filled $t_{2g}$ and empty $e_g$ orbitals is large. The complex absorbs higher-energy light towards the blue-violet end of the spectrum and transmits yellow light.

   In the high-spin aqua complex, the energy gap is much smaller. It absorbs lower-energy light towards the red end of the spectrum and transmits pale green light. …

Concept: Complex Formation & Colour

The colour difference arises from Crystal Field Theory (CFT) — specifically, the nature of the ligand and its effect on d-orbital splitting.

Method: Crystal Field Theory — Ligand Spectrochemical Series

Step 1: Identify the metal ion and its d-electron count

• Both complexes contain Fe²⁺ (iron in +2 oxidation state).
• Fe²⁺ has the electronic configuration: $[Ar]\,3d^6$.

Step 2: Determine the geometry and ligand field

• Both complexes are octahedral (coordination number 6).
• In an octahedral field, the 3d orbitals split into:
  • $t_{2g}$ (lower energy: $d_{xy}, d_{xz}, d_{yz}$)
  • $e_g$ (higher energy: $d_{z^2}, d_{x^2-y^2}$)

Step 3: Apply the Spectrochemical Series

The spectrochemical series ranks ligands by their ability to split d-orbitals:

• $H_2O$ is a weak field ligand → small splitting ($\Delta_{\text{oct}}$ is small).
• $CN^-$ is a strong field ligand → large splitting ($\Delta_{\text{oct}}$ is large).

Step 4: Determine electron configuration in each case

• $[Fe(H_2O)_6]^{2+}$ (weak field, small $\Delta$):

  • Electrons fill according to Hund's rule (high-spin).
  • Configuration: $t_{2g}^4\, e_g^2$ (4 unpaired electrons).

• $[Fe(CN)_6]^{4-}$ (strong field, large $\Delta$):

  • Electrons pair up in lower $t_{2g}$ orbitals (low-spin).
  • Configuration: $t_{2g}^6\, e_g^0$ (0 unpaired electrons).

Step 5: Relate to colour …

Here are the common mistakes students make when explaining the colour difference between $[Fe(CN)_6]^{4-}$ and $[Fe(H_2O)_6]^{2+}$, along with how to avoid each.

Mistake 1: Saying the colour is due to the metal ion alone

The error:

Students often say “Iron(II) is green” or “Iron(II) is yellow,” implying the colour comes only from the $Fe^{2+}$ ion. This ignores the role of the ligand.

Why it’s wrong:

The colour of a transition metal complex arises from d-d transitions — electrons moving between split d-orbitals. The energy gap ($\Delta$) depends on the ligand field strength, not just the metal ion.

How to avoid:

Always mention that the ligand determines the splitting energy. For the same metal ion ($Fe^{2+}$), different ligands give different colours.

• $CN^-$ is a strong field ligand → large $\Delta$ → absorbs higher energy light (violet/blue) → appears yellow.
• $H_2O$ is a weak field ligand → small $\Delta$ → absorbs lower energy light (red region) → appears pale green (the complementary colour).

Key point: Colour is a complex property, not a metal-only property.

Mistake 2: Confusing the oxidation state of iron

The error:

Some students think $[Fe(CN)_6]^{4-}$ contains $Fe^{3+}$ because cyanide is often associated with ferricyanide ($[Fe(CN)_6]^{3-}$).

Why it’s wrong:

The charge on the complex is $4-$. Cyanide ($CN^-$) has a charge of $-1$ each.

Let $x$ be the oxidation state of Fe:

Both complexes contain $Fe^{2+}$ (d⁶ configuration).

How to avoid:

Always calculate the oxidation state using the overall charge and ligand charges. Write it down step-by-step in exams.

Mistake 3: Ignoring the spin state (high-spin vs low-spin)

The error:

Students treat both complexes as having the same electron arrangement in d-orbitals.

Why it’s wrong:

• $CN^-$ is a strong field ligand → causes large splitting → electrons pair up in lower orbitals → low-spin (t₂g⁶, eg⁰).
• $H_2O$ is a weak field ligand → small splitting → electrons remain unpaired as per Hund’s rule → high-spin (t₂g⁴, eg²).

Different spin states mean different d-orbital occupancy, which changes the energy of d-d transitions and thus the colour.

How to avoid:

Mention the spectrochemical series and decide spin state before discussing colour. For $Fe^{2+}$:

• Strong field → low-spin
• Weak field → high-spin

Mistake 4: Forgetting to mention d-d transitions

The error:

Giving vague answers like “because of different ligands” without explaining the mechanism.

Why it’s wrong:

The examiner expects you to link ligand strength → splitting energy → wavelength of light absorbed → complementary colour observed.

How to avoid:

Use this chain in your answer:

Ligand strength → Crystal Field Splitting Energy ($\Delta$) → Energy of absorbed photon → Colour observed (complementary)

For example:

• $[Fe(CN)_6]^{4-}$: strong field → large $\Delta$ → absorbs violet → appears yellow. …