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Q5.21:
([Fe(CN)_{6}]^{4-}) and ([Fe(H_{2}O)_{6}]^{2+}) are of different colours in dilute solutions. Why?

Solution :

1. Analysis of Electronic Configuration and Oxidation State

Both complex ions contain Iron in the $+2$ oxidation state ($Fe^{2+}$). The atomic number of $Fe$ is $26$. The electronic configuration of $Fe^{2+}$ is $[Ar] 3d^6$.

  • In $[Fe(CN)_6]^{4-}$, $CN^-$ is a strong-field ligand.
  • In $[Fe(H_2O)_6]^{2+}$, $H_2O$ is a weak-field ligand.

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

According to the Crystal Field Theory (CFT), the $d$-orbitals of the central metal ion split into two sets: $t_{2g}$ (lower energy) and $e_g$ (higher energy) in an octahedral environment. The magnitude of splitting, denoted as $\Delta_o$, is dependent on the nature of the ligand [Per the Spectrochemical Series].

3. Electronic Distribution and Transitions

Feature $[Fe(CN)_6]^{4-}]$ $[Fe(H_2O)_6]^{2+}]$
Ligand Strength Strong Field ($CN^-$) Weak Field ($H_2O$)
Splitting Magnitude Large ($\Delta_o > P$, where $P$ is pairing energy) Small ($\Delta_o < P$)
Configuration $t_{2g}^6 e_g^0$ (Low Spin) $t_{2g}^4 e_g^2$ (High Spin)
d-d Transition High Energy (Visible region: shorter $\lambda$) Low Energy (Visible region: longer $\lambda$)

4. Theoretical Justification of Color

The color of coordination compounds arises from $d-d$ electronic transitions. When white light falls on the complex, specific wavelengths are absorbed to promote an electron from the lower energy $d$-orbitals to the higher energy $d$-orbitals [Per the Principle of Complementary Colors].

The energy absorbed ($\Delta E$) is inversely proportional to the wavelength ($\lambda$) of the light absorbed, given by the Planck-Einstein relation: $\Delta E = \frac{hc}{\lambda}$.

Because $CN^-$ is a strong field ligand, it causes a larger splitting ($\Delta_o$), requiring higher energy (shorter wavelength) for excitation. $H_2O$ causes smaller splitting, requiring lower energy (longer wavelength). Consequently, the absorbed wavelengths are different, resulting in the observation of different complementary colors.

Weak Field Strong Field Large $\Delta_o$ Small $\Delta_o$

Final Solution: The difference in colors arises because the strong-field ligand ($CN^-$) causes a larger crystal field splitting ($\Delta_o$) compared to the weak-field ligand ($H_2O$). Consequently, the $d-d$ transitions in these complexes involve different amounts of energy, resulting in the absorption of different wavelengths of visible light and the reflection of different complementary colors.


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