`[Fe(CN)_(6)]^(4-)` and `[Fe(H_(2)O)_(6)]^(2+)` are of different colours in dilute solutions why?

Options

A. `CN^(-)` is a strong field ligand and `H_(2)O` is a weak field ligand hence magnitude of CFSE is different
B. both `CN^(-)` and `H_(2)O` absorb same wavelength of energy
C. complexes of weak field ligands are generally colourless
D. the sizes of `CN^(-)` and `H_(2)O` are different hence their colours are also different .

Answer

To understand why the complexes \([Fe(CN)_{6}]^{4-}\) and \([Fe(H_{2}O)_{6}]^{2+}\) exhibit different colors in dilute solutions, we can break down the explanation into several steps:

### Step-by-Step Solution:

1. **Identify the Complexes**:
- We have two complexes: \([Fe(CN)_{6}]^{4-}\) and \([Fe(H_{2}O)_{6}]^{2+}\).
- Both complexes contain iron (Fe) in the +2 oxidation state.

2. **Determine the Ligands**:
- The ligand in the first complex is cyanide (\(CN^{-}\)), and in the second complex, it is water (\(H_{2}O\)).
- It is important to note that these ligands have different field strengths.

3. **Classify the Ligands**:
- Cyanide (\(CN^{-}\)) is classified as a strong field ligand.
- Water (\(H_{2}O\)) is classified as a weak field ligand.

4. **Crystal Field Theory**:
- According to crystal field theory, ligands cause the d-orbitals of the central metal ion (Fe in this case) to split into different energy levels.
- For octahedral complexes, the d-orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g\) (higher energy).

5. **Crystal Field Splitting Energy (\(\Delta\))**:
- The splitting energy (\(\Delta\)) is higher for strong field ligands compared to weak field ligands.
- Therefore, in \([Fe(CN)_{6}]^{4-}\), the crystal field splitting energy is greater than in \([Fe(H_{2}O)_{6}]^{2+}\).

6. **Absorption of Light**:
- The color of a complex is determined by the wavelengths of light it absorbs. The energy difference between the split d-orbitals corresponds to specific wavelengths of light.
- Since \([Fe(CN)_{6}]^{4-}\) has a higher \(\Delta\), it absorbs light of a different wavelength compared to \([Fe(H_{2}O)_{6}]^{2+}\).

7. **Resulting Colors**:
- Because the two complexes absorb different wavelengths of light, they will appear as different colors in dilute solutions.

### Conclusion:
The difference in colors between \([Fe(CN)_{6}]^{4-}\) and \([Fe(H_{2}O)_{6}]^{2+}\) arises from the different crystal field splitting energies caused by the strong field ligand \(CN^{-}\) and the weak field ligand \(H_{2}O\).