The [Cr(H₂O)₆]³⁺ ion is violet, and [Cr(CN)₆]^3- is yellow. Explain this difference using crystal field theory. Use the colors to order H₂O and CN^- in the spectrochemical series.

Verified step by step guidance

1. Step 1: Understand that the color of a complex ion is due to the absorption of light which promotes an electron from a lower energy d-orbital to a higher energy d-orbital. The color we see is the complementary color of the light absorbed.
2. Step 2: Recognize that the crystal field theory explains the color of transition metal complexes in terms of the splitting of their d-orbitals into two sets of different energies when ligands approach the metal ion. The difference in energy between these two sets of d-orbitals corresponds to the energy of light absorbed.
3. Step 3: Realize that the extent of splitting of the d-orbitals, and hence the color of the complex, depends on the nature of the ligands. Ligands that cause a large splitting of the d-orbitals are known as strong-field ligands, while those that cause a small splitting are known as weak-field ligands.
4. Step 4: Infer from the given colors that [Cr(H₂O)₆]³⁺ absorbs light of higher energy (shorter wavelength) than [Cr(CN)₆]^3-. This is because violet light is the complementary color of yellow light, which is of lower energy (longer wavelength). Therefore, H₂O is a weaker field ligand than CN^-.
5. Step 5: Conclude that in the spectrochemical series, which orders ligands according to their ability to split the d-orbitals, H₂O comes before CN^-.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes by considering the effect of surrounding ligands on the d-orbitals of the metal ion. When ligands approach the metal ion, they create an electric field that splits the degenerate d-orbitals into different energy levels. The extent of this splitting depends on the nature of the ligands and their arrangement around the metal ion.

Spectrochemical Series

The spectrochemical series is a list that ranks ligands based on the strength of the field they produce when coordinating to a metal ion. Strong field ligands, like CN^-, cause a larger splitting of the d-orbitals, leading to higher energy transitions and different colors. Conversely, weak field ligands, such as H₂O, result in smaller splitting and lower energy transitions, which can be observed in the color of the complexes.

Color and d-Orbital Splitting

The color observed in transition metal complexes is a result of the specific wavelengths of light absorbed during electronic transitions between split d-orbitals. The energy difference between these orbitals corresponds to specific colors in the visible spectrum. For example, the violet color of [Cr(H₂O)₆]³⁺ indicates that it absorbs light in the yellow-green region, while the yellow color of [Cr(CN)₆]^3- suggests it absorbs light in the violet region, reflecting the differences in ligand field strength.