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Ch.21 - Transition Elements and Coordination Chemistry
All textbooksMcMurry 8th EditionCh.21 - Transition Elements and Coordination ChemistryProblem 21.105
Chapter 21, Problem 21.105

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.
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.
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.
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-.
Step 5: Conclude that in the spectrochemical series, which orders ligands according to their ability to split the d-orbitals, H2O comes before CN-.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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The study of ligand-metal interactions helped to form Ligand Field Theory which combines CFT with MO Theory.

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<sup>-</sup>, cause a larger splitting of the d-orbitals, leading to higher energy transitions and different colors. Conversely, weak field ligands, such as H<sub>2</sub>O, result in smaller splitting and lower energy transitions, which can be observed in the color of the complexes.
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Activity Series Chart

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(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> indicates that it absorbs light in the yellow-green region, while the yellow color of [Cr(CN)<sub>6</sub>]<sup>3-</sup> suggests it absorbs light in the violet region, reflecting the differences in ligand field strength.
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d Orbital Orientations
Related Practice
Textbook Question

What hybrid orbitals are used by the metal ion and how many unpaired electrons are present the complex ion [VCl4]- with tetrahedral geometry?

(a) sp3; 2 unpaired electrons

(b) sp3; 3 unpaired electrons

(c) sp3d2; 3 unpaired electrons

(d) sp3d2; 4 unpaired electrons

Textbook Question

What is the electron configuration of Co2+ and how many unpaired electrons are in the free transition metal ion?

(a) [Ar]3d54s2; 5 unpaired electrons

(b) [Ar]3d54s2; 1 unpaired electron

(c) [Ar]3d7; 3 unpaired electrons

(d) [Ar]3d7; 1 unpaired electron

Textbook Question

Draw a crystal field energy-level diagram for the 3d orbitals of titanium in [Ti(H2O)6]3+]. Indicate the crystal field splitting, and explain why is [Ti(H2O)6]3+] colored.

Textbook Question

For each of the following complexes, draw a crystal field energy-level diagram, assign the electrons to orbitals, and predict the number of unpaired electrons. 

(a) [CrF6]3-

(b) [V(H2O)6]3+

(c) [Fe(CN)6]3-

Textbook Question

Draw a crystal field energy-level diagram, assign the electrons to orbitals, and predict the number of unpaired electrons for each of the following.

(a) [Cu(en)3]2+

(b) [FeF6]2-

(c) [Co(en)3]3+ (low spin) 

Textbook Question

The Ni2+(aq) cation is green, but Zn2+(aq) is colorless. Explain.