Problem 10 - Chemistry: The Central Science

Question

Two Fe(II) complexes are both low spin but have different ligands. A solution of one is green and a solution of the other is red. Which solution is likely to contain the complex that has the stronger-field ligand? [Section 23.6]

Step-by-Step Solution

Answer

The red solution is likely to contain the complex with the stronger-field ligand. Its red color indicates that it absorbs cyan light, which has a higher energy and shorter wavelength than the magenta light absorbed by the green complex. This larger d-orbital splitting suggests a stronger-field ligand in the red complex.

Step 1: Recall crystal field theory

Crystal field theory is a model used to describe the electronic structure of transition metal complexes, taking into account the influence of the surrounding ligands. In this theory, the ligand field splits the metal's d-orbitals differentially, leading to the creation of a high-energy and low-energy set of orbitals. As a result of the energy gap formed between these sets, the complex will absorb light at wavelengths corresponding to the difference in energies, leading to a color attributed to its complementary color.

Step 2: Recall the spectrochemical series of ligands

To determine which complex has the stronger-field ligand, we must recall the spectrochemical series, which is the classification of ligands based on their field strength. Strong-field ligands cause a larger splitting of the d-orbitals, resulting in a higher crystal field energy difference, while weak-field ligands cause smaller splitting. The spectrochemical series is as follows: I- < Br- < Cl- < F- < OH- < H2O < NCS- < SCN- < EDTA < NH3 < en < NO2- < CN- < CO

Step 3: Examine the relation between color and ligand strength

Based on the crystal field theory, a larger splitting in the d-orbitals will cause the absorbed light energy to have a higher frequency, and by extension, a shorter wavelength. Therefore, the color of the absorbed light will be closer to the blue end of the visible light spectrum. Conversely, the color of the transmitted light, which we see as the color of the solution, will be complementary to the absorbed color. The complementary color rule is as follows: - Red ↔ Cyan - Green ↔ Magenta - Blue ↔ Yellow When the transmitted color is red, the complex is absorbing cyan light, and when it is green, it is absorbing magenta light.

Step 4: Identify the stronger-field ligand complex

Based on the color of the solutions, analyze the possible absorbed colors: - The green complex absorbs magenta light, which has a lower frequency and a longer wavelength than cyan light. - The red complex absorbs cyan light, which has a higher frequency and a shorter wavelength than magenta light. As the red complex absorbs light with higher energy (shorter wavelength) than the green complex, the d-orbital splitting is larger in the red complex, indicating a stronger-field ligand. Therefore, the complex that has the stronger-field ligand is the red one.

Key Concepts

Spectrochemical Series

The spectrochemical series is a list of ligands ranked by their ability to split the d-orbitals of a central metal ion in transition metal complexes. This series is essential for understanding which ligands exert strong or weak fields when they coordinate with metals. The series follows a general order based on field strength:

• Weak-Field Ligands: I^-, Br^-, Cl^-, F^-, OH^-, H₂O, NCS^-
• Intermediate Ligands: EDTA, NH₃, en (ethylenediamine), NO₂^-
• Strong-Field Ligands: CN^-, CO

A strong-field ligand causes significant splitting of the metal's d-orbitals. This large splitting means that electrons can pair up in lower energy orbitals rather than occupy higher energy levels, influencing the spin state of the complex.
To predict the color outcome and electronic structure, knowing the position of ligands in this series is crucial.

Transition Metal Complexes

Transition metal complexes are formed when transition metals bind with ligands. These complexes are characterized by their diverse structures and properties, heavily influenced by the surrounding ligands. Transition metals have partially filled d-orbitals which allows them to form complex ions with various ligands.
In these complexes, the arrangement and type of ligands determine properties such as magnetism, color, and geometry.

• The metal ion acts as a central pivot, coordinating with other molecules or ions known as ligands.
• These ligands can affect the overall stability and reactivity of the complex.
• The geometry of complexes depends on factors like the number and sizes of ligands and the charge of the metal ion.

Understanding these dynamics is crucial for applications in fields like catalysis, material science, and bioinorganic chemistry.

Ligand Field Splitting

Ligand field splitting describes the process where the degeneracy of the d-orbitals in transition metal centers is lifted when ligands approach and interact with the metal. Ligands create an electrostatic field causing the energy levels of the d-orbitals to split into two groups: typically called the 't_2g' and 'e_g' orbitals in an octahedral coordination.

• The degree of splitting and the energy gap depends on the nature and strength of the ligands involved as demonstrated in the spectrochemical series.
• Strong-field ligands cause greater splitting and often lead to low-spin complexes, where all lower energy orbitals are completely filled before any electrons fill the higher ones.
• Weak-field ligands cause smaller splittings leading often to high-spin complexes where electrons singly occupy the larger number of orbitals before pairing occurs.

Ligand field theory expands upon this, incorporating orbital shape and molecular symmetry to explain the complex energetics further.

Color and Light Absorption in Complexes

The colors observed in transition metal complexes are a result of the light absorption characteristics governed by the split d-orbitals. When white light passes through or is reflected by a complex, specific wavelengths are absorbed to promote electron transitions between the split orbitals, primarily from the t_2g to the e_g.
This energy difference corresponds to specific portions of the visible spectrum, and the color seen is the complementary color to the absorbed wavelength. For instance:

• If a complex appears red, it absorbs light in the cyan region (higher energy/frequency).
• A green-appearing complex absorbs its complementary color in the magenta range (lower energy).

Thus, the colors provide insightful clues about the energy levels involved and the ligand field strength. Understanding these principles helps in predicting and manipulating the properties of metal complexes in various applications.