Question

Explain why \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (blue) and \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (pink) have different colors. Which complex has its absorption bands at longer wavelengths?

Short answer

\(\left[\mathrm{CoCl}_{4}\right]^{2-}\) absorbs longer wavelength (lower energy) light; \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) absorbs shorter wavelength (higher energy) light.

Step-by-step solution

Understand Coordination Complexes

Coordination complexes are molecules that consist of a central metal atom or ion bonded to surrounding molecules or ions (ligands). In this problem, we have two cobalt complexes: \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) and \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\). These different ligands lead to changes in the energy levels of the d-orbitals, affecting the color.

Identify Ligands Involved

In \(\left[\mathrm{CoCl}_{4}\right]^{2-}\), chlorine acts as the ligand. In \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\), water molecules serve as ligands. Ligands affect the color by changing the energy difference between the d-orbitals in the metal.

Understand Crystal Field Splitting

Crystal Field Theory explains that ligands cause the d-orbitals of the metal ion to split into different energy levels. The difference in these energy levels corresponds to the absorbed light's wavelength, which, consequently, determines the color of the complex.

Compare Ligand Field Strength

Chloride ions are weak field ligands, causing a small splitting of the d-orbitals. Water, on the other hand, is a stronger field ligand, causing a larger splitting. This discrepancy in field strength impacts the color and absorption wavelength of each complex.

Relate Splitting to Color and Wavelength

A large splitting, as in \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\), requires higher energy (shorter wavelength) light to be absorbed, making it appear pink. For \(\left[\mathrm{CoCl}_{4}\right]^{2-}\), lesser splitting leads to absorption of lower energy (longer wavelength) light, hence it appears blue.

Determine Which Has Longer Wavelength Absorption

Since \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) absorbs at a longer wavelength (lower energy) than \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\), it retains its blue color.

Key concepts

Crystal Field Theory

Crystal Field Theory provides a framework for understanding how ligands affect the energy levels of metal ions in coordination complexes. When ligands approach a central metal ion, such as cobalt in our examples, the surrounding electronic field causes the d-orbitals to split into different energy levels. This splitting is because the electrostatic interaction between the negatively charged ligands and the d-electron clouds alters their energy levels.

The specific pattern and magnitude of splitting depend on several factors:

• The geometry of the complex (e.g., tetrahedral or octahedral).
• The nature and field strength of the ligands involved.
• The charge and identity of the metal ion.

By analyzing these factors, we can predict the colors of coordination complexes based on the resultant difference in energy states of the d-orbitals.

Ligands

Ligands play a crucial role in determining the properties of coordination complexes. They are ions or molecules that donate a pair of electrons to the central metal atom to form coordination bonds. Different ligands have varying abilities to affect d-orbital splitting, which directly impacts the color and absorption characteristics of the complex.

For example, in \([ ext{CoCl}_4]^{2-}\), chlorine ions act as ligands, while water molecules serve this role in \([ ext{Co(H}_2 ext{O)}_6]^{2+}\). The field strength of a ligand refers to how strongly it impacts the d-orbitals:

• Chloride is classified as a weak field ligand, causing minimal d-orbital splitting.
• Water, being a stronger field ligand, induces more significant splitting.

This variation in field strength is a key reason for the different colors observed in such complexes.

d-Orbitals Splitting

The concept of d-orbitals splitting underpins the explanation for the diverse colors of coordination complexes. In Crystal Field Theory, the interaction between ligands and d-orbitals results in an energy difference within the d-electron shells. This process is essential to understanding why complexes absorb particular wavelengths of light.

In an octahedral complex like \([ ext{Co(H}_2 ext{O)}_6]^{2+}\), the symmetrically placed ligands cause the five d-orbitals to split into two sets with different energy levels. This splitting creates an energy gap, \( riangle\), which corresponds to the energy of visible light absorbed by the complex. The magnitude of this gap depends on:

• The spatial arrangement of ligands around the metal ion.
• The nature of the ligands, determining the field strength.
• Electrostatic influence on the d-orbitals.

A smaller splitting leads to absorption of lower energy, longer wavelength light, resulting in a blue appearance for \([ ext{CoCl}_4]^{2-}\). Larger splitting entails absorption of higher energy, shorter wavelength light, giving \([ ext{Co(H}_2 ext{O)}_6]^{2+}\) its pink color.

Cobalt Complexes

Cobalt complexes exemplify the principles of coordination chemistry and crystal field effects. Cobalt can form a variety of complexes with different colors due to the changeable nature of its d-orbital splitting, influenced by different ligands.

The cobalt complex \([ ext{CoCl}_4]^{2-}\) appears blue because the weaker chloride ligands cause minimal splitting of the d-orbitals, which results in absorption of longer wavelength (lower energy) light.
Meanwhile, \([ ext{Co(H}_2 ext{O)}_6]^{2+}\) appears pink due to the strong field effect of the water ligands, which creates larger splitting and absorption of shorter wavelength (higher energy) light.

Cobalt's ability to form complexes with such varying properties showcases the versatility and interest in transition metal coordination chemistry. Understanding these mechanisms not only allows chemists to predict the behavior and appearance of complexes but also to apply these principles in various fields such as material science and catalysis.