Question

The \(\mathrm{Cr}^{3+}\) ion forms octahedral complexes with two neutral ligands \(\mathrm{X}\) and \(\mathrm{Y}\). The color of \(\mathrm{Cr} \mathrm{X}_{6}^{3+}\) is blue while that of \(\mathrm{Cr} \mathrm{Y}_{6}^{3+}\) is yellow. Which is a stronger field ligand, X or Y?

Short answer

Ligand \(\mathrm{Y}\) is the stronger field ligand.

Step-by-step solution

Understand Octahedral Complexes

In octahedral complexes, the central metal ion is surrounded by six ligands. The arrangement of ligands affects the splitting of d-orbitals of the central metal ion, which in turn influences the color of the complex.

Understand Crystal Field Splitting

Crystal field theory explains how the presence of ligands affects the energy levels of d-orbitals in transition metal ions. In an octahedral field, the d-orbitals split into two sets: three lower-energy t2g orbitals and two higher-energy eg orbitals. The energy difference between these two sets is called the crystal field splitting, denoted as \(\Delta_{o}\).

Relate Color to Crystal Field Strength

The color of a complex is determined by the wavelength of light absorbed, which corresponds to the energy of the crystal field splitting, \(\Delta_{o}\). Larger splitting leads to absorption of higher-energy (shorter wavelength) light and the complex exhibits the complementary color.

Apply to the Given Complexes

The complex \(\mathrm{Cr} \mathrm{X}_{6}^{3+}\) appears blue, indicating absorption of orange light (lower energy). The complex \(\mathrm{Cr} \mathrm{Y}_{6}^{3+}\) appears yellow, indicating absorption of violet light (higher energy).

Determine the Stronger Field Ligand

Since the \(\mathrm{Cr} \mathrm{Y}_{6}^{3+}\) complex absorbs higher energy light, the ligand \(\mathrm{Y}\) causes a larger crystal field splitting \(\Delta_{o}\) than ligand \(\mathrm{X}\). Therefore, ligand \(\mathrm{Y}\) is the stronger field ligand compared to \(\mathrm{X}\).

Key concepts

Crystal Field Splitting

Crystal field splitting is a key concept in ligand field theory that describes how ligands influence the energy levels of metal ions in a complex. When ligands approach a metal ion, the electrostatic interactions cause the five degenerate d-orbitals to split into different energy levels.
In an octahedral field, this splitting occurs into two groups:

• Three orbitals with lower energy are called the \(t_{2g}\) orbitals.
• Two orbitals with higher energy are called the \(e_{g}\) orbitals.

The energy difference between these orbitals is referred to as \(\Delta_{o}\), the octahedral splitting energy. This splitting is crucial for understanding the chemical and physical properties of the resulting complexes.

Octahedral Complexes

Octahedral complexes are a common and important structure in coordination chemistry. They consist of a central metal ion surrounded by six ligands arranged symmetrically at the corners of an octahedron.
This geometry is significant because the arrangement of these ligands around the metal ion causes a distinct pattern of d-orbital splitting, as explained by crystal field splitting theory.
The octahedral arrangement is the basis for predicting and rationalizing many properties of transition metal complexes, including magnetism, spectroscopic behavior, and reactivity. Understanding octahedral complexes allows chemists to design compounds with desired chemical behaviors.

Color and Light Absorption

The color observed in transition metal complexes is linked directly to the absorption of light as a result of crystal field splitting. When a complex absorbs light, it promotes electrons from the lower energy \(t_{2g}\) orbitals to the higher energy \(e_{g}\) orbitals, a process which corresponds to specific wavelengths of light.
The absorbed wavelength determines the color that is missing from the spectrum of the light that is transmitted or reflected from the complex. The remaining light, which is the complementary color, is what we observe.

• For example, if a complex absorbs light in the orange region of the spectrum, the complementary color, blue, will be seen.
• Similarly, if the complex absorbs violet light, it will appear yellow.

This understanding helps chemists predict and manipulate the colors of complexes under different conditions.

Strong Field Ligands

Ligands are classified into two categories: strong field and weak field, based on how they affect the crystal field splitting energy \(\Delta_{o}\).
Strong field ligands:

• Cause a large \(\Delta_{o}\), leading to greater splitting between the \(t_{2g}\) and \(e_{g}\) orbitals.
• Often result in low-spin configurations where electrons favor filling lower energy orbitals first, minimizing the number of unpaired electrons.

Conversely, weak field ligands cause smaller \(\Delta_{o}\), resulting in less splitting. In the given example, ligand \(Y\), forming a yellow complex, causes absorption of violet (higher energy) light, indicating it is a strong field ligand compared to ligand \(X\), which forms a blue complex.