Question

The compound \(\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{2}\) is green, whereas \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\) is violet. Predict the predominant color of light absorbed by each compound. Which compound absorbs light with the shorter wavelength? Predict in which compound \(\Delta\) is greater and whether \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{NH}_{3}\) is the stronger field ligand. Do your conclusions agree with the spectrochemical series?

Short answer

The compound \(\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{2}\) absorbs red light, while \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\) absorbs yellow light. The shorter wavelength absorbed is by the violet complex, \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\). The stronger field ligand is \(\mathrm{NH}_{3}\), resulting in a greater crystal field splitting energy, \(\Delta\), in this complex. These conclusions agree with the spectrochemical series.

Step-by-step solution

Understanding color absorption

When a compound appears green, it's because it reflects or transmits green light, which indicates that the compound absorbs the color complementary to green. Similarly, if a compound appears violet, it reflects or transmits violet light and absorbs the color that is complementary to violet.

Identify complementary colors

For green, the complementary color is red, which is on the longer wavelength end of the spectrum. For violet, the complementary color is yellow, which is on the shorter wavelength end of the spectrum.

Determine which compound absorbs shorter wavelengths

Since the green compound primarily absorbs red light and the violet compound primarily absorbs yellow light, we can conclude that the violet compound (\(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\)) absorbs light with a shorter wavelength than the green compound (\(\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{2}\)).

Determine the stronger field ligand and the compound with greater \(\Delta\)

Since the violet compound (\(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\)) absorbs shorter wavelengths, it must have a greater crystal field splitting energy, \(\Delta\), because shorter wavelengths of light have higher energy. Therefore, the stronger field ligand must be \(\mathrm{NH}_{3}\), as it results in a greater \(\Delta\) in the complex.

Compare with the spectrochemical series

In the spectrochemical series, ligands are ordered based on their ability to produce large crystal field splitting energies. When comparing the ligands given in the problem, we would find that \(\mathrm{NH}_{3}\) indeed is a stronger field ligand than \(\mathrm{H}_{2} \mathrm{O}\), confirming our conclusion from step 4. To summarize: 1. The green compound \(\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{2}\) predominantly absorbs red light, whereas the violet compound \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\) predominantly absorbs yellow light. 2. The violet compound absorbs light with a shorter wavelength. 3. The stronger field ligand is \(\mathrm{NH}_{3}\), and the complex with \(\mathrm{NH}_{3}\) has a greater crystal field splitting energy, \(\Delta\). 4. Our conclusions agree with the spectrochemical series.

Key concepts

Color and Wavelength Absorption

The vibrant colors observed in coordination compounds, like the green of \( \mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_{6} \mathrm{Cl}_2 \) or the violet of \( \mathrm{Ni}\left(\mathrm{NH}_3 \right)_6 \mathrm{Cl}_2 \), are due to the absorption of certain wavelengths of light. When a compound appears a certain color, it reflects that color's wavelength while absorbing its complementary hue.
For example, if the compound appears green, it predominantly absorbs red light, which lies on the opposite side of the spectrum. Conversely, a violet-colored compound will mostly absorb yellow light. This understanding helps to predict color absorption simply based on the appearance of the compound. Knowing these color pairs is essential:

• Green absorbs red
• Violet absorbs yellow

By connecting color perception with wavelengths, we better grasp which wavelengths are absorbed and thus better understand the nature of a compound's interactions with light.

Spectrochemical Series

The spectrochemical series is a powerful tool that ranks ligands based on their ability to split the d-orbitals in transition metal complexes. This series aids in predicting the strength of a field exerted by different ligands, determining crystal field splitting energy \( \Delta \), which directly influences the colors we see.
The series essentially places stronger field ligands, which cause a greater \( \Delta \), at the higher end of the list. For example, common ligands placed in order are:

• \( \mathrm{I}^- \) (weak field)
• \( \mathrm{Br}^- \)
• \( \mathrm{Cl}^- \)
• \( \mathrm{H}_2 \mathrm{O} \)
• \( \mathrm{NH}_3 \)
• \( \mathrm{CN}^- \) (strong field)

This ranking supports that \( \mathrm{NH}_3 \) is a stronger field ligand than \( \mathrm{H}_2 \mathrm{O} \), resulting in greater splitting and confirming its impact observed in the violet color of the \( \mathrm{Ni}(\mathrm{NH}_3)_6 \mathrm{Cl}_2 \) complex.

Ligand Field Strength

Ligand field strength refers to the ability of a ligand to affect the arrangement and energy of d-orbitals in a metal complex. This strength is pivotal in dictating the extent of d-orbital splitting, leading to different observable properties, like color.
Stronger field ligands, like \( \mathrm{NH}_3 \), cause a greater d-orbital splitting, enhancing the energy difference \( \Delta \). This results in the absorption of higher-energy (shorter wavelength) light, lending to different colors in comparison to weaker field ligands like \( \mathrm{H}_2 \mathrm{O} \).
The clear distinctions between ligand field strengths emphasize the role ligands play, not just in the color we see but also in the overall electronic configuration and stability of the complex itself.

Crystal Field Splitting Energy

Crystal field splitting energy, denoted as \( \Delta \), is the difference in energy between split d-orbitals in a metal complex in the presence of a ligand field. This phenomenon explains much about the optical properties and the geometry of coordination compounds.
When ligands approach a metal ion, they create an electrostatic field that disrupts the degenerate nature of d-orbitals. These orbitals split into two energy states—\( t_{2g} \) and \( e_g \) in an octahedral field, for example. The energy gap \( \Delta \) between these states dictates which wavelengths of light the compound can absorb.
A larger \( \Delta \) implies absorption of higher energy (shorter wavelength) light, resulting in compounds like \( \mathrm{Ni}(\mathrm{NH}_3)_6 \mathrm{Cl}_2 \) appearing violet. This contrasts with \( \mathrm{Ni}(\mathrm{H}_2 \mathrm{O})_6 \mathrm{Cl}_2 \), where a smaller \( \Delta \) results in the absorption of lower energy red light, giving it a green appearance. Understanding \( \Delta \) is crucial for predicting and explaining the color and behavior of transition metal complexes.