Problem 94 - Chemistry: An Atoms-Focused Approach

Question

Aqueous solutions of copper(II)-ammonia complexes are dark blue. Will the color of the series of complexes \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{(6-x)}\left(\mathrm{NH}_{3}\right)_{x}^{+}\) shift toward shorter or longer wavelengths as the value of \(x\) increases from 0 to \(6 ?\)

Step-by-Step Solution

Answer

Answer: As the value of x increases from 0 to 6, the color of the complex shifts towards shorter wavelengths. This is because ammonia is a stronger ligand than water, leading to an increased energy splitting of the d-orbitals. Consequently, the complex absorbs higher energy (shorter wavelength) visible light for electronic transitions within the d-orbitals.

Step 1: Understand the complex and crystal field theory

The complex ions we are analyzing have the general formula \(\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{(6-x)}\left(\mathrm{NH}_{3}\right)_{x}^{+}\). As x increases, the number of water ligands decreases, and the number of ammonia ligands increases. Crystal field theory explains how the energies of the d-orbitals of a metal ion can be affected by ligands in a complex. In the presence of ligands, the d-orbitals are split into different energy levels, and the energy difference between these levels determines the color of the complex.

Step 2: Compare ligand strength of water and ammonia

Ligand strength determines the energy split of the d-orbitals. According to the spectrochemical series, ammonia (NH3) is a stronger ligand than water (H2O). Therefore, a complex with ammonia as its ligand will have a larger energy split in its d-orbitals as compared to a complex with water as its ligand.

Step 3: Determine the effect of increasing the number of ammonia ligands on color

As x increases in the complex \(\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{(6-x)}\left(\mathrm{NH}_{3}\right)_{x}^{+}\), the number of ammonia ligands also increases. Consequently, the energy splitting of the d-orbitals in the complex will increase. As the energy difference between the d-orbitals increases, the complex absorbs a higher energy (shorter wavelength) of visible light for electronic transitions within the d-orbitals. This means the color of the complex shifts towards shorter wavelengths as x increases from 0 to 6.

Key Concepts

Complex Ions

Complex ions are fascinating structures formed when metal ions associate with one or more ligands. Ligands are molecules or ions that can donate a pair of electrons to the metal ion, establishing a coordinate bond. This interaction creates a range of beautiful colors in complexes, visible in substances like gemstones and certain solutions.
An example of a complex ion is \(\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{(6-x)}\left(\mathrm{NH}_{3}\right)_{x}^{+}\), where copper acts as the central metal ion and water (\(\mathrm{H}_{2}\mathrm{O}\)) and ammonia (\(\mathrm{NH}_{3}\)) serve as ligands.

• Central Metal Ion: Typically a transition metal, such as copper, which is capable of forming bonds with ligands.
• Ligands: These provide electrons; examples include water and ammonia.

The coordination of these components determines the color of the complex due to the specific arrangement and interaction of ligands with the metal's d-orbitals.

Ligand Strength

Ligand strength is a crucial factor in determining the properties of complex ions. It refers to the ability of a ligand to cause the splitting of the metal’s d-orbitals' energy levels.
Ammonia is a stronger ligand than water, meaning it can cause a greater energy split in d-orbitals of a central metal ion when compared to water.
This strength difference is evident through:

• Higher Energy Split: Stronger ligands like ammonia lead to a larger gap in energy between the split d-orbitals.
• Effect on Color: The greater the energy split, the higher energy light (shorter wavelength) absorbed, influencing the color we perceive.

In practice, this means as ammonia replaces water as a ligand in the copper complex, the light absorbed shifts to a shorter wavelength. Thus, impacting the observed color of the solution through the phenomenon of crystal field splitting.

Spectrochemical Series

The spectrochemical series is a useful tool for predicting the relative strength of ligands based on their ability to split d-orbital energies. This series lists ligands in order of increasing field strength, which is crucial for understanding why certain ligands produce certain colors in complexes.
Important aspects of the spectrochemical series include:

• Ranking of Ligands: For example, ammonia is stronger than water, as it is higher on the list.
• Implications for Color Shifts: Transition metals with stronger ligands showcase a greater d-orbital energy split, changing the wavelengths of absorbed light.

In the example of \(\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{(6-x)}\left(\mathrm{NH}_{3}\right)_{x}^{+}\), increased ammonia results in the absorption of shorter wavelengths, thus changing the solution's color as described in the spectrochemical context.