Question

The complex ion \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) has an absorption maximum at around \(800 \mathrm{~nm}\). When four ammonias replace water, \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{2+}\), the absorption maximum shifts to around \(600 \mathrm{~nm} .\) What do these results signify in terms of the relative field splittings of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) ? Explain.

Short answer

The shift of the absorption maximum from \(800 \mathrm{~nm}\) in the complex ion \(\left[\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) to \(600 \mathrm{~nm}\) in the complex ion \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{2+}\) signifies that the field splitting produced by ammonia ligands is larger than that produced by water ligands. This is because the lower absorption maximum indicates a larger crystal field splitting when ammonia ligands are present, reflecting a stronger field produced by ammonia compared to water.

Step-by-step solution

Understanding the given complexes

We are given two complex ions, the first one is \(\left[\mathrm{Cu}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\), having six water molecules as ligands. The second complex ion is \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{2+}\), where four water molecules are replaced by ammonia molecules. The absorption maximum for the first complex is around \(800 \mathrm{~nm}\), and for the second complex, it is around \(600 \mathrm{~nm}\).

Relate absorption maximum to energy levels

The absorption maximum corresponds to the energy difference between the orbitals involved in the d-d transition. This energy difference is related to the crystal field splitting, which depends on the strength of the field produced by the ligands. A higher absorption maximum indicates a larger energy difference, which in turn indicates a larger crystal field splitting.

Compare the field splittings

The first complex with water ligands has an absorption maximum of around \(800 \mathrm{~nm}\) and the second complex with four ammonia ligands has an absorption maximum of around \(600 \mathrm{~nm}\). Since the absorption maximum of the second complex is lower than that of the first complex, this means the crystal field splitting is larger in the second complex when ammonia ligands are present.

Analyze the effect of ligand replacement

The larger field splitting in the second complex means that ammonia produces a stronger field as compared to water. The replacement of the four water molecules with ammonia causes a shift of the absorption maximum from \(800 \mathrm{~nm}\) to \(600 \mathrm{~nm}\), indicating that the field produced by ammonia ligands is stronger than that produced by water ligands.

Conclusion

Based on the given information about the absorption maximum of the two complex ions, we can infer that the field splitting produced by ammonia ligands is larger than that produced by water ligands. This is signified by the shift of the absorption maximum from \(800 \mathrm{~nm}\) to \(600 \mathrm{~nm}\) when four water molecules are replaced by ammonia molecules in the complex ion.

Key concepts

Complex Ions

Complex ions are entities formed from a central metal atom or ion bonded to one or more molecules or ions, referred to as ligands. The bond is typically coordinate covalent, where the ligands donate a pair of electrons to the metal. These interactions give rise to unique chemical and physical properties, distinguishing complex ions from the individual atoms or molecules from which they are formed.

Understanding complex ions is crucial because they are prevalent in a variety of chemical reactions, including biological processes and industrial applications. In the given example, \( \left[\mathrm{Cu}\left(\mathrm{H}_2\mathrm{O}\right)_6\right]^{2+} \) and \( \left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\left(\mathrm{H}_2\mathrm{O}\right)_2\right]^{2+} \) are both complex ions with copper as the central atom. Water and ammonia act as ligands, affecting properties like color and reactivity due to their distinct interactions with the copper ion.

Ligand Field Theory

Ligand field theory (LFT) is a modification of the crystal field theory that considers the covalent, as well as the ionic aspects of the bonding in complexes. This theory offers a more detailed understanding of how ligands affect the electron distribution around the central metal ion, leading to crystal field splitting.

According to LFT, ligands create an electric field that splits the degenerate (same energy) d-orbitals of the metal ion into groups with different energies. These energy differences are key in determining the colors and chemical behavior of the complexes. The act of ligands, such as water and ammonia interacting with copper ions, changes the energy levels of the d-orbitals, influencing properties like the absorption spectra observed in our exercise.

Absorption Spectroscopy

Absorption spectroscopy is a technique used to study the absorption of light by chemical substances. It helps in identifying the energy gap between the ground state and the excited state of an electron. A substance will absorb light at specific wavelengths depending on this gap.

The observed color of a complex ion is actually the complement of the color it absorbs. For instance, when we mention that the absorption maximum for the \( \left[\mathrm{Cu}\left(\mathrm{H}_2\mathrm{O}\right)_6\right]^{2+} \) complex is around 800 nm, it indicates that it absorbs light in the infrared region, which results in a perceived color change. As absorption spectroscopy reveals shifts in these wavelengths, we can deduce changes in the electron configuration within the complex ion, commonly triggered by the substitution of ligands.

d-d Transitions

d-d transitions are electronic transitions between d-orbitals of a metal ion split in energy by the presence of a ligand field. When a transition metal ion is surrounded by ligands, the degenerate d-orbitals split into two or more energy levels. An electron may move from a lower energy d-orbital to a higher energy d-orbital by absorbing a photon of light that corresponds to the energy difference between these orbitals.

In the context of our exercise, the shift of the absorption maximum from 800 nm to 600 nm suggests a shorter wavelength (higher energy) of light is absorbed for the electronic transition in \( \left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\left(\mathrm{H}_2\mathrm{O}\right)_2\right]^{2+} \) compared to \( \left[\mathrm{Cu}\left(\mathrm{H}_2\mathrm{O}\right)_6\right]^{2+} \) complex. This is indicative of a larger energy gap for d-d transitions in the presence of ammonia ligands, denoting a stronger ligand field that ammonia exerts on the copper ion compared to water.