Question

The complex ion \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) has an absorption maximum at around 800 \(\mathrm{nm}\) . When four ammonias replace water, \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+},\) 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

In conclusion, the absorption maximum of Cu(NH3)4(H2O)2^2+ at around 600 nm compared to 800 nm for Cu(H2O)6^2+ signifies that the field splitting of NH3 is greater than that of H2O. This is because the lower wavelength indicates a larger energy difference between the d-orbitals in Cu(NH3)4(H2O)2^2+, meaning NH3 creates a stronger crystal field around the central Cu ion than H2O.

Step-by-step solution

Understanding Crystal Field Theory (CFT)

Crystal Field Theory (CFT) is a model that helps in understanding the electronic structure of complex ions. It describes the interaction of the central metal ion and the ligands surrounding it. The interaction between the central metal ion and the ligands causes the energy levels of d-orbitals to split into different energy levels, which is known as the field splitting.

Relating absorption wavelength to field splitting#:tag_content# When a complex absorbs light, an electron is excited from lower energy d-orbitals to higher energy d-orbitals. The energy difference between these orbitals is directly related to the absorption wavelength. The smaller the energy difference is, the more significant absorption wavelength. Mathematically, this can be represented as: \[ ΔE = h \nu = \dfrac{hc}{λ} \] where ΔE is the energy difference between the d-orbitals, h is the Planck's constant, ν is the frequency of absorbed light, c is the speed of light, and λ is the wavelength of absorbed light.

Step 3: Observing the absorption wavelengths of given complex ions#:tag_content# We have two complex ions: 1. Cu(H2O)6^2+ with an absorption maximum at around 800 nm 2. Cu(NH3)4(H2O)2^2+ with an absorption maximum at around 600 nm Since the absorption maximum is inversely proportional to the energy difference, we can conclude that the energy difference between the d-orbitals in Cu(NH3)4(H2O)2^2+ is larger than that of Cu(H2O)6^2+.

Interpreting the results in terms of field splitting

As we have concluded that the energy difference between the d-orbitals in Cu(NH3)4(H2O)2^2+ is larger than that of Cu(H2O)6^2+, it means that the field splitting due to NH3 ligands is more significant than that of H2O ligands. Therefore, NH3 creates a stronger crystal field around the central Cu ion than H2O. In conclusion, these results signify that the field splitting of NH3 is greater than that of H2O, as the absorption maximum shifts to lower wavelength (600 nm) when four NH3 ligands replace water (with an absorption maximum at around 800 nm) in the complex ion.

Key concepts

Complex Ions

In the realm of chemistry, complex ions play a vital role in understanding the behavior of compounds containing a central metal ion bonded to various molecules or ions known as ligands. A complex ion is formed when ligands donate pairs of electrons to a central metal ion, forming a coordinate covalent bond. This setup alters the electronic environment around the metal ion, influencing many properties, including color and stability.

Complex ions can form through various metals and ligands, resulting in diverse structures and properties. The nature and power of these ligands significantly affect the properties of the complex ion. For example:

• The type of ligand (e.g., water, ammonia) influences the strength of the metal-ligand interaction.
• Ligands can alter the electronic arrangement of the central metal ion, causing differences in properties like color and magnetic behavior.

In the exercise, we're observing the impact of water and ammonia ligands on a copper ion's electronic structure. By exchanging water molecules in the coordination sphere with ammonia, the properties of the complex change, reflecting key aspects of Crystal Field Theory.

Absorption Wavelength

The absorption wavelength of complex ions gives us deep insights into their electronic configurations. When a complex ion is exposed to light, it can absorb specific wavelengths, causing electrons to jump from lower energy orbitals to higher energy ones. This phenomenon is directly tied to the energy difference between these orbitals.

Each absorbed wavelength corresponds to a specific photon energy, and this energy (ΔE) can be calculated using the equation:\[ \Delta E = \frac{hc}{\lambda} \]where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. Therefore, a longer wavelength corresponds to a smaller energy gap, and a shorter wavelength corresponds to a larger energy difference.

In the context of our exercise:

• The transition observed at 800 nm for \(\mathrm{Cu} \left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) indicates a smaller energy gap.
• The shift to 600 nm for \(\mathrm{Cu} \left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+}\) suggests a larger gap due to stronger ligand interaction with ammonia.

Such shifts in absorption wavelength reveal invaluable information about the electronic transitions within the complex ions.

Ligand Field Splitting

Ligand field splitting is a central concept in understanding the behavior of complex ions. This splitting occurs when ligands approach and interact with the central metal ion, causing the d-orbitals of the metal ion to split into different energy levels.

The degree of splitting, often called the ligand field strength, depends on:

• The nature of the ligands themselves.
• Their ability to donate electrons and form bonds with the metal ion.

Different ligands create varying fields, influencing the electronic configuration of the metal ion's d-orbitals. This is crucial in predicting properties like color and magnetic behavior of the complex ion.

In our exercise:

• Replacing water with ammonia in the copper complex increases ligand field splitting.
• Ammonia, compared to water, is a stronger field ligand, causing greater splitting of the copper ion's d-orbitals.

This larger splitting results in a shorter absorption wavelength, indicating stronger electronic interactions and a significant change in the complex's properties. Understanding ligand field splitting is essential for predicting and explaining the behavior of coordination complexes.