Question

Estimate the ligand field splitting for (a) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) \(\left(\lambda_{\max }=295 \mathrm{~nm}\right),(b)\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\left(\lambda_{\max }=435 \mathrm{~nm}\right)\), and (c) \(\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}\left(\lambda_{\max }=540 \mathrm{~nm}\right)\), where \(\lambda_{\max }\) is the wavelength of the most intensely absorbed light. (d) Arrange the ligands in order of increasing ligand field strength.

Short answer

Ligand field splitting energies: (a) \( \Delta_{\mathrm{CN}^{-}} \) > (b) \( \Delta_{\mathrm{NH}_3} \) > (c) \( \Delta_{\mathrm{H}_2O} \) ; therefore, the ligands in order of increasing strength are water < ammonia < cyanide.

Step-by-step solution

Introduction to ligand field splitting

Ligand field splitting energy, denoted by \( \Delta \), can be estimated by using the absorbed light wavelength at its maximum (\( \lambda_{\max} \) ) based on the relationship \(\Delta = \frac{hc}{\lambda}\), where \(h\) is Planck's constant and \(c\) is the speed of light.

Calculation for \( \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-} \)

Use the \( \lambda_{\max} = 295 \text{ nm} \) to calculate the ligand field splitting for Cobalt hexacyanide. Convert the wavelength to meters by multiplying by \(1 \times 10^{-9} \). Then, use the given equation to calculate \( \Delta \) in joules.

Calculation for \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \)

Use the \( \lambda_{\max} = 435 \text{ nm} \) to calculate the ligand field splitting for Cobalt hexaammine. As before, convert the wavelength to meters and apply the same equation to find \( \Delta \) in joules.

Calculation for \( \left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} \)

Use the \( \lambda_{\max} = 540 \text{ nm} \) to calculate the ligand field splitting for Cobalt hexaaqua. Convert the wavelength to meters and calculate \( \Delta \) using \( \frac{hc}{\lambda} \).

Convert energies to similar units for comparison

If necessary, convert all values of \( \Delta \) to the same energy unit, e.g., electron volts (eV), for an easier comparison.

Arrangement of ligands

Based on the calculated ligand field splitting energies, arrange the ligands in the order of increasing ligand field strength. A larger \( \Delta \) value corresponds to a stronger field ligand.

Key concepts

Spectrochemical Series

The spectrochemical series is a list that ranks ligands based on their ability to split the d-orbital energies of transition metal ions within complexes.

Ligands that cause a greater splitting of these energies are considered 'strong field' and those that cause less splitting are termed 'weak field'. The series is crucial in predicting the color, magnetic properties, and geometry of metal complexes.

For instance, cyanide (CN-) is typically at the strong field end, while water (H2O) is weaker in field strength.

Connection to the Exercise

In the given exercise, the differing absorption wavelengths suggest varying field strengths for the ligands. Cyanide, with its shorter wavelength absorption, indicates a strong field ligand, whereas water suggests a weaker field. The exercise requires the understanding of the spectrochemical series to explain these differences.

Crystal Field Theory

Crystal Field Theory (CFT) explains the interaction between the transition metal ions and their ligands from an electrostatic viewpoint.

When ligands approach a metal ion, they interact with the d-orbitals of the metal, causing a split in energy levels. This results in two sets of orbitals: higher-energy 'eg' and lower-energy 't2g'.

The magnitude of this splitting is known as the 'ligand field splitting energy' and influences properties like color and magnetism.

Ligand Field Splitting in Practice

In our exercise, the application of CFT through the formula \( \Delta = \frac{hc}{\lambda} \) connects the absorbed light's wavelength to the field splitting energy, an integral concept in understanding transition metal complexes.

Transition Metal Complexes

Transition metal complexes consist of a central transition metal ion surrounded by molecules or anions called ligands.

These complexes are fascinating due to their diverse structures and properties that arise from the d-orbitals.

• The coordination number and geometry of the complex depend on the size, charge, and electron configuration of the metal ion as well as the nature of the ligands.
• The color results from the difference in energy between split d-orbitals when an electron jumps from a lower to a higher energy d-orbital as it absorbs a photon of light.
• Varying ligand field strengths lead to different colors and intensities of absorption in spectroscopy.

Implications for the Calculation

During the exercise, the ability to estimate ligand field splitting is essential for understanding the differences between the given cobalt complexes.

Absorption Spectroscopy

Absorption spectroscopy is a technique used to study the absorbing characteristics of substances.

In the context of metal complexes, when white light passes through a solution containing a transition metal complex, specific wavelengths get absorbed depending on the ligand field splitting. The remaining light transmits or reflects, and the solution appears colored—the complementary color of the absorbed light.

The absorbed wavelength (\( \lambda_{\max} \) ) is related to the energy of the electronic transitions between d-orbital levels.

Significance of Wavelength in the Exercise

The given exercise involves using the wavelength of maximum absorption to calculate the ligand field splitting energy, demonstrating a practical use of absorption spectroscopy in analyzing transition metal complexes.