Question

(a) The values of \(\epsilon_{\max }\) for the most intense absorptions in the electronic spectra of \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) and \(\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}\) differ by a factor of about \(100 .\) Comment on this observation and state which complex you expect to exhibit the larger value of \(\varepsilon_{\max }\) (b) In the clectronic spectrum of a solution containing \(\left[\mathrm{V}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+},\) two bands are observed at 17200 and \(25600 \mathrm{cm}^{-1} .\) No absorption for the \(^{3} A_{28} \leftarrow^{3} T_{1 g}(F)\) transition is observed. Suggest a reason for this, and assign the two observed absorptions. (c) Red crystalline \(\left[\mathrm{NiCl}_{2}\left(\mathrm{PPh}_{2} \mathrm{CH}_{2} \mathrm{Ph}\right)_{2}\right]\) is diamagnetic. On heating to \(387 \mathrm{K}\) for 2 hours, a blue-green form of the complex is obtained, which has a magnetic moment of \(3.18 \mu_{\mathrm{B}}\) at \(295 \mathrm{K}\). Suggest an explanation for these observations and draw structures for the complexes, commenting on possible isomerism.

Short answer

(a) \\([\mathrm{CoCl}_4]^{2-}\\) likely has the larger ε_max. (b) Allowed octahedral transitions are observed. (c) Geometry shift causes paramagnetism in heated form, suggesting isomerism.

Step-by-step solution

Understanding ε_max

The molar absorptivity (ε_max) is directly related to the intensity of an absorption band in the electronic spectrum of a metal complex. Generally, complexes with π-bonding ligands or with more extensive d-π* transitions tend to have high ε_max. For \([\mathrm{CoCl}_4]^{2-}\), which is a tetrahedral complex, the distorted coordination causes more intense d-d transitions, usually leading to higher ε_max compared to octahedral complexes like \([\mathrm{Co(OH}_2)_6]^{2+}\). Thus, tetrahedral cobalt complexes are expected to show more intense absorptions.

Analyzing Vanadium Complex Spectrum

The electronic spectrum of \([\mathrm{V(OH}_2)_6]^{3+}\) shows two bands, but does not show the \(^3 A_{2g} \leftarrow ^3 T_{1g}(F)\) transition. This transition requires a change in electron spin state, which is symmetry forbidden and usually weak.The two bands at 17,200 and 25,600 cm⁻¹ can be assigned to allowed octahedral transitions: \(^3 T_{1g}(F) \rightarrow ^3 T_{2g}\) and \(^3 T_{1g}(F) \rightarrow ^3 T_{1g}(P)\) transitions, respectively, which involve electron re-arrangement within d-orbitals.

Explanation for Nickel Complex's Behavior

The red \([\mathrm{NiCl}_2(\mathrm{PPh}_2\mathrm{CH}_2\mathrm{Ph})_2]\) is diamagnetic, indicating a square planar geometry, where all electrons are paired, making it low spin.Upon heating, it converts to a blue-green, paramagnetic form with a magnetic moment of 3.18 μ_B, indicating a change to a tetrahedral or octahedral geometry, such as a \([\mathrm{Ni}_3]\) coordination which is high spin. The change in magnetic properties is due to alteration in ligand field strength and geometry, showing possible geometric isomerism.

Key concepts

Molar Absorptivity (ε_max)

Molar absorptivity, denoted as \( \epsilon_{\text{max}} \), is a measure of how strongly a chemical species absorbs light at a particular wavelength. It is crucial for understanding the intensity of absorption bands observed in the electronic spectra of transition metal complexes. The higher the \( \epsilon_{\text{max}} \), the more intense the color.

• Tetrahedral complexes, such as \( [\text{CoCl}_4]^{2-} \), typically exhibit stronger absorptions due to d-d electronic transitions that are partly allowed. This results in higher values of \( \epsilon_{\text{max}} \).
• Octahedral complexes, like \( [\text{Co(OH}_2)_6]^{2+} \), generally have lower \( \epsilon_{\text{max}} \) because the symmetry reduces the overlap and effectiveness of these transitions.

Therefore, the tetrahedral cobalt complex \( [\text{CoCl}_4]^{2-} \) is expected to have a significantly larger \( \epsilon_{\text{max}} \) compared to the octahedral \( [\text{Co(OH}_2)_6]^{2+} \). The difference by a factor of 100 that the exercise mentions indicates this relationship quite clearly.

Tetrahedral vs. Octahedral Complexes

The geometries of transition metal complexes can dramatically influence their properties, including their electronic spectra and magnetic characteristics. Understanding the differences between tetrahedral and octahedral complexes is key to predicting their behavior.

• Tetrahedral complexes have four ligands, with bond angles of approximately 109.5 degrees. They usually show more intense absorption due to d-d transitions because of the lower symmetry, which allows for some relaxation in selection rules.
• Octahedral complexes, on the other hand, have six ligands forming 90-degree angles with each other. They are more stable and common. The regular arrangement leads to fewer intense d-d transitions due to symmetry restrictions.

These differences play a crucial role in dictating the observed electronic spectra and also contribute to differing molar absorptivity values. Tetrahedral complexes, therefore, often appear more vividly colored, as observed with the cobalt complexes.

Magnetic Properties of Nickel Complexes

Nickel complexes can exhibit different magnetic properties based on the configuration and geometry around the nickel center. For \( [\text{NiCl}_2(\text{PPh}_2\text{CH}_2\text{Ph})_2] \), the initial red form is diamagnetic, indicating all electrons are paired, suggesting a low-spin configuration.

• Square Planar Geometry: The diamagnetic nature suggests a square planar geometry, where electron pairing is maximized.
• Upon heating, this complex changes color to blue-green and becomes paramagnetic, having a magnetic moment of \( 3.18 \mu_{\text{B}} \). This indicates the presence of unpaired electrons, hence a shift to a high-spin configuration.
• Possible Geometries: In this state, the nickel complex could be in a tetrahedral or possibly octahedral form, both allowing for the presence of unpaired electrons.

Changes in coordination can alter the ligand field strength and thus the spin state of the complex. This phenomenon provides insights into the dynamic nature of transition metal complexes and their sensitivity to environmental conditions such as temperature.

Transition Assignments in Vanadium Complexes

Vanadium complexes like \( [\text{V(OH}_2)_6]^{3+} \) exhibit specific transitions in their electronic spectra. Each transition corresponds to changes in the arrangement of d-electrons in response to energy from absorbed light.

• The observed bands at \( 17,200 \) and \( 25,600 \ \text{cm}^{-1} \) can be assigned to specific d-d transitions within an octahedral field. These are the \(^3 T_{1g}(F) \rightarrow ^3 T_{2g} \) and \(^3 T_{1g}(F) \rightarrow ^3 T_{1g}(P) \) transitions.
• The absence of the \(^3 A_{2g} \leftarrow ^3 T_{1g}(F) \) transition is due to its forbidden nature in terms of spin state change and symmetry, making it weak and often unobserved.

This highlights the intricate nature of electronic transitions in transition metal complexes, where selection rules and symmetry drastically influence the observable spectrum. Understanding these assignments aids chemists in predicting and explaining the behavior of similar complexes.