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(a) The electronic absorption spectrum of \(\left[\mathrm{Ni}(\mathrm{DMSO})_{6}\right]^{2+} \quad\left(\mathrm{DMSO}=\mathrm{Me}_{2} \mathrm{SO}\right) \quad\) exhibits three absorptions at 7728,12970 and \(24038 \mathrm{cm}^{-1} .\) Assign these absorptions. (b) \(\mathrm{CuF}_{2}\) has a distorted rutile structure (four \(\mathrm{Cu}-\mathrm{F}=193 \mathrm{pm}\) and two \(\mathrm{Cu}-\mathrm{F}=227 \mathrm{pm}\) per \(\begin{array}{lllll}\text { Cu } & \text { centre } ) ; & {\left[\mathrm{CuF}_{6}\right]^{2-}} & \text { and } & {\left[\mathrm{NiF}_{6}\right]^{3-}} & \text { are }\end{array}\) distorted octahedral ions. Explain the origins of these distortions. (c) Dissolution of vanadium metal in aqueous HBr leads to a complex 'VBr \(_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) '. X-ray diffraction data reveal that the compound contains a complex cation containing a centre of symmetry. Suggest a formulation for the compound, and a structure for the cation.

Step by step solution

01

Assign Absorptions for [Ni(DMSO)鈧哴虏鈦�

The absorption spectrum of \([\mathrm{Ni(DMSO)}_{6}]^{2+}\) can be assigned based on the splitting of \(d\) orbitals in the octahedral field. Nickel(II) has a \(d^8\) configuration. The observed absorptions at 7728, 12970, and 24038 cm鈦宦� can be assigned to transitions: \(^3A_2g \rightarrow ^3T_{2g}\), \(^3A_2g \rightarrow ^3T_{1g}(F)\), and \(^3A_2g \rightarrow ^3T_{1g}(P)\) respectively.

02

Explain Origin of Distortions in CuF鈧�

Copper(II) in \([\mathrm{CuF}_{6}]^{2-}\) often shows a Janh-Teller distortion due to its \(d^9\) configuration. This results in unequal \(Cu-F\) bond lengths. The shorter \(Cu-F\) bonds (193 pm) and longer bonds (227 pm) agree with this distortion effect. For \([\mathrm{NiF}_{6}]^{3-}\), with a \(d^7\) configuration, similar distortions arise due to electronic repulsions in lower energy states causing variations in bond lengths.

03

Suggest a Formulation and Structure for 'VBr鈧� 路 6H鈧侽'

Based on the dissolution reaction and the description of a symmetry center, the complex can be formulated as \([\mathrm{V(H_2O)_6}]^{3+}[\mathrm{Br}_3]^-\). The center of symmetry suggests a regular octahedral geometry, where vanadium is coordinated by six water molecules in the cation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electronic Absorption Spectrum

The electronic absorption spectrum is a crucial concept in coordination chemistry. It helps to understand how transition metal complexes absorb visible or ultraviolet light. This absorption leads to transitions between different energy levels.
In the context of \([\mathrm{Ni}(\mathrm{DMSO})_{6}]^{2+}\), the observed absorption peaks occur at different wavelengths. These peaks correspond to electronic transitions within the d-orbitals. Transition metals like nickel have partially filled d-orbitals. When light is absorbed, electrons can move from a lower energy d-orbital to a higher energy one.
For example, the absorptions at 7728 cm鈦宦�, 12970 cm鈦宦�, and 24038 cm鈦宦� in Ni虏鈦� complexes correspond to transitions labeled by terms like \(^3A_2g \rightarrow ^3T_{2g}\). These complex symbols describe how electrons rearrange in the orbital energy levels of nickel in this octahedral field.

Crystal Field Theory

Crystal field theory (CFT) is a model describing the electronic structures of transition metal complexes. It accounts for the splitting of d-orbitals in a coordination compound.
Imagine the metal ion centered among surrounding ligands. These ligands act like electric fields due to their negative charges or lone pairs. In an octahedral complex, for instance, this electric field causes the five degenerate d-orbitals in a free metal ion to split into two energy levels.

• Upper energy level: \(e_g\), containing two orbitals
• Lower energy level: \(t_{2g}\), containing three orbitals

The energy difference between these levels is termed the "crystal field splitting energy". This splitting helps us understand why certain transitions occur at specific energies. It impacts everything from the color of the complex to its magnetic properties.

Jahn-Teller Distortion

The Jahn-Teller effect is an important phenomenon in transition metal chemistry. It predicts geometrical distortion in any non-linear molecule with degenerate electronic states, particularly for d鈦� configuration metals like copper(II) in certain complexes.
Taking \([\mathrm{CuF}_{6}]^{2-}\) as an example, the distortion results in unequal bond lengths. Here, four of the Cu-F bonds measure 193 pm and two measure 227 pm. This distortion minimizes the overall system's energy.
This effect is not limited to copper only. It can also affect other configurations, like \([\mathrm{NiF}_{6}]^{3-}\), due to electronic repulsion. The Jahn-Teller distortion is crucial for predicting the geometry and properties of metal complexes, including why they might deviate from perfect symmetry.

X-ray Diffraction

X-ray diffraction (XRD) is a pivotal tool in determining the structure of crystal-based compounds. When X-rays hit a crystal, they scatter in specific patterns based on the crystal's arrangement of atoms.
By analyzing these patterns, scientists can determine the positions of atoms within a compound. This technique is practical for complex systems like metal salts and hydrates. For example, the description of a vanadium bromide complex revealed its structure using XRD.
The technique provided insight into the geometry surrounding the vanadium cation. It confirmed that the \([\mathrm{V(H_2O)_6}]^{3+}\) cation is likely regular octahedral, with water molecules symmetrically arranged around vanadium. Such structural details are critical for understanding chemical properties and reactivity.

Transition Metal Complexes

Transition metal complexes are chemical compounds featuring a central transition metal and surrounding ligands. These ligands can be atoms, ions, or molecules that donate electron pairs to the metal.
The nature of these complexes involves metals with incompletely filled d-orbitals. These metals can form various coordination compounds due to their diverse oxidation states and coordination numbers.

• The geometry of these complexes can vary, but octahedral, tetrahedral, and square planar are common shapes.
• Ligands influence properties such as color, magnetism, and electron distribution within the complex.

Studying metal complexes enables us to predict behaviors, reactivity, and applications in areas like catalysis and material science.