Problem 62 - Chemistry: The Central Science

Question

Draw the crystal-field energy-level diagrams and show the placement of electrons for the following complexes: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-}\), (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) (a high-spin complex), (c) \([\text { Ru(bipy) }]^{3+}\) (a low-spin complex), (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral), (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-},(f)\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\). S in the spectrochemical series?

Step-by-Step Solution

Answer

In summary, the crystal-field energy-level diagrams and electron placements for the given complexes are: (a) \([\text{VCl}_{6}]^{3-}\): Octahedral, high-spin; 2 electrons in \(t_{2g}\) orbitals. (b) \([\text{FeF}_{6}]^{3-}\): Octahedral, high-spin; 3 electrons in \(t_{2g}\) and 2 in \(e_{g}\) orbitals. (c) \([\text{Ru(bipy)}]^{3+}\): Octahedral, low-spin; 5 electrons in \(t_{2g}\) orbitals. (d) \([\text{NiCl}_{4}]^{2-}\): Tetrahedral; 3 electrons in \(e\) and 5 in \(t_{2}\) orbitals. (e) \([\text{PtBr}_{6}]^{2-}\): Octahedral, low-spin; 6 electrons in \(t_{2g}\) orbitals. (f) \([\text{Ti(en)}_{3}]^{2+}\): Octahedral, low-spin; 2 electrons in \(t_{2g}\) orbitals.

Step 1: Determine the Electron Configuration

The vanadium ion in this complex has a +3 oxidation state, so it has the electron configuration of [Ar] 3d^{2}.

Step 2: Determine the Geometry and Splitting Pattern

The complex is octahedral, and in octahedral complexes, the d-orbitals are split into two sets: \(e_{g}\) (dx2-y2, dz2) and \(t_{2g}\) (dxy, dyz, dxz). Since Cl- is a weak field ligand, the complex is high-spin.

Step 3: Draw the Diagram and Place the Electrons

In high-spin complexes, electrons fill the orbitals according to Hund's rule. We would first fill the \(t_{2g}\) orbitals and then the \(e_{g}\) orbitals. So, in this case, the two electrons go into the \(t_{2g}\) orbitals, one in each orbital. (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\)

Step 4: Determine the Electron Configuration

The iron ion in this complex has a +3 oxidation state and has an electron configuration of [Ar] 3d^{5}.

Step 5: Determine the Geometry and Splitting Pattern

The complex is octahedral, so it has the same \(e_{g}\) and \(t_{2g}\) splitting pattern as in (a). The problem states that this is a high-spin complex.

Step 6: Draw the Diagram and Place the Electrons

The electron filling follows Hund's rule, which results in three electrons in the \(t_{2g}\) orbitals and two in the \(e_{g}\) orbitals. (c) \([\text { Ru(bipy) }]^{3+}\)

Step 7: Determine the Electron Configuration

The ruthenium ion in this complex has a +3 oxidation state, so it has an electron configuration of [Kr] 4d^{5}.

Step 8: Determine the Geometry and Splitting Pattern

The complex is octahedral, so it has the same \(e_{g}\) and \(t_{2g}\) splitting pattern as in (a). The problem states that this is a low-spin complex.

Step 9: Draw the Diagram and Place the Electrons

In low-spin complexes, electrons first occupy the lower-energy orbitals before any pairing takes place. Therefore, all five electrons are in the \(t_{2g}\) orbitals, with two orbitals having two electrons and one having just one electron. (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\)

Step 10: Determine the Electron Configuration

The nickel ion in this complex has a +2 oxidation state, so it has an electron configuration of [Ar] 3d^{8}.

Step 11: Determine the Geometry and Splitting Pattern

The complex is tetrahedral, so the d-orbitals are split into two sets: \(e\) (dxy, dyz, dxz) and \(t_{2}\) (dx2-y2, dz2).

Step 12: Draw the Diagram and Place the Electrons

The electron filling follows Hund's rule, resulting in three electrons in the \(e\) orbitals and five in the \(t_{2}\) orbitals. (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-}\)

Step 13: Determine the Electron Configuration

The platinum ion in this complex has a +4 oxidation state, so it has an electron configuration of [Xe] 4f^{14} 5d^{6}.

Step 14: Determine the Geometry and Splitting Pattern

The complex is octahedral and Pt(IV) is a strong field, so this is a low-spin complex with an \(e_{g}\) and \(t_{2g}\) splitting pattern.

Step 15: Draw the Diagram and Place the Electrons

In this low-spin complex, the electrons first occupy the lower-energy orbitals, the \(t_{2g}\) subset. Therefore, all six electrons are in the three \(t_{2g}\) orbitals. (f) \(\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\)

Step 16: Determine the Electron Configuration

The titanium ion in this complex has a +2 oxidation state, so it has an electron configuration of [Ar] 3d^{2}.

Step 17: Determine the Geometry and Splitting Pattern

The complex is octahedral, so it has the same \(e_{g}\) and \(t_{2g}\) splitting pattern as in (a). Since en is a moderately strong field ligand, this is a low-spin complex.

Step 18: Draw the Diagram and Place the Electrons

In this low-spin complex, both electrons occupy the lower-energy \(t_{2g}\) orbitals.

Key Concepts

Octahedral Complexes

Octahedral complexes consist of a central metal ion surrounded by six ligands arranged at the corners of an octahedron. This geometry creates a unique environment that affects the energy levels of the metal ion's d-orbitals, leading to a phenomenon known as crystal field splitting. In an octahedral field, the d-orbitals split into two groups: three t2g orbitals with lower energy and two eg orbitals with higher energy. This splitting pattern is crucial for determining the electronic structure and properties of the complex.

When electrons occupy these split d-orbitals, their arrangement follows specific rules based on the nature of the ligands, which can be either strong field (low-spin) or weak field (high-spin). Understanding the electron configuration in these complexes is vital as it influences their color, magnetic properties, and reactivity.

High-Spin and Low-Spin Complexes

The difference between high-spin and low-spin complexes is determined by the strength of the field produced by the ligands. High-spin complexes occur when the metal is surrounded by weak field ligands, which results in a smaller splitting of the d-orbitals. Electrons prefer to occupy the higher energy eg orbitals to maintain unpaired spins as per Hund's rule, leading to a maximum number of unpaired electrons.

On the other hand, low-spin complexes form with strong field ligands that produce a larger splitting of the d-orbitals. In this scenario, electrons fill the lower energy t2g orbitals first, and pairing occurs even if empty eg orbitals are available, resulting in a minimal number of unpaired electrons. These nuances in electron arrangement have profound effects on the chemical behavior of the complex.

Electron Configuration

Electron configuration refers to the distribution of electrons in the atomic or molecular orbitals of an element or compound. For transition metal complexes, the configuration is expressed in terms of the number of electrons in the d-orbitals. The knowledge of the oxidation state of the metal ion and its electronic configuration in its free ion state (before complexation) is essential to determine how the d-orbitals will be filled once the metal forms a complex.

In the context of crystal field theory, the electron configuration is influenced by the splitting of the d-orbitals into t2g and eg sets. Whether the complex is high-spin or low-spin alters the electron placement and directly impacts the magnetic and optical properties of the complex.

d-Orbital Splitting

d-Orbital splitting is at the heart of crystal-field theory. It explains the separation of the five degenerate d-orbitals into subsets with different energy levels upon the approach of ligands to a metal ion. In an octahedral crystal field, this splitting results in the lower-energy t2g orbitals and the higher-energy eg orbitals. The energy gap between these subsets, known as the crystal field splitting energy (Δoct), determines whether a complex adopts a high-spin or low-spin electron configuration.

Factors like the nature of the ligands and the metal ion's charge can affect the magnitude of Δoct. Ligands are often ranked according to their ability to split these orbitals on the spectrochemical series, with strong-field ligands inducing greater splitting and favoring low-spin arrangements, while weak-field ligands induce lesser splitting and favor high-spin arrangements.

Hund's Rule

Hund's rule, also known as the rule of maximum multiplicity, is a guiding principle for electron distribution in degenerate orbitals such as the t2g and eg sets in transition metal complexes. According to this rule, electrons occupy empty orbitals singly before they pair up. Electrons in singly occupied orbitals keep parallel spins as far as possible, which minimizes electron-electron repulsions and lowers the total energy of the atom or ion.

Applying Hund's rule in the context of crystal field theory helps predict the magnetic properties of complexes, as the number of unpaired electrons determines whether the complex will be diamagnetic (all electrons paired) or paramagnetic (one or more unpaired electrons). When combined with the knowledge of the ligand field strength, Hund's rule reveals whether a complex is high-spin or low-spin.