Problem 64 - Chemistry: The Central Science in SI Units, Global Edition

Question

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

Step-by-Step Solution

Answer

In summary, the crystal-field energy-level diagrams for the given complexes are as follows: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-}\): Octahedral, t2g: ↑ ↓ ↑, eg: - (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) (high-spin): Octahedral, t2g: ↑ ↓ ↑, eg: ↑ ↑ (c) \(\left[\mathrm{Ru}(\text { bipy })_{3}\right]^{3+}\) (low-spin): Octahedral, t2g: ↑ ↓ ↑ ↓ ↑ ↓, eg: - - (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral): e: ↑↓ ↑↓ ↑↓, t2: ↑ ↑ - (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-}\): Octahedral, t2g: ↑↓ ↑↓ ↑↓, eg: ↑ ↑ (f) \(\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\): Octahedral, t2g: - - -, eg: - -

Step 1: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-}\)

Central ion: V (Vanadium), Electronic configuration: [Ar] 3d^3 4s^2 Charge: 3+, Final electron configuration: [Ar] 3d^2 The complex is octahedral, so the d-orbitals get split into two sets: t2g and eg, with t2g at lower energy and eg at higher energy. Electron configuration in the crystal field: - Two electrons will first fill the three t2g orbitals (one in each, following Hund's rule), and no electrons in eg. - Energy level diagram: t2g: ↑ ↓ ↑, eg: -

Step 2: (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) (a high-spin complex)

Central ion: Fe (Iron), Electronic configuration: [Ar] 3d^6 4s^2 Charge: 3+, Final electron configuration: [Ar] 3d^5 The complex is octahedral, so the d-orbitals get split into two sets: t2g and eg. Since it's a high-spin complex, the energy difference between t2g and eg is small, allowing the electrons to occupy the higher energy eg orbitals following Hund's rule. Electron configuration in the crystal field: - Three electrons fill the t2g orbitals and two go to the eg orbitals. - Energy level diagram: t2g: ↑ ↓ ↑, eg: ↑ ↑

Step 3: (c) \(\left[\mathrm{Ru}(\text { bipy })_{3}\right]^{3+}\) (a low-spin complex)

Central ion: Ru (Ruthenium), Electronic configuration: [Kr] 4d^7 5s^1 Charge: 3+, Final electron configuration: [Kr] 4d^4 The complex is octahedral, so the d-orbitals get split into the two sets: t2g and eg. It's a low-spin complex, meaning a large energy difference between t2g and eg, so electrons prefer to fully occupy the lower energy t2g orbitals before going to the eg orbitals. Electron configuration in the crystal field: - Four electrons fill the t2g orbitals completely, and no electrons in eg. - Energy level diagram: t2g: ↑ ↓ ↑ ↓ ↑ ↓, eg: - -

Step 4: (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral)

Central ion: Ni (Nickel), Electronic configuration: [Ar] 3d^8 4s^2 Charge: 2+, Final electron configuration: [Ar] 3d^8 The complex is tetrahedral. In this case, the d-orbitals get split into two sets: e (double) and t2 (triplet), with e at lower energy and t2 at higher energy. Electron configuration in the crystal field: - Six electrons fill the two e orbitals and two go to the three t2 orbitals (following Hund's rule). - Energy level diagram: e: ↑↓ ↑↓ ↑↓, t2: ↑ ↑ -

Step 5: (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-}\)

Central ion: Pt (Platinum), Electronic configuration: [Xe] 4f^14 5d^9 6s^1 Charge: 2+, Final electron configuration: [Xe] 4f^14 5d^8 The complex is octahedral, so the d-orbitals get split into t2g and eg sets. Electron configuration in the crystal field: - Five electrons will first fill the three t2g orbitals, and three go to the two eg orbitals (following Hund's rule). - Energy level diagram: t2g: ↑↓ ↑↓ ↑↓, eg: ↑ ↑

Step 6: (f) \(\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\)

Central ion: Ti (Titanium), Electronic configuration: [Ar] 3d^2 4s^2 Charge: 2+, Final electron configuration: [Ar] 3d^0 The complex is octahedral, so the d-orbitals get split into t2g and eg sets. Since there are no d-electrons for the Ti(II) ion, the energy level diagram will have no occupied orbitals. Electron configuration in the crystal field: - No electrons in t2g and eg. - Energy level diagram: t2g: - - -, eg: - -

Key Concepts

Octahedral Complex

In the world of coordination chemistry, an octahedral complex refers to a molecule or ion surrounded by six ligands arranged at the vertices of a regular octahedron. This configuration is common for transition metal complexes and significantly influences their properties.

The ligand field splits the five degenerate d-orbitals of the central metal atom into different energy levels. In an octahedral field, these split into two sets: the lower energy set known as the t2g orbitals and the higher energy set known as the eg orbitals. This separation is due to the differing orientations of the d-orbitals relative to the surrounding ligands.

Here's what occurs in an octahedral complex:

• The t2g orbitals ( d_{xy}, d_{xz}, d_{yz}) align between the axes and experience less repulsion from the ligands
• The eg orbitals (d_{x^2-y^2}, d_{z^2}) directly face the ligands and experience more repulsion

This splitting is critical when discussing the electronic structure and magnetic properties of a complex. It also impacts the color and reactivity of the compound.

Electron Configuration

Understanding the electron configuration of the central metal ion in a complex is fundamental in predicting the behavior and properties of the complex. Electron configuration provides insight into the distribution of electrons among an atom or ion's orbitals.

For a metal in an octahedral complex:

• Its d-electrons will occupy the t2g and eg orbitals resulting from crystal field splitting
• The filling order of these orbitals depends on the energy difference, Δ, between t2g and eg orbitals

In a high-spin octahedral complex, Δ is small, so electrons will fill all the orbitals with the maximum number of unpaired electrons before any pairing occurs. Conversely, in a low-spin complex, Δ is large, leading to paired electrons in the lower energy t2g orbitals before populating the eg orbitals. This difference in electron arrangement significantly affects the magnetic and spectral properties of the complex.

Energy Level Diagram

An energy level diagram visually represents the arrangement and energy distribution of electrons within a complex. In crystal field theory, this diagram displays how the energy levels of d-orbitals split in the presence of a ligand field.

The t2g and eg sets depict the energy differences in octahedral complexes. When drawing an energy diagram:

• The horizontal lines represent the energy levels for t2g and eg orbitals
• Arrows indicate electrons, with each arrow showing one electron, pointing up or down to denote spin

Higher energy lines correspond to the eg orbitals, and lower ones to the t2g orbitals.

By examining an energy level diagram, you can determine the number of unpaired electrons, predict the magnetic properties, and understand potential transition pathways in a complex. This approach provides vital information to chemists on how to tailor and synthesize complexes with desired properties.