Question

Draw the \(d\) -orbital splitting diagrams for the octahedral complex ions of each of the following. a. \(\mathrm{Zn}^{2+}\) b. \(\mathrm{Co}^{2+}\) (high and low spin) c. \(\mathrm{Ti}^{3+}\)

Short answer

a. Zn²⁺: \(t_{2g}\) - ↑↓, ↑↓, ↑↓; \(e_g\) - ↑↓, ↑ b. Co²⁺: Low-spin: \(t_{2g}\) - ↑↓, ↑↓, ↑↓; \(e_g\) - ↑↑, 0 High-spin: \(t_{2g}\) - ↑, ↑, ↑; \(e_g\) - ↑, ↑ c. Ti³⁺: \(t_{2g}\) - ↑, 0, 0; \(e_g\) - 0, 0

Step-by-step solution

Find the electron configuration for each ion

To determine the electron configuration for each ion, we first need to know the atomic number of each element. Then, we can use the loss of electrons to find the electron configuration for the ion. a. Zn²⁺: Zinc has 30 electrons in its neutral state. When it loses 2 electrons, the configuration is as follows: \([Ar] 3d^8\) b. Co²⁺: Cobalt has 27 electrons in its neutral state. When it loses 2 electrons, the configuration is as follows: \([Ar] 3d^7\) c. Ti³⁺: Titanium has 22 electrons in its neutral state. When it loses 3 electrons, the configuration is as follows: \([Ar] 3d^1\)

Draw the d-orbital splitting for octahedral complexes

In an octahedral complex, the energy level of the d-orbitals splits into two sets: \(t_{2g}\) orbitals (lower energy) and \(e_g\) orbitals (higher energy). The \(t_{2g}\) orbitals include the \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals, while the \(e_g\) orbitals include the \(d_{z^2}\) and \(d_{x^2 - y^2}\) orbitals. We will fill the electrons according to the electron configurations obtained in step 1. a. Zn²⁺: \([Ar] 3d^8\) Place 8 electrons in the d-orbitals, respecting the Hund's rule and the Pauli exclusion principle: \(t_{2g}\): ↑↓, ↑↓, ↑↓ \(e_g\) : ↑↓, ↑ b. Co²⁺: \([Ar] 3d^7\) Place 7 electrons in the d-orbitals: Low-spin: \(t_{2g}\): ↑↓, ↑↓, ↑↓ \(e_g\) : ↑↑, 0 High-spin: \(t_{2g}\): ↑, ↑, ↑ \(e_g\) : ↑, ↑ c. Ti³⁺: \([Ar] 3d^1\) Place 1 electron in the d-orbitals: \(t_{2g}\): ↑, 0, 0 \(e_g\) : 0, 0

Key concepts

Octahedral Complex

An octahedral complex is a coordination compound in which a central metal atom is surrounded by six ligands arranged at the corners of an octahedron. Ligands are molecules or ions that can donate a pair of electrons to the metal atom to form a chemical bond.

In octahedral complexes, the metal's d orbitals are surrounded symmetrically by the ligands. This arrangement causes an electrostatic interaction which leads to the splitting of the d orbitals into two different energy levels. This splitting is essential for understanding the color, magnetism, and chemical reactivity of transition metal complexes.

• The lower energy set of orbitals is called the \(t_{2g}\) orbitals, which include the d_xy, d_yz, and d_xz orbitals.
• The higher energy set is termed the \(e_g\) orbitals, consisting of d_z^2 and d_x^2−y^2 orbitals.

The energy difference between these two sets is known as the crystal field splitting energy, denoted as \(Δ_o\). This value influences the electronic structure and behavior of octahedral complexes.

Electron Configuration

Electron configuration is the distribution of electrons in an atom's orbitals. It helps predict the atom's chemical properties, bonding abilities, and geometry.

For transition metal ions, the electron configuration is determined by removing electrons from the highest energy orbitals first, typically the s and then d orbitals. Here's how the ions in our exercise configure:

• For Zn²⁺: Starting from zinc's neutral state \([Ar] 3d^{10} 4s^2\), losing two electrons results in \([Ar] 3d^8\).
• For Co²⁺: From cobalt's \([Ar] 3d^7 4s^2\), losing two 4s electrons gives \([Ar] 3d^7\).
• For Ti³⁺: Titanium \([Ar] 3d^2 4s^2\) loses three electrons (two 4s and one 3d), resulting in the configuration \([Ar] 3d^1\).

Accurately determining the electron configuration is crucial for analyzing d-orbital splitting and predicting other properties like magnetism.

High Spin vs Low Spin

High spin and low spin refer to the electronic configuration pattern within the split d orbitals in a complex. This concept primarily applies to transition metal complexes, including octahedral ones.

The choice between high spin and low spin is influenced by the strength of the ligand field, characterized by the crystal field splitting energy \(Δ_o\) and the pairing energy. Ligands can be weak or strong field:

• Weak field ligands: These cause a smaller \(Δ_o\). Electrons prefer to occupy the higher energy \(e_g\) levels before pairing in the \(t_{2g}\) orbitals, resulting in a high-spin state. Example: Co²⁺ with seven d electrons can fill each orbital singly, making all spins high.
• Strong field ligands: These increase \(Δ_o\), encouraging electron pairing in the lower energy \(t_{2g}\) orbitals, leading to a low-spin state. Example: the electrons in Co²⁺ might pair in the \(t_{2g}\) orbitals before occupying the \(e_g\) orbitals.

Understanding whether a complex adopts a high or low spin configuration affects its magnetic properties and the color it exhibits.

Transition Metal Ions

Transition metal ions form when transition metals lose electrons to achieve a more stable state. This partially filled d subshell is what characterizes them and affects their chemistry.

These ions often participate in the formation of coordination compounds, like octahedral complexes. Their unique electron configurations facilitate various oxidation states and complex formation, offering a palette of colors in their compounds due to d-d electron transitions.

• Variable oxidation states: Transition metals can exhibit multiple stable oxidation states, enabling them to form a wide variety of compounds.
• Colorful compounds: The presence of unpaired d electrons and d orbital splitting in complex ions results in a rich diversity of colors, useful for identifying specific metal ions.
• Magnetic properties: Their magnetic characteristics depend largely on their electron configuration and whether they adopt high or low spin states.

The study of transition metal ions is crucial in understanding many biological and industrial processes, influencing everything from enzymes to catalysts.