Problem 61 - Chemistry: The Central Science

Question

Draw the crystal-field energy-level diagrams and show the placement of \(d\) electrons for each of the following: (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}\) (four unpaired electrons), (b) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (high spin), (c) \(\left[\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2+}\) (low spin), (d) \(\left[\mathrm{IrCl}_{6}\right]^{2-}\) (low spin), (c) \(\left[\mathrm{Cr}(\mathrm{cn})_{3}\right]^{1+}\), (f) \(\left[\mathrm{NiF}_{6}\right]^{4-}\).

Step-by-Step Solution

Answer

The crystal-field energy diagrams for the given complexes are as follows: (a) \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{4}]^{2+}\): Weak ligands, small splitting; electrons filled as ↑↓ in t2g(dxz, dyz), ↑ in t2g(dxy), ↑ in eg(dx²-y²). (b) \([\mathrm{Mn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\): Weak ligands, small splitting; electrons filled as ↑↓ in t2g(dxz, dyz, dxy), ↑ in eg(dx²-y², d²z²). (c) \([\mathrm{Ru}(\mathrm{NH}_{3})_{3}(\mathrm{H}_{2}\mathrm{O})]^{2+}\): Strong ligands, large splitting; electrons filled as ↑↓ in t2g(dxz, dyz, dxy), ↑↓ in eg(dx²-y²) - low spin. (d) \([\mathrm{IrCl}_{6}]^{2-}\): Intermediate ligands, large splitting; electrons filled as ↑↓ in t2g(dxz, dyz, dxy) - low spin. (e) \([\mathrm{Cr}(\mathrm{CN})_{3}]^{1+}\): Strong ligands, large splitting; electrons filled as ↑↓ in t2g(dxz, dyz, dxy). (f) \([\mathrm{NiF}_{6}]^{4-}\): Weak ligands, small splitting; electrons filled as ↑↓ in t2g(dxz, dyz, dxy) and eg(dx²-y², d²z²).

Step 1: (a) Cr#\({^{2+}}\)

The electron configuration of neutral Chromium (Cr) is [Ar] 3d5 4s1. When it loses 2 electrons, the electron configuration is [Ar] 3d4.

Step 2: (b) Mn#\({^{2+}}\)

The electron configuration of neutral Manganese (Mn) is [Ar] 3d5 4s2. When it loses 2 electrons, the electron configuration is [Ar] 3d5.

Step 3: (c) Ru#\({^{2+}}\)

The electron configuration of neutral Ruthenium (Ru) is [Kr] 4d7 5s1. When it loses 2 electrons, the electron configuration is [Kr] 4d6.

Step 4: (d) Ir#\({^{4+}}\)

The electron configuration of neutral Iridium (Ir) is [Xe] 4f14 5d7 6s2. When it loses 2 electrons due to the negative charge, the electron configuration is [Xe] 4f14 5d5.

Step 5: (e) Cr#\({^{1+}}\)

The electron configuration of neutral Chromium (Cr) is [Ar] 3d5 4s1. When it loses 1 electron, the electron configuration is [Ar] 3d5.

Step 6: (f) Ni#\({^{2+}}\)

The electron configuration of neutral Nickel (Ni) is [Ar] 3d8 4s2. When it loses 2 electrons due to the negative charge, the electron configuration is [Ar] 3d8. Step 2: Determine the type of ligand and crystal field Due to the different ligands, each complex presents different ligand field strengths. In general, we can classify aqua and fluoride as weak-field ligands; ammine and cyanide as strong-field ligands, and halogen as an intermediate ligand. Step 3: Draw the crystal-field energy-level diagrams and place the electrons Considering the types of ligand, the crystal-field energy-level diagram for weak-field ligands (t2g and eg split) - octahedral complexes. For strong-field ligands, the energy difference will be larger. Now, let's fill the electrons according to the ligand field strength and d electron configuration.

Step 7: (a) The crystal-field diagram for \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{4}]^{2+}\)

Due to weak ligands, the splitting is small. We fill the 4 d electrons as follows: ↑↓ in t2g(dxz, dyz), ↑ in t2g(dxy), ↑ in eg(dx²-y²).

Step 8: (b) The crystal-field diagram for \([\mathrm{Mn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\)

Due to weak ligands, the splitting is small. We fill the 5 d electrons as follows: ↑↓ in t2g(dxz, dyz, dxy), ↑ in eg(dx²-y², d²z²).

Step 9: (c) The crystal-field diagram for \([\mathrm{Ru}(\mathrm{NH}_{3})_{3}(\mathrm{H}_{2}\mathrm{O})]^{2+}\)

Due to strong ligands, the splitting is large. We fill the 6 d electrons as follows: ↑↓ in t2g(dxz, dyz, dxy), ↑↓ in eg(dx²-y²) - low spin configuration.

Step 10: (d) The crystal-field diagram for \([\mathrm{IrCl}_{6}]^{2-}\)

Due to intermediate ligands, we assume a relatively large splitting. We fill the 5 d electrons as follows: ↑↓ in t2g(dxz, dyz, dxy) - low spin configuration.

Step 11: (e) The crystal-field diagram for \([\mathrm{Cr}(\mathrm{CN})_{3}]^{1+}\)

Due to strong ligands, the splitting is large. We fill the 5 d electrons as follows: ↑↓ in t2g(dxz, dyz, dxy).

Step 12: (f) The crystal-field diagram for \([\mathrm{NiF}_{6}]^{4-}\)

Due to weak ligands, the splitting is small. We fill the 8 d electrons as follows: ↑↓ in t2g(dxz, dyz, dxy) and eg(dx²-y², d²z²).

Key Concepts

Crystal-Field Splitting

Crystal-field splitting is a fundamental concept in coordination chemistry that explains how the energy levels of metal d orbitals are affected by the surrounding ligands. When metal ions form complexes with ligands, the d orbitals, which are originally degenerate (at the same energy level), split into two sets of orbitals with different energies. This splitting occurs because the electric fields generated by nearby ligands exert an uneven force on the d electrons.
For octahedral complexes, which have six ligands symmetrically arranged around the metal, the five d orbitals split into two groups: the t2g (comprising dxy, dxz, dyz) and eg (comprising dx²-y², dz²) orbitals. The t2g orbitals are lower in energy because they experience less repulsion from the ligands than the eg orbitals, which point directly at the ligands and therefore are higher in energy.
Understanding the extent of this splitting is crucial, as it affects the electronic configuration of the metal ion and can significantly influence the properties of the complex, such as its color and magnetic properties. How the electrons are distributed between the t2g and eg levels determines whether the complex is high spin or low spin, a concept deeply intertwined with the strength of the ligands involved.

d Electron Configuration

The d electron configuration refers to the arrangement of electrons in the d orbitals of a transition metal ion. The specific arrangement or 'filling' of these electrons affects the overall stability, magnetic properties, and color of the complex. For instance, when a transition metal forms a complex, its electrons will fill the lower-energy t2g orbitals before the higher-energy eg orbitals, according to Hund's Rule and the Pauli Exclusion Principle.

• Hund's Rule states that electrons will fill an empty orbital before they pair up with another electron.
• The Pauli Exclusion Principle states that no two electrons in the same atom can have identical quantum numbers, meaning all electrons must have unique states.

These rules dictate the observed patterns in electron configurations across various complexes. In an octahedral field, typically the t2g level will be filled first, followed by the eg level. However, in cases where field splitting is large enough and pairing energy is lower than the splitting energy, electrons may pair up in the t2g orbitals, resulting in a low spin configuration.

Ligand Field Strength

Ligand field strength is a measure of a ligand's ability to split the d orbitals of a metal ion. The strength of a ligand's field is determined by its electronic properties and spatial arrangement. Broadly, ligands are classified according to their field strength into two main categories: strong-field and weak-field ligands.

• Strong-field ligands, such as CN- (cyanide) and NH3 (ammine), are powerful at imposing crystal-field splitting due to their ability to donate electron density effectively to the metal ion. They result in a large energy difference between t2g and eg orbitals and tend to lead to low-spin configurations.
• Weak-field ligands, including H2O (aqua) and F- (fluoride), cause a smaller splitting energy gap, often leading to high-spin configurations because the energy cost to pair electrons in the t2g orbitals is higher than placing them in the higher-energy eg orbitals.

The choice of ligand can drastically change the electronic structure of a complex, thereby altering its reactivity, magnetism, and other key properties. Understanding the strength of ligand fields is also crucial for predicting the geometries of complexes based on the Crystal Field Stabilization Energy (CFSE).

Octahedral Complexes

Octahedral complexes are a type of coordination complex where six ligands surround a central metal ion in an octahedral geometry. This arrangement is prevalent due to its symmetrical shape, which minimizes repulsion between the ligands and stabilizes the complex.
The crystal-field splitting pattern for an octahedral complex places the t2g orbitals at a lower energy level than the eg orbitals, creating an energy gap known as the crystal-field splitting energy (Δo). The magnitude of this splitting is affected by the nature of the ligands and the metal ion. When populating the d orbitals with electrons, one must consider both the number of d electrons for the specific metal ion and the strength of the ligands.
The magnetic properties of octahedral complexes are determined by the arrangement of the electrons in these split d orbitals. If the electrons remain unpaired, the complex is termed 'high-spin'; when electrons are paired, it is 'low-spin'. These differences have practical implications in areas such as catalysis and magnetic resonance imaging (MRI) contrast agents, and the terms 'high-spin' and 'low-spin' are crucial descriptors in inorganic and coordination chemistry.