Complete the exercises below. Draw the crystal-field energy-level diagrams and show the placement of d electrons for each of the following: c. [Ru(NH₃)₅(H₂O)]²⁺ (a low-spin complex).

Verified step by step guidance

1. Identify the central metal ion and its oxidation state. Ruthenium (Ru) is the central metal ion. In the complex [Ru(NH₃)_5(H₂O)]^{2+}, the overall charge is +2. Ammonia (NH₃) and water (H₂O) are neutral ligands, so the oxidation state of Ru is +2.
2. Determine the electron configuration of the Ru^{2+} ion. Ruthenium (Ru) has an atomic number of 44, so its electron configuration is [Kr] 4d^7 5s^1. For Ru^{2+}, remove two electrons, typically from the 5s and 4d orbitals, resulting in [Kr] 4d^6.
3. Consider the geometry and crystal field splitting. The complex is octahedral, which means the d orbitals will split into two sets: t_{2g} (lower energy) and e_g (higher energy).
4. Since the complex is low-spin, the electrons will pair in the lower energy t_{2g} orbitals before occupying the higher energy e_g orbitals. Place the six d electrons in the t_{2g} orbitals.
5. Draw the crystal-field energy-level diagram. Illustrate the splitting of the d orbitals into t_{2g} and e_g levels, and show the placement of the six electrons in the t_{2g} orbitals, indicating that all are paired.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects the energy levels of its d orbitals. In an octahedral complex, such as [Ru(NH₃)₅(H₂O)]²⁺, the d orbitals split into two energy levels: the lower-energy t₂g and the higher-energy e_g. This splitting is crucial for determining the electronic configuration and magnetic properties of the complex.

Low-Spin vs. High-Spin Complexes

Low-spin and high-spin complexes refer to the arrangement of electrons in the d orbitals of transition metal complexes. Low-spin complexes, like [Ru(NH₃)₅(H₂O)]²⁺, occur when the ligand field is strong enough to pair electrons in the lower energy orbitals before occupying the higher ones. This results in fewer unpaired electrons and typically leads to a diamagnetic complex.

Ligand Field Strength

Ligand field strength is a measure of the ability of a ligand to split the d orbital energies of a metal ion. Strong field ligands, such as NH₃, cause a significant splitting of the d orbitals, favoring low-spin configurations. In contrast, weak field ligands lead to smaller splitting and can result in high-spin configurations, influencing the overall stability and reactivity of the complex.