Complete the exercises below. The complex [Mn(NH₃)₆]²⁺ contains five unpaired electrons. Sketch the energy-level diagram for the d orbitals, and indicate the placement of electrons for this complex ion. Is the ion a high-spin or a low-spin complex?

Verified step by step guidance

1. Step 1: Identify the oxidation state of manganese in the complex [Mn(NH₃)_6]^{2+}. Since NH₃ is a neutral ligand, the oxidation state of Mn is +2.
2. Step 2: Determine the electron configuration of Mn^{2+}. Manganese (Mn) has an atomic number of 25, so its electron configuration is [Ar] 3d^5 4s^2. For Mn^{2+}, remove two electrons from the 4s orbital, resulting in [Ar] 3d^5.
3. Step 3: Sketch the energy-level diagram for the d orbitals. In an octahedral field, the d orbitals split into two sets: t_{2g} (lower energy) and e_g (higher energy).
4. Step 4: Place the five d electrons in the energy-level diagram. Since the complex has five unpaired electrons, each electron will occupy a separate orbital, filling the t_{2g} and e_g orbitals singly before any pairing occurs.
5. Step 5: Determine if the complex is high-spin or low-spin. The presence of five unpaired electrons indicates that the complex is a high-spin complex, as all d orbitals are singly occupied before any pairing occurs.

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 like [Mn(NH₃)₆]²⁺, the d orbitals split into two energy levels: the lower-energy t₂g and the higher-energy e_g orbitals. The extent of this splitting is influenced by the nature of the ligands and the metal ion's oxidation state.

High-Spin vs. Low-Spin Complexes

High-spin and low-spin complexes refer to the arrangement of electrons in the d orbitals based on the strength of the ligand field. High-spin complexes have more unpaired electrons due to weaker field ligands that do not cause significant splitting, while low-spin complexes have fewer unpaired electrons as stronger field ligands lead to greater splitting, allowing electrons to pair up in lower energy orbitals.

Electron Configuration of Transition Metals

The electron configuration of transition metals is crucial for determining their magnetic properties and oxidation states. For manganese in [Mn(NH₃)₆]²⁺, the electron configuration is [Ar] 3d⁵ 4s², and upon losing two electrons to form the ion, it becomes [Ar] 3d⁵. The presence of five unpaired electrons indicates that this complex is high-spin, as the electrons occupy higher energy orbitals before pairing.