Complete the exercises below. For each of the following metals, write the electronic configuration of the atom and its 3+ ion: a. Fe. Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex, and show the placement of the d electrons for each 3+ ion, assuming a weak-field complex. How many unpaired electrons are there in each case?

Verified step by step guidance

1. Step 1: Determine the atomic number of iron (Fe), which is 26, and write its electronic configuration using the Aufbau principle: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6.
2. Step 2: For the Fe^3+ ion, remove three electrons from the highest energy orbitals. Since 4s and 3d are close in energy, remove two electrons from 4s and one from 3d, resulting in the configuration: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5.
3. Step 3: Draw the crystal-field energy-level diagram for an octahedral complex. In an octahedral field, the five d orbitals split into two sets: t2g (lower energy, three orbitals) and eg (higher energy, two orbitals).
4. Step 4: Place the five d electrons of Fe^3+ in the t2g and eg orbitals according to Hund's rule, which states that electrons will fill an empty orbital before pairing up. In a weak-field complex, the electrons will remain unpaired as much as possible.
5. Step 5: Count the number of unpaired electrons in the d orbitals of Fe^3+. Since there are five d electrons and they are distributed among the t2g and eg orbitals with maximum unpairing, determine the number of unpaired electrons.

Key Concepts

Electronic Configuration

Electronic configuration describes the distribution of electrons in an atom's orbitals. For transition metals like iron (Fe), the configuration is crucial for understanding their chemical properties and behavior in complexes. The electronic configuration of Fe is [Ar] 4s² 3d⁶, and for its 3+ ion, it loses three electrons, resulting in [Ar] 3d⁵.

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, the d orbitals split into two energy levels: t2g (lower energy) and eg (higher energy). This theory helps predict the electronic structure and magnetic properties of metal complexes based on ligand strength.

Unpaired Electrons and Magnetism

Unpaired electrons in an atom or ion contribute to its magnetic properties. In the context of transition metal complexes, the number of unpaired electrons can indicate whether the complex is paramagnetic (attracted to a magnetic field) or diamagnetic (not attracted). For the Fe3+ ion in a weak-field complex, the d electrons will occupy the higher energy eg orbitals, leading to a specific count of unpaired electrons.