How many unpaired electrons are present in each of the following? (a) \(\left[\mathrm{CoF}_{6}\right]^{3-}\) (high spin) (b) \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}\) (low spin) (c) \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}(\text { low spin })\) (d) \(\left[\mathrm{MnCl}_{6}\right]^{4-}\) (high spin) (e) \(\left[\mathrm{RhCl}_{6}\right]^{3-}\) (low spin)

Electron configuration is the arrangement of electrons in an atom's or ion's orbitals, which are defined by quantum numbers. Imagine it as a map that shows where each electron lives within an atom. Understanding electron configuration is essential for predicting the chemical, electrical, and magnetic properties of an atom.

For transition metals, the configuration can vary based on oxidation states, as electrons are removed from the highest energy levels first. In the complexes from the exercise, we start with the basic electron configuration of the neutral atom (using the periodic table) and then adjust it based on the metal's oxidation state determined in the exercise. The 'd' orbital electrons are the ones involved in bonding and magnetism, hence they are the primary focus for these transition metal complexes.

The oxidation state, often referred to as oxidation number, is a measure of the degree of oxidation of an atom in a chemical compound. Think of it as an imaginary charge that an atom would have if all bonds were purely ionic. To find the oxidation state of the metal in a coordination complex, like the examples in the exercise, you subtract the sum of the ligands' charges from the overall charge of the complex.

This is crucial because the oxidation state of the metal affects its electron configuration, which in turn dictates properties such as color, magnetism, and reactivity. In our exercise, different oxidation states of cobalt, manganese, and rhodium dictate the number of electrons in the 'd' orbitals and hence the number of unpaired electrons.

Spin complexes relate to the spin of electrons in the d-orbitals of transition metals. When we refer to 'high spin' and 'low spin' complexes, we're talking about the arrangement of electrons in these orbitals, which can have a significant impact on the properties of the complex, including color and magnetism.

High spin complexes occur when a metal ion is surrounded by weak-field ligands, which don't exert enough energy to pair up the electrons. As a result, electrons fill all the orbitals singly before any pairing occurs. Conversely, low spin complexes form when strong-field ligands are present, and electrons pair up in lower energy orbitals first, leading to fewer unpaired electrons. This has been applied in our exercise to predict the number of unpaired electrons in each complex.

Hund's Rule is like a guideline for filling subshells with electrons. It tells us that electrons will fill each degenerate orbital in a subshell singularly before pairing up. The rule is all about maximizing the number of unpaired electrons and minimizing repulsion between them.

Imagine a bus with seats in pairs (representing orbitals): people (electrons) would rather sit alone than next to someone. Only when all seats have one person, do people start sitting next to each other. This is what Hund's Rule suggests for electrons and it affects the properties of atoms, ions, and molecules significantly. In coordination chemistry, Hund's Rule helps predict the number of unpaired electrons in high spin complexes, leading to the exercise solutions given.