Name the following complex ions. a. \(\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}^{2+}\) c. \(\mathrm{Mn}\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)_{3}^{2+}\) b. \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\) d. \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{NO}_{2}^{2+}\)

Coordination chemistry involves the study of molecules that are formed by the combination of central metal atoms or ions and surrounding groups of molecules or ions known as ligands. These molecules, known as coordination compounds or complex ions, have unique properties and structures. The central metal atom or ion, usually a transition metal, serves as the hub for the coordination entity, and its coordination number indicates the number of bonds formed with ligands.

For example, in the complex ion \textbf{Ru(NH\(_3\))\(_5\)Cl}\(^{2+}\), ruthenium acts as the central metal ion, coordinating with five ammonia molecules and one chloride ion.

Ligands are ions or neutral molecules that bond to a central metal atom or ion in a coordination compound through a process called coordination. They can be either mono-dentate, bonding through a single site, or poly-dentate, offering multiple bonding sites to the central metal. Depending on the charge, size, and electron-donating ability of the ligand, they can influence the properties of the complex ion.

In the coordination compound \textbf{Fe(CN)\(_6^{4-}\)}, six cyanide (CN\(^-\)) ions surround the central iron ion, each acting as a mono-dentate ligand by coordinating through its carbon atom.

The oxidation state is a theoretical charge that an atom would have if all bonds to atoms of different elements were entirely ionic. In coordination compounds, determining the oxidation state of the central metal is crucial for correct nomenclature. It's derived from the overall charge of the complex and the known charges of the ligands.

Take for instance the complex \textbf{Mn(NH\(_2\){CH}\(_2\){CH}\(_2\)NH\(_2\))\(_3^{2+}\)}. Since the ethylenediamine ligand is neutral, the oxidation state of manganese is +2 to balance the 2+ charge of the entire complex ion.

Transition metals are elements found in the d-block of the periodic table, which are characterized by their ability to form multiple oxidation states and complex ions. They have unfilled d-orbitals and readily engage in coordination bonds with various ligands. Transition metals are often at the center of coordination compounds due to their versatile electronic configurations that enable them to accept electrons from ligands.

For instance, cobalt in the complex ion \textbf{Co(NH\(_3\))\(_5\)NO\(_2\)}\(^{2+}\) demonstrates its transitional metal characteristics by coordinating with five ammonia molecules and one nitrite ion, leading to a rich diversity of geometries and other chemical properties.