Give the coordination number for each metal ion in the following compounds: (a) \(\left[\mathrm{Co}\left(\mathrm{CO}_{3}\right)_{3}\right]^{3-}\) (note that \(\mathrm{CO}_{3}^{2-}\) is bidentate in this complex) (b) \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (d) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]\left[\mathrm{PtCl}_{4}\right]\) (e) \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]\left(\mathrm{NO}_{3}\right)_{3}\) (f) \(\left[\mathrm{Pd}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Br}_{2}\right]\) (square planar) (g) \(\mathrm{K}_{3}\left[\mathrm{Cu}(\mathrm{Cl})_{5}\right]\) (h) \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]\)

Ligands are molecules or ions that bind to a central metal atom to form a coordination complex. They are crucial in the formation of these complexes as they provide the necessary electrons for bonding. Ligands can be monodentate, meaning they donate one pair of electrons to the metal from one donor atom, like ammonia (NH₃), or they can be bidentate or even polydentate, with multiple atoms to bind to the metal, offering two or more pairs of electrons, respectively.

For example, ethylenediamine (({en}) is a common bidentate ligand which has two nitrogen atoms that can each donate a pair of electrons to a metal atom. When determining the coordination number of a metal in a complex, it's important to consider the denticity of the ligands because it directly affects the total number of binding sites the metal atom can accommodate.

Coordination compounds, also known as complexes, are molecules that consist of a central metal atom or ion surrounded by ligands. These compounds are unique due to their structural and chemical properties and are found in many areas of chemistry, including biological systems and industrial processes. The central metal atom can have different states of oxidation, and it's the ligands that determine the overall charge of the coordination compound.

The geometric arrangement of the ligands around the central metal atom is known as the coordination geometry, and this can be tetrahedral, square planar, octahedral, and other less common shapes. The coordination number—the total number of ligands bonded directly to the central metal ion—along with the charge and identity of the ligands, are fundamental characteristics that influence the color, magnetism, and reactivity of the coordination compounds.

Transition metals are elements found in the d-block of the periodic table and are characterized by their ability to form complexes with variable oxidation states and coordination numbers. They have partially filled d-orbitals, which allows them to form stable coordination compounds with diverse geometries.

Common transition metals that feature in coordination chemistry include cobalt (Co), copper (Cu), and chromium (Cr). These elements are highly versatile and can form bonds with a wide array of ligands, resulting in a rich chemistry with applications ranging from biological enzymes to catalysts in industrial processes. Understanding the behavior of transition metals within complexes is essential for predicting their chemical behavior, as well as for designing new molecules for specific functions, such as medicinal drugs or materials with special physical properties.