Give systematic names for the following formulas: (a) \(\mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\) (b) \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Br}\right] \mathrm{Br}_{2}\)

In coordination chemistry, the central metal ion plays a pivotal role. It's the metallic atom or ion at the center of the coordination complex. Typically, this metal ion is surrounded by molecules or ions, known as ligands, which are bonded to it via coordinate covalent bonds.
Identifying the central metal ion is the primary step in naming coordination complexes. For example, in \[ \mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right] \], the central metal ion is silver (Ag). Similarly, in \[ \mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\], the central metal ion is cadmium (Cd). Recognizing this allows you to correctly assess the surrounding ligands and the complex's overall structure.

The oxidation state of the central metal ion in a coordination complex is crucial for systematic naming. The oxidation state signifies the charge of the metal ion in the complex. Determining it involves balancing the total charge of the complex with the known charges of the ligands.
For instance, in the complex \[ \mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right] \], the potassium cation (K) has a +1 charge. Each cyanide ligand (CN) has a -1 charge. Thus, the silver ion (Ag) must be in the +1 oxidation state to balance the charge.
Similarly, for \[ \mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right] \], sodium contributes a +2 charge total (as there are two Na+ ions). Each chloride ligand (Cl) contributes a -1 charge. Therefore, cadmium must be in the +2 oxidation state.
In the complex \[ \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2}\mathrm{O}\right) \mathrm{Br}\right] \mathrm{Br}_{2}\], the Co ion has to account for the charge provided by Br (as Br-). By considering the neutral charge of NH3 and H2O, and the ionic charges of Br-, cobalt's oxidation state is determined as +3.

Ligand naming involves identifying and properly naming each ligand bonded to the central metal ion. Ligands can be neutral molecules like water (H2O) or ammonia (NH3), or they can be anions like chloride (Cl-) or cyanide (CN-).
For systematic naming, each type of ligand has a specific name:

• Water (\text{H}_2\text{O}) is called 'aqua.'
• Ammonia (\text{NH}_3) is called 'ammine.'
• Chloride (\text{Cl}^-) is 'chloro.'
• Cyanide (\text{CN}^-) is 'cyano.'

When there are multiple identical ligands, prefixes such as 'di-', 'tri-', 'tetra-', etc., are used to indicate their number.
For example: In \[ \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2}\mathrm{O}\right) \mathrm{Br}\right] \mathrm{Br}_{2}\], the ligands include four ammines, one aqua, and one chloro ligand. This makes naming clear and standardized.

Anionic complexes occur when the coordination complex carries a negative charge. When naming anionic complexes, modify the name of the central metal to end in '-ate.'
For instance, \[ \mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right] \] is an anionic complex. Here, 'silver' changes to 'argentate,' denoting the negative charge. The full name becomes 'potassium dicyanoargentate(I).'
Another example is \[ \mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right] \]. The cadmium complex is anionic, so 'cadmium' changes to 'cadmate.' The full name in this case is 'sodium tetrachlorocadmate(II).'
When writing these names, always consider the oxidation state of the central metal ion, represented in Roman numerals at the end of the name (e.g., argentate(I), cadmate(II)). This ensures clarity and precision in chemical nomenclature.