Give the coordination numbers and write the formulas for each of the following, including all isomers where appropriate: (a) tetrahydroxozincate(II) ion (tetrahedral) (b) hexacyanopalladate(IV) ion (c) dichloroaurate(I) ion (note that aurum is Latin for "gold") (d) diamminedichloroplatinum(II) (e) potassium diamminetetrachlorochromate(III) (f) hexaamminecobalt(III) hexacyanochromate(III) (g) dibromobis(ethylenediamine) cobalt(III) nitrate

The coordination number of a central metal ion in a complex refers to the number of ligand atoms that are directly bonded to the metal ion. It effectively indicates the total number of coordinate bonds formed between the central atom and the ligands in the coordination sphere.

For instance, in the provided exercise, tetrahydroxozincate(II) ion has a coordination number of 4 because it forms four bonds with hydroxide ions. Similarly, hexacyanopalladate(IV) and hexaamminecobalt(III) have coordination numbers of 6, conforming to octahedral geometries. Understanding the coordination number is crucial as it impacts the geometric arrangement and potential isomerism of a complex, therefore, it is one of the foundational concepts in coordination chemistry.

Isomerism in coordination compounds includes structural and stereoisomers. Structural isomerism occurs when the components within a complex can form different structural arrangements, while for stereoisomers, the connectivity is the same but the spatial arrangement of ligands differs.

In the exercise, isomerism is exemplified in diamminedichloroplatinum(II) that can exist as cis or trans isomers due to its square planar geometry. The cis isomer has the two ammine ligands adjacent to each other, while in the trans isomer, they are opposite each other. Recognizing potential isomerism in coordination compounds is essential, as isomers can have vastly different chemical and physical properties.

The geometric arrangement of ligands around a central metal atom is determined by the coordination number, which dictates the most stable shape for a complex. Common geometries include linear, tetrahedral, square planar, and octahedral arrangements.

For example, the dichloroaurate(I) ion, with a coordination number of 2, has a linear geometry, whereas the tetrahydroxozincate(II) ion, with a coordination number of 4, has a tetrahedral geometry. Proper understanding of these geometrical shapes helps predict molecular shapes, bond angles, and the potential reactivity of the complex compounds.