Write the formula for each of the following compounds, being sure to use brackets to indicate the coordination sphere: (a) hexamminechromium(III) nitrate (b) tetraamminecarbonatocobalt(III) sulfate (c) dichlorobis(ethylenediamine)platinum(IV) bromide (d) potassium diaquatetrabromovanadate(III) (e) bis(ethylenediamine) zinc(II) tetraiodomercurate(II)

Coordination chemistry revolves around the study of coordination compounds, which are substances that have a central metal atom or ion bonded to a group of molecules or anions called ligands. These ligands can be neutral molecules like water (H₂O) or ammonia (NH₃), or charged ions like chloride (Cl^-). The ligands are bonded to the metal center through coordinate covalent bonds, where both electrons in the bond originate from the same atom, usually the ligand.

These complexes can have various geometries such as square planar, tetrahedral, or octahedral based on the number and spatial arrangement of ligands around the central metal. Coordination compounds are described using coordination numbers, which tell us the number of ligand-donor atoms bonded to the metal ion. For instance, in hexamminechromium(III) nitrate, chromium has a coordination number of six because it is surrounded by six ammonia molecules.

In coordination chemistry, it's also crucial to understand the naming of compounds. For example, 'hexammine' signifies six ammonia ligands, and 'dichlorobis' suggests two chlorine ligands and two molecules of a bidentate ligand like ethylenediamine. Understanding these naming conventions is key to writing correct formulas for such compounds.

Writing chemical formulas for coordination compounds requires knowledge of the complex's composition and the rules for naming such structures. The central metal is written first, followed by the ligands within square brackets to denote the coordination sphere. Ligands are generally written alphabetically, and their number is indicated by prefixes such as di-, tri-, tetra-, etc. Multi-atomic ligands like ethylenediamine are often encapsulated in parentheses.

When writing these formulas, it is also important to indicate the oxidation state of the metal, which is given in Roman numerals within the name and placed after the metal within the chemical formula. For example, the (III) in hexamminechromium(III) nitrate indicates that chromium has a +3 oxidation state. The charge of the entire coordination complex is balanced by counter-ions, like nitrate (NO₃^-) or sulfate (SO₄^2-), which are written outside the brackets. If necessary, these counter-ions are written as multiples, to balance the charge of the complex, as seen in the chemical formula \[ [Cr(NH₃)₆] (NO₃)₃ \].

The oxidation state (also called oxidation number) is a concept in chemistry that describes the degree of oxidation of an atom in a chemical compound. It is a hypothetical charge that an atom would have if all its bonds to atoms of different elements were 100% ionic.

Oxidation states are typically represented by integers, which can be positive, negative, or zero. In coordination compounds, knowing the oxidation state of the central metal ion is essential to deduce the correct formula of the complex. For example, in the coordination compound dichlorobis(ethylenediamine)platinum(IV) bromide, the IV after platinum indicates that platinum is in the +4 oxidation state. The overall charge on the coordination sphere must be balanced by the counter-ions present outside the brackets.

Calculation of oxidation states within coordination complexes can be done by using the known charges of the ligands and applying the rule that the sum of the oxidation states within a neutral molecule must be zero, or must match the charge if the molecule is an ion. This method helps in determining the number of counter-ions needed to balance the charge of the complex as seen in the provided exercise.