Concept: Chemistry (Coordination Compounds) - IUPAC Nomenclature and Formulation.
Step 1: Identify the central metal ion and its oxidation state. The name ends in "cobaltate(III)", which tells us the central metal is Cobalt (Co) and its oxidation state is exactly . The "ate" suffix indicates that the complex coordination sphere itself carries a net negative charge (anionic complex).
Step 2: Identify the ligands and their total charge. The prefix "hexanitro" signifies the presence of six "nitro" ligands. The nitro ligand is the ion bonding through the nitrogen atom. (Note: if it were bonding through oxygen, it would be named "nitrito-O" and written as ). Since there are six of them, the total charge from the ligands is .
Step 3: Calculate the net charge on the coordination sphere. The net charge on the complex sphere is the sum of the oxidation state of the central metal and the total charge of the ligands:
Net Charge = (Oxidation state of Co) + (Total charge of 6 )
Net Charge = .
Thus, the complex anion is .
Step 4: Determine the number of counter ions needed for neutrality. The compound is a sodium salt. The sodium ion is an alkali metal cation, , with a constant charge. To perfectly balance the charge of the complex anion, we need exactly three cations.
Step 5: Assemble the complete chemical formula. Combine the three sodium cations with the complex anion. In chemical formulas, the cation is always written first, followed by the anion.
This yields the final chemical formula: . $ $