Final answer:
The formula for tris(ethane-1,2-diamine) chromium(III) chloride is [Cr(en)3]3Cl3, where Cr stands for chromium with a +3 charge, 'en' is the abbreviation for ethane-1,2-diamine, and Cl is the chloride anion.
Step-by-step explanation:
The formula for tris(ethane-1,2-diamine) chromium(III) chloride follows the IUPAC norms for naming coordination compounds. The central metal in this complex is chromium with an oxidation state of III, which is indicated by the Roman numeral in parentheses. Tris indicates that there are three ethane-1,2-diamine ligands attached to the chromium. Ethane-1,2-diamine is a bidentate ligand, meaning it binds through two donor atoms to the central metal. The entire complex is a cation with a +3 charge because chromium is in the +3 oxidation state.
The ethane-1,2-diamine ligand is represented by 'en', so with three of these, we have 'en3'. Combining this information, the complex part of the formula becomes [Cr(en)3]3+. Since the complex is a cation, it must be balanced with anions. As 'chloride' is present, we use Cl- for each of the three units required to neutralize the charge, resulting in three chloride ions.
The complete chemical formula for tris(ethane-1,2-diamine) chromium(III) chloride is therefore [Cr(en)3]3Cl3.