In the complex ion [Co en 2Br2]^+, the central metal ion is cobalt Co . To determine the coordination geometry and oxidation state of cobalt, we need to analyze the ligands surrounding it.There are two ethylenediamine en ligands and two bromide Br ligands. Ethylenediamine is a bidentate ligand, meaning it can form two coordinate covalent bonds with the central metal ion. Therefore, the two en ligands will form a total of four coordinate covalent bonds with cobalt. The two bromide ligands will each form one coordinate covalent bond with cobalt, resulting in a total of six coordinate covalent bonds around the cobalt ion.Since there are six ligands surrounding the cobalt ion, the coordination geometry is octahedral.Now, let's determine the oxidation state of cobalt. The ethylenediamine ligands are neutral, so they do not contribute to the oxidation state of cobalt. The two bromide ligands each have a charge of -1, so their total charge is -2. The overall charge of the complex ion is +1. Therefore, the oxidation state of cobalt must be +3 to balance the charges:Co^x + 2 en + 2 Br^- = [Co en 2Br2]^+x - 2 = +1x = +3So, the central metal ion, cobalt, has an oxidation state of +3 and an octahedral coordination geometry in the complex ion [Co en 2Br2]^+.