* Cobalt (III) ion: This means cobalt has a +3 charge (Co³⁺).

* Bromide ion: Bromine has a -1 charge (Br⁻).

To balance the charges, we need three bromide ions for every cobalt (III) ion:

* Co³⁺ + 3Br⁻ → CoBr₃

Therefore, the chemical formula for the compound formed between cobalt (III) and bromide ion is CoBr₃.