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Why is ##FeBr_3## a lewis acid?
As you probably know, a is a compound that is capable of accepting electron pairs.
If you look at ##FeBr_3##, the first thing that should stand out is the fact that you've got a transition metal, ##Fe##, bonded to a highly element, ##Br##.
This difference in creates a partial positive charge on the ##Fe##, which in turns allows it to accept an electron pair. Remember that transition metals are capable of expanding their in order to accomodate more electrons, so a good rule of thumb is that formed by transition metals paired with highly electronegative will most likely be Lewis acids.
##FeBr_3## is used as a catalyst in the bromination of benzene because of its strong Lewis acid character.
Without going into detail, the bromine (##Br_2##) molecule reacts with ##FeBr_3## and donates a pair of electrons to it. This polarizes ##Br_2##, making it a better electrophile (more attracted to electrons).