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In the reaction of aluminum bromide with ionized sodium bromide, which compound is the Lewis acid?
In other words you ask which is the electron pair acceptor. Clearly, it is aluminum.
The Lewis concept of acidity designates acids as electron pair acceptors, and bases as electron pair donors. For the reaction:
##AlBr_3 + Br^(-) rarr AlBr_4^-##,
clearly the bromide ion is the base, the electron donor, and aluminum, the acid, the electron-pair acceptor. How would designate the reaction of ##BCl_3## with chloride ion in these terms?