Since the reaction shown in the question is an acid - base reaction in the Lewis sense; the Lewis acid here is AlCl3 while the Lewis base here is Cl^- .
A Lewis acid is a substance that accepts electron pair while a Lewis base donates an electron pair.
Now consider the given reaction; AlCl3 +Cl^- ------> AlCl 4 ^-. The Lewis acid here is AlCl3 while the Lewis base here is Cl^- .
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