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There are two different definitions of acids and bases. The Lewis definition of an acid is that is a species that accepts an electron pair. The Bronsted definition of an acid is that an acid is a proton donor. The Lewis definition of a base is a species that donates an electron pair. The Bronsted definition of a base is that a base is a proton acceptor.
A Lewis acid is defined as accepting an electron pair while a bronsted acid is defined as donating a proton. A lewis base is defined as donating an electron pair while a bronsted base is deifned as accepting a proton. Note that in water, the "proton" defers to a hydronium ion such as in the case of HCl reacting in water.
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