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Bronsted acids are proton, or H+ donators. Bronsted bases are proton acceptors. Conjugate acids are bronsted bases that have accepted a proton. Conjugate bases are bronsted acids that have donated a proton. Lewis acids are electron acceptors, while lewis bases are electron donators.
They're basically all referring to the same thing, but just approach it differently. Lewis acids are molecules that accept an electron pair, while lewis bases donate an electron pair. Bronsted acids donate a proton, while Bronsted bases accept a proton. Conjugate acids and bases are a little different, because they are specific to reactions. They are the result of a base becoming an acid or an acid becoming a base. For example, HCl is an acid, and when it dissociates in water its conjugate base would be chlorine (which is a very weak base, but still a base).
A conjugate acid is the species that is formed after the base accepts a proton, and a conjugate base is formed after an acid donates a proton. Bronsted acids are defined as H+ donors while Lewis acids are defined as electron pair acceptors.
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