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In an acid-base reaction, the conjugate acid/base are on the products side of the equation. Essentially, the conjugate acid is the base with a hydrogen ion added to it. The conjugate base what is remaining after the original acid has donated a proton during the acid-base reaction.
A conjugate acid is a species formed by the reception of a proton (H+) by a base, so basically it is a base with a hydrogen ion added to it. On the other hand, a conjugate base is what is left over after an acid has donated a proton during a chemical reaction.
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