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Conjugate acids/bases are the compounds formed from a reaction involving an acid/base. You identify them by figuring out what compound on the reactant side is an acid/base and then finding the compound that looks like it on the product side. Acids form conjugate bases and bases form conjugate acids.
conjugates are the molecules formed when the acid/base either donates or accepts a hydrogen ion. For example in the HCL molecule HCL is an acid and the product Cl is the conjugate base. I recommend reading the textbook on this topic as it is very helpful.
It's also important to note that the stability of the conjugate base is a good indicator of the strength of the acid. Cl-, Br-, I-, for example, are all relatively stable anions, so their conjugate acids (HCl, HBr, HI) are strong.
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