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How do I identify the conjugate acid and base?

Answer
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Hint: In order to identify the conjugate acid and conjugate base, we must first know what a conjugate acid and base is. For that we must have an idea about the Bronsted-Lowry acid base theory.

Complete answer:
Let us first understand about Bronsted-Lowry acid base theory. This is an acid-base reaction theory. This theory is said to be an extended version of the Arrhenius theory of the acid-base reaction. Based on this theory an acid and base will react with one another and there will be exchange of the proton acid. Due to this exchange of the proton, the acid will form a conjugate base and the base will form a conjugate acid.
In other words, we can say that the acid will donate the \[{H^ + }\]ions, to form a conjugate base and the base will accept the \[{H^ + }\] ions to form a conjugate acid.
Let us now explain this with an example.
Hydrochloric acid will react with an ammonia base to give conjugate base and conjugate acid respectively.
\[HCl + N{H_3} \rightleftharpoons NH_4^ + + C{l^ - }\].
\[N{H_3}\]will accept a proton to form a conjugate acid which is \[NH_4^ + \].
\[HCl\]will donate a proton to form a conjugate base which is \[C{l^ - }\].

Note: The Bronsted-Lowry acid which is strong will have a tendency to strongly donate the protons and form a weak conjugate base.
The Bronsted-Lowry acid which is weak will have a weak tendency to donate the protons and will form a strong conjugate base.