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How do you determine conjugate acids and bases?

Answer
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Hint: The concept of conjugate acid and conjugate base is from the Bronsted-Lowry definition for acids and bases. The acid and conjugate base pair differs only by one proton.

Complete answer:
So in the question it is given that how do we determine conjugate acids and conjugate bases. To understand the difference between these two terms first we should know the Bronsted-Lowry approach of acids and bases.
We know that in chemistry there are mainly three main concepts of approaching or explaining which one is acid and which is base.
The three concepts are Arrhenius concept, Bronsted-Lowry concept and the Lewis concept.
The Bronsted-Lowry concept of acid accounts for the above given terms, conjugate base and conjugate acid.
In the Bronsted-Lowry concept, the acids are those species that give or donate protons (p+) in the solution and bases are those species that accept the protons.
And we say that when an acid and base undergoes reactions, two species conjugate base and conjugate acid is formed.
Specifically the base and conjugate acid pair and acid and conjugate base pair are formed which differ by one proton.
-The acid and conjugate base differ by one protons and as we know that there should be more H+ions in acid and the compound with more H+ions is called the acid and the conjugate base will have one H+less than the acid.
-Similarly the base and conjugate acid differ by one protons ie the compound with lessH+ions will be the base and the one with more H+will be the conjugate acid.
Yes, the concept is quite confusing, let’s see an application of the concept for better clarity.
Let’s study a reaction,
H2CO3+OHHCO3+H2O
Here the pairs formed are H2CO3 and HCO3 which is an acid-conjugate base pair, here both the species differ by one H+and the conjugate base has oneH+less than that of the acid.
The next pair of base –conjugate acid is OHandH2O, where the base which is OHhas one proton less than the conjugate acid formed which isH2O.
H2CO3(Acid)+OH(Base)HCO3(Conjugatebase)+H2O(Conjugateacid)
Hence, we can summarize that the conjugate base is a species which will have less number of protons than the acid and conjugate acid is the species which has greater number of protons than the base.

Note: If the question is asked to write the conjugate base for a given acid then the simplest way to solve these types of problems remove one H+ and calculate the charge and write the species. If conjugate acid is acid for base then add up one H+ ion, balance the charge and write the obtained species. The strong acid will form a weak conjugate base and vice versa. Similarly a strong base will form a weak conjugate acid and vice versa.