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What is the conjugate base of $ HS{O_4}^- $ ?

Answer
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Hint: Conjugate base is the substance formed when an acid loses a hydrogen ion. Considered a base because it gains a hydrogen ion to reform the acid. It can be represented as:
Acid $ + $ Base $ \rightleftharpoons $ Conjugate Base $ + $ Conjugate Acid.
A cation can be a conjugate acid and anion can be a conjugate base.

Complete answer:
The Bronsted-Lowrey theory state that, when an acid and a base react with each other, the acid forms its conjugate base, and the base forms its conjugate acid by exchange of a proton (The hydrogen cation, or $ {H^ + } $ ).
Example- $ HCl + {H_2}O \to {H_3}O + C{l^ - } $ water acts as a base (accepting $ {H^ + } $ ) because $ HCl $ is a stronger acid.
But in reaction, $ N{H_3} + {H_2}O \to N{H_4} + O{H^ - } $ water acts as an acid (donates $ {H^ + } $ to ammonia) because water is a stronger acid than ammonia.
 $ HS{O_4}^ - $ Is in fact the conjugate base of the sulfuric acid. $ {H_2}S{O_4} $ is an acid so it donates a proton and after donating a proton it will be $ HS{O_4}^ - $ . The reaction is
 $ {H_2}S{O_4} \to HS{O_4}^ - + {H^ + } $ . $ HS{O_4}^ - $ is a base since it has the ability to accept a proton but it is a conjugate base to $ {H_2}S{O_4} $ since it is formed by the $ {H_2}S{O_4} $ after donating a proton.
But, $ HS{O_4}^ - $ is an acid itself. When in water, it removes the $ {H^ + } $ proton, it becomes a conjugate base $ S{O_4}^{2 - } $ . The conjugate base means it has to add $ {H^ + } $ proton back in a backward reaction.
The reaction in water: $ HS{O_4}^ - + {H_2}O \to S{O_4}^{2 - } + {H_3}{O^ + } $ . Even if $ HS{O_4}^ - $ has a negative charge, it will never accept a $ {H^ + } $ ion to form $ {H_2}S{O_4} $ again. That is because sulfuric acid is a stronger acid and completely dissociates in water. That’s why sulphate ions would be the conjugate base formed.
 $ HS{O_4}^ - $ Is acid and $ S{O_4}^{2 - } $ is conjugate base
 $ {H_2}O $ is base and $ {H_3}{O^ + } $ is conjugate acid.

Note:
The conjugate acid of a base is the compound formed after the Bronsted base accepts a proton.
 $ S{O_4}^{2 - } + {H^ + } \to HS{O_4}^ - $ , that is bisulfate ion $ HS{O_4}^ - $ is conjugate acid of sulfate ion. (Bronsted base: a proton acceptor.) It is not possible to put this ion $ HS{O_4}^ - $ into solution as it has to accompany something like sodium hydrogen sulfate $ (NaHS{O_4}) $ or calcium sulfate $ (CaHS{O_4}) $ .