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What is the conjugate acid of $HCO_3^ - $ ?

Answer
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Hint: A conjugate acid has one more hydrogen atom and one more positive charge than the base from which it was made. A conjugate base has one less hydrogen atom and one more - charge than the acid from which it was made.

Complete answer:
An acid is any hydrogen-atom-containing material (molecule or ion) that can release a proton or hydrogen ion to any other substance, while a base is any substance (molecule or ion) that can accept a proton from any other substance to form the conjugate acid base pair.
Conjugate acids and bases pairs are made up of members that can be formed from each other by gaining or losing protons. One conjugate pair consists of a stronger acid and a weaker base, while another consists of a stronger base and a weaker acid.
When a base absorbs a proton or a ${H^ + }$ ion, a conjugate acid is formed. So, what we need to know to decide the conjugate acid for a given base is that
$Base + {H^ + } \to $ Conjugate acid of that base
The basis in our case is hydrogen carbonate, or $HC{O_3}$ ; if we write the equation down, we get
$HCO_3^ - + {H^ + } \to {H_2}C{O_3}$
Hence, Carbonic acid, or ${H_2}C{O_3}$ , is the hydrogen carbonate conjugate acid.

Note:
${H_2}C{O_3}$ is a weak acid that is acidic. In the presence of acid, it undergoes partial dissociation, yielding ${H^ + }$ and $HCO_3^ - $ (bicarbonate) ions. As a diprotic acid, carbonic acid can form two kinds of salts: bicarbonates and carbonates.