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What is the conjugate acid of ${HPO_2}^{2-}$.

Answer
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Hint: When an acid loses a proton, then the resulting molecule is a conjugate base. When a base accepts a proton, then the resulting molecule is a conjugate acid. Remember that protons are the chemical currency of acid-base reactions.

Complete step by step answer:
The result of an acid donating a proton or a base accepting a proton gives us conjugate bases and conjugate acids.
${\text{HA}} \to {{\text{A}}^ - }$
${\text{B}} \to {\text{HB}}$

In the first reaction, ${\text{HA}}$ is an acid. It donates ${{\text{H}}^ + }$ and forms conjugate base ${{\text{A}}^ - }$. In the second reaction, ${\text{B}}$ is a base. It accepts ${{\text{H}}^ + }$ and forms conjugate acid ${\text{HB}}$. Acids are proton donors whereas bases are proton acceptors. By applying this knowledge on ${HPO_2}^{2-}$, we can write the reaction as:
${{\text{H}}_2}{\text{PO}}_2^ - \to {\text{HPO}}_2^{2 - } + {{\text{H}}^ + }$

Therefore, from the above reaction we can say that the conjugate acid of ${HPO_2}^{2-}$ is ${{\text{H}}_2}{\text{PO}}_2^ - $.

Note: Remember that the acids on the left side of the chemical reaction will have a conjugate base on the right side of the chemical reaction. Bases on the left side of the chemical reaction will have a conjugate acid on the right side of the chemical reaction. According to the Bronsted-Lowry theory of acids and bases, a conjugate acid-base pair will have two compounds that differ by the presence of a proton ${{\text{H}}^ + }$. When a proton is added to a base, we get a conjugate acid. When a proton is removed from an acid, we get a conjugate base. Note that, if acid is stronger then the conjugate base is weaker. The only difference between a conjugate acid-base pair is a proton ${{\text{H}}^ + }$.