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What is the conjugate base of $HN{O_2}$?

Answer
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Hint: The term 'conjugate base' is usually used in conjunction with the term 'conjugate acid' in the chemical world, and it comes from the Brønsted-Lowry theory of Acids and Bases.
The Brønsted-Acid is a proton donor, while the Brønsted-Base is a proton acceptor. These definitions mean that a chemical reaction is needed to distinguish between the 'donor' and 'acceptor' substances. The root of the application can be traced back to the ' Brønsted -Lowry' principle of acids and bases.

Complete step by step answer:
By extracting a proton \[\left( {{H^ + }} \right)\]from any Brønsted-Lowry acid, the conjugate base can be identified (every Brønsted-Lowry acid has a conjugate base, and vice versa).
Let's look at the chemical reaction where nitrous acid reacts with water:
\[HN{O_2}\left( {aq} \right) + {H_2}O\left( l \right) \rightleftharpoons NO_2^ - \left( {aq} \right) + {H_3}{O^ + }\left( {aq} \right)\]
Here, to form \[NO_2^ - \] and the hydronium ion, \[{H_3}{O^ + }\] the Brønsted-Lowry acid \[HN{O_2}\], has donated a proton to \[{H_2}O\]. This is the forward reaction and in the reverse reaction, \[NO_2^ - \] is now the Brønsted-Lowry base (conjugate of \[HN{O_2}\]) because it accepts a proton from hydronium (conjugate acid of \[{H_2}O\]) to form nitrous acid again.
So, the conjugate base of \[HN{O_2}\] is \[NO_2^ - \]

Note:
In an aqueous solution, a monoprotic acid donates either one proton or hydrogen atom per molecule. Monoprotic acids include \[HN{O_2}\], also known as nitrous acid, is a weak acid that only occurs in the form of nitrite salts in solution \[\left( {NO_2^ - } \right)\]. Remember that the presence of one hydrogen distinguishes a Conjugate Base from an Acid of the Conjugate Base. That is, adding one hydrogen to any anion produces the conjugate base's acid.
Generally:
\[Anio{n^ - } + {H^ + } \Rightarrow H - Anion\]
\[Anio{n^ - } \Rightarrow \]Conjugate Base of the acid \[H - Anion\]