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An example of a reversible reaction is:
(A) $AgN{{O}_{3}}_{\left( aq \right)}+NaC{{l}_{\left( aq \right)}}\to AgC{{l}_{\left( s \right)}}+NaN{{O}_{3\left( aq \right)}}$
(B) $2N{{a}_{\left( s \right)}}+2{{H}_{2}}{{O}_{\left( l \right)}}\to 2NaO{{H}_{\left( aq \right)}}+{{H}_{2\left( g \right)}}$
(C) $2KCl{{O}_{3\left( s \right)}}\to 2KC{{l}_{\left( s \right)}}+3{{O}_{2\left( g \right)}}$
(D) $N{{H}_{4}}H{{S}_{\left( s \right)}}\to N{{H}_{3\left( g \right)}}+{{H}_{2}}{{S}_{\left( g \right)}}$

Answer
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Hint: Have a look at all the options given in the question and determine in which reaction the equilibrium will shift to the left side, that is, towards the reactants side. Also, take a look at the stability of reactants and products to get the answer.

Complete step by step solution:
- In the question, we need to find the reversible reaction. So, let’s take a look at the reactions given in the options.

(A) $AgN{{O}_{3}}_{\left( aq \right)}+NaC{{l}_{\left( aq \right)}}\to AgC{{l}_{\left( s \right)}}+NaN{{O}_{3\left( aq \right)}}$
In this reaction, a stable white precipitate of silver chloride, AgCl is obtained. Silver chloride is very stable and won’t spontaneously react with sodium nitrate. So, this reaction is irreversible.

(B) $2N{{a}_{\left( s \right)}}+2{{H}_{2}}{{O}_{\left( l \right)}}\to 2NaO{{H}_{\left( aq \right)}}+{{H}_{2\left( g \right)}}$
In this reaction, sodium reacts with water. We know that sodium is highly reactive in air and water and reacts violently to form sodium hydroxide. Sodium hydroxide is hygroscopic and dissolves in water forming sodium ion, $N{{a}^{+}}$ and hydroxyl ions, $O{{H}^{-}}$. Also, hydrogen gas escapes into the atmosphere. So, this reaction is irreversible.

(C) $2KCl{{O}_{3\left( s \right)}}\to 2KC{{l}_{\left( s \right)}}+3{{O}_{2\left( g \right)}}$
In this reaction, potassium chlorate decomposes to give potassium chloride and oxygen. This reaction occurs when potassium chlorate is heated strongly. Here, oxygen gas escapes into the atmosphere leaving behind KCl salt only. So, this reaction is irreversible.

(D) $N{{H}_{4}}H{{S}_{\left( s \right)}}\to N{{H}_{3\left( g \right)}}+{{H}_{2}}{{S}_{\left( g \right)}}$
In this reaction, ammonium hydrosulfide or ammonium bisulfide decomposes to give ammonia and hydrogen sulfide. In this reaction, both the reactions as well as products are equally stable. Ammonia reacts readily with hydrogen sulfide to form ammonium hydrosulfide. So, this reaction will exist in equilibrium. Therefore, this reaction is reversible.
-Therefore, an example of reversible reaction is $N{{H}_{4}}H{{S}_{\left( s \right)}}\to N{{H}_{3\left( g \right)}}+{{H}_{2}}{{S}_{\left( g \right)}}$

Therefore, option (D) is the correct answer.

Note: Remember the reaction will be reversible only if the products formed react with each other under the same reaction conditions to form the product. If either of the products formed escapes into the air or is a stable precipitate then the reaction will be irreversible.