Question
Answers

Which of the following represent a double displacement reaction?
A.$2{H_2} + {O_2}\xrightarrow{{}}2{H_2}O$
B.$2Mg + {O_2}\xrightarrow{{}}2MgO$
C.$AgN{O_3} + NaCl\xrightarrow{{}}AgCl \downarrow + NaN{O_3}$
D.${H_2} + C{l_2}\xrightarrow{{}}2HCl$

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Hint: A double displacement reaction is a type of reaction in which exchange of parts between two ionic compounds takes place. In this reaction cations and anions of two compounds switch their positions to generate two new compounds.

Complete step by step answer:
As the name suggests in a double displacement reaction, two compounds exchange their parts to give two new compounds. So two different compounds have to react with each other and swipe their parts during the reaction. Let us take the above reactions one by one to identify whether it is a double displacement reaction or not.
A.$2{H_2} + {O_2}\xrightarrow{{}}2{H_2}O$
In this reaction two components are reacting to give a single compound. It is a combination reaction and not a double displacement reaction as no displacements are happening between the reactants.
B.$2Mg + {O_2}\xrightarrow{{}}2MgO$
In this reaction two components are reacting to give a single compound one is a metal and other a non metal. It is also a combination reaction and not a double displacement reaction.
C.$AgN{O_3} + NaCl\xrightarrow{{}}AgCl \downarrow + NaN{O_3}$
In this reaction two components are reacting to give two compounds. The silver nitrate reacts with sodium chloride to precipitate silver chloride. Sodium nitrate is also produced in the reaction. The silver cation is bonded to nitrate ion in reactant but bonded to chloride ion in product. Similarly sodium cation is bonded to chloride ion in reactant and bonded to nitrate ion in product. Hence some kind of interchange has taken place between the reactants to yield two different products. So this reaction includes a double displacement.
D.${H_2} + C{l_2}\xrightarrow{{}}2HCl$
In this reaction, two components gases are reacting to give a single compound. It is a combination reaction and not a double displacement reaction as no displacements are happening between the reactants.

So option C is the correct answer.

Note: In reactions where two products are formed from two or more reactants, they are not referred to as combination reactions. Normal combustion reactions can also be referred to as combination reactions. For example, if carbon is burnt in presence of oxygen to give carbon dioxide on full combustion.