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Ashish mixed a solution of soluble silver nitrate and soluble sodium chloride. The products formed are:
a.) Soluble silver chloride and soluble sodium nitrate.
b.) Insoluble silver chloride and insoluble sodium nitrate.
c.) Insoluble silver chloride and soluble sodium nitrate.
d.) Soluble silver chloride and insoluble sodium nitrate.

Answer
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Hint: Try to recall that in a double displacement reaction, two ionic compounds react and the positive ions (cation) and negative ions (anions) of the two reactants (must be ionic compounds) exchange their places, forming two new products (ionic compounds). Now by using this you can easily find the correct option from the given ones.

Complete step by step answer:
It is known to you that both silver nitrate and sodium chloride are ionic compounds and they are soluble in water.
Also, it is known to us that when two ionic compounds are mixed then they undergo double displacement reaction i.e. the cations and anions switch between two reactants to form new products.
When soluble silver nitrate is mixed with soluble sodium chloride, then first \[NaCl\]decomposes to give \[N{{a}^{+}}\] and \[C{{l}^{-}}\]ions and \[AgN{{O}_{3}}\]to\[A{{g}^{+}}\]and \[N{{O}_{3}}^{-}\] ions. Then, \[A{{g}^{+}}\]combines with \[C{{l}^{-}}\]to form \[AgCl\]and \[N{{a}^{+}}\] combines with\[N{{O}_{3}}^{-}\]to form \[NaN{{O}_{3}}\]. The double displacement reaction between \[NaCl\]and\[AgN{{O}_{3}}\]is as follows:
\[NaCl(aq)+AgN{{O}_{3}}(aq)\to AgCl(s)+NaN{{O}_{3}}(aq)\].

From the above double displacement reaction, it can be easily seen that the one product is silver chloride (\[AgCl\]) which is insoluble in water and the other product which remains soluble in water is sodium nitrate (\[NaN{{O}_{3}}\]).
So, the correct answer is “Option C”.

Note: It should be remembered to you that the double displacement reaction also known as double decomposition reaction is different from other reactions as there is absolutely no change in oxidation states of any of the components, atoms or radicals i.e. it is not a redox reaction.