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Identify the type of reaction:
$Fe+CuS{{O}_{4}}(aq)\to FeS{{O}_{4}}(aq)+Cu(s)$

Answer
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Hint: When elements from the reactants take each other’s place, or replace each other in their aqueous salt solutions to form the products, then the reaction is termed a displacement reaction. It is of two types, single and double displacement.

Complete step-by-step answer:
We are given a reaction where iron, Fe, reacts with copper sulfate, to form ferrous sulfate and solid copper. In this reaction Ferrous displaces Copper from its aqueous salt solution of copper sulfate, so this is a type of displacement reaction. As iron replaces copper.
Ferrous is able to displace copper from its aqueous salt solution because ferrous is more reactive than copper. According to the activity series of elements, ferrous is placed before copper, therefore it is more reactive, and displaces copper.
Hence, the type of the given reaction is displacement reaction.
Additional information: Displacement reaction occurs in two ways; one is the single displacement as discussed above, while double displacement occurs when there is exchange of two ions between the reactants. These reactions often result in forming a precipitate. For example, $BaC{{l}_{2}}+N{{a}_{2}}S{{O}_{4}}\to BaS{{O}_{4}}\downarrow +2NaCl$, in this reaction, barium and sodium replaces each other forming a precipitate of barium sulfate, hence the reaction is double displacement.

Note: The reaction between ferrous and copper sulfate mentioned in the question can be depicted through an activity. It is performed by dipping an iron nail into copper sulfate solution, after some time you will observe that the blue color of copper sulfate solution changes to pale green due to iron replacing copper.