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Why are the dissolution of anhydrous copper sulphate exothermic, and the dehydration of $ CuS{O_4} \cdot \;5{H_2}O $ endothermic?

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Hint: To answer this question, first we have to know about dissolution and dehydration. And also about the exothermic and endothermic. The dissolution is the chemical process in which solutes in gaseous, liquid, or solid phase dissolve in a solvent to form a solution. Whereas dehydration reactions are the chemical reactions in which a water molecule is lost, such as that during the synthesis of an organic compound.

Complete answer:
The process of dissolving is the exothermic process as more energy is released when water molecules bond to the solute than to pull the solute apart. As more energy is released than is used, the molecules of the solution move rapidly, making the rise in temperature.
For hydration of anhydrous copper sulphate:
 $ CuS{O_4}\left( s \right) + excess\;water\;{H_2}O\left( l \right) \to C{u^{2 + }}\left( {aq} \right) + SO_4^{2 - }\left( {aq} \right) $
Here in this chemical reaction, visible colour change is observed. $ C{u^{2 + }}\left( {aq} \right) $ is a coordination complex, that is probably $ {\left[ {Cu{{\left( {O{H_2}} \right)}_6}} \right]^{2 + }} $ .
On the other hand, the endothermic process which includes an increase in the enthalpy of the system. In this type of process, a closed system usually absorbs thermal energy from its surroundings, which is heat transferred into the system.
When we take the blue hydrate, $ CuS{O_4} \cdot \;5{H_2}O $ and place it in water, there are strong ionic bonds between the sulphate and copper ions which must be broken for dissolution.

Note:
Water is dissolved in copper sulphate, heat is produced due to which the water present boils. As heat is produced, thus the reaction is exothermic. Exothermic reaction is the reaction in which the heat energy is produced.