Question

The heat of solution of anhydrous $CuS{{O}_{4}}$ is $-15.9KCal$ and that of $CuS{{O}_{4}}.5{{H}_{2}}O$ is $2.8KCal$ . Calculate the heat of hydration of $CuS{{O}_{4}}$.

Answer 1

Hint: Heat of hydration is defined as the amount of energy released when one mole of ions undergoes hydration process. Here, the solvent used is water. It is a specific form of energy of dissolution. Anhydrous salts combine with water and produce hydrates.

Complete step-by-step answer: The heat of solution of anhydrous $CuS{{O}_{4}}$ is $-15.9KCal$
Let us write the reaction:
$CuS{{O}_{4}}\left( s \right)+aq\to CuS{{O}_{4}}\left( aq \right)$
This is equation 1.
Here, $aq$ is aqueous solution.
$\Delta {{H}_{1}}=15.9KCal$
The heat of solution of anhydrous $CuS{{O}_{4}}.5{{H}_{2}}O$ is $-2.8KCal$
Let us write the reaction:
$CuS{{O}_{4}}.5{{H}_{2}}O+aq\to CuS{{O}_{4}}\left( aq \right)+5{{H}_{2}}O$
Here, $aq$ is aqueous solution.
$\Delta {{H}_{2}}=2.8KCal$
Now, we will reverse this reaction so that both the sides of the reaction become equal.
$CuS{{O}_{4}}\left( aq \right)+5{{H}_{2}}O\to CuS{{O}_{4}}.5{{H}_{2}}O+aq$
This is equation2.
$\Delta {{H}_{2}}=-2.8KCal$
Now we will add equation 1 and equation 2 we get,
$CuS{{O}_{4}}\left( s \right)+aq+CuS{{O}_{4}}\left( aq \right)+5{{H}_{2}}O\to CuS{{O}_{4}}\left( aq \right)+CuS{{O}_{4}}.5{{H}_{2}}O+aq$
Now we will cancel out, we get
$CuS{{O}_{4}}\left( s \right)+5{{H}_{2}}O\to CuS{{O}_{4}}.5{{H}_{2}}O$
As we have added equation 1 and equation 2, we will therefore add up the heat of hydration.
$\Delta H=\Delta {{H}_{1}}+\Delta {{H}_{2}}$
$\Delta H=-15.9+\left( -2.8 \right)$
$\Delta H=-18.7KCal$
The heat of hydration of $CuS{{O}_{4}}$ is $-18.7KCal$
Additional information:
Water of crystallization is defined as the amount of fixed number of molecules present in a formula unit of salt. Water of crystallization is also known as water of hydration. It is formed by purified crystals from an aqueous solution. Hydrates are defined as the crystal salts with water of crystallization.

Note: It is to note that when an anhydrous copper sulphate is dissolved in water it results in the formation of copper sulphate pentahydrate. The anhydrous copper sulphate is white powder whereas the product formed that is copper sulphate pentahydrate is blue prism crystals. Copper sulphate pentahydrate decomposes before melting.The heat of hydration is measured in $KCal$ .