Calculate the enthalpy of hydration of anhydrous copper sulphate`(CuSO_4)` into hydrated copper sulphate `(CuSO_4 cdot 5H_2O)`. Given that the enthalpies of solution of anhydrous copper sulphate and hydrated copper sulphate are `-66.5 and + 11.7 kJ mol^(-1)` respectively.

Explanation

We are given
(i) `CuSO_(4)(s) + aq rarr CuSO_(4)(aq), Delta_(sol) H= - 66.5 kJ mol^(-1)`
(ii) `CuSO_(4) . 5H_(2)O(s) +aq rarr CuSO_(4)(aq), Delta_(sol) H= + 11.7 kJ mol^(-1)`
we aim at `CuSO_(4) (s) + 5H_(2)O(l) rarr CuSO_(4).5H_(2)O(s), Delta _(hyd) H= ?`
Eqaution (i) can be written in two steps as`:`
`(ii) CuSO_(4) (s) +5H_(2)O(l) rarr CuSO_(4).5H_(2)O(s) , Delta H= Delta H_(1) kJ mol^(-1)`
(iv) `CuSO_(4). 5H_(2)O(s) + aq rarr CuSO_(4)(aq) , Delta H = DeltaH_(2) kJ mol^(-1)`
According to Hess's law, `Delta H_(1) + Delta H_92) = - 66.5 kJ mol^(-1)`
Further, equations (ii) and (iv) are same `:. Delta H_(2) = + 11.7 k J mol^(-1)`
Putting this value above, we get `Delta H_(1) + 11.7 = - 66.5 ` or `Delta H_(1) = - 66.5- 11.7 kJ = - 78.2 kJ mol^(-1)`
Thus, equation (iii) may be written as
`CuSO_(4)(s) + 5H_(2)O(l) rarr CuSO_(4). 5H_(2)O(s), Delta _(hyd) H- 78.2kJ mol^(-1)`
This is what we aimed at . Hence, the required value of the enthalpy of hydration is`Delta _(hyd) H = - 78.2k J mol^(-1)`.