At `25^(@)C`, when 1 mole of `MgSO_(4)` was dissolved in water, the heat evolved was found to be 91.2 kJ. One mole of `MgSO_(4) . 7H_(2)O` on dissolution gives a solution of the same composition accompanied by an absorption of 13.8 kJ. The enthalpy of hydration, i.e., `DeltaH_(h)` for the reaction
`MgSO_(4)(s) + 7H_(2)O(l)rarrMgSO_(4) . 7H_(2)O(s)` :

Options

A. `-105 kJ//"mol"`
B. `-77.4 kJ//"mol"`
C. 105 kJ/mol
D. None of these

Answer

A

Explanation

Given that
`MgSO_(4)(s)+nH_(2)OrarrMgSO_(4)(nH_(2)O),`
`Delta_(r )H_(1)=-91.2 " kJ"//"mol ....(i)"`
`MgSO_(4).7H_(2)O(s)+(n-7)H_(2)OrarrMgSO_(4)(nH_(2)O)`
`Delta_(r )H_(2)=13.8 " kJ"//"mol ....(ii)"`
Equation (i) - (ii)
or `DeltaH_("hyd")=Delta_(r )H_(1)-Delta_(r)H_(2)`
`=-91.2 " kJ"//"mol"-13.8 " kJ"//"mol"`
`=-105" kJ"//"mol"`