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. `105kJ//mol`
D. `77.4 kJ//mol`

Answer

A

Explanation

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