Concrete is produced form a mixture of cement, water and small stones. Small amount of gypsum, `CaSO_(4).2H_(2)O` is added in coment production to impove the subsequent hardening of concrete. The elevated temperature during the production of cement may lead to the formation of unwanted hemihydrate `CaSO_(4)(1)/(2)H_(2)O` according to reaction.
`CaSO_(4)2H_(2)O(s) rarr CaSO_(4)(1)/(2)H_(2)O(s)+(3)/(2)H_(2)O(g)`
The `Delta_(f)H^(Theta) of CaSO_(2).2H_(2)O(s),CaSO_(4)(1)/(2)H_(2)O(s),H_(2)O(g)`
are `-2021.0 kJ mol^(-1), -1575.0 kJ mol^(-1)` and `-241.8 kJ mol^(-1)`, respectively. The respective values of their standard entropies are `194.0, 130.0` and `188.0 J K^(-1)mol^(-1)`. The values of `R = 8.314JK^(-1)mol^(-1) = 0.0831L` bar `mol^(-1)K^(-1)`.
Answer the following questions on the basis of above information.
Heat change occuring during conservation of `1kg` of `CaSO_(4).2H_(2)O(s)` (molar mass `172g mol^(-1))` of `CaSO_(4)(1)/(2)H_(2)O(s)` is equal to

Options

A. `484 kJ mol^(-1)`
B. `400 kJ`
C. `-484.0 kJ mol^(-1)`
D. `-1000 kJ`

Explanation

`DeltaH^(Theta) = DeltaH_(P)^(Theta) - DeltaH_(R)^(Theta): (for 1 mol)`
`= [-1575.0 kJ mol^(-1) -(3)/(2) xx 241.8]`
`-[-2021.0 kJ mol^(-1)]`
`= +83.3 kJ mol^(-1)`
For `1kg CaSO_(4). 2H_(2)O`
Number of moles `= (1000)/(172) = 5.81`
`:.` Heat change for `5.81 mol of CaSO_(4).2H_(2)O`
`= 5.81 xx 83.3 kJ mol^(-1)`
`= 484 kJ mol^(-1)`