Concrete is produced form a mixture of cement, water and small stones. Small amount of gypsum, `CaSO_(4).2H_(2)O` is added in cement production to improve 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 occurring during conversion 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

To solve the problem, we need to calculate the heat change occurring during the conversion of 1 kg of `CaSO4.2H2O(s)` to `CaSO4(1/2)H2O(s)` using the given enthalpy of formation values.

### Step 1: Write the reaction and identify the enthalpy change
The reaction is given as:
\[ \text{CaSO}_4 \cdot 2\text{H}_2\text{O}(s) \rightarrow \text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O}(s) + \frac{3}{2}\text{H}_2\text{O}(g) \]

The enthalpy change (\(\Delta H\)) for the reaction can be calculated using the formula:
\[
...