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.
The value of `DeltaG^(Theta)` for the reaction at `298K` is

Options

A. `120 kJ mol^(-1)`
B. `17.92 kJ mol^(-1)`
C. `-180 kJ mol^(-1)`
D. `10 kJ mol^(-1)`

Explanation

To find the value of ΔG° for the reaction at 298 K, we will follow these steps:

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

### Step 2: Calculate ΔH°
Using the formula:
...