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)` at 298K. 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 equilibrium for reaction is

Options

A. `=0`
B. ` lt 1`
C. `gt 1`
D. `=1`

Explanation

To solve the problem, we need to calculate the equilibrium constant (K) for the reaction given the enthalpy and entropy values of the substances involved. We will follow these steps:

### Step 1: Write the Reaction
The reaction we are considering 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 the Change in Enthalpy (ΔH)
Using the standard enthalpy of formation values:
...