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 equilibrium pressure of water vapour in closed vessel containing `CaSO_(4)2H_(2)O(s),CaSO_(4)(1)/(2)H_(2)O(s)` and `H_(2)O(g)` at `298K` (Antilog `-3.14 = 7.24 xx 10^(-4))` is

Options

A. `17.35 xx 10^(-4)` bar
B. `2.15 xx 10^(-4)` bar
C. `8.10 xx 10^(-3)` bar
D. `7.00xx10^(-4)` bar

Answer

C

Explanation

`DeltaH^(@)=DeltaH^(@) -DeltaS^(@)=17920 J "mol"^(-1) " "implies " "DeltaG^(@) =-2.303 RT " log" K_(p)`
log `K_(p)=(DeltaG^(@))/(2.303 RT) = 7.22 xx 10 ^(-4) (P_(H_(2)O))^(3//2) " "implies " " P_(H_(2)O) = 8.1 xx 10^(-3)` atm