Concerete is produced from a mixture of cement , water, sand and small stones. It consists primarily of calcium silicates and calcium aluminates formed by heating and grinding of clay and limestone. In later steps of cement production a small amount of gypsym , `CaSO_(4).2H_(2)O` is added to improve subsequent hardening of concrete . The use of elevated temperature during the final production may lead to formation of unwanted hemihydrate, `CaSO_(4).1//2H_(2)O.` Consider the following reaction:
`CaSO_(4).2H_(2)O(s) rarr CaSO_(4).(1)/(2) H_(2)O(s)+(3)/(2)H_(2)O(g)`
The following themodynamic data apply at `25^(@)C` standard pressure : 1 bar
`{:("Compound","DeltaH_(f(KJ//mol))^(@),S^(@)(JK^(-1)mol^(-1))),(CaSO_(4).2H_(2)O(s),-2021.0,194.0),(CaSO_(4).(1)/(2)H_(2)O(s),-1575.0,130.5),(H_(2)O(g),-242.8,188.6):}`
R=8.314 `JK^(-1)mol^(-1)`
Equillibrium pressure (in bar) of water vapour in closed vessel containing `CaSO_(4).2H_(2)O(s),CaSO_(4).(1)/(2) H_(2)O(s),H_(2)O(g)` at `25^(@)`C

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